THEORY

UNPUBLISHED//THEORY

PUBLISHED//THEORY

Embodied Meaning In John Adams' El Niño

Curriculum//Ear-Training

The following first-year undergraduate ear-training curriculum is one that was built and implemented successfully by Dr. Bruce Roter, Kari Francis, and myself. It develops the ear in traditional western common-practice, contemporary, and music industry-related sound structures. Areas of development include melodic dictation/transcription, chord progression recognition, harmonic dictation (including voice-leading and harmonies), and rhythmic dictation (one line, as well as two- and three-line drum dictation/transcription.) We are making it open-source, so feel free to make use of it yourself in your undergraduate classroom setting. (Student version and sound files provided here. Instructor copy will be made available on or after May 6, 2021.)

first semester ear-training (student version)

first semester ear-training (audio)

Homeworks 1–7

first semester ear-training (audio)

Homeworks 8–14

first semester ear-training (audio)

Homeworks 15–21

First Semester Ear-Training (Instructor Version)

second semester ear-training (student version)

second semester ear-training (audio)

Homeworks 1–7

second semester ear-training (audio)

Homeworks 8–14

second semester ear-training (audio)

Homeworks 15–21

second Semester Ear-Training (Instructor Version)

Music Theory ideas in incubation (informal notes)

1. Flexible scale-degrees 6 and 7 as

opposed to the 3 standard forms of the

minor scale (a la Gary S.

Karpinski's presentation in the
Manual for Ear Training and Sight
Singing)

2. Triadic cadence names that are more

specific than "progressive" and

"conclusive" when they don't fit into

traditional cadence

nomenclature; subdominant

cadence (ends on IV, iv) supertonic

cadence (ends on ii); supertonic-tonic

cadence (ii–I), etc.

3. Secondary Modal Borrowing: For

example, consider the following harmonic progression: C F#ø7 B7b9 Emaj7...the

progression continues in C major. From the

perspective of E major, where this chord

progression ends, the preceding two

chords can be seen as a iiø7 V7b9 from E

minor (the parallel minor of E major). This is

an instance of modal borrowing; however, it

is from the perspective of a chord which is

not a tonic, but a locally tonicized chord

(which incidentally is not the expected Em

or iii chord in the more global C major).

From this perspective, the Emaj7 is a

Picardy 3rd and maj7 borrowed from E

minor's parallel major. However, Picardy

3rds are usually the purview of tonic

chords, not any and all possible triads. This

situation then, proposes two different

instances of modal borrowing, both with a

"secondary" quality to them. The ii-V is an

instance of secondary modal borrowing

since it is borrowing from the parallel minor

of a tonicized chord. The tonicized chord is

an instance of "secondary" modal

borrowing in the sense that it achieves the

possibility of a Picardy third only as a very

localized tonic rather than a global one.

4. Double function in the cadential

V7sus chord.

5. Melodic Dictation In Pedagogy: Why

Contour Matters In Taking Melodic

Dictation. Some students will insist that

they "got the right note" if, for instance, they

move from sol up to do at the conclusion of

a melodic line when, in fact, it moved

from sol down to do. The pitch class is

correct while the pitch is incorrect and the

contour is incorrect. Would the rest of the

world recognize these types of scenarios

as the "correct" tunes if we took well-known

tunes and completely altered the registers

and directionality of the melodic lines of our

favorite well-known songs? Obviously this

is taking the same concept to the point of absurdity, but by so doing it does help

make the point that we need to be able to

hear directionality as a basic listening

component in melodic

dictation/transcription.

6. Pedagogy: Making Explicit The

Reasons For Note Specificity. Some

students have a tendency to see a teacher

who requires note specificity as the sign of

a bullheaded instructor rather than viewing

such specificity as a practical necessity of

all musicians. For example, a student might

say "I know I said the answer was A C E G,

but of course you know I meant Ab C E Gb.

Same thing. You are so specific." Explicitly

pointing out (and even demonstrating) to

students the musical situations in which the

lack of specificity completely breaks down

in terms of achieving compositional and

performance accuracy which would be

demanded of any musician in any musical

scenario may effectively break students of

such habits.

7. Distinguishing swing at the beat

division level and beat subdivision

level: At the beat division level, the beat is

divided into two unequal parts (long-short)

somewhere between two straight eighths

per beat and straight triplet eighths in

which the first two eighths are tied while the

third is not. At the beat subdivision level,

the divided beat (8th note, assuming a

quarter note beat unit) is divided into two

unequal parts (long-short) somewhere

between two straight 16ths per 8th and

straight triplet 16ths in which the first two

16ths are tied while the third is not.

8. Help! I can't hear intervals! A multi-

contextualization process for

scaffolding the aural recognition of

intervals. An example: The basic idea is

varying small contexts for individual

intervals we are studying. Let's take the

major 2nd for example. I'll use a referent of

C Major.

a. Play the major 2nd melodically, then

harmonically.

b. Play it as an add-note chord: C major, then

Cadd2

c. Play the major 2nd melodically, then

harmonically.

d. Play C major with a doubled root (C-E-G-

C), then Cadd9

e. Play the major 2nd melodically, then

harmonically.

f. Play a whole-tone scale beginning on C

(WT-0)

g. Play the major 2nd melodically, then

harmonically.

h. Play a whole-tone 4-note cluster chord with

a bass note of C.

i. Play the major 2nd melodically, then

harmonically.

j. Play C and D as a M9.

k. Play C4, D5, C5 melodically.

l. Play C4, D4, C4 melodically.

m. Play C4, D4, C4, Bb3 melodically to orient

it to a different key context (new tonal

center.)

n. Play a Gsus4 (G-C-D) going to G major (G-

B-D) *4-3 suspension.

o. Play Gsus 4 without resolving it.

p. Play a major 9 (C-D)

q. Play Cmaj9

r. Play a major 9 (C-D)

s. Play C9

t. Play a major 9 (C-D)

u. Play a C-9

v. Play a major 9 (C-D)

w. Play a Cø9

x. Play a major 9 (C-D)

y. Play a Cº9

z. Play a major 9.

aa. Play a Csus2, then C (CEG)

In this way, we can help them not be so "hit or

miss" with intervals, but scaffold their listening

experience through small musical contexts for those intervals. We can simultaneously

introduce them to sounds (both traditional and

contemporary) that make use of those

intervals.

9. Measuring Strength Of, And

Conformance To, Tonic Perception In

Melody: Create various melodies intentionally

crafted with the intent of measuring how much

listener conformance to (or deviation from) the

perception of a particular tonic(s) occur(s)

depending upon the structure of a given

melody.

10. Examples Of Negative Musical Space

In Pitch And Rhythm (and Timbre?):

This idea comes from Bert Ligon in his

textbook entitled Jazz Theory Resources (p.

23) where he states "Negative space is

implied space created by a positive image.

Visual artists depend on the recognition of

negative space. The concept of negative

space is also important in music. Any pitches

that are played (positive space) may imply

other pitches that are not played. A certain

pitch may be stressed by playing a number

of pitches around that pitch that point to that

pitch, while never actually playing the pitch.

...As with pitches, any rhythm that is played

(positive space) may imply a rhythm not

played (negative space)." Perhaps an

example would be a ii-V which implies a

certain tonic resolution, but never actually

provides it. Another example could be

running a major scale from low do up to

high ti and then simply stopping. In certain

contexts, we may feel an implication

that ti implies a resolution to do, whether or

not this implication is actualized. When these

types of implication are not realized, they are

examples of negative musical space.

Informal Thoughts On Semiotics: Means Of Communication

(These thoughts are indebted to Kofi Agawu, Patricia Attiba, Care Bears, Diana Deutch, Robert Hatten, David Huron, Inside Out 2—Ennui character, Timothy Koozin, Lego Movie 2, James Lyke, Tony Caramia, Geoffrey Haydon, Ronald Chioldi, Mary Poppins, Jace Mosher, Zachary Mosher, Renee Kathleen Gonzales Mosher, Charles Sanders Pearce, Petikan, Janna K. Saslaw, Rob Schultz, Indre Viskontas, Kristen Wallentinsen, and more.)

Consistent mouth sounds (two subcategories: (a) "unpitched"—though emphasis, use of pauses between words, repetition as a signal of intentionality (Deutch and Viskontas), word order and the general contour can indicate meaning and question, statement, amount of emphasis attributed, choice of specific words that are synonyms to various degrees can have various amounts of overlap in meaning, noting that denotation and connotation can shift over time with usage and context, etc. and (b) tone languages in which around five? tones are used in relative contour and are attached to the meaning of the words themselves, (c) whistle languages (Diana Deutch refers to them in Indre Viskontas's Cadence, Season 1: Episode 1 or 2), (d) music as a language, (e) Morse code as a language, (f) texture used in consistent ways to express meaning as a language (Braille), (g) flag movements such as those used at Signal Point during the U.S. Civil War, (h) any visual art medium is communicative of meaning(s)

Consistently-drawn shapes (two subcategories: (a) pictorial, as in Chinese characters that indicate entire words) and (b) spelling languages in which the drawings represent sounds strung together to make words; subcategory: capitalization can be used to indicate weight, value, importance, draw attention to, yell, show excitement

Punctuation as meaning are consistently-drawn shapes attributing the dependency of one idea upon another idea (comma), the amount of connectedness between ideas in a single thought (semicolon), the communication that a basic idea has concluded at some level of depth (period), the idea that a string of connected thoughts go together at a deeper level (paragraph indentation), (same concept on out to chapter, book, volumes in a set)

Facial expressions

Bodily movements

Conducting as gesture to evoke mood and character

Hand Gestures: Sign language: there are many, not just ASL; these are hand motions used in consistent ways to express meaning; these, I believe, can be of the. spelling or "pictorial" ("whole-word-based") variety; for example, you can spell your name, but you can also make one symbol for the word "sunset"

Gestural communication in non-human species: examples include cat tail motions, ear direction, echolocation, distance from other organisms, placement of body so as to position for the best line of sight toward all traffic-flow directions, fight-flight-frisson response (a la David Huron talks), dog tail wagging (situational with multiple meanings), types of barks, fish communication moving away from electrodes, dolphin communication (extensively documented—communication distance is also significant), whale song (likewise extensively documented—communication distance is also significant), birdsong, crickets, cicadas, bees

Sarcasm and Irony as meaning: Change of tone, pitch, contour, and non-denotative aspects of words and word combinations, and/or context, cause word meanings to mean their opposite (irony). Verbal examples: Anything stated by Ennui in Inside Out 2. Musical and verbal example: "Stay Awake" from Mary Poppins in which the denotative meaning of the words (lyrics) state that you should "Stay awake, Don't rest your head. Don't lie down upon your bed. While the moon drifts in the skies, Stay awake, Don't close your eyes." Simultaneously, the musical cues are those of a lullaby. The musical cues achieve Mary Poppins' purpose of having the children go to sleep while the verbal cues satisfy the children's obstinate defiance. In opera, theatre, and film, we see music providing information to the audience about the character of the individuals on stage which the other characters on stage are not privy to since the other characters on stage are only imagined to have access to the words being spoken while the audience hears the deeper message in the music. The information provided to the audience is based upon the director(s)' hopes that the music will affect the audience in a particular way, allowing them to know whether the individual is to be seen valiantly or villainously (or any other affect the director(s)' might be attempting to convey).

Segmentation, grouping, accent placement as meaning:

Examples in spoken language:

-"Care-A-Lot, we care a lot." (from Care Bears)

-"Queen Watevra Wa'Nabi" ["Queen Whatever I Want To Be"] (from Lego Movie 2)

In music, this is expressed through items like placement of rests, articulations, breath marks, changing metric locations of a repeated riff (examples in minimalism, post-minimalism, rock, jazz, pop, CCM, and more), dynamics (and micro-dynamics—the smaller un-notated note-to-note dynamics that help musicians shape phrases effectively).

Informal Thoughts On Directionality And Numbering Systems

(These thoughts are indebted to Brent Auerbach, Louise Becker, Cadwallader and Gagne, Thomas Christenesen et al., Alan Forte, Gary S. Karpinski, Timothy Koozin, Lerdahl and Jackendoff, Lippius, Justin London, Padgett, Janna K. Saslaw, Arnold Schoenberg, Craig Sikes, John Snyder, Joseph N. Straus, Dmitri Tymoczko, Indre Viskontas, Elizabeth Wallace, and more.)

Pitch is "higher" when it vibrates at a faster frequency, "lower" when it vibrates at a slower frequency.

The sun "rises" and "sets".

Guitar Directionality and Numbering Systems: As you move "higher" on the fretboard, you move closer to your body. As you move "lower" on the fretboard, you move away from your body. Guitar "numbering" systems use T, 1, 2, 3, 4 (thumb, index finger, middle finger, ring finger, pinky). (In classical settings, p (pulgar—Latin for thumb), i (indece—Latin for index), m (medio—Latin for middle), and a (anular—Latin for ring) are used to label fingers. A chord chart diagram for fretting a chord visualizes the guitar fretboard as if you were holding the guitar vertically and facing you. It also limits the frets shown to basically those necessary to fret the chord. If "higher" on the neck of the guitar, it will indicate the fret number you are looking at as the first fret shown. The counting system for frets is fret zero equates to an open string (not usually stated in this way) and each fret "ascending" the fretboard increases by one. (When we "fret" a note, we do not literally place our fingers on the fret, we place them "in front of" (just further away from the "body" of the guitar on the "neck" of the guitar than) the fret we indicate. Guitar tablature uses "lower" on the page to indicate a "lower"-sounding string (though as we typically play a guitar, the "lowest"-sounding string is "higher" (or higher from the ground as a reference point). Traditional music notation also uses lines on a page in a "lower" sound finding its location "lower" on the page.

Piano Directionality and Numbering Systems:

As you move "higher" on the keyboard, you move to the right of your body as a reference point. As you move "lower" on the keyboard, you move to the left of your body as a reference point. Piano "numbering" systems use 1, 2, 3, 4, 5 (thumb, index finger, middle finger, ring finger, pinky). A piano chart diagram may place dots on the locations of the notes to be played in a given chord. Typically, the amount of the keyboard shown is about an octave or a little more, or just framing the visual space needed to show which notes will be played. (A post-tonal numbering system might indicate either C as zero and "ascend" numerically by half-step (yet another counting system: steps—whole and half-steps related to diatonic (fuzzy mod7-based system which uses letters and inflections of those letters as "stand-ins" for numbers) versus chromatic (mod12-based system like our modern calendar; also note that our Arabic counting system is base 10 or mod-10 relating to the number of digits on our hands) counting methods based perhaps on the constuction of the music to be played to it) to B or choose the chord root as a zero starting point and "ascend" numerically from there. The piano chart will take the keyboard and rotate it toward you as if it were facing you on the page. It maintains the same right-left directionality as the piano keyboard itself. If a particular register is desired, one could indicate this by using octave designations in addition to pitch-class lettering.

Note the following piano, guitar, and calendar numbering comparison-contrasts "side-by-side":

Piano: 1 (thumb), 2 (index finger), 3 (middle finger), 4 (ring finger), 5 (pinky)

Guitar system 1: p (thumb), i (index finger), m (middle finger), a (ring finger), *pinky unused?

Guitar system 2: T (thumb), 1 (index finger), 2 (middle finger), 3 (ring finger), 4 (pinky)

2 Interchangeable Calendar Counting Systems (Illustrated Here with examples of Years followed by Centuries Counting Methods (equal sign placed in between the two counting systems): 0-99 = 1st century; 2000s=21st century

Directionality in Schenkerian Analytical Practice: "deeper" levels of structure on a Schenkerian graph are shown "higher" on the page; the "background" is at the "top" of the page and moves toward the "foreground" at the "bottom" of the page

"Hypometer"-Meter-Hypermeter: Meter and hypermeter are given two distinct terms, but are continuous concepts/experiences. Both terms have to do with the regular interaction of multiple levels of pulse streams. Meter is typically more closely associated with the levels of pulse streams notated by note values we have standard symbols for. As we move into pulse streams related by longer timespans that exceed the human temporal perception window, (and require pulse streams present within that temporal perception window in order to perceive), we begin to count these pulse streams in "measures" or "formal sections", etc. The same concept could be extended in the opposite direction by moving into "hypometer", which we might understand as moving into relationships between multiple levels of pulse streams that are too fast to our perception to be considered reasonable for distinct note values on sheet music. (As you move to faster and faster pulse streams, at some point a type of perceptual "fusion" occurs in which the distinct attack points are so fast that we perceive them as a steady tone, much like the visual analogue of a nickelodeon.

Directionality in Theology: We often tend to refer to God as "up" even as the globe is "round".

Informal Thoughts On Building-Out An Open-Ended Index Of Pop And Jazz Harmonies

(These thoughts are indebted to Alan Forte, Micheal Houlahan and Philip Tacka, Mark Levine, David Liebman, Stefan Caris Love, Felipe Salles, Joseph N. Straus, and more.)

