colortone series experiments

"The" giant loop of pitches / #15 and beyond. Ever wonder whether our equal tempered resource is a finite set of musical elements, i.e., just so many pitches or chords? Or if there is a perfect closure to our system of music? Well, the following discussions examine various elemental properties of the ancient overtone series and how we find this naturally occurring phenomena reshaped within our modern system of equal temper to create a looping cycle of pitches, chords and tonalities with perfect closure. Perfect? Yep. Cool with this?

Here the discussion quickly moves beyond the everyday practical realm of application towards the more esoteric or abstract, for rarely do we see this kind of extended approach in any of the American styles, and when we do, it is often in the freer, more obscure, modern jazz or new age musical environments. I'm not all to sure which path within the text got you to this page, for there are many, but if you're looking for the "sharp 15th and beyond" story or how a certain intervalic symmetry creates a closed or set looping of the entire 12 pitches and creating the combined 24 major and minor key schemes of equal temper, this is the place. For the following ideas are not only cool in their potential to see a more complete "birds eye view" of the closure of our equal tempered resource, but perhaps also will illuminate new ways of combining the same elements that we have come to love in creating our own styles and versions of American music.

So where does these "experiments" come from? Years ago, while attending college, one of the requirements for the baccalaureate degree I was completing was a course in basic vocal techniques. The professor, Dr. Allen Frank, was what back then was known in the jazz world as a "cocktail" pianist. This cat plays so beautifully. Anyway, on entering the class each session, while students were getting settled etc., Dr. Frank would be seated at the piano casually doing his thing. As the class settled down to begin, Dr. Frank oftentimes ended his improvisations with an extended tonic arpeggio. One time, while enjoying these improvisations, as the last pitches were sounded, I realized that I could not identify aurally / theoretically what had been played. After that class, I asked Dr. Frank what was the arpeggiated figure used to end his improvisations. He passed along to me the idea of the sharp fifteenth ( #15 ) as being an extension of the tonic arpeggio, this being the next "correct" sounding chord tone pitch after the thirteenth ( 13 ). Here are the tonic arpeggio pitches as just described based on the root C. Example 1.

After a brief discourse about the relationship between the naturally occurring overtone series and the well tempered system of our modern day piano, Dr. Frank encouraged me to explore these upper partials. Thus, the following "experiments" are concerned with the upper extensions of the One ( I major 7 ), Two ( ii -7 ) and Five ( V 7 ) chord types. Starting out as an experiment to simply ascertain chordal intervals above ( 13 ), not only was this color tone riddle solved but a totally giant new sphere of melodic and harmonic opportunity eventually was revealed to me.

Interested to recreate the experiment? It's rather easy. Using a well tuned piano, depress and hold the pitch sustain pedal ( the one on the left underneath ) and gently arpeggiate the pitches of a C major chord from the lowest possible C on the piano and extend upward using a major 3rd / minor 3rd sequence of pitches. The resulting pitches are listed in chart #1. Repeat the process starting on the pitch D for the minor Two chord type, this time using the interval sequence of the minor 3rd / major 3rd, click chart #2 for my results. Same process for the Five chord, starting with the pitches of the G 7 arpeggio, which initially does not follow either the major 3rd / minor 3rd or it's reverse interval sequence. Click chart #3 for the dominant arpeggio core pitches.

Here's the idea. Using each of the three chord types to generate an "arpeggio core", the pitches in the charts were the ones that "sounded most correct" to my ears, and as the results tend to imply, seem to be theoretically ok. From analysis of these pitches emerged the cycling of all of the pitches into the 12 major and 12 minor key centers of equal temper. So what? Well, coolness emerges in that when using either of the major 3rd / minor 3rd interval formulas, a consistent cycling and evolution of keys between the major and minor environments is created, which when completed, not only includes all of the 12 pitches of the chromatic scale, but each of the 12 major and 12 minor key centers are represented. These key centers simply evolve into another as the cycle of pitches unfolds. Really? Yep.

Any glitches? Only when the tritone, as found within the dominant color of Five chord type, is used to create the sequence. To create the tritone including dominant colors, we "break" the consistent cycle of major 3rd / minor 3rd. Interesting in that after we pass this break in the cycle, the pitches ( by my way of hearing things ) naturally settle back into the consistent pitch cycle as found with the tonic / One or Two chord types. So, there seems to be an influence outside the naturally occurring cycle of major and minor thirds or it's inverse within equal temper when wanting to create the dominant color. Potentials of this? Well, basically a key scheme whereby there is no tritone intervals associated in a given key center, a tonality without a tritone if you will.

So what do we gain by this endeavor? Well, perspective of the resource and maybe a new way of expressing our ideas. Perhaps a new sense of tonality that doesn't necessarily rely on the tritone color for the creation of aural tension, opening into a new palette of colors for expression. But without a tritone ... Exactly, things change in a hurry in all of the current levels of evolution in all of the styles of American music without the tritone, so much of the typical American sound simply goes away. Maybe we are looking at the tonality that will create the top 40 hits in the year 2525. Are folks using this approach in creating their music as you read this, i.e., today? Yep, we often find this music referred to as "new age" or "modern jazz", much of which is tonally softer, less definite in it's cadential motions and perhaps more of an abstract mixing of the aural colors.

