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UNPUBLISHED//THEORY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.

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)

Application is no longer available.

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

Application is no longer available.

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

Application is no longer available.

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

Application is no longer available.

light (SATB Brief choral warm up)

Application is no longer available.

emergence (piano)

Application is no longer available.

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"

Application is no longer available.

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"

Application is no longer available.

jazz composition assignment
"stay"

Application is no longer available.

latin class composition assignment
"senora"

Application is no longer available.

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

Application is no longer available.

rain

Application is no longer available.

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

Application is no longer available.

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

Application is no longer available.

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

Application is no longer available.

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

Application is no longer available.

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)

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quest (string duo—cello part)

Application is no longer available.

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)

Application is no longer available.

emergence (piano)

Application is no longer available.

chorale prelude

Application is no longer available.

figurated prelude

Application is no longer available.

fugue

Application is no longer available.

too deep for words (two sopranos and piano)

Application is no longer available.

Invention

Application is no longer available.

minuet

Application is no longer available.

three-voice counterpoint (trio sonata style)

Application is no longer available.

triple invertible counterpoint

Application is no longer available.

Selected Compositions (charts)

Anthem of hope

Application is no longer available.

My savior-shepherd-king

Application is no longer available.

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

Application is no longer available.

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

Application is no longer available.

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)