What if we considered creating an open-ended index of pop and jazz harmonies using a hybrid post-tonal approach alongside common current voicings? We could place the normal order (normal form) number alongside the pop label. The reason I say open-ended is because pop and jazz harmonic usage may (and does) change over time. For example, G7#9,b13 could be expressed alongside (02478)/4. The second of these two labels is in normal order (normal form), but not prime form and has a slash-chord look to it as is used in pop music labels. It might be helpful in this hybrid approach to leave the post-tonal label in normal order rather than putting in prime form in order to highlight a sound-over-sight approach. The slash-chord approach to the notation allows us to understand which of these tones in this sonority is to be understood as the bass-root, as bass and root are often synonymous (though certainly, not always) in much jazz literature. Following the two chord labels, we could then show pictures of some common voicings of the chord as possibilities, noting that other arrangements of the tones might be selected or become more popular voicings. One voicing that could be shown for the example above could voice the chord as G (m7) F (+3) A# (m2) B (d4) Eb.

An example from popular music might be a Bbadd4. This pop chord label could be expressed alongside (0457)/0 rather than its inversion in prime form (0237), again, prioritizing a sound-over-sight approach.

Informal "What If"?

(These thoughts are indebted to Joseph N. Straus, brilliant.org lesson on polar coordinate graphing, and more.)

Currently, our equal-temperament system is a mod12-based system. What if we created (unless it already exists and I'm not aware of it) a mod8-based equal-temperament system, thusly.

C=0, C three-quarters sharp (or D half-flat)= pi/4, D sharp (or Eb)=pi/2, E half-sharp (or F half-flat)= 3pi/4, F# (or Gb)=pi, G half-sharp (or A three-quarters flat)=5pi/4, A=3pi/2, A three-quarters sharp (or B half-flat)= 7pi/4

Let's try it out, start making some physical and software instruments that are based on this system, and start acclimatizing our ears to the myriad of sound worlds we could create with it (or any other modular equal-temperament systems)!

Possible Reconsideration Of Some Music-Theoretic Terminologies?

(These thoughts are indebted to William E. Caplin, Andrew Davis, Hepakoski and Darcy,

Stefan Kostka and Dorothy Payne, and more.)

Should we consider re-evaluating music-theoretic terminologies which may have negative connotations and updating those terms with more neutral terminologies? Some examples for consideration might include the following: (I have put the terms we might consider changing in italics.)

-Authentic Cadence

-Imperfect Authentic Cadence

-Perfect Authentic Cadence

-Centric

-Deformation

-Minimalism

-Nonfunctional harmonic structures
-Normal Form (Normal Order)

-Retardation

-Retrogression

Informal Thoughts On Music, The Arts, And Aesthetics In Therapeutic Usage

(These thoughts are indebted to Art Pharmacy, Susan Magsamen and Ivy Ross, 1 Samuel 16:14-23, Lisa Sanders,

Alexander Scriabin, Craig and Debbie Sikes, Elizabeth Wallace, Jordan Winkler, and more.)

(*Disclaimer: I am not a music therapist. Nor do I have the professional background or licensure for the statements below. These statements are my informal opinions based upon literature I have read and observational experience.)

When approaching music, the arts, and aesthetics in therapeutic usage, consider the following thoughts:

-"Modulate" musical approach in real-time during live music performance (or DJing live with recorded music) based upon your detailed attention to non-verbal communication from your listeners in order to better meet their needs. Look for non-verbal signs of: (a) peace--fear (no (or low) anxiety--high anxiety, (b) happiness--discontentedness, (c) alertness/focus/attentiveness/energy/engagement--sleepiness/boredom/distractedness, or others. Look to see if there is need for emotional catharsis, for "being with" them in a sad situation, a space for hopeful and/or joyful music (and at what level of intensity and in what mixtures). The goal here is to "see" your listeners and monitor your "seeing" of them consistently as you best attempt to meet their needs in these ways. Use music which might best relate to your listeners in tone and/or text, including all parameters of music in your consideration (and the environment in which the music takes place). You should "modulate" any parameter(s) in real-time as you sense and observe the changing emotive-thought states of your listeners.

-Other non-musical environmental factors to take into consideration:

-aesthetics of the room

-use of (and intensities of, where this applies):

-lighting

-colors

-room temperature

-air-flow--stagnation

-humidity--dryness

-spaciousness of the room, its size, its shape, its corners

-amount of open space--amount of used space in room

-location of individuals in room

-location of entryways and exits

-scents in the room, as well as the amount of saturation of those scents, including the even distribution

of the amount of saturation of those scents

-amount of sound decay in the room (how sonically "wet" or "dry" is the room and/or each instrument

or voice?)

-try giving your listeners a reassuring texture to hold in their hands

-natural light (amount of), including outdoor scenery view, accessibility to it, and how it interacts with

all the other elements here described

-some knowledge of those you will be playing for in determining your choices in the elements here

described

Informal Thoughts On Everyday Contexts In Which Music

Positively Influences Behavior

(These thoughts are indebted to a lecture I heard at an ICMPC (International Conference On Music Perception

And Cognition) session, and more.)

(*Disclaimer: The particular musical attributes may not be one-size-fits-all.)

When considering the plethora of ways that music positively influences behavior, consider the following:

-Music As Extending Our Capacity For Patience

-Music as mitigation of road rage (aiding in reduction of traffic accidents)

-Music as extending our ability to patiently wait in lines (in elevators, supermarket lines, theme park lines, or any

other place we find it necessary to wait)

-Music As Extending Our Body's Energy

-Music keeping you from getting sleepy on long road trips

-Music motivating you to exercise, extending the amount of time that you are motivated to exercise once you get

started, and musical tempo at most salient pulse stream contributing to the pacing of your exercise

Informal Thoughts On Music As Evocation Of Time And/Or Place

(These thoughts are indebted to lectures I heard at a session of the Popular Music Interest Group at SMT (Society for Music Theory), Kofi Agawu, Timothy Chenette, Matthew Dirst, Napua Greig, Robert Hatten, David Huron,

Inside Out 2—Nostalgia character, Stefan Caris Love, Kuana Torres Kahele, Israel Kamakawiwo'ole (aka Braddah Iz), The Lego Movie, James Ford Murphy, Katherine Svistoonoff, Edna Thoreson, Richard Twiss, Indre Viskontas, Wikipedia.com, and more.)

(Similar to the way a scent can seem to almost "take us back to a certain place and time" in incredibly vivid detail (For example, among the many associations (multivalence) I have with the smell of pine needles, it can "take me back" in this way to my grandmother's cabin in Ruidoso, NM that we frequented when I was a child.), music and musical timbre can similarly evoke a sense of place. (In this context, what I mean by place is "location" in addition to all of the other para-associations (multivalence to various intensities depending on current context) that we may have to that particular place. Note that this may be somewhat of community-shared sense of place, but also with important nuances for individuals based upon their own personal histories. It is also multivalent for each community and individual. By this I mean that though pine needles evoke my grandmother's cabin in Ruidoso, NM, there are many other associations which it may call to mind as I have many other experiences with them—Christmas trees, slalom snow-skiing at Ski Apache, the Pine Village at Yankee Candle Company in Deerfield, MA, etc.)

When considering the many ways that music may evoke a sense of "place", it is also incredibly important to honor the origins and histories of the music and musical timbres that we are considering. Sometimes, we may not know. This provides ample opportunities for education and areas of research for both myself and others. Below are a small list of examples to consider.

–Out-of-tune piano as a signifier for old western bar-room scene

–Steel drums as a signifier for the Caribbean

–Ukuleles as a signifier for the Hawaiian islands (Again, as with all of these examples, there is potential for multivalence. With this particular example, more recent and increasing use of the ukulele within at least U. S. elementary music classrooms, if not as well in other locations around the world, the association with the ukulele and the elementary music classroom also evokes another layer of "place". A third layer of place is found in the incorporation of the ukulele into "pop" music with pieces including Israel Kamakawiwo'ole's (Braddah Iz's) use of the instrument in his medley of "Somewhere Over The Rainbow/What A Wonderful World". A fourth layer of "place" is found in its use in short films like Disney's short film Lava. Multivalence. Origins are important. History is important. Honoring one another is important.)

–Banjo as a signifier for bluegrass and Appalachian music, originally from Africa. (Multivalence. Origins are important. History is important. Honoring one another is important.)

–Organ as a signifier of Christian church music is also utilized in pop, rock, and jazz music. It was also used live in early silent films and perhaps later recorded for silent films rebroadcast on television. Additionally, it has been used live and later recorded at carnivals in the merry-go-rounds. Multivalence. Origins are important. History is important. Honoring one another is important.)

–Early music performers will often now intentionally perform on period instruments for the reason of hearing the music in as close a manner as possible to the ways in which the original listeners would have heard it, evoking a type of historical sense of "place". (*Disclaimer: We acknowledge that though this does bring us closer to the ways they may have heard it, they did not have the same biographical listening history that we do.)

–The particular "sound" of a recording itself (micing techniques, recording approaches, use of particular recording technologies, and more, from a given time period)

Informal Thoughts On Music And The Brain: Music As An Aid In Memory Formation And Retention

(These thoughts are indebted to the Animaniacs television series, Diana Deutch, Gary S. Karpinski's Music Cognition and Perception class and readings, ICMPC (International Conference on Music Cognition and Perception)— presentation-performance of members of the deaf community as a part of the conference, Susan Magsamen and Ivy Ross, Martha Jane Thoreson Mosher, Carmen Shirley Bunn Mosher, Pearson Silver-Burdett, Preschool Prep video series, Switched At Birth television series, "Music In The Brain" by Anne Trafton, which can be read at https://mcgovern.mit.edu/2015/12/16/music-in-the-brain/, "Your Brain On Music: The Sound System Between Your Ears" article found at the Trump Kennedy Center, which can be read at https://www.kennedy-center.org/education/resources-for-educators/classroom-resources/media-and-interactives/media/music/your-brain-on-music/your-brain-on-music/your-brain-on-music-the-sound-system-between-your-ears/, Cadence podcast—Indre Viskontas, observing those with hearing aids and members of the deaf community, and more.)

Brain research has shown that music is not solely processed in one region of the brain (See the article linked above entitled "Your Brain On Music: The Sound System Between Your Ears" found at the Trump Kennedy Center), though "...a neural population in the human auditory cortex that responds selectively to sounds people typically categorize as music, but not to speech or other environmental sounds." has been located. (See the article linked above entitled "Music In The Brain" by Anne Trafton.). Perhaps the way that music connects multiple areas of the brain together makes it quite powerful in allowing us to "make connections" that we otherwise would be unable to make, which may help us as humans in all domains of our lives.

In addition, music seems to last quite a long time in our memories (With Alzheimer's patients, music has been shown to be one of the "last parts of the memory to go".), which may give it potential for making our memories in other domains that are connected to music last longer as well. In other words, there is evidence that music aids both in memory formation and retention. Here are some examples of this, below:

-"The Alphabet Song" (Roman alphabet, used in U. S. schools) aids us in remembering a string of 26 letters (This is a much longer string of information than is typical to retain without music. Also note that "chunking" information, a process in which we can group or subsume smaller amounts of information into larger meaningful "chunks", typically occurs at a maximum of 7 +/- 2 items (or "chunks") of information. This particular song uses its musical phrasing to group the letters of the alphabet into "chunks" of this size. For example, the first phrase is "A, B, C, D, E, F, G" (7 letters), "H I J K L M N O P" (9 letters (7+2) or 7 pulses at same pulse stream), etc. Other cultures likely have songs for recalling their alphabets as well. (Most of us can likely still sing our alphabet song, though if you are reading this, you were likely taught it years ago, and it is doubtful that you put it on your playlist yesterday—with likely exceptions.)

-Preschool Prep video series for children incorporates music into the learning process in its presentation of Letters, Colors, Numbers, Digraphs, Blends, Sight Words and seemed to be quite effective for learning within our family.

-"The Sun Is A Mass Of Incandescent Gas" and "Beep Beep, Here Comes A Satellite" were "science songs" I was taught as a child, which have acted as strong memory aids for me.

-The Animaniacs television series has songs which aid in the memory of (a) the countries of the world, (b) the U. S. states and capitals, (c) the planets of our solar system, and likely others I do not currently recall.

-Pearson Silver-Burdett includes a song in their elementary music curriculum entitled "Fifty-Nifty United States" that aid children in remembering all the U. S. states.

Continued research in these areas should prove fruitful. It might also be particularly helpful to focus some of our future research on assisting those with cochlear implants and other hearing aid devices in order to develop musically-robust models of sound for them for the purposes of facilitating their memory retention and deepening their musical enjoyment.

What Would It Look Like If We Expressed All Major Keys Enharmonically? (Just For The Fun Of It)

(These thoughts are indebted to Daniel Huey, Gary S. Karpinski, a lesson entitled "Identify and Represent Proportional Relationships from into Math (Grade 7) by Edward B. Burger, Juli K. Dixon, Timothy D. Kanold, Matthew R. Larson, Steven J. Leinwand, and more.)

When we learn our major scales and their tonics' relationships to the Circle of Fifths, we learn 12 sonically-distinct major scales; however, we learn 15 major scales with respect to our traditional notation system (because we traditionally express 3 of those 12 scales enharmonically as well). What would it look like if we extended the enharmonically-expressed key concept to every major scale? Below, you will see three expressions of each key area.

B-sharp major: B sharp, C double-sharp, D double-sharp, E sharp, F double-sharp, G double-sharp, A double-sharp, B sharp [12 sharps]

C major: C, D, E, F, G, A, B, (C) [0 sharps and 0 flats]

D double-flat major: D double-flat, E double-flat, F flat, G double-flat, A double-flat, B double-flat, C flat, (D double-flat) [12 flats]

F double-sharp major: F double-sharp, G double-sharp, A double-sharp, B sharp, C double-sharp, D double-sharp, E double-sharp, (F double-sharp) [13 sharps]

G major: G, A, B, C, D, E, F sharp, G [1 sharp]

A double-flat major: A double-flat, B double-flat, C flat, D double-flat, E double-flat, F flat, G flat (A double-flat) [11 flats]

C double-sharp major: C double-sharp, D double-sharp, E double-sharp, F double-sharp, G double-sharp, A double-sharp, B double-sharp (C double-sharp) [14 sharps]

D major: D, E, F#, G, A, B, C#, (D) [2 sharps]

E double-flat major: E double-flat, F flat, G flat, A double-flat, B double-flat, C flat, D flat, (E double-flat) [10 flats]

G double-sharp major: G double-sharp, A double-sharp, B double-sharp, C double-sharp, D double-sharp, E double-sharp, F triple-sharp, (G double-sharp) [15 sharps]

A major: A, B, C#, D, E, F#, G#, (A) [3 sharps]

B double-flat major: B double-flat, C flat, D flat, E double-flat, F flat, G flat, A flat, (B double-flat) [9 flats]

D double-sharp major: D double-sharp, E double-sharp, F triple-sharp, G double-sharp, A double-sharp, B double-sharp, C triple-sharp, (D double-sharp) [16 sharps]

E major: E, F#, G#, A, B, C#, D#, (E) [4 sharps]

F flat major: F flat, G flat, A flat, B double-flat, C flat, D flat, E flat, (F flat) [8 flats]

A double-sharp major: A double-sharp, B double-sharp, C triple-sharp, D double-sharp, E double-sharp, F triple-sharp, G triple-sharp, (A double-sharp) [17 sharps]

B major: B, C sharp, D sharp, E, F sharp, G sharp, A sharp, (B) [5 sharps]

C flat major: C flat, D flat, E flat, F flat, G flat, A flat, B flat, C flat [7 flats]

E double-sharp major: E double-sharp, F triple-sharp, G triple-sharp, A double-sharp, B double-sharp, C triple-sharp, D triple-sharp, (E double-sharp) [18 sharps]

F sharp major: F sharp, G sharp, A sharp, B, C sharp, D sharp, E sharp, (F sharp) [6 sharps]

G flat major: G flat, A flat, B flat, C flat, D flat, E flat, F, (G flat) [6 flats]

B double-sharp major: B double-sharp, C triple-sharp, D triple-sharp, E double-sharp, F triple-sharp, G triple-sharp, A triple-sharp, (B double-sharp) [19 sharps]

C sharp major: C sharp, D sharp, E sharp, F sharp, G sharp, A sharp, B sharp, (C sharp) [7 sharps]

D flat major: D flat, E flat, F, G flat, A flat, B flat, C, (D flat) [5 flats]

E sharp major: E sharp, F double-sharp, G double-sharp, A sharp, B sharp, C double-sharp, D double-sharp, (E sharp) [11 sharps]

F major: F, G, A, Bb, C, D, E, (F) [1 flat]

G double-flat major: G double-flat, A double-flat, B double-flat, C double-flat, D double-flat, E double-flat, F flat, (G double-flat) [13 flats]

A sharp major: A sharp, B sharp, C double-sharp, D sharp, E sharp, F double-sharp, G double-sharp, (A sharp) [10 sharps]

B flat major: B flat, C, D, E flat, F, G, A, (B flat) [2 flats]

C double-flat major: C double-flat, D double-flat, E double-flat, F double-flat, G double-flat, A double-flat, B double-flat, (C double-flat) [14 flats]

D sharp major: D sharp, E sharp, F double-sharp, G sharp, A sharp, B sharp, C double-sharp, (D sharp) [9 sharps]

E flat major: E flat, F, G, A flat, B flat, C, D, (E flat) [3 flats]

F double-flat major: F double, flat, G double-flat, A double-flat, B triple-flat, C double-flat, D double-flat, E double-flat, (F double-flat) [15 flats]

G sharp major: G sharp, A sharp, B sharp, C sharp, D sharp, E sharp, F double-sharp, (G sharp) [8 sharps]

A flat major: A flat, B flat, C, D flat, E flat, F, G, (A flat) [4 flats]

B triple-flat major: B triple-flat, C double-flat, D double-flat, E triple-flat, F double-flat, G double-flat, A double-flat, (B triple-flat) [16 flats]

*Moving in a sharpward direction (clockwise) around the Circle of Fifths increases the sharp collection by one with each click up to 19 sharps (where we stopped with B-double sharp major); it decreases the flat collection by one with each click. Moving in a flatward direction (counterclockwise) around the Circle of Fifths increases the flat collection by one with each click up to 16 flats (where we stopped with B triple-flat major); it decreases the sharp collection by one with each click.