How far back does this "modern" approach go in the history of music? Perhaps the first real incarnate of this sound, i.e., tonality without a tritone, that we have a written record of today, is in the later operatic music of European composer Richard Wagner. Mr. Wagner created a "wash" of moving color, using melodic motifs to represent the various characters and their personalities to tell his stories, some performances of which are said to have lasted a couple of days! Hours of cadentially unresolving sounds. Were John Coltrane's "sheets of sound" heading in this direction? Maybe. Is this "tonality without a tritone" potentially a portal towards aurally portraying the evolving consciousness of the souls on this cool planet towards a more enlightened, loving awareness of each other? Just might be.

So, what do we do with the data collected from these experiments within this text? Once the pitches and the arpeggios by chord type are created, the rest of the discussion centers upon running these "arpeggio cores" through a couple of different filters, and simply seeing what shakes out. Triads are extracted, we simply examine 3 note segments of the core, building the 3 note colossus so essential to the creation of our music. Next is to extend the triad into 7th chords, examining 4 note segments of the arpeggio cores and creating lines of tonal convergence. Exploring this 4 note grouping was my initial pathway into this experiment, as at the time in my studies I was centering in on the idea of categorizing chords by type. Creating a seven note core becomes the last focus, filtering the core arpeggio into "groups of 7", then creating a scale configuration from the arpeggio. We then employ these scales in composing music. Oh, are you hip to the 7 / 5 / 12 concept of viewing our musical resources?

Results of the overtone series experiments.

1) Both the One and Two chord types, although starting on different pitches and using a different but consistent interval sequence, yielded identical results. The loop of pitches created is a giant 7 octave arpeggio, in which every pitch of the chromatic scale appears twice before looping back on to it's starting point. How many octaves on the standard piano keyboard? The distinction between these two different but similar chord types is essentially in the major 3rd / minor 3rd or minor 3rd / major 3rd interval sequence between their pitches. Coolness emerges with these chord types in a cycling of fifths with the triad filter, polytonal implications with the 7th chord filter and a consistent cycling of 12 major and 12 minor keys when the 7 note filter is applied. Interesting perhaps to note here that the major tonality is Lydian based while the minor is Dorian. Curious huh? Especially with the popularity of the Ionian / Aeolian pairing in American music?

2) Within the Five chord type, the symmetry of the major 3rd / minor 3rd sequence is momentarily disrupted by one pitch, the minor seventh, which when paired with the major 3rd, creates a tritone pitch relationship. We use the 3rd and 7th of almost any chord to determine chord type yes? Upon reaching the 7th degree and upward within the dominant core, the sequence then slips back into the symmetry of the major 3rd / minor 3rd cycle ( by my way of hearing things anyway ). Triads are examined. Using the 4 pitch / 7th chord filter, we discover a series of chord eight chord substitutions which are organized into a convergence diagram, chart #4, the components of which are analyzed in chart #5. A brief explanation of each entry, suggestions for scale choices and sample convergence ideas are included. Groups of seven pitches are examined from the dominant perspective. These discussions close with a profile of the experiment.

3) A chord summary chart is created by using the 4 pitch / 7th chord filtering of each of the 3 cores done simultaneously. Each of the four note segments paired together creating some interesting convergence pathways. See chart #6.

So why are these concepts potentially important for the creative musician? Can segments of the these theoretical concepts be extracted from the whole and used to create new forms of melodies and harmonic progressions? Is this part of what the modern serialists composers base their work on? For the American jazz artist, the idea of creating new melodic and harmonic schemes and the expanding the existing musical forms, is oftentimes at the historical core of artistic evolution. For at whatever level, a true joy for the player of any style of American music is in the continual searching and evolution of one's "voice", the gradual development of their ability to tell their stories within some of the most exciting musical settings ever imagined.

Can we base our musical adventures in polytonality in these principles? That's kinda the idea with this study of the cycle of pitches. Polytonal options seem to spring forth from weaving these extended arpeggios together. Just the idea of a naturally occurring cycling of keys within equal temper is to me so totally cool and exciting. Years ago while at work, my improvised melodic line "accidentally" slipped into this natural key cycle. I ended up being up a half step and had changed tonalities, but I sort of heard the line go there so I played it. I thought it sounded cool. Needless to say, I got a few looks. I remember hearing the bass player say, Yo Db!, as we were playing the A section of "Body and Soul." They probably thought I was lost, ha, was I ever. Anyway, the polytonal world does exist and one way to view it's theory is in these cycles of the pitches. Whether there is anything there for you artistically is up to you to find, but that's the cool part right? What was the last important theoretical breakthrough in American jazz music? Where is the next one?

So with this in mind, perhaps explore the pitch cycles of each of the three chord type arpeggios as time permits, examine the results and look for coolness to expand your own palette of colors.

"If I have seen further, it is by standing on the shoulders of giants" Sir Issac Newton