major colortones

Chart # 1. Creating the core arpeggio in chart form based in C major using the major third / minor third cycle of pitches within the consistent intonation of equal temper, looping at 24 pitches. Example 1.

continuing upward...

continuing upward...

Here is the sound of the above pitches, ascending then descending. Example 1a.

So, 24 occurences / intervals to complete one cycle, interesting that enharmonic spellings of the pitches naturally emerge from the major / minor 3rd interval sequence eh? Here are the pitches of the arpeggio in example 1 above, simply reformatted into one line. Although only presented in one occurrence in linear form, perhaps try to think of it as a continuum or loop of pitches.  Example 1b.

This simple idea of "loops of pitches" becomes a key to understanding how equal temper is a balanced and theoretically "closed" system of tonal organization. Notice the motion by perfect fifth between every other pitch, creating the cycle of fifths? Here are the pitches by 5th. Example 1c.

Running the core arpeggio of the tonic group of pitches through the triad filter. Here the alternating 12 major and 12 minor triads emerge. Simply follow the different colored, three note groups of pitches gradually downward and to the right then back to the top and repeat the process. Example 2.

Ran out of space at the end, sorry, again software limitations. The triad A C E completes the cycle. Thus, the triads emerge. Note the major / minor cycling in their quality. Here is the sound of the above 24 triads, transposed up or down by octave to keep things within a comfortable range of the bass and treble clefs. Example 2a.

Shedding chart for the alternating sequence of major and minor triads. Example 2b.

Click the icon for a practice loop of the above sequence with the scales. Example 2c.

Same loop, you add the melodic lines. Example 2c.

Creating four note groups brings forth the 7th chord. Example 3.

These 24 alternating major / minor 7th chords find their way onto the tonal convergence chart #6. Here is the sound of the above sequencing of seventh chords. Example 3a.

By looping this group seven times and then extracting groups of 7 pitches, each of the 12 major and 12 minor key centers emerge. The following chart again uses 5 different colors to help separate the scales and reads left to right, top to bottom. Example 4.

Extracting the groups of seven pitches, creating the 12 Lydian major and 12 Dorian minor scales, we again create the major / minor sequencing. From the above chart, do you notice how the upper part of the arpeggiated Lydian group naturally evolves upward into the Dorian color by half step, creating a cycle used to include all of our 24 tonal centers? That C Lydian evolves into C# Dorian which becomes C# / Db Lydian then up to D Dorian? Is the flip side of this cool? Dorian to Lydian, i.e., minor to major? Just might be eh? Simply alternating between the Lydian and Dorian colors. So very cool. Perhaps this is a new concept for the advancing theorist? Here we weave the tonalities together using this "tonal evolutionary principle". Staying within a comfortable range, we combine scales over chords and follow the half step evolutionary motion as illuminated above. Example 4a.

Could we reverse the direction of the evolving tonal centers, or move backwards? C to B etc? Of course, but you knew that right? Chart 1a. Here are the above scale pitches written out by letter names. Example 4c.

So, if the major scale is so popular in creating the American melodies why doesn't appear on the chart? Well it does, it's just that the major scale is created from within the Lydian and Dorian modes, similar to how we can extract these modes from the major scale n'est pas?

So, how can all this figure in stylistically? Well, perhaps it is like comparing the resource potential associated with our brains? Out of the total resource of my personnel hard drive, my average i.q. is supposed to mean that I am using about 10 to 15% of what's available perhaps? So, same with my music? Out of 24 key centers, if I play a folk, blues or rock tune, I'm generally going to hang in one key, or about 4% of the available resource. In jazz tunes I often play, visiting four or five key centers is not that uncommon, although two or three keys is more the norm, so between 8 and 18% or so. So, even with visiting 5 key centers in one song, that still leaves 19 tonal destinations or about 80% of the resource untouched? Exactly. So what might this mean for your music?

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