Informal Notes On The Use Of A "Taste" Metaphor To Express Consonance-Dissonance Perception

(These thoughts are indebted to a conversation with my wife (Renee' Kathleen Gonzales Mosher) about taste-testing foods at a local farmers' market, informal feedback from students in music theory classes on interval perception of consonance-dissonance, and more.)

What if we tried putting our sense of taste to use as a metaphor to describe our consonance-dissonance perception? People have different tastes for foods and drinks, so we could use our taste bud palettes as analogous to our aural palette for consonance-dissonance. Doing so would allow us to acknowledge individual differences (perhaps based in whole or in part on our personal historical listening backgrounds) in the following areas:

(a) harmonic perception of intervals

(b) harmonic perception of 3-or-more-note sonorities

Looking at consonance-dissonance perception through this lens could also allow for our aural perceptions to change over time as often our tastes for certain foods and/or drinks change over time as well.

Informal Notes On "Musikenglish" and/or "Musiklanguage"

(These thoughts are indebted to the B-A-C-H motive, J. R. R. Tolkien's The Silmarillion, serialism, total serialism, discussions and readings from Rob Schultz's Motivic Analysis class, music note-reading worksheets from elementary music class that spell words like "cabbage", etc., and more.)

What if we converted every tone of a quarter-tone scale into a letter of the alphabet in order to use our music to "play" words? We would have 24 characters to work with if we removed the letter "c" from the alphabet (allowing the soft "c" to be spelled with an "s" in its place and allowing the hard "c" to be spelled with a "k") and removed the letter "q" from the alphabet (allowing "kw" in its place). Melodic lines could then spell out words. Segmentation from one word to the next could be achieved through the use of rests. Simultaneities would be self-contained words that we could read from the lowest-to-highest-sounding note. If more registers are needed for particular words, we could have instruments that play together and indicate in what order to read those instruments' contributions to the words.

*The example here is based upon use of a mod24 system adapted to the 26-letter English alphabet, but could be applied to any modular space in order to correspond to an alphabet of any size (length).

Informal Notes On "...And Heaven And Nature Sing"—Animal And Plant Speech And/Or Song (And Effects Of Speech And/Or Song On Plants)

(These thoughts are indebted to Colossians 1:16–23, Job 12:7–8, Luke 19:40, Numbers 22: 21–34, Psalm 19:1–4a, Romans 8:21–22, St. Francis of Assisi, Kerry Dearborn, Diana Deutch, Jane Goodall, National Geographic, George Bernard Shaw's Pygmalion (My Fair Lady), Indre Viskontas, Eric Whitacre's "The Seal Lullaby", Wild Dolphin Project and Google's DolphinGemma (AI machine learning model), "Is There a Role for Sound in Plants?" by Filippo Del Stabile, Vittoria Marsili, Luca Forti, and Laura Arru, and more.)

Below, you will read a description of some of my thoughts on how we might decode the language(s) of dolphins (and/or other creatures). Some disclaimers here: (a) It appears that a lot of work has already been done to this end with some animals, in particular with dolphins via the Wild Dolphin Project and their use of Google's DolphinGemma (AI machine learning model). (b) I have no formal training in this area of research; I simply find it fascinating. (c) There is much work to be done on this (these) topic(s), though a rigorous literature review would be necessary to know where to effectively jump into this (these) topic(s).

-record sounds

-organize sounds from broad to fine categorical groupings

-whistles, clicks, blowhole sounds, etc. (as the largest groupings)

-under (for example) whistles, organize these sounds by pitch, pitch contour, width of pitch contour, length of sound, rate of pitch change, energy

expended and at what rate within the sound, etc.

-under (for example) clicks, organize these sounds by how many clicks occur in a given time spacing, the number of clicks, the distribution of the clicks

within the time frame (clustering of clicks within the timeframe), acceleration or deceleration of clicks within the time span, intensity: waxing or waning

or staying fairly constant, pitch contour to the clicks, are the clicks "voiced"—engaging vocal folds—or "unvoiced"—not engaging them

-under (for example) blowhole sounds, organize these sounds by pitch height, width or thickness of the sound, amount of open/spread or closed or tall

sound to the sound, amount of spray or air expended or amount of mixture

-consider that these could be syllables? words? word picture statements as in full-thought sentences? etc. To this end, try seeing how dolphins may combine them in groups of two or more sounds. Look for any consistent combinations here. Make these comparisons with video as well to see how non-sonic communication may interact as part of a consistent meaning for these sounds. Also, check dolphin actions that may consistently go with these sounds, etc.

-Note that all dolphins may not have the same language as all humans do not either. They may be regionally localized (distributed) to various points, though perhaps related.

-Also, record these sounds from many dolphins within a region so that you can generalize about these sounds in a way where one sound with one meaning might sound different in different dolphins because of the physical structure differences among them.

-Further, any sounds they may make outside of the range of human hearning, translate into the range of human hearing, but take the original pitch height into consideration in your analysis.

-Might there be musical and/or deep emotive value (further aesthetic value) to the patterns of sounds and silences they make?

-Value of similar approach to other animals outside of dolphins which may have been less studied or not studied at all?

-Though some work has been done, further work would be very helpful in studying the effects of speech and/or music on plants and perhaps looking at the ways in which they communicate via sound (acoustic perception and communication). (According to "Is There a Role for Sound in Plants?" by Filippo Del Stabile, Vittoria Marsili, Luca Forti, and Laura Arru, "...plants not only respond to sound, they actually seem to emit sound as well.")

Informal Notes On Personalized Music For Smart Household Appliances

(These thoughts are indebted to a discussion I heard on the radio between two DJs while I was waiting to get a haircut, and more.)

What if we could program personalized playlists via Spotify or another music platform which could connect to smart household appliances in order to vivify our daily experiences. A few examples might include the following:

-You arrive home and open the front door. You start hearing Chris Martin singing "Home, home, where I wanted to go." from "Clocks" by Coldplay (among a larger repository of songs which could be set up to play when you open your front door either randomized or played in an order you set up).

-It's Tuesday night and you put in your refrigerator's app that Tuesday night's dinner is Taco Tuesday. You open the door to the refrigerator and music from Los Tigres del Norte begins to play while you take out the Mexican food ingredients.

-You turn on the stove and Selena begins to sing.

-After dinner, you decide to have ice cream for dessert. As you open the door to the freezer you hear "The snow glows white on the mountain tonight, Not a footprint to be seen" from Frozen's "Let It Go".

-After dinner, you decide to take a bath. As you turn the water on you hear, "Splish, splash. I was takin' a bath, long about a Saturday night, yeah." from Bobby Darin's "Splish Splash".

-Now it's time to head to bed. You open your pajama drawer and hear "And oh, my dreams, It's never quite as it seems, Never quite as it seems." from "Dreams" by The Cranberries.

Informal Notes On Including Games, Gaming, and Gamification Elements In Our Teaching Of Music Theory And Aural Skills

(These thoughts are indebted to Michael R. Rogers, John Snyder, former students, and more.)

*Disclaimer: I have not done a literature review on this topic, so ideas presented here may not be novel. It is also my understanding that gamification is currently a broader trend across educational disciplines, not specific to music theory and aural skills.

"In every job that must be done, there is an element of fun. You find the fun aaaaand "snap", the job's a game!"—Mary Poppins from Mary Poppins

Games, gaming, and gamification of any content matter allow us to present that content in such a way that motivates student learning, makes it fun, memorable, and engaging, and further encourages future attendance, collaboration with peers, and "stick-to-it-ive-ness" (mental staying power with content matter). Below are just a few examples and/or possibilities in music theory and/or aural skills:

--Make reviewing of material in advance of an exam a game show (music theory): Divide the class into two teams. A representative from each team takes a seat facing away from the board. Put examples to work on the board in two separate locations (one for each team). Once the examples are ready, say "Go!". The team representatives get up from their chairs and run to the board. They work the examples as quickly as they can and return to the seat they got up from. The first team representative back to their seat with the correct solution(s) wins a point for their team. Repeat this process until all students have had an opportunity to play. You can decide if teams can help the representatives or not. First team to "X" wins. Congratulate everyone for working hard and playing hard—make it fun for all!

--Team dictations (aural skills): Divide into any number of teams (perhaps 3 or 4 to a team is a reasonable size). Have the teams come up to the whiteboard within their own areas so they have enough space to take down a dictation. Play the dictation and have each team write the music you have played. You determine number of playings and amount of time between playings. The students work within their teams to notate what you've played. First team to complete the dictation accurately and say "Final answer." wins. Congratulate everyone for working hard and playing hard—make it fun for all!

--Community dictations (aural skills): All students remain in their seats while you play a dictation. Each student is individually working on the dictation on their own staff paper from their seats. Allow for a little time to pass after the first playing (you determine the amount of time). Then state that you would like to allow for someone to contribute the first X amount of notes or beats. A volunteer comes and writes the beginning of the dictation on the whiteboard. If it needs correcting, do not correct it unless it is unable to be corrected by another student from the class. (*With this game, it is important to convey in advance that we are workshopping. It is not for a grade. We are working as a team. There is no shame in writing something incorrectly and being corrected by a peer. This is all part of the learning process for all of us. There is a certain amount of trust and camaraderie that must be developed in the playing of this game—which is also a good thing!) Play the dictation again. Allow for some more time to pass. Invite a new student contributor to add a certain amount of notes or beats to the dictation. Continue this process of allowing the class to collectively form the dictation on the board until all are satisfied that what they have on the board matches the sound of what you've played.

--Use of supplemental online resources like teoria.com for some homework assignments on rudimental concepts (music theory). These resources can allow for the students to practice a concept until their accuracy and speed with that concept reach a point of fluency. They also receive immediate feedback on their accuracy throughout their practice.

--Use of Quizlets in reviewing select materials (music theory)

--Music theory and aural skills RPGs (music theory and aural skills knowledge and skills put to use within the game help you advance in the game)?

Informal Notes On Extending The Idea Of Intervallically-Based Chord Labeling In Compositional Contexts Which Seem To Be Based Upon Voicing As A Paramount Focal Point

(These thoughts are indebted to Stefan Kostka, Stefan Caris Love, Felipe Salles, and more.)

*Disclaimer: This is not a novel idea, but simply an extension of a labeling system that I've seen in Materials and Techniques of 20th-Century Music by Stefan Kostka.)

Within a diatonic context, (below I will use C major as a demonstration and three-note sonorities as a demonstration) we may indicate the number of notes in a given harmonic sonority followed by the general interval (from within its diatonic sound world) being replicated followed by the bass-root note and referent diatonic sound world.

Diatonic context derived from: C D E F G A B C; sonority: C D E; label: 3 x 2 on C maj diatonic

Diatonic context derived from: C D E F G A B C; sonority: C E G; label: 3 x 3 on C maj diatonic

Diatonic context derived from: C D E F G A B C; sonority: C F B; label: 3 x 4 on C maj diatonic

Diatonic context derived from: C D E F G A B C D; sonority: C G D; label: 3 x 5 on C maj diatonic

Diatonic context derived from: C D E F G A B C D E F; sonority: C A F; label: 3 x 6 on C maj diatonic (*yes, some will be recognizable triadic inversions;

resist seeing/hearing them this way within a context focused on intervallically-based voicings)

Diatonic context derived from: C D E F G A B C D E F G A; sonority: C B A; label: 3 x 7 on C

Within a chromatic context, we may indicate the number of notes in a given harmonic sonority followed by the specific interval being replicated followed by the bass-root note.

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B; sonority: C C#/Db D; label: 3 x ic1 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B; sonority: C D E; label: 3 x ic2 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B; sonority: C D#/Eb F#/Gb; label: 3 x ic3 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B; sonority: C E G#/Ab; label: 3 x ic4 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B; sonority: C F A#/Bb; label: 3 x ic5 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C; sonority: C F#/Gb C; label: 3 x ic6 on C (*could be seen as 2 x ic6 on C with doubling of "C" at

octave)

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C C#/Db D; sonority: C G D; label: 3 x ic7 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C C#/Db D D#/Eb E; sonority: C G#/Ab E; label: 3 x ic8 on C (*yes, again, some will be recognizable

triadic inversions; resist seeing/hearing them this way within a context focused on intervallically-based voicings)

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C C#/Db D D#/Eb E F F#/Gb; sonority: C A F#/Gb; label: 3 x ic9 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C C#/Db D D#/Eb E F F#/Gb G G#/Ab; sonority: C A#/Bb G#/Ab; label: 3 x ic10 on C

C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb; sonority: C B A#/Bb; label: 3 x ic11 on C

Informal Notes On Use Of Algorithms (Or Recipes) For Rudimentary Skills In Music Theory

(These thoughts are indebted to Help Your Kids With Computer Coding: A Unique Step-By-Step Visual Guide, From Binary Code To Building Games (authors include Carol Vorderman, Jon Woodcock, Sean McManus, Craig Steele, Claire Quigley, and Daniel McCafferty; previous music theory courses, and more.)

Help Your Kids With Computer Coding defines an algorithm as a set of simple instructions for performing a task. Merriam-Webster defines recipe as (1) a set of instructions for making something from various ingredients, (2) a formula or procedure for doing or attaining something.

Students of music theory rudiments could find use of explicitly written-out algorithms (or recipes) incredibly helpful as they work with new musical materials. As they develop increasing speed and fluency with a musical topic through repeated practice, outlined versions of these algorithms (recipes) become helpful in weaning them off the need for the complete algorithm. As fluency with the musical material is approached, the need for the algorithm or outline to be explicit is eliminated since the process has become internalized.

Building A Major Scale

(ingredients: knowledge of musical note names, knowledge of the definition of the term "scale", knowledge of locations of note names on modern clefs, knowledge of sharps and flats, knowledge of the locations of notes on a keyboard, knowledge of the term "step", knowledge of the distinction between types of step: half-steps and whole-steps; knowledge of the half- and whole-step formula for the major scale structure (WWHWWWH))

(Complete algorithm. No part of the following process has been internalized.)

1. Pick a starting note.

2. Place the starting note on the staff in the appropriate location.

3. Place your second note a whole step above your starting note.

4. Place your third note a whole step above above your second note.

5. Place your fourth note a half step above your third note.

6. Place your fifth note a whole step above your fourth note.

7. Place your sixth note a whole step above your fifth note.

8. Place your seventh note a whole step above your sixth note.

9. Place your eighth note a half step above your seventh note.

(Outline. The process is understood. Only the overall plan is necessary as a scaffold.)

1. Pick a starting note.

2. Add successive ascending notes that conform to the structure WWHWWWH. (You should end on starting note 8va.)

(Fluency. Major scales are internalized.)

1. Pick a note.

2. Build its major scale.

More Informal Notes On Embodied Learning At The Keyboard

(These thoughts are indebted to Timothy Koozin, and more.)

Have you ever had this experience? I memorized this piece of music a while back. I don't really remember it, but my hands do. So you end up able to play it. (Muscle memory)

What if we could put muscle memory to use intentionally in our approach to the teaching of keyboard skills?

We can, for example, internalize the various ways a major chord can feel physically. Zooming in on this example, a close voicing major chord in root position can fall into six categories of "feel" to the hands (even as they all fall into the same intervallic structure of a major third below, a minor third atop, and a perfect fifth as the bounding interval). Below are the 6 "feel" categories for this example.

Category 1: white note-white note-white note (wh-wh-wh): C major, F major, G major

Category 2: black note-white note-black note (bl-wh-bl): C#/Db major, D#/Eb major, G#/Ab major

Category 3: white note-black note-white note (wh-bl-wh): D major, E major, A major

Category 4: black note-black note-black note (bl-bl-bl): F#/Gb major

Category 5: black note-white note-white note (bl-wh-wh): A#/Bb major

Category 6: white note-black note-black note (wh-bl-bl): B major

All chord shapes can be categorized in like manner to the system shown by this above example.

Chord progressions too can be approached in this way. Let's use a three-voice right hand texture as an example. We can think of our approach to the chord progression from the standpoint of parsimonious voice leading, emphasizing economy of means. For example, a I-vi-IV-ii-cad64-V7-I in any major key in a 3+1 texture could have the right hand voiced as follows:

Begin with the notes as such (stated from lowest to highest voice, only RH voices shown; LH would cover notes implied by the above harmonic progression):

EGC (action required to move to next sonority: bounding voices remain, middle voice moves up by step within the key)--> EAC (action required to move to next sonority: top two voices remain, bottom voice moves up by step within the key)--> FAC (action required to move to next sonority: bottom two voices remain, top voice moves up by step within the key)--> FAD (action required to move to next sonority: all three voices slide down by step within the key)--> EGC (action required to move to next sonority: middle voice remains, outer voices contract by step within the key)--> FGB (action required to move to next sonority: middle voice remains, outer voices expand by step within the key)--> EGC.

Informal Notes On Contour, Pulse Streams, Groove, And Similarities Of Effect Across Instruments

(These thoughts are indebted to Timothy Koozin, Rob Schultz, John Snyder, Kristen Wallentinsen, and more.)

One of Merriam-Webster's definitions of groove is "a pronounced enjoyable rhythm". Grove Music Online includes "vital drive and rhythmic propulsion" in its definition. Many consider groove from the standpoint of a composite interlocking rhythmic effect created by the repeated rhythmic coordination of several instruments working together to create an overall rhythmic feel that is fairly palpable. I would like to consider general contour points as a stand-in for the several instruments noted in this last approach to groove. In other words, when a certain contour point is sounded, imagine that contour point to actually be the sounding of a particular "instrument". I will then show how these repeated contour shapes are created by the drum set (my first example), the acoustic guitar (my second example), and the piano (my third example). *Disclaimer: Some will likely see these as "accompaniment patterns" as opposed to "grooves", and that's OK by me at this point as at some level I think what I am exploring here in this nascent stage is the similarity between a drum set as an accompanist and more strongly pitched instruments which have overlap with the drum set in their approach to accompanying.

A Sample Drum Set's Collective Contour Points and Overall Shape (rough outline)

Contour Point 6: Cymbals

Contour Point 5: Snare

Contour Point 4: Tom 1

Contour Point 3: Tom 2

Contour Point 2: Tom 3

Contour Point 1: Kick Drum

(Basic Rock Beat in 4/4; Kick on beats 1 and 3, Snare on beats 2 and 4, Hi-hats (Cymbals) every eighth note)

6: C C C C C C C C

5: S. S

1: K K

Travis Picking On An Acoustic Guitar—Collective Contour Points and Overall Shape (rough outline—chords and their particular constituent notes may change as the chords change, but do not matter for the purposes of groove contour and overall shape)

Contour Point 6: String 1 (highest-sounding/thinnest string)

Contour Point 5: String 2

Contour Point 4: String 3

Contour Point 3: String 4

Contour Point 2: String 5

Contour Point 1: String 6 (lowest-sounding/thickest string)

(Travis picking uses a low, high, mid-low, mid-high contour repetition pattern)

D major chord

6 (string 1): F# F#

5 (string 2): D D

4 (string 3): A A

3 (string 4): D

2 (string 5): A

1 (string 6):

*Notice above that there are two iterations of the contour. The bass notes of D (string 4) and A (string 5) function as the low point in the four-point contour. The fact that the bass note changed does not matter from the standpoint of the groove contour or overall shape.

Alberti bass pattern in left hand of the piano (again, the particular chords used or chord changes do not affect the overall shape)

Contour point 3: high note of chord

Contour point 2: middle note of chord

Contour point 1: low note of chord

(Alberti bass uses a low, high, middle, high contour repetition pattern.)

G major chord

3: D D

2: B

1: G

Informal Notes On Scalar Shapes Embodied At The Keyboard Through Various Techniques Via Muscle Memory Emphasis As Pedagogical Reinforcement

(These thoughts are indebted to Elizabeth Wallace, Timothy Koozin, and more.)

You are trying to learn your scales at the keyboard. Let's say you're working on major scales in particular. Assuming you know your major scales intellectually from music theory class and could verbally state the notes of any major scale in order, do you know them in an embodied physical sense at the piano keyboard, for example? In working on this embodied knowledge, it is once again important to recognize patterns for a number of reasons, but specifically here for the purposes of grouping scales with identical fingerings so that if you know the fingering for one scale, you can apply that same knowledge to any other scale that reproduces that same fingering pattern. This significantly cuts down on cognitive (and embodied) load. Use patterns to your cognitive and embodied advantage. Let's focus on what some instructors refer to as Group 1 major scales. Group 1 major scales all use the following fingerings.

Right Hand (ascending read left to right; descending read right to left): 1 2 3 1 2 3 4 (5)/1 *The 5 in parentheses indicates you would use your pinky as the top note of your scale when you have decided to turn around and descend; otherwise, you would use your thumb in order to progress to the next register.

Left Hand (ascending read left to right; descending read right to left): (5)/1 4 3 2 1 3 2 1. *The 5 in parentheses indicates you would use your pinky as the starting note of your scale as you begin your ascent; otherwise, you would use your thumb in order to progress to the next register.

Group 1 major scales that use the above fingerings include C major, G major, D major, A major, and E major. Combine your intellectual knowledge of the notes in these particular scales with the embodied Group 1 fingerings at the piano keyboard and you've got it. This may be enough. However, in the case that our fingers need reinforcement, we may try a few physical techniques that emphasize to our hands the shapes we want to create and recreate.

Cluster chord-scale approach:

Recognizing that our right hand pattern is essentially two shapes: (a) 123 and (b) 1234 on repeat, we can make cluster chords out of these two shapes and run them over the entire range of the piano keyboard. For example in C major, find the lowest CDE and play them as a chord with 123. Follow that up with FGAB played as a chord with 1234. Repeat this process moving all the way to the top of the piano keyboard and back down. (Do the same technique with other Group 1 scales in your right hand.)

Recognizing that our left hand pattern is essentially two shapes: (a) 4321 and (b) 321 on repeat, we can make cluster chords out of these two shapes and run them over the entire range of the piano keyboard. *In starting, we will begin our first octave with 54321 since 5 initiates the scale in the left hand.* In C major, 54321 plays CDEFG in the lowest register as a chord. Follow that up with ABC played as a chord with 321. Beginning in the next register, play DEFG as a chord with 4321, then ABC with 321, now repeating the 4321, 321 chordal process moving all the way to the top of the piano keyboard and back down. (Do the same technique with other Group 1 scales in your left hand.)

Time-weight-over/under exaggeration approach:

With this technique we draw attention to the moments in the sequence in which we have to either tuck our thumb under another finger or cross a finger over our thumb. We do this by physically leaning into these moments with extra weight in the hands and by lengthening these notes to add a temporally marked quality to these moments. This again, is a technique for learning through exaggerated embodied motions. Once the scales are internalized, you would want to even out the weight of each note and make the timing between note attacks equidistant.

RH alone: 1 2 3---- 1---- 2 3 4---- 1---- etc.

LH alone: (5)/1 4 3 2 1---- 3---- 2 1----4---- 3 2 1---- etc.

Informal Notes On Arhythmic To Rhythmic To Rhythmic-At-Tempo Tw0-Handed Piano Practice As A Technique For Learning

(These thoughts are indebted to Elizabeth Wallace, and more.)

Hands-alone practice at the piano is often incredibly important and it does a lot to solidify what each particular hand will do when it is put together, but it is certainly not a given that because you can perform something hands alone that you can perform it hands together. So as we put something hands together, we pay particular focused attention to precisely the sensations we physically feel as both hands create this shape right now, vertically, at the same moment in time. It may be necessary to begin this process arhythmically. If so, find your starting hand position. Mentally prepare yourself for which fingers in each hand will be depressed simultaneously, activating the weight of those fingers until you are ready to strike that shape at the keys. Once mentally and physically prepared for the first simultaneity, strike. Now look at the next simultaneity and repeat this same process. If practicing arhythmically, do not concern yourself with how long each simultaneity takes. Focus on pitch accuracy and attention to the physical feeling of playing that particular shape that you are focused upon. After you've successfully played two sonorities, try playing them back-to-back. Again, initially don't worry about the time it takes to get from one shape to the next. Rather, focus on the physical sensations of playing one sound, changing shape, and playing the next sound accurately. Once this is achieved with a consistent accuracy, introduce a very slow tempo and rhythmic accuracy within it. Your body now knows the shapes. Try very gradually working up to knowing those shapes at a consistent speed. As your accuracy becomes consistent at that speed, slowly increase the speed until you are at tempo. Take this concept and continually expand your approach and continuation window (prior to and following the harmonic moment with which you began).

Informal Notes On The Essence Of Community (Through The Lens Of (Musical) Ensembles)

(These thoughts are indebted to my communities, colleagues, and students, both past and present. If past, know you are ever-present with me; if present, I am grateful for the gift of your presence.)

-everyone belongs

-everyone is seen and accepted

-a place of calm

-a place of connection

-a place you can just be

-being heard

-being listened to

-listening to

-a place where we are all imperfect people, but we care about each other completely and always choose restoration when we get it wrong

-supportive

-all of us are for you, not against you

-a place of equality and equity

-a place where we share each others’ joys and hardships

-a sense of “we’ve got time for you, all the time in the world", and if you need our time, that doesn’t feel like an imposition, but an honor to gift you our time

-a place of play, joy, creativity, spontaneity

-a place of inclusion, not exclusion: You are welcome here. Me?, Yes, you. But I…, Yes, absolutely you.—wholeheartedly and individually, and each person is valued in this way. Always.

-A place we can express shared meaning together through song and music to the very best of our abilities without judgment, but instead with support.

-A place where our music can express all the feels— our ups, our downs, our ins, our outs, our I don’t knows, our emotional mixtures—all of our emotional complexities.

-A place we can’t wait to get to. A place we don’t ever want to leave.

-A place with doors that are always open and lights that are always on because we are always waiting expectantly for you to arrive.

-A place without “us” v. “them” because we are all always—all of us—"us”.

Informal Notes On "Hey! Who Turned Out The Lights?"—Kinesthetic Learning At The Piano Keyboard

(These thoughts are indebted to eye tracking studies, Dr. Gary S. Karpinski, Dr. Elizabeth Wallace, and more.)

As we learn at the piano, one of the things we can become aware of is that as we are at a certain point in our learning process, our eyes quickly shift between sheet music and our hands at the keyboard itself many times. "What notes am I supposed to play?" We quickly scan the score for the moment in the piece we are about to play and quickly take in all of the notes that need to be played in the next instant. Before we play, our eyes shoot downward to our hands. "Is my right hand positioned correctly for each note it will play?" We quickly shoot our eyes over to our left hand. "Is my left hand positioned correctly?" Then we may trust it and play the sound. That instant of sound is created correctly or incorrectly and a similar type of process repeats. The amount of information that must be taken in at once in "real time" is significant. Treble clef with multiple notes sounding at once. Bass clef with multiple notes sounding at once. All of this represents only one moment in time, so we must not only have fairly instantaneous recall of our notes in both clefs, but also be able to scan ahead of the next few moments in time and use our working memory to maintain a mental image of what sounds are upcoming. This will allow us to spend just a few moments longer looking at our hands when needed to focus on actually making those shapes at the keyboard and sounding them. The process over time becomes slightly more fluid as we shift between quick moments of time imaging larger swathes of music and more quickly finding those shapes at the keyboard with our hands. As we develop at the keyboard, however, we need to begin to develop an internal spatial image of our hands and their relationship to the keyboard itself so that we can minimize the need to look at our hands and the keyboard at all. One way to develop this skill is to take a scale, a chord progression, a brief excerpt that you can transpose, an interval, a short piece that you've memorized and literally turn out the lights in your practice room. This forces you to find the sounds that your mind's ear is looking for with a kinesthetic knowledge of your hands' size(s) and shape(s) and their relationship to the keyboard itself. These two entities should over time become "hand in glove" where your body simply knows where the note is, where the chord is, how it feels to take an octave and leap two octaves upward, etc. Start small. Be gentle on yourself when it comes to errors as there will be much error fixing in this type of practice (less and less over time). Start with shapes and sizes that are only near your body's center, the center of the keyboard, and require minimal shifts in hand positions. Then move gradually to more extreme positional shifts. (For example, a small shift would be from a C major chord in the 4th register (C4, E4, G4) to an F/C (C4, F4, A4). A larger shift would be a shift from Bb3 and Bb4 played simultaneously followed by a leap to Bb5 and Bb6. The goal is to make the keyboard such an extension of the body that it "feels like home". This kind of work over time will allow you to minimize the need to look down at your hands as you read music and also as you play by memory. So, "Hey! Who Turned Out The Lights?" You should.

Informal Notes On Alternatives To Traditional Musical Notation/Graphic Scores

(These thoughts are indebted to 20th/21st century experimentation in graphic notation, Ableton Live, brilliant.com, contour theory, historical musical notational developments, Dave Liebman, player piano rolls, Conlon Nancarrow, Rob Schultz, Dmitri Tymoczko, and more.)

Below, you will see a Cartesian graph in which the x-axis represents a steady pulse stream in eighth notes with the 8th note made equal to 160 beats per minute and the y-axis represents pitch height by a stable distance in half-steps (ic1). The plots may either be "dots" which indicate that pitch (or those pitches) at that moment in time or "lines" which indicate the pitches are sounded for the number of eighth notes they pass through on the x-axis. The system is flexible in that the time points on the x-axis may equate to any bpm and the pitch height on the the y-axis may equate to any scalar formation or interval class cycle of one's choosing (including uneven steps ("fuzzy categories") that accommodate for M2 v. m2, etc, gapped scales, non-octave repeating scales, or other scales of your own creation).

Pitch height (ic1) (up/down)

C5 . ______ ______

B4 .

A#/Bb4

A4 ______ ______

G#/Ab4

G4 . .

F#/Gb4

F4 ______

E4 . . ______

D#/Eb4

C#/Db4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pulse stream (left to right)

(8th notes; 8th note=160bpm

Informal Notes On Musical Works Made Of Negative Musical Space

(These thoughts are indebted to many.)

Imagine a musical pitch system. For our purposes, we'll use a diatonic C major system with pitch-classes C, D, E, F, G, A, B, (C). If, in our imagined work, we played the chord C major, we can imagine the negative musical pitch-class space as all the other pitch classes available in the system. Since C major is made of the pc set [C, E, G], the negative musical pitch-class space in that diatonic system is the pc set [D, F, A, B]. We could conceive of realizing musical works which perhaps maintain other musical parameters of a pre-composed piece, substituting out the negative space for each sonority. Voicings would be up to our compositional design. Other parameters could be maintained. The "new piece" could be understood as the negative pc space of the original piece. This same negative musical pitch-class space could be applied to other parameters creatively as well either individually or in combination.

Informal Notes On The Proposed Use Of Even-Further-Layered Musical Analytical Systems

(These thoughts are indebted to Thomas Christensen, Stefan Caris Love, Gary S. Karpinski, Jean-Philippe Rameau, Felipe Salles, and more.)

When we do harmonic analysis of musical passages, we layer two historical systems—figured bass and Roman numeral analysis. Figured bass is concerned with the intervals above a given bass note. It prefigures chord theory altogether. A bass note is written on the staff and Arabic numerals below the staff indicate to the performer what intervals above that bass note should be supplied for the sonority's realization. Traditional chord theory, which came later, understands sonorities from the vantage point of sonorities stacked in thirds. Once arranged into this position, the bass note is then understood as the "root" of the chord from which we name the chord. In terms of musical function, we then relate that chord to its root's position in the prevailing major or minor scale relative to a governing tonic of the passage or piece. The chord can then be assigned a numeric value indicated by a Roman numeral. Further, that Roman numeral can indicate the specific structure of the chord with capital Roman numerals indicating that the quality of the chord is major and lowercase Roman numerals indicating that the chord is minor. Sometimes addendums to these Roman numerals are added to triads to further indicate qualities such as augmented (+) or diminished (º). I would like to propose a further addendum to the use of seventh chords in order to further clarify their structure. We already do this with diminished seventh chords built upon the leading tone. In the major mode, we can build a viiø7. The half-diminished label (ø) tells us that the structure of the triad is diminished while the seventh is minor. In the minor mode, we can build a viiº7. The fully-diminished label (º7) applies the "degree" symbol to both the triad and the seventh as the "degree" symbol without an appending "7" means a diminished triad, but with the "7" following is understood to refer in both directions to the triad and seventh of the chord. However, I would like to recommend clarity, for example, among the I7, IV7, and V7 chords derived from the major mode. Via their functional labels as just shown, they would appear to all be of identical structure, but we know they are not. The V7 is a major-minor seventh chord; it consists of a major triad with a minor seventh above its root. The I7 and IV7 are major-major seventh chords; they consist of major triads with major sevenths above their roots. As we are comfortable with the analytical clarity afforded through layering figured bass and traditional chord theory, I would like to recommend that we further pull from pop chord labels into this analytical amalgam for the I7 and IV7 chords above described in particular. If we were in the key of C major, the I7 would get a pop label of Cmaj7 (or a delta symbol in the place of "maj"); the IV7 would get a pop label of Fmaj7. The "maj" label refers to the quality of the chord seventh, while the root label by itself is understood as shorthand for a major triad. I recommend we simply pull the "maj" label (and/or delta label) into functional analytical practice where these chords arise. I7 could easily be labeled Imaj7 and IV7 could easily be labeled IVmaj7. In jazz contexts, these labels do get used for this type of clarity. I think we could also benefit from them in analysis of Common-Practice-Era Western Art Music since at least IVmaj7, though certainly far less common than V7, does exist in the literature and the Imaj7 exists as a theoretical construct that comes up in our pedagogy when illustrating diatonic seventh chords which can be built from each degree of the major scale. As theoretical constructs, when illustrating seventh chords derived from the "three forms of" the minor scale, we could also include imaj7 (a minor triad with a major seventh which can be seen as derived from the harmonic or melodic minor scale), the III+maj7 (an augmented triad with a major seventh which can be seen as derived from the harmonic or melodic minor scale), and the IV7 (a major triad with a minor seventh which can be seen as derived from the melodic minor scale—inclusion of this chord as a theoretical possibility would also necessitate the use of "maj" in the IVmaj7 derived from the major mode to distinguish it from this theoretical chord; also note that within the blues tradition, the labels I7, IV7, and V7 do indeed all refer to major-minor seventh chords as the labels appear to indicate). Use of these labels for further clarity also allow for students to see them as possibilities in their own compositions even as they derive materials from familiar scale systems. It also assists in allowing us to broaden the scope in the undergraduate music theory sequence of the areas of repertoire we include outside of CPWAM. In settings where we do this, these chords then can become more than simply theoretical constructs, but options used in other repertoires and possibilities in current neo-tonal settings.

Informal Notes On Self-Awareness During Piano Practice

(These thoughts are indebted to many.)

Piano practice can be a joy. We can find joy in the process. We can find joy in practice. We can find joy in the performance. It is simultaneously a discipline, and we also can find joy in the discipline. You don't ever simply instantly arrive as the perfect pianist able to play any and everything always, no matter how long you have played the instrument. Skill levels are in a constant state of increase and decrease in this area or that area. Our love of the music and the instrument cause us to approach it as a lifelong journey and in itself as a practice. There is joy in this and hard work—and the joy of observing our hard work make a difference in the quality of our abilities with the instrument. All of this said, when we come to the practice room we don't come mindlessly. We come with intentionality. From one practice session to the next, some of our specific goals may be different, but we are working on some things—hopefully several different things. As we practice, our constant musical-awareness and self-awareness are incredibly important in terms of effective use of our practice time. In other words, we should be constantly monitoring both what is happening musically and what is happening within ourselves. As you practice, be checking in on your enjoyment of the process as you engage with a particular passage. Check in on your energy levels, your level of joy, anger, frustration, boredom, enthusiasm, focus, satisfaction. As you are practicing with particular strategies for improvement, are you seeing a reasonable musical performance quality increase in the passagework or are you beginning to see diminishing returns for the effort put in or perhaps even regression in the quality of your performance of a given passage (or the technique you are using to approach improving said passage). If you are in the zone, go after it; you are in the flow or a sweet spot of developmental improvement. If you are sensing that is not what is happening and you are seeing the quality of output slow or decrease while your frustration increases or your engagement decreases, it may be time to either take a short break, focus on your breath, go for a short walk to clear the head, change repertoire or focal areas of your practice, stand up and stretch, or take some other form of either mental break or change in focal activity. This will allow a mental reset, more productive and enjoyable practice, and a fresh engagement with the material that will prove more fruitful upon your return to the passagework that was causing you difficulty. Practice well.

Informal Notes On Music, Learning, and Theory Of "Place"

(These thoughts are indebted to Daniel Levitin, Elizabeth Wallace, and more.)

To my best current understanding, music has a strong ability to evoke a sense of "place". You hear a song playing that you first heard in a particular place and you can sometimes literally reconstruct all memories associated with the place you heard it. This can also be multi-layered. I can hear Debussy's Deux Arabesques and recall multiple places that I've heard the pieces. To use this ability, perhaps we should practice our instruments and study for quizzes and exams in multiple places because the reverse is also true. I can be sitting in the kitchen and want to go grab an item from the car and then forget what I was going to get once I get to the car. Upon returning to the kitchen, I recall what I wanted to get from the car perhaps because I thought of it in that "place". In practicing our instruments and studying for quizzes and exams, it may be helpful to study and practice where we will be taking the exam or performing our repertoire. That way the memories of what we are studying are present in that location. In addition, so as not to simply learn for the sake of the exam, but rather to allow the concepts and/or musical materials to travel with us outside of the specific location, we should study and practice our instruments in many different places so that our brains realize it is the informational content and musical content we are seeking to hold onto regardless of place.

Informal Notes On Alternate Ways Of Being Tonal Music: A Moment With Impressionism, Blues, Jazz, and 20th-and-21st-Century Popular Musics

(These thoughts are indebted to Brent Auerbach, T. Dennis Brown, Timothy Chenette, David Huron, Gary S. Karpinski, Stefan Caris Love, Drew Nobile, David Orr, Salvatore Macchia, Austin Patty, Felipe Salles, Lisa Sanders, Rob Schultz, Craig Sikes, Mark Spicer, Dmitri Tymoczko, John Wykoff, and more.)

Unpack the differences in terms like tonal versus centric
- Understanding that the level of detail that is given to analysis of what we traditionally refer to as tonal music is also worth this level of analytical attention when it comes to music that uses scalar systems beyond the CPWAM major/minor usage of the term. Rather than simply labeling this music as tonal and its tonal center as a tonic, it is often more common to label this music as centric, assigning a tonal center or centric note, but not being necessarily willing to label the tonal center a tonic because the harmonic and scalar language do not conform to the prior practice of particular works of particular composers from a particular era.
Unpack the differences in terms like harmonic progression, harmonic succession, and harmonic retrogression.

Understanding what we mean by the terms harmonic progression, harmonic retrogression, and harmonic succession. They seem to have differing connotations. Using the term progression appears to indicate that the choices in our chords are advancing, indicating that using such chord patterns makes them somehow more fitting to quality music. Retrogression appears to indicate that we are choosing chord patterns that are moving backwards or perhaps that using such chord patterns makes them somehow less fitting to quality music. Succession appears to indicate that we are simply aimless in our stringing along chord after chord. I will paraphrase my own personal take away from a video interview I heard of John Cage. Tones do not want to go to other tones; chords do not want to go to other chords; we may want them to go particular places, but this is based upon our own biographical listening histories (and social pressures based upon what we are told is “good music”) rather than the fitness of the melodies or harmonies themselves.

Unpack the differences in the level of detail important for analysis at the microscopic musical level such as:
- microtimings important to various expressions of musical swing (which are not all identical, but cluster around era, band, and individual, as opposed to simply labeling them with straight eighth notes and indicating that they are to be swung as if all musical swing is the same)
- Bent notes, blue notes, growls, rips, sound effects (natural and synthetic, recorded and live, also including earcons), elements of spatialization, use of vibrato (including when it is engaged within the timespan of the note, how wide the vibrato it is (and changes in this aspect), and the rate of speed of the undulation (and changes in this aspect)), proportion of breath-tone, and other non-discreet pitches which are important to the sounds of genres outside of (and inside of) standard CPWAM literature, but often not notated or easily accessible on all instruments
Unpack the perhaps unspoken differences in view among types of musical notation and aural traditions
How do we view the quality of music once we find that it is written on modern traditional sheet music, a lead sheet, a chord chart, a non-standard notational format (such as a graphic notation—though these are all in a sense graphic notations), or not notated at all? Do our views with respect to this question need reassessment?

Below is a figure which illustrates a possible way of viewing music from the whole tone scale. In such a case, "C" would function as the tonic and the other chords would be used in relation to "C" as the orienting note. A composer could use the primacy effect, the recency effect, repetition, reiteration, use at registral extremes in the texture, doublings (triplings, etc.) of the note, drones, and perhaps other ways to reinforce it in order to make certain that this is indeed still heard as the central tone around which the others are related. The composer should let the ear be the guide in doing this. (*It should also be noted that biographical listening history may also play into which note is heard as a tonic with respect to other listeners as I have seen a live experiment conducted in which some musicians heard one tone in a sounded musical passage as a reference point while other musicians in the room heard a different note as the reference point—see Drew Nobile's, Mark Spicer's, (and other theorists') work on the concept of the Double Tonic Complex in popular music.)

In the figure above, one may view these triads from a pop chord symbol approach on top of the grand staff; under the grand staff, one may view these same triads from a functional (how the chords relate to a given tonic) tonal viewpoint. In a scale such as WT-0 (0, 2) with "C" as a tonic, one will please note three things: (1) prior to the Roman numerals in some chords, there are directional arrows in use, (2) A#+ and Bb+ are both shown despite the fact that these chords would sound identical to one another, and (3) I have spelled all chords in stacked thirds. With respect to item 1, I am choosing to use the major scale as a reference point for the root locations of each chord. While this may seem odd, our mod-12 chromatic scale is traditionally used with a 7-letter-name system which allows for downward and upward inflections of those seven names. Since the major scale is such a common structure to many of our ears (mine included), I have chosen to use it in this instance as the point from which to inflect notes and chords upward and/or downward with respect to it. With respect to item 2, I have shown both versions of the final chord in the scale because our 7-letter-name system will create a gap in letter names at some point in a scale made of 6 scale tones. The composer is free to choose where to place the gap. With respect to item 3, though enharmonicism is completely an option, I have chosen here to spell these chords in 3rds consistently even when it causes some notes to require double sharps (etc.) for the "logic" of it (or the consistency of it, or the familiarity we have with spelling chords in 3rds).

Just Another Basic Analysis Of A Musical Excerpt?

(These thoughts are indebted to Brent Auerbach, Charles Burkhardt, L. Poundie Burstein, Timothy Cutler, Michael Horvit, Gary S. Karpinski, Timothy Koozin, Stefan Kostka, Stefan Caris Love, Robert Nelson, Matthew Santa, Joseph Straus, and more.)

Below, you will see a six-bar musical example I've written. It looks fairly basic and requests that the analyst label the key, the harmonies with Roman numerals and figured bass, embellishing tones, the harmonic sequence that takes place, and the cadence. However, in what initially seems a straightforward analytical exercise, we quickly encounter a number of complexities.

The first complexity involves non-chord tones. (I prefer the term embellishing tones which Burstein and Straus use.) Within our key of Bb major, we see a tonic triad governs the first bar of music; however, how do we understand the C-natural in the melody in m.1, b.2? Perhaps this is an easy answer. It is an appoggiatura since it is approached by leap and left by step. That would certainly be a correct reading. That being said, there are other contexts in which we use terms like register transfer and coupling in order to discuss connections we hear between octaves, a way of hearing not only pitch but pitch-class. The Bb4 on m.1, b.1 becomes a Bb5 on m.1, b.3. before returning back to the 4th octave registration, effectively allowing our ears to hear these 4th and 5th registers as aurally linked or connected in some manner. If then we were to collapse or flatten these two registers because of the way in which they are being used, the line in m. 1, b.1–3 becomes Bb-C-Bb and C functions as a neighbor tone. In addition, our contemporary ears are unable to unhear all the music we have heard in our current historical situatedness and so perhaps despite the anachronism in such a reading, our ears may hear this entire measure (particularly if performed with the sustain pedal) as a Iadd2 chord in which the C is simply part of the overall sound of the chord (or a Iadd9 if we do indeed want to draw attention to the registral disparity between the right and left hands). We can recognize both that this is not how listeners in the Romantic-era would have heard it (although I composed it two days ago as opposed to in the Romantic-era, lol) and also recognize that our ears can and sometimes do. We will return to other instances of embellishing tones I wish to consider within a larger overall discussion momentarily.

The second complexity involves our understanding of harmonic sequences. If I simply made the statement that the harmonic sequence is a sequence in descending thirds, as in Pachelbel's "Canon in D", I don't think I would have many that would argue against that reading. We move from I (Bb) down to V (F) up to vi (Gm) down to iii (Dm) etc. The overall pattern is a two-chord pattern copied and then pasted down by third within the key. It can summarily be labeled as D3(D4,A2). (In reading this notation of the sequence, it means that to achieve an overall downward trajectory of a descending third in terms of chord roots, we take two moves to get there—a root that descends by fourth and then ascends by second (within the key). The complexity arrives in the second-to-last (penultimate) measure. Where does the sequence end? If we continued the sequence further than I stated above, we would have the following: I (Bb) down to V (F) up to vi (Gm) down to iii (Dm) up to IV (Eb) down to I (Bb) down to V (F). In looking at the penultimate measure, we see that indeed, the chords do follow this pattern and don't break it until the final measure as we cadence on our tonic triad of Bb major. Is this an incorrect reading? My guess is that in the second to last measure, many want to hear something more traditional akin to a IV-cad64-V-I. Could both readings be correct? Also on the downbeat of m.5, what if we used a common substitute for IV such as a ii6? Now this calls into question whether or not we always only are talking about chord roots when we are talking about harmonic sequences. What if it were a ii65? What if it were a IVadd6? Further, beat 3 of this same measure is often thought of as a dominant functioning chord where scale-degree 5 (the F in the bass) is really the root and the other two tones are thought of as embellishing tones (the Bb and D) which fall by step into their actual "functioning" positions on beat 4. At the same time, it is also a tonic triad in its spelling and does indeed continue the harmonic sequence. Do both readings have validity? Are they two ways we can hear this?

This complex moment (the penultimate measure) also brings back our understanding of embellishing tones in the melody. What is the F5 in the melody on beat 2? The entire melody is a sequence with small variations upon each iteration. If we saw the C6 on m.1, b.2 as an appoggiatura, then it would make sense that this would be too. It is approached by leap and left by step as well; however, it does not resolve to a chord tone. If I use my contemporary ears (which are the ears I have by my historical situatedness), I could hear it as a IVadd2 or a IVadd9 anachronistically (but not really because it was written two days ago while imitating a 19th-century practice). Again, what if the chord were a common sub such as ii6, would the full sonority be a ii11 in first inversion? Would it be a IVadd6,add9? I could hear these being possibilities even as I also hear the characteristic use of the appoggiatura. The most weird thing to me is that this excerpt does not sound all that out-of-the-box to me for a Romantic-era sound world.

Moving on to beat 3 of the penultimate measure, what is the Eb5 in the melody? Is it an accented passing tone? It can't be if the F prior is an embellishing tone. It also has the effect on my ears of a 4-3 suspension, but it was not approached by common tone...unless we invoke register transfer again, which we could. But that reading would understand this chord as a I64, not a V64 (or cad64) at a cadence. If understood as a V64 with the F in the bass as the root, does the Eb in the melody then become a seventh? It does resolve downward by step as we teach that sevenths do.

The third complexity involves the cadence. As I see it, there are three possible readings. My guess at the most traditional reading is to understand it as a PAC. This reading understands beats three and four of the penultimate measure as a cadential 64 to 53 and finishing with a root position tonic triad with tonic in the melody as well. The points to consider, however are that it breaks with the left hand figuration which has been taking place for the rest of the piece. The left hand pattern was set up with the root that governed the measure on downbeats. In the penultimate measure, it is Eb (sd4) which governs the measure, not F (sd5). If we say that the F3 in the chords of the penultimate measure's beats 3 and 4 are indeed the governing harmonic root, then why do we then ignore the bass positions of the chords in the last measure on beats 2–4 as they have the same F3.

The second way we could see the cadence is as an IAC, although an odd one. In this reading, we say that the F3 in the penultimate measure is indeed governing these harmonies, despite its movement into an "inner voice". It then would state that the chords in the final measure on beats 2–4 need to be read the same way and so the final chord's sound is indeed inverted despite ending on a not-so-traditional "I64".

The third way we could view the cadence is as a plagal cadence (PC). This view retains the downbeats of each measure as the driving harmonic force for the measure and so despite the "inner voice" motion to the dominant on beats 3 and 4 of the penultimate measure, it would understand that motion as happening at a "lower level" of structure.

A fourth complexity involves meter. Sometimes it is advantageous to view simple duple and simple quadruple meters as interchangeable. In this particular musical example, I don't think they are. If we rewrote this piece in 2/4 with twice as many measures and left everything else the same, would accompaniment patterns such as this really be equally well expressed in either meter or would the expression in 2/4 cause performers to accent the music distinctly?

Music is complex.

Composer Notes For "Space-Time-Movement-Stillness" By David Mosher And All Performer-Creators Of The Piece

(This piece is indebted to Tibetan singing bowls, Christian meditation musicians, Gary S. Karpinski, Joseph N. Straus, 20th-century aleatoric and indeterminate works, and more.)

Instrumentation: This piece is for an unspecified musical instrument or group of instruments (understanding the voice as a musical instrument as well) of the performer-creator's (or performer-creators') choice.

Directions: Select any 5-note set of pitches (pentatonic). This may be any combination of 5 pitches, not just the ones we typically think of as "the" pentatonic scale (sds 1, 2, 3, 5, and 6 of the major scale), although this 5-note set is perfectly acceptable to use as well if you so choose. Play any note or note combination from the set as you feel led by the Holy Spirit of God. If you do not yet feel led to play a sound, sit peacefully in silence until you do, then play the sound(s) you feel led to play. Timing and the strength with which you play the notes should also be done in this manner. The amount of ring or the timing of damping the sound and note overlap amounts, where applicable, should also be done in this manner. The piece in some sense should continue on eternally into the way you live your entire life. That being said, you may cease playing the piece for a time in your physical body and go about your day when you feel led by the Holy Spirit of Jesus to do so.

The performer-creators could also be creative with use of other sensory modalities in the domains of light, fragrance, taste, and/or texture. Light, for example, could be operated through a light board operating colored lights which operate on faders and would be performed in a similar manner to the directions above in the sonic domain.

If you find yourself, for any number of reasons, uncomfortable understanding your movements and cessations of movements as issuing forth from the Spirit of God, please do not in any way allow this to hinder you from participating in this piece if you have the desire to participate in it. Perhaps, if this describes you, understanding your movements and cessations of movements in terms of acting on a positively-valenced impulse to move or a positively-valenced impulse to rest, a positively-valenced desire to gesture or a positively-valenced desire to stillness may better welcome you to participation in this piece today. Above all, if (and only if) you desire to participate-cocreate this piece, feel free to understand your participation in whatever fashion makes the most sense to you and sets you most at ease today. Holistic peace to you, my friend. Welcome.

Informal Notes On "Hey DJ, Make Us A Sonic Quilt!"

(These thoughts are indebted to Dorothy Bullard, Stefan Caris Love, Zachary Mosher, Rob Schultz, Frank Zappa, previous students, previous graduate students in my cohort, and more.)

*I begin this entry with a large disclaimer and acknowledgement of ignorance with regard to the worlds of DJing and quilting. If the analogy below misses the mark, I ask forgiveness in advance.

When a person makes a quilt, their imagination is captured by a fabric or a pattern or fabrics and patterns that they have a vision for in combination as they imagine putting them into adjacencies and juxtapositions and at opposing corners and in different shapes all coming together under an overarching vision for the whole of the quilt they will design. Disparate objects come together and make a new composite object that didn't exist before as they are brought together. Something beautiful. Something new.

This image of an artist strikes me as analogous to the artwork of a DJ, a sonic quilter, as it were. DJs find and collect a large variety and repository of songs. They imagine an event for which they will DJ and envision what pieces might work together over a large time span that would be most meaningful for those participating in the event. In real-time, DJs will choose a song they think will speak to the participants. They will real-time monitor engagement with the piece and do real-time editing—looping moments they think will create impact (changing the original form of the piece to fit the needs of the moment, a type of improvisation), changing tempo to effect mood, crossfading from one song to the next to either change up the mood or inject added energy into the space, etc. Song adjacency and overall arc (trajectory and curating of pieces throughout the event) also shape meaning in terms of how we understand them in relation to one another—contextual understanding (This occurs to participants consciously and/or subconsciously.). Changing order within a song (such as looping or repeating a section of the form) or from song to song (perhaps you originally heard a given piece in the context of its original album) or in the overall arc of the event (think of the event itself as analogous to a concept album) recontextualizes the sonic objects, allowing for new understandings. (To use another analogy, ordering books of the Bible in terms of (1) our best current archaeological knowledge of age of production, (2) by our best understandings of literary genre(s),

(3) by traditional order of the Tanakh (Torah, Nevi'im, and Ketuvim) as the CJB orders the Hebrew Bible, or other orderings, shape our understandings as if turning a prism in the light.)

Thanks to our quilters and thanks to our DJs for being artists that create something new, something beautiful.

Informal Notes On The Need For The Doubly-Augmented Unison

(These thoughts are indebted to attempting to mass transpose scales in a music software program, and more.)

As I have been working in a music software program, building scales and attempting to group piano fingering patterns for those scales in order to aid student learning of those scales, I have found it incredibly helpful to copy a scale, paste it, and then transpose it by the interval necessary to put it in the new key, updating the key signature for the scale so as to relocate the accidentals that ensue into the key signature. In so doing, I have run into the need for an interval which I have up to this point not had a practical need for using, but now do see such a need. The interval is the doubly-augmented unison. Read that again. Yes, the doubly-augmented unison. I had already written out the A# harmonic minor scale and now wanted to write the Ab harmonic minor scale. I wanted to use the copy-paste-transpose method which I described above rather than re-typing out every single note again in the new key, but doubly-augmented unison as a transpositional distance does not exist in the options. So instead, my workaround was to transpose down by augmented unison from A# harmonic minor to A harmonic minor and then again from A harmonic minor to Ab harmonic minor. Doable, but one extra step. Here's to the doubly-augmented unison for practicality's sake! ;)

Informal Notes On Piano Fingering Grouping Logics In Major And Harmonic Minor Scales

(These thoughts are indebted to perhaps "common" knowledge, Carmen Shirley Bunn Mosher, Louise Becker, Mrs. Padgett, Patty Arambula,

Dr. Elizabeth Wallace, and more.)

Major and Harmonic Minor scale fingerings on the piano may be grouped according to the following principles:

Group I Scales: C major and C harmonic minor, G major and G harmonic minor, D major and D harmonic minor, A major and A harmonic minor, E major and E harmonic minor

-RH: 12312341231234(5): read left to right shows the ascent; read right to left shows the descent; the underlined portions show finger

crossovers or crossunders; 5 indicates the turnaround point

-LH: (5)43213214321321: read left to right shows the ascent; read right to left shows the descent; the underlined portions show finger

crossovers or crossunders; 5 indicates the initiating point

Group II Scales: F# major/Gb major, C# major/Db major, Bb major and Bb harmonic minor/A# harmonic minor, Ab major and Ab harmonic minor/G#harmonic minor, Eb harmonic minor

-Group II fingerings use the following principles:

-(a) 234 RH for groups of three black keys ascending (432 RH for groups of three black keys descending)

432 LH for groups of three black keys ascending (234 LH for groups of three black keys descending)

-(b) for each set of two white notes between the sets of 3 or 2 black notes, use the thumb (or 1) on the appropriate note in the key

*In Group II scales that don't use all of the 3 black keys laid out together on the piano or the 2 black keys grouped

together on the piano (Bb major, Ab major as examples), those black keys that are used correspond to the fingers that you would use under
"principle (a)" above.

Group III Scales: no complete members, only hybrid usage of its principles; the principles only have application for the RH; there is no LH membership; for hybrids, see Hybrid Scales below

-Group III fingerings use the following principles:

-RH: thumb after black note or black note group ascending; thumb before black note or black note group descending, *exception at the leading tone,

which uses the 2nd finger

Group IV Scales: no complete members, only hybrid usage of its principle; the principle only has application for the LH; there is no RH membership; for hybrids, see Hybrid Scales below

Hybrid Scales:

-Group I/II Hybrids:

-F major: RH is Group II; LH is Group I

-B major/Cb major: RH is Group I; LH is Group II

-Group III/II Hybrids:

-F# harmonic minor: RH is Group III; LH is Group II

-C# harmonic minor: RH is Group III; LH is Group II

-Group II/IV Hybrid:

-Eb major: RH is Group II; LH is Group IV

*A note to the scale practitioner: Standardized fingerings for scales are not meant to be inhibitors to your freedom on the instrument as a pianist, but rather are pre-worked out for you in order to ease your fluency in navigating large swathes of the keyboard quickly and easily and with an eye toward ergonomics.

Informal Notes On "It's Electric!"

(These thoughts are indebted to John Campbell, and more.)

We have electric keyboards and synths that can modify their timbres to great amounts as well as electric guitars and electric drums that can do similar timbral changes. We also have electric violins, cellos, and double basses (not sure if we have electric violas?) of which I am uncertain as to the degree of timbral modification these allow. What if the entire orchestra (or simply all instruments both inside of a standard orchestral instrumental collection and outside of it—including the voice) could have electric counterparts to their acoustic originals (not in replacement of) in order to allow for an incredibly wide (exponential increase in) range of expressive and timbral possibilities outside of, and in addition to, those they already have in their acoustic forms? Perhaps the EWI (electronic wind instrument) is the kind of thing I am thinking of at least for wind instruments, but with a physical body and operation that as closely as possible keeps the physicality of the acoustic instrument in tact; and it should allow for the expressive range of, for example, a Nord piano keyboard or an electric guitarist with an incredibly large set of options in foot pedals and/or instant live real-time access to mind-staggering amounts of software patches. We could allow each instrument to have synthetic instrument capabilities, premade sounds, as well as allowing for significant modifications to those sounds throughout the sound envelope—attack, sustain, decay, release, in addition to room ambiance controls (wet-dry room amounts). We could allow for creating your own synthetic sounds—either novel in their timbre or with various degrees of modifications to known acoustic or more common electronic instrument sounds. This would allow for each orchestra (or ensemble of any kind) to really create quite distinctive collective timbral palettes, either unique to their sound as an ensemble, much as many popular music groups have a "sound" of their own (sound stamp) or unique to each piece or performance of a given piece.

*Somewhat related note: What if MIDI input for software instruments in DAWs like Logic, ProTools, etc. were equally set up for each of these electric instruments rather than only through MIDI piano keyboards? Why not through MIDI sitar or MIDI erhu? (Apologies if this is already the case to a larger degree than I am currently aware of. If not, let's do it!)

Informal Notes On Value And Music

(These thoughts are indebted to many.)

When assessing the value of something, I have often been told to consider a counterfactual or perhaps an alternative reality in which the item under question is absent from lived experience. Here is a brief series of thoughts which may spur creative thought around the value we place on or don't place on music. (The same thought exploration could and should be applied to all the arts individually and collectively as well, though the following will briefly consider just music.)

A World With No Music

-Live music is gone. Recorded music is gone. Musical notation of any kind is gone. There is no such thing as a musical instrument. There is no such experience as using any object musically. We don't sing tunes in our heads. We don't hum. We don't sing. Singing happy birthday at birthday celebrations is simply not a thing. Worship services are spoken only. The book of Psalms, the Magnificat, The Song of Moses and Miriam, Song of Songs are all nonexistent (as well as perhaps all poetic books of the Bible and sections of poetry which may have been sung). Church bells don't ring. Wedding ceremonies are devoid of any musical components as are the dances that follow in wedding receptions. Any and all types of cultural celebrations are sans music in contributing to celebration. Funerals have no music to aid in our grief expressions. We don't find songs with or without words that connect to our souls or connect our souls to one another because the songs don't exist. There is no such expression. Sonic expressions of culture, history, imagination, community of various instantiations in which song brings us together around these ideas are totally absent in these settings. There is no band. There is no choir. There is no orchestra. There are no ensembles. There are no teens creating their own garage bands. There are no music festivals. There are no summer concert series. Cities cannot rally around their symphony orchestras or opera companies because these are nonentities. Movies have no songs, no orchestral scores, no sound effects—everything is simply spoken. In video games, your character navigates the RPG in absolute silence. Musicals occur sans music as well. Seasonally, we find no holiday music aiding in creating the seasonal and/or religious aesthetic. Elevators operate in more silence than they already do. Restaurants and businesses are hopelessly silent as well, other than the sound of air conditioners or heaters (which are unable to be heard musically either). Videos on social media are always spoken only. No such thing as a music app. What are wax cylinders, records, tapes, CDs, streaming music? These concepts are not present in this reality. Music stores—nope. Teaching lessons? Nope again. Advertisements have no jingles. Sporting events have no music to pump you up. Music cannot function to help us express love, joy, laughter, pain, catharsis, or be used in any personally or collectively therapeutic sense because it doesn't exist. Even the natural world is somehow absent of musicality. If birds do make sounds, our brains cannot process anything aesthetically pleasing about the sounds they make; that, or they sound more spoken as well. Even the speech cannot be understood by our brains rhythmically in any way. We don't have musical capacity in this world. This could go on, but I'm not sure I could at the moment. Do we like this world? Do we miss the musical world at all? A little bit? A lot? How much do we miss it? Do we value music? To what extent? How expendable is it? How essential is it? Do we treat it like it is?

Informal Notes On Alternative Ways Of Being Tonal

(These thoughts are indebted to Gary S. Karpinski, and many.)

The following figure and text associated with it should be understood in the context of a previous "Informal Notes On..." entitled "Informal Notes On Alternate Ways Of Being Tonal Music: A Moment With Impressionism, Blues, Jazz, and 20th-and 21st-Century Popular Musics". Related specifically to the figure in this entry, several points are worth noting. (Other important related points may be found in the previous "article" I just referenced.) All tones represented here are derived from the whole tone scale, specifically WT-0 (0, 2). The type of harmonic entity which serves as the basic structure is the seventh chord, specifically an augmented triad with a minor seventh (one of two standard altered dominant seventh chords which can both be understood as derived from a whole tone scale, the other being the "V7b5"). Above the staves, I have opted for two ways which could be used to notate these chords in a pop chord label style. Pop label option A, as shown, is to label it with the root of the chord followed by the number 7, which together would indicate a Mm7 chord; however, after the 7 is appended a ↑5. The ↑ is a modification used by Karpinski in his Manual for Ear Training and Sight Singing textbook. The arrow up or down indicates that the note is raised or lowered. This is in use rather than the more pop and jazz traditional "b5" or "#5" approach. Though "b5" and "#5" are in standard usage in these repertoires, and therefore should be understood by musicians, the arrow notation allows us more specifically to recognize that altering a note upward or downward by semitone does not always yield a sharp or a flat; it depends upon context. The other pop notation I have shown (pop label option B) is a letter name that indicates the root of the chord followed by the "+" symbol, indicating that the triad is augmented. The appended 7 is placed in parentheses thusly, (7). The reason for this is so that performers don't understand the "+" symbol as applicable both to the triad and the 7th as you would in a fully-diminished seventh chord with the "º" label. The parentheses thus allow us to understand the 7 as the standard m7 which you would assume when no symbol is applied to it. Underneath the staves there are two options for functional labels. They work in exactly the same manner as I have described for the pop labels with the exception that the Roman numerals are used to indicate their scalar relationship to a given note understood as a tonic.

*It is also perhaps important to note that above, I've used the term "altered dominant", which I have often heard used. This term is a shorthand for a standard modification of a Mm7 chord built upon the 5th scale degree of the major or minor scale (the dominant scale degree); the standard modification is to alter the fifth of the chord, which would normally be sd2 in either the major or minor scale, either upward or downward by a semitone. If one is in a major mode context and moves the fifth of the chord upward by semitone and allows for enharmonicism, one could view the new chord as borrowing sd3 from the parallel minor; if one is in a minor mode context, this tone is already available diatonically, again, allowing for enharmonicism. If one is in a major or minor mode context and moves the fifth of the chord downward by semitone, one could view the new chord as borrowing sd2 from the parallel Phrygian mode. (This expanded concept of modal borrowing, which includes parallel modes beyond just the parallel major and minor modes, including borrowing from any parallel mode of the major scale—or perhaps even other scalar structures—may prove highly useful analytically in a surprising number of traditionally tonal and neo-tonal contexts. (It may prove useful in some contexts approached via Neo-Riemannian theory as well. For example, within a C major context, a move from a C major chord to an Eb minor chord—a doubly-chromatic mediant chord relationship—could be understood via Neo-Riemannian theory as a PRP transformation, but could also be understood as borrowing from the parallel Locrian; similarly, within that same C major context, a move from a C major chord to an F#/Gb major chord (enharmonicism allowed) could be understood via both lenses; in transformational theory, it could be seen as a PRPR transformation, while expanded modal borrowing could view it as pulling the triad from the parallel Locrian once again.) Using an example that is not normally approached via a Neo-Riemannian lens, but rather as N or bII, we have the Neapolitan chord. Use of this chord could be understood as borrowing from the parallel Phrygian.) Returning to my original point about "altered dominant" or "V7b5" or "V7#5", these terms fit better within a major/minor system in which we are building the Mm7 chord on sd5. Within this whole-tone context, the augmented triad with minor seventh that we are featuring is built on every degree of the scale; the fifth scale degree also is not what we traditionally understand as the "dominant" scale degree because it is not a P5 above the tonic. It seems best, then, to refer to these with the labels shown in the figure, rather than understanding them as "dominants" within this tonal and scalar context.

Informal Notes On Alternative Ways Of Being Tonal: C Octatonic (0,2)

(These thoughts are indebted to many.)

The type of harmonic entity which serves as a basic referential structure in the figure above is the three-note chord stacked in fourths. The octatonic scale has eight tones, but exists within a system in which note names have seven unique letters, so one letter name is duplicated with an inflection. As I have chosen to render the scale above, both F and F# exist; all other notes of the scale have unique letter names. Above the staff, I have chosen to label these chords by combining two systems and somewhat altering the second of the two. The label "3x4 on 'insert note name here'" indicates that there are 3 notes to the chord, that they are stacked in fourths, and that the note which should be understood as the "bass-root" is the letter name at the end of the label. The second system affixed to the label comes from pitch-class set theory. It rearranges the tones of the chord in their most compact positioning, treats the lowest tone in this arrangement as "0", and simply counts numerically up to the next note in the chord. This chord position (note arrangement) is called normal order or normal form. I have opted to apply the labels at this point in the process rather than putting the chords into traditional prime form, an arrangement which compares the normal order with its same interval structure read in the opposite direction. (For example, a C major chord, CEG, would be the most tightly-packed arrangement of those notes, thus in normal order. C would be set to "0", arriving on E would be arriving on "4", arriving on G would be arriving on "7", so the normal order would be (047); however, taking the same tightly-packed structure and reading from G as "0" down to E, E would become "3" and C would become "7". Reading this same structure would yield (047) from "bottom to top" and (037) from "top to bottom". Traditional set theory would label the chord (037) because it reads in a more compact manner to the left side of the label. From a visual standpoint, it's like taking a hat (a basic structure) and turning it upside down and understanding that it is still a hat no matter how you turn it. The problem, in my opinion here (and I believe for many others as well), is that it does not really line up with the way a human brain processes the sonic experience (to my current knowledge and personal experience). If we label a C major chord as (037), what else is a (037)? C minor is also a (037) where C is set to 0, Eb is 3 and G is 7. I hear a qualitative difference (Gestalt difference, holistic difference) between a major chord and a minor chord. I do not sonically experience them at all in the same way I experience seeing a hat as right-side up or upside-down. The auditory and visual domains function differently in this regard for me. I can certainly hear constituent intervals—I can hear a minor 3rd, a major 3rd, a perfect fifth—but placing a major 3rd below a minor 3rd and the resulting bounding perfect 5th is again qualitatively distinct to me from a minor 3rd below a major 3rd with a resulting bounding perfect 5th. This is why I propose using normal form as a label more closely aligned to sonic experience.

To use a term in a slightly different manner than we traditionally use it, the chords are all "diatonic". Traditional usage of this term means that they conform to the key signature. Perhaps a new term is in order within this context as there are no key signatures set up for octatonic collections; key signatures were set up for major and minor keys (major and natural minor, specifically). Whether this might indicate that we need expanded key signatures and/or a new definition for "diatonic" is an important question. Here, I will use the term "diatonic" to simply mean that all of the chords correspond to the scale from which they are derived—the C OCT 0-2 collection.

It is, to me, interesting to note that even within "quartal" harmonies, we end up with some structures that we more commonly hear (and perhaps think of more quickly) in their tertian harmonic form. A few examples include 3x4 on F# (047) which sounds like a B major chord in second inversion, but is spelled in quartal fashion. 3x4 on G# (037) sounds like an F minor chord in first inversion, but is spelled in quartal fashion. 3x4 on B (026) sounds like an incomplete B7 chord (missing the fifth of the chord, as is very common), but is spelled in quartal fashion. It should be noted that how one spells their octatonic scale, as in where the duplicated letter name with inflection is located, affects both the spelling of the chords and the resulting sounds of the chords because what constitutes quartal stacking is based upon spelling. For example, if I had spelled my scale with Gb instead of F# (followed by G#), the quartal chord on Gb would be spelled Gb, C, F instead of F#, B, Eb—different chords and different sounds. Both of these chords are possible within the collection, but spelling plays into what structures you build and the resultant chords and their sounds.

Lastly, below the staves, I have applied functional labels consistent with the pop labels above the staves. The functional labels are identical to the pop labels other than indicating how the chords relate to the tonic of C as scale-degree 1. Again, note that use of enharmonicism determines how we understand scale degree. I have, as previously, opted to use the major scale as a referent when using up/down arrows to indicate raised or lowered scale degrees due to my own (and many others) strong biographical listening experiences that likely root the major scale more deeply in me than other scalar structures.

Informal Notes On Alternative Ways Of Being Tonal: The Symmetrical Expanding-Contracting Hexatonic—C Sym Exp-Cont Hexa (0,1)

(These thoughts are indebted to many.)

The term hexatonic classifies it under an umbrella category of 6-note scales: two others that I am aware of are (a) the whole-tone scale, which replicates interval-class 2s from tonic to tonic, and (b) the augmented scale, which alternates the replication of an ic1 followed by an ic3 (or the reverse, depending upon mode (or rotation)). Next, let's explore how it is symmetrical. The scale evenly divides the octave by splitting the chromatic scale (the notes traditionally available, for example, on a piano keyboard) from one instantiation of a given letter name to the next note with the same letter name an octave above (in this case, from C to C). The halfway point between these two Cs is F#. C to F#=C [0],C#/Db [1] , D [2], D#/Eb [3], E [4], F [5], F# [6], and is the same semitonal distance as F# to C, where F# [as here for illustration is set to 0], G [1], G#/Ab [2], A [3], A#/Bb [4], B [5], C [6]. So there are 6 semitones from C to F# and also from F# to C. It is also important to note that F#, which does indeed divide the octave evenly, is also the midpoint of the scale itself; from C to C within the scale, there are three notes before F# and three notes after F#, so it both divides the octave evenly and divides the scale itself evenly. There is one further area of symmetry which I will address as I cover the next descriptors in the name of the scale.

The term expanding-contracting views the scale in both a left-to-right manner and a right-to-left manner. Reading the successive intervals in the scale in a left-to-right manner, we encounter the following interval succession: C to Db=ic1 (m2), Db to Eb=ic2 (M2), Eb to F#=ic3 (+2 or enh. m3), F# to A=ic3 (m3), A to B=ic2 (M2), B to C=ic1 (m2). Removing the letter names and only looking at the intervallic succession between them, we see the following pattern: ic1, ic2, ic3, ic3, ic2, ic1. Notice in this succession that the intervals begin with an ic1, successively expand by semitone to an ic3; then they restate the ic3 and successively contract by semitone back to an ic1. The intervals expand and contract per the name I've chosen to apply to the scale. The axis of symmetry is between the two statements of ic3 (in our rendering, on the note F#, which also divided our octave and the number of notes in the scale). Another way to think about this is to say, if F# is our midpoint we can go up by ic3 to the following note (A) or down by ic3 to the previous note (Eb); from A we go up an ic2 (B) and from Eb we go down an ic2 (Db); finally, from B we go up an ic1 (C) and from Db we go down an ic1 (C). The scale is symmetrical in all of these ways.

I have also chosen to explore some of the harmonic possibilities which can be derived from this scale (3-note chords explored only). I will only highlight some points here. System 2 considers secundal harmonies (clusters), which are understood generally as adjacent scale degrees. A point should be made here that with the gap of a 3rd on either side of the midpoint of the scale, not all adjacent notes in the scale actually lead to chords in seconds unless you choose to enharmonically spell them that way. They might then also be viewed as mixed interval chords. Some enharmonic spellings are explored in this system, particularly when an alternate spelling highlights a possible more familiar tertian hearing of the sonority. In all systems, I have put "pop chord labels" (my term in most of these instances as I doubt you will find these in any current charts) above the staves and functional labels (as per my description in previous "articles") below the staves.

System 3 considers tertian harmonies, by which I generally mean using every other note of the scale. Again, enharmonicism may allow for exceptions here which I have tried to make allowances for by indicating that secundal and quartal sonorities can show up via this method as well. Even though "tertian", I have mostly opted to use the [number of tones] x [interval being replicated] on [insert letter name here] approach in conjunction with an affixed normal order (expressed with parentheticals like you would typically see a prime form—for reasoning, please see my previous "article" on that topic). In one case I did use a traditional Roman numeral label. Either option may work where the chord actually conforms to our expectations of Roman numerals. *A momentary aside: The [number of tones] x [interval being replicated] on [insert letter name here] approach in conjunction with an affixed normal order has the function of honoring both the importance of voicing to a sonority, particularly in instances like clusters and quartal and quintal harmonies in which the voicing is part of the effect the composer is often looking to highlight as well as the importance of providing us with the precise and tightest arrangement of the notes in play for precision in analytical comparison between one chord and another for classification purposes. Back to "tertian" examples in System 3, I think it interesting to highlight that the 3x3 on sd↑4 (027) and the 3x3 on sd7 (027) are made of the exact same notes in different arrangements. They also look and sound like an F#sus4 and a Bsus2, respectively. This also brings up an interesting discussion on voicing, bass-root, and pop chord labeling and hearing depending upon context, which will need to be saved for another time.

System 4 explores quartal sonorities by spelling. Not all possibilities are shown here. Enharmonics are used. In this system, I did not use the "skip two notes in the scale and use enharmonics when necessary" approach. I rather used each note in the scale as the bass note for a quartally-spelled sonority, regardless of the number of notes skipped and with use of enharmonics when needed. More possibilities could certainly be explored here. It is interesting to me to note that several chords do indeed sound tertian: the 3x4 on sd↓3 (046) sounds like an Ebø7 without a chordal third; the 3x4 on sd↑4 (047) sounds like a B major chord in second inversion; the 3x4 on sd6 (037) sounds like an F#m chord in first inversion; the 3x4 on sd7 (026) sounds like a B7 without a chordal fifth.

System 5 explores quintal sonorities by spelling. Not all possibilities are shown here. Enharmonics are used. In this system, I did not use the "skip three notes in the scale and use enharmonics when necessary" approach. I rather used each note in the scale as the bass note for a quintally-spelled sonority, regardless of the number of notes skipped and with use of enharmonics when needed. More possibilities could certainly be explored here. It is interesting to me to note that the 3x5 on sd↓3 (047) sounds like a B major chord in first inversion; the (3)x5 on sd↑4 sounds like a tritone dyad with the bass-root doubled enharmonically at the octave (which it is); 3x5 on sd6 (026) sounds like a B7 in third inversion without a chordal fifth.

I hope, whether this scale is novel or already in use in music of which I am unaware, that composers are able to creatively make use of the possibilities that this structure makes possible. Perhaps at some point, I too may try my hand at writing some music with it.

*One final aside: In some cases in the figure, you may see a label like this—3x(3+2) on C. This label means that there are three notes in the chord and that the chord is made up of a third on the bottom with a second above it, and finally, that the structure is built on C. The entity is diatonic (in the sense of conforming to the scale) and there is also a normal form associated with such labels so one can make certain that the correct specific notes are in use.

Informal Notes On “Skating and Music—That’s So Punk Rock!”

(These thoughts are indebted to Mark Dean, Bob Dylan, Damon Kelly, Charlie Mackesy, Darrow L. Miller, and others.)

For a time in the 1990s, I was a skater. Long story short, a friend got into skating and asked me if I wanted to skate with him, and I was drawn to it. There was no “making the team” or not, there was no entry bar, there was no hierarchy or pecking order or questions I had to answer correctly, just did I want to. If I did, come on. That appealed to me. Disclaimer: This is not a wholesale endorsement of all things skating. There are aspects to the skating community with which I interacted that were less than ideal. That being said, aspects I enjoyed within the skating community were that skaters were like cats—you come and go as you please; split off as you please; learn from whom it looks like, from observation, you could learn from; there was complete approachability with everyone around; there was a sense of community, of people who liked being together, but it was organically organized and, again, with complete freedom to come and go as you please.

Interacting with the 1990s world around us at the time in our area, we found we were in a world around us that sought our erasure. There was no good place to be, to exist. If we were on the sidewalks, these were meant for pedestrians so we should not be there. If we were on the streets, these were meant for cars so we should not be there. If we were in parking lots, business owners would tell us to leave and then have “no skateboards” signs up the following week. Empty community swimming pools which would not be used for eight more months in any way were locked gates, which skaters had no problem climbing, until barbed wires were placed atop those gates in order to keep us out. You get the idea—erasure.

The music for this community at the time was punk rock—it emotionally hit for us. It was fast, it was energetic, it was full like a wall of sound, it had grit, it was bold, brave, and unafraid, it was honest and unapologetic. It was related to what we thought of as the “garage bands” of our time which shared many of the above-described characteristics of skating.

Let’s return now for a moment to the concept of erasure. I will begin a brief philosophical discussion on an aspect of music here. My disclaimer up front is that this is in no way a wholesale endorsement to go and listen to all music and throw away our discernment. Rather, I would say we should be incredibly discerning about our music. That being said, I have read passages from books and articles which have a tendency to take the approach of being offended by perhaps even entire genres of music and in effect calling for their deletion, their erasure. While there is certainly no lack of music out there which does not cause us to celebrate each and every aspect of it, and we absolutely should be discerning in our music—in fact, I find myself preoccupied with doing my best to pay attention to what music I listen to quite often—I wonder what would happen if at times, we chose to step out of just our initial emotional reaction to it, and instead stepped back and thought about it in a slightly different way.

Why does this music exist? If it is an entire genre of music, what is it about this genre that is speaking to people? Who is it speaking to? What personal expression is taking place here? Is there hurt in this music? If there is, what is the deeper reason for this pain? Is there anger and frustration in this music? Why might those who relate to it be frustrated? Is it possible that some of these reasons come from some legitimate concerns, perhaps able to be expressed plainly, perhaps part of the 90% of the iceberg that is under the surface of the water. Do we have enough care for the people that this music speaks to in order to care about them and what they are thinking and feeling and processing? Could it be that life experience is so complex at times that even though in music with lyrics, lyrics are being articulated, that the music itself and its holistic characteristics are getting at something deeper that people who love this genre are feeling but perhaps can’t put into words? If a perspective that I don’t relate to is present in this music, could I lean in, love the person better, ask more questions out of curiosity and care rather than judgment? Could I possibly learn something through this music that I don’t know? Could it somehow teach me something? Could asking these questions bring us together more than separate us? Are there aspects about this music that I do relate to, that I value, that we as listeners have in common in order to allow music to bring us together rather than separate us, as we claim it does? Can we find a space to choose with discernment, guarding our hearts, some music that we might otherwise be inclined to apply erasure to, and listen with a heart that beats for the image bearer who made it and the image bearers who seem to “get it” so that we might “get” some aspect of them, and perhaps in so doing they might “get” an aspect of us they might not get otherwise, and maybe in so doing bring us closer to one another with a heart of love and care for one another.

In music and in life, what if rather than erasure, we could communicate in some form to one another (all one anothers without exception) these words that I'm drawn to by Charlie Mackesy: "Always remember you matter, you're important and you are loved, and you bring to the world things no one else can."

Informal Notes On Instrument Usage In The Aural Skills Classroom

(These thoughts are indebted to Jason Hooper, Taka and Houlahan, Justin London, Edward Sarath, and others.)

I will begin here by stating that there may be nothing genuinely "new" in this entry. I have, perhaps embarrassingly, a need to catch up on current scholarship in the music theory field, which I aim to do. That being said, my experience tells me that whether or not the scholarship is new, the "put the ideas from the scholarship into practice" is likely not happening at the scale that it could.

The topic is instrument usage in the aural skills classoom. My experience has been that this has historically been taboo. My understanding as to the reason it has been taboo is that if, for example, you are sight-singing from a piece of sheet music in front of you, your ear and brain working together need to decode the notes on the page in order to auralize what the sheet music is showing and then you use your vocal apparatus to realize it accurately in sound. In the aural skills classroom, we are heavily invested in the aspect of that process that involves the ear and brain working together in decoding music. However, it has traditionally been argued that the best, and/or only way for us to know if the brain is actually doing what it is supposed to do in decoding is to have it actualized out loud through the voice. Playing sheet music, even if it is sight-reading sheet music, is seen as "cheating" in the sense that it is understood as a type of "button pushing". I see the notes on the page and I know what "buttons" to push down on my instrument to make those sounds. In that approach, the ear and brain do not need to be decoding the sound of what the sheet music in front of them is showing. The instrumentalist could in some sense be completely surprised by the sounds coming out of their instrument in a way that causes the ear and brain to only "hear" it after it has been realized on the instrument.

Understanding the validity in the above description, we do run into issues when we have instrumentalists in our aural skills classes who have perhaps never really sung in their lives and are now feeling the immediate pressure of being graded in some way with respect to their singing in a college classroom. It can, and has been argued, that we are not really grading on the beauty of the singing in the way that we would at a vocal jury for a voice major, but rather on pitch and rhythmic accuracy so instrumentalists are not left thinking that the beautiful voices of the vocal majors automatically put them ahead in the aural skills classroom. This line of thinking could continue in this discussion along lines of intonation and other related topics. I will not delve into this at the moment.

All of this being said, is there any place for instrumental usage within the aural skills classroom at any point or under any circumstances? Yes, indeed there is. When we think of vernacular (popular) musics and the jazz tradition, we are often working in musical worlds that exist in some respects in a type of "aural skills" world in the sense that often there is no written music. They are typically aural traditions, or aural traditions first, or aural traditions primarily. The written music takes a big backseat to the sonic world in these settings. It is often the case that vernacular musicians and jazz musicians have very strong ears perhaps in part because of working in almost totally sonic-only environments (or with minimal or lesser primacy of attachment to the page). How then wouldn't there be a way for instruments to be a part of the aural skills classroom in developing our ears?

One method I have seen and used from time to time is a structured exercise like this. Students bring their instruments to class. Students come up with a brief lick that they will play given some confines by the teacher which restrict the lick to being made up of aural materials which we've already encountered in class. Once everyone has their lick, we put on a backing track in the key I've asked those licks to be in, typically a rhythm section vamp on a tonic-dominant drone or something basic like that to keep as a reference point over atop which the licks will be heard. A volunteer plays their lick. There is no written music for the rest of the class to reference. The class' job is to aurally decode what was played, so we sit in the sound of the backing track until a hand is raised and that volunteer attempts to accurately play back the lick. If it is accurate on that person's instrument, it means the lick was indeed decoded correctly. We repeat the process with each student's lick. For vocalists in the room, decoding an instrumental lick means they must sing it back on solfege or in scale-degrees to show they have truly decoded it; in this context, simply singing it back on a neutral syllable would not indicate they necessarily understood the structure of it.

I think we could continue to flesh out more and more how we could appropriately incorporate instrumental usage within the aural skills classroom in meaningful and inclusive ways.

Informal Notes On Timbral Usage In The Aural Skills Classroom

(These thoughts are indebted to former colleagues from The College Of Saint Rose with whom I informally discussed this topic, Anna Gonzales, First Nations Version New Testament, The Complete Jewish Bible, Albert Nyuke (who gave me and my wife our Mankanyan names—Mphantan Nyuke and Danti Bampoki), Jean Luc, Simon,Rosalie, Ange Bernard, Gerard Kali, Hyassenth, Rigobert, Jan, Sidi Sou, Patricia Attiba, Samba, Joe, Victorien, Tim Gaved of SIL, Sheila (ethnomusicologist in Ziguinchor, Senegal), the Casamance, Dakar, Gorree Island, the oral translation of the Mankanyan Bible, and others.)

Another area in which I believe we can grow as aural skills instructors in helping our music students develop their ears has to do with how we approach dictation. To my knowledge, the overwhelming majority of dictations are played on the piano. In an earlier entry, I mentioned brain research having to do with the way the brain takes in the totality of its environment when learning. In that entry, I recommended studying in multiple places in order for the brain to latch onto the content we are hoping to acquire without being quite so tied to place. I want to remember what I've learned whether I'm at home or at school or on vacation or wherever I am. (Recall the familiar concept of thinking of something you want to go get in the other room, but when you arrive in the room, you've forgotten what you went into that room to get. Then upon returning to the place you were when you thought of it, you again recall what you wanted to retrieve.) Along these lines, though again, this is born out of experience and observation, and not out of particular literature that I've read, we also want our students to hear the aural materials we are teaching them irrespective of timbral context. If I'm playing a I-vi-IV-V-I harmonic progression, my students might have learned this pretty well in class by hearing it played on the piano. Could they recognize it in a string quartet playing it in a rhythmicized manner rather than in isochronous whole notes at the piano at a whole note per chord harmonic rhythm? Could they recognize it in an electric guitar and electric bass playing it with distortion? Could they recognize it on an ethereal ambient synthetic timbre? Could they recognize it arpeggiated in scat singing by an acapella vocal ensemble? Could they recognize it in a band, choral, or orchestral setting? We want our students to be able to take these skills out of the aural skills classroom/lab setting and be able to hear these aural materials all around them wherever they hear music—in their own repertoire, at concerts they attend, in audio streaming, etc. And in these musical settings, those materials are going to show up in a variety of timbres and timbral combinations (and in different meters, tempi, and figurations and textures as well). *Relatedly, I come back to the Rob Paravonian stand-up comedy example of the "Pachelbel" harmonic sequence showing up in all kinds of guises, genres, musical settings (I only wish that for my timbral point to be made here that he wasn't performing all of them on acoustic guitar, though I think we can imagine their original timbral contexts even as he renders these pieces on acoustic guitar.—I'm providing the link to his stand-up routine; there is some language content, so be forewarned. https://www.youtube.com/watch?v=JdxkVQy7QLM) I think some of what makes his stand-up routine funny is that most everyone is probably somewhat shocked to realize that all of these disparate works are making use of exactly the same harmonic progression. My point is, I don't want our students to be surprised. I want them to hear these structures everywhere in the musical worlds around them.

There are a number of ways we might approach unattaching our student's ears from piano-only dictations. One is to assign upcoming dictations to students in the class in this manner. Northumbria plays the flute. You hand Northumbria a melodic dictation which you ask her to play for the class at the next meeting. You have some choral students in your class: one sings soprano, another alto, another tenor, another bass. You assign them a harmonic dictation that they will perform on a given date for the class on a neutral syllable (or have them create their own text). Agamemnon plays the electric guitar. Have Agamemnon prepare a dictation for an upcoming class. You get the point. Allow the timbral variety inherent in any aural skills class to be utilized to their own aural benefit in this way. (I am talking to myself here as well as I need to grow in this area.)

Another way you can approach timbral variety in the presentation of dictations and transcriptions is through the use of a MIDI keyboard and music software program such as Logic. Bring your portable MIDI keyboard and laptop with you to class. When it comes time for dictation, select from the seemingly never-ending repository of timbral possibilities from the software's virtual instrument library.

With timbral (metric, tempo, figuration, textural) variety added to the mix, our students will begin to hear the aural materials we are working on in class outside of class as well in any and all kinds of musical situations they will encounter as musicians.

Informal Notes On The Use Of Guitar Within The Academy

(These thoughts are indebted to informal conversations with colleagues and students at Lee University, Stephen Goacher, Timothy Koozin, and others.)

When I was an undergraduate student, my primary instrument was piano and my secondary instrument was guitar. I recall that at the time, having a secondary in guitar was something of a question at my institution. Thankfully, they decided that it was ok for me to have as my secondary instrument. (Again, to my embarrassment, it would be better if I got back into regularly practicing it. Seriously.) Along these lines, I recall having a conversation with my jazz band instructor (an ensemble in which at one time I played the electric bass, and later, the piano) in which I expressed my frustration with the fact that there was any question as to whether the guitar would be allowed as a legitimate secondary instrument. I recall that he reassured me that the guitar would indeed be more respected in the academy over time. He encouraged me by saying that when he was an undergraduate at UCLA, he was not allowed to be a saxophone major; he could play the saxophone, but majored in clarinet instead. He said that later, saxophone was indeed allowed as a primary instrument of study at UCLA. I am grateful for that conversation; it was truly an encouragement.

Fast forward, and a question. We have class piano courses that every music major takes because even if a musician is not a piano major, there are a multitude of situations in which a professional musician will find themselves in which they will need a number of basic competencies on the piano. Thankfully, this is generally recognized in colleges and universities with music programs everywhere. But could it be that the guitar has also become something that at least musicians with certain professional aims should gain some level of basic competency on? For now, I am thinking particularly of music industry (or commercial music) majors, singer-songwriters, music education majors, as well as those in music and worship degrees. So many industry genres rely and/or have relied heavily on the guitar as a central instrument in and to their approach. Many worship leaders lead by singing and playing guitar. And, generally speaking, worship leaders would do well in serving their congregations to be able to understand the guitar at least enough to be able to work with musicians and worship music volunteers who understand music embodied through the lens of this instrument. Many singer-songwriters write in tandem with their guitar. Industry and/or commercial genres are chalked full of guitar-driven musical works. In music analysis, one can often tell that particular music has been composed at the guitar because of the choices in chord progressions and how these work with the ease of finger movements and open strings on the guitar (many times working in tandem with the CAGED system, perhaps a capo and/or a half capo, power chords, emphasis on fourths/fifths related to the instrument's tuning, and solos which allow for the hand to remain within a relatively stable location(s) on the neck). In music education, I used to teach class guitar to 4th and 5th graders on smaller-sized guitars. We learned some chords like "easy G" (strings 1–3 or 1–4), "easy C" (strings 1–3) or "medium C" (strings 1–4), D7, and "easy Em" (strings 1–3) or regular Em (all 6 strings). (You might also be able to add D and "easy G7" (strings 1–3 or 1–4). We used these to play and sing as a group along with a packet of about 30 children's folk songs. This is a great way to get young students started in simultaneous singing and playing as a combined skill set. Music educators would benefit greatly in being able to teach elementary students such skill sets. In all of the above scenarios, we don't need these college students to be the next Stevie Ray Vaughan, but some basic competencies would be incredibly helpful to them within their professional lives. A caveat here is that I at this time do not have a recommendation for how we add yet another item to a music major's plate. Perhaps opening this conversation up, however, may allow others within the academy who see some merit to this proposal to aid in fleshing out those important questions.

Relatedly, industry (commercial) guitar majors, should not be without ensemble homes. Guitar ensembles, and genre-specific industry (commercial) ensembles should be generally available as options for these students to develop their craft in a variety of settings. Composition and analysis courses related to the standard repertoire in these genres should also be readily available to our students.

*By way of a sidenote, if you take the CAGED system, and rearrange the notes thusly, CDEGA, the roots of these chords spell out the notes of a major pentatonic scale. If you rearrange them thusly, ACDEG, you have a minor pentatonic scale. Both are important scales. The minor pentatonic as a scale is very important to rock-based musics. Much rock-based music is guitar-driven music. There is also much rock-based guitar-driven music that makes use of chromatic mediant relationships in its chord progressions, which again, is likely born out of the embodied setup of the instrument itself and ease of playing it as above described. Examples from CAGED which create chromatic mediant chord relationships include: Cmaj to E maj, C maj to A maj, E maj to G major. The Mixolydian's characteristic "flat sd7" is also contained here. If you have a key center of "A", the "G" is your subtonic. If you have a key center of "E", the "D" is your subtonic. If you have a key center of "D", the "C" is your subtonic. Rock's "bVI"-"bVII"-"I" is also born out of this system. With a key center of "E", this chord progression would be "C" (bVI), "D" (bVII), "E" (I).

selected compositions (traditional scores)

Peregrination

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Cruciatu animi

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rain

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a little-known way through the forest (woodwind trio—full score)

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a little-Known way through the forest (woodwind trio-flute part)

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a little-Known way through the forest (woodwind trio—clarinet in B-flat part)

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a Little-known way through the forest (woodwind trio—bassoon part)

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do not be conformed (SATB choral score)

Application is no longer available.

quest (string duo)

Application is no longer available.

quest (string duo—violin part)

Application is no longer available.

quest (string duo—cello part)

Application is no longer available.

heroic (brass quartet)

Application is no longer available.

elsewhere (Trio-Flute, Viola, double bass)

Application is no longer available.

cello and piano duo

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light (SATB Brief choral warm up)

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emergence (piano)

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chorale prelude

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figurated prelude

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fugue

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too deep for words (two sopranos and piano)

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Invention

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minuet

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three-voice counterpoint (trio sonata style)

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triple invertible counterpoint

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Selected Compositions (charts)

Anthem of hope

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My savior-shepherd-king

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12-Bar Blues class composition assignment
"I Got The Almost There Blues"

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Broadway class composition assignment
"a wolf is quite the breed"

Application is no longer available.

country class composition assignment
"It's gonna be a real good day"

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jazz composition assignment
"stay"

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latin class composition assignment
"senora"

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rock class composition assignment
("I Make it real")

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R&B class composition assignment
"Our love is off the ground"

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"pop" class composition assignment
"You're the journey. You're the goal."

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gamelan class assignment

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gamelan fusion composition assignment

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Music theory paper idea to further flesh out
"Some aspects of music which translate across cultural, stylistic, and historical boundaries"-david Mosher

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Latin Jazz composition

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world music: Irish vernacular
"An irish blessing" (a musical setting)

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world music: guzheng fusion
"drink the sunshine"

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t0ward a creative Temporal experiment

A sloth experiences the first four bars of J.S. Bach's Prelude in C major, WTC Bk. 1, prelude 1 (on vibraphone, 8vb)
16th note approx. 5bpm

Sloth Speed WTC Bk 1 Prelude 1 - 4_22_26, 12.03 PM

00:00 / 12:48

A peregrin falcon experiences the first four bars of J.S. Bach's Prelude in C major, WTC Bk. 1, prelude 1 (on celtic tin whistle, 8va)
16th note approx. 3,960bpm

Peregrin Falcon WTC Bk 1, Prelude 1

00:00 / 00:04

Low-to-High pitch discrimination thresholds
(wide-to-narrow-to same note)

00:00 / 00:10

equal-tempered microtonal scales

quarter-tone scale (c3 to C4) (Interval class 0.5)

relative solmization syllables for quarter tones are not standardized.
Some use "oo" in reference to raised tones and "uh" in reference to lowered tones. I will use "oo" to mean quarter tone sharp, "Ah" (as in "apple") to mean three-quarter tone sharp, "ih" (as in "igloo"") to mean quarter tone flat, and "uuH" (as in "book") to mean three-quarter tone flat.

quarter-tone scale (c3 to C4) (Interval class 0.5)

C3 ("do")

00:00 / 00:04

C Half-sharp 3 ("Doo" or "Ruuh")

C half-sharp 3

00:00 / 00:04

C sharp 3 ("Di" or "ra")

C sharp 3

00:00 / 00:04

D half-flat 3 ("DAh" or "Rih")

D half-flat 3

00:00 / 00:04

D3 ("re")

00:00 / 00:04

D half-sharp 3 ("Roo" or "MuuH")

D half-sharp 3

00:00 / 00:05

D sharp 3 ("Ri" or "Me")

D sharp 3

F sharp 3

00:00 / 00:04

G half-flat 3 ("FAH" or SiH")

G half-flat 3

00:00 / 00:04

G3 ("Sol")

00:00 / 00:04

G half-sharp 3 ("Soo" or "Luuh")

G half-sharp 3

00:00 / 00:04

G sharp 3 ("Si" or "Le")

beat divides evenly in two parts (50 : 50) (as in even eighth notes in a 4/4 meter)
Example:

choose some examples of particular amounts of swing between a 50 ; 50 divided beat and a 67 : 33 divided beat

beat divided approx 67 : 33 (as in a quarter note followed by an eighth note in a 12/8 meter)
Example

choose some examples that move toward the beat dividing 75 : 25 as in a dotted eighth followed by a sixteenth note in a 4/4 meter

THEORY

UNPUBLISHED//THEORY

PUBLISHED//THEORY

Embodied Meaning In John Adams' El Niño

Curriculum//Ear-Training

first semester ear-training (student version)

first semester ear-training (audio)

Homeworks 1–7

first semester ear-training (audio)

Homeworks 8–14

first semester ear-training (audio)

Homeworks 15–21

First Semester Ear-Training (Instructor Version)

second semester ear-training (student version)

second semester ear-training (audio)

Homeworks 1–7

second semester ear-training (audio)

Homeworks 8–14

second semester ear-training (audio)

Homeworks 15–21

second Semester Ear-Training (Instructor Version)

Music Theory ideas in incubation (informal notes)

selected compositions (traditional scores)

Peregrination

Application is no longer available.

Cruciatu animi

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rain

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a little-known way through the forest (woodwind trio—full score)

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a little-Known way through the forest (woodwind trio-flute part)

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a little-Known way through the forest (woodwind trio—clarinet in B-flat part)

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a Little-known way through the forest (woodwind trio—bassoon part)

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do not be conformed (SATB choral score)

Application is no longer available.

quest (string duo)

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quest (string duo—violin part)

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quest (string duo—cello part)

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heroic (brass quartet)

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elsewhere (Trio-Flute, Viola, double bass)

Application is no longer available.

cello and piano duo

Application is no longer available.

light (SATB Brief choral warm up)

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emergence (piano)

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chorale prelude

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figurated prelude

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fugue

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too deep for words (two sopranos and piano)

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Invention

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minuet

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three-voice counterpoint (trio sonata style)

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triple invertible counterpoint

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Selected Compositions (charts)

Anthem of hope

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My savior-shepherd-king

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12-Bar Blues class composition assignment "I Got The Almost There Blues"

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Broadway class composition assignment "a wolf is quite the breed"

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12-Bar Blues class composition assignment
"I Got The Almost There Blues"

Broadway class composition assignment
"a wolf is quite the breed"

country class composition assignment
"It's gonna be a real good day"

jazz composition assignment
"stay"

latin class composition assignment
"senora"

rock class composition assignment
("I Make it real")

R&B class composition assignment
"Our love is off the ground"

"pop" class composition assignment
"You're the journey. You're the goal."

Music theory paper idea to further flesh out
"Some aspects of music which translate across cultural, stylistic, and historical boundaries"-david Mosher

world music: Irish vernacular
"An irish blessing" (a musical setting)

world music: guzheng fusion
"drink the sunshine"

A sloth experiences the first four bars of J.S. Bach's Prelude in C major, WTC Bk. 1, prelude 1 (on vibraphone, 8vb)
16th note approx. 5bpm

A peregrin falcon experiences the first four bars of J.S. Bach's Prelude in C major, WTC Bk. 1, prelude 1 (on celtic tin whistle, 8va)
16th note approx. 3,960bpm

Low-to-High pitch discrimination thresholds
(wide-to-narrow-to same note)