The implications are staggering, if not blasphemous. We are at core now in truth saying that we do not believe there are twelve distinct individual key centers available to us in the Western musical system. We are saying something truly outrageous; that there are only three key centers.

For if the key centers of roots a minor third apart: C, Eb, F#, and A = one key center, and C#, E, G, and Bb= the next key center, and D, F, G#, and B = the last key center, (it repeats itself again at Eb...) then we have only three distinct key centers to really choose from.

But how can this even be possible?

At the very least, I concede key centers a minor third apart have distinct intervallic characteristics that render them not literally identical to one another. Any music student can point out to me the serious number of notes that are patently not the same in the C major and F# major scales, for example. But what if these key center groups actually are so related that modulation from one of them to the other within the group was so weak, it hardly constituted a change of key at all, at least in practice? Has that even been done?

In Figure 1, the ubiquitous I-VI-II-V turnaround in the keys of C, Eb, F#, and A majors are demonstrated to be easily utilized interchangeably yielding differing but entirely musical results, and often already recognized and commonly accepted practice (in this example it seems, especially in the field of Brazilian music).

Yet, how would a music teacher explain for example the last harmonic sequence presented, namely Amaj7—D#m7—Dm7—C#7? Will the D#m7, instead of being simply what it is, be thought as a partial chord of some other convoluted twisted harmonic mechanism in a tortured attempt to explain this harmonic movement, without resorting to the Grand Unified Field? Will the C# Dominant chord resolving into the key of A major (#IVm7-Imaj, already a head scratcher) be thought of as theoretically anomalous, but common in some backward or unschooled styles of hoi-polloi musics? One would have to present a rather long and circuitous route to describe such a straightforward chord motion as this, if using only present-day known harmonic theory. While this new theory is based on standard harmonised scale theory, it fully accounts for any known instance of deviation from it, as I will try to prove in this and upcoming articles.

Figure 1

Part 1b

I have managed to chart out every possible combination of chords that function as subdominant to dominant to tonic movement given a single key center, or rather a single set of cyclic key centers. It is my preference to call it a polytonal center. Poly, since it not singular; yet center is singular. A compound singularity, as it were.

1)
II-V-I

Dmin7th G7th Cmaj7

2)
IIm—bVii7—I

Dm7—Bb7—Cmaj7

3)
IIm7—III7th—I

Dm7—E7th—Cmaj7

4)
IVm-b7thdom- I

Fmin7—Bb7—Cmaj7

5)
Ivm7—V7th—I

Fm7—G7th—C

IVm7—bII7th—I

Fm7—Db7—Cmaj7

7)
IVm7—III7th—I

Fm7th—E7th—Cmaj7th

8)
b6thm7 b7th7th Imaj7

Abm7—Bb7th—Cmaj7th

9)
bVim7—V7th—I

Abm7—G7th—Cmaj7

10)
Viim7—bVii7th—Imaj7

Bmin7—Bb7th—Cmaj7

11)
Viim7(b5)—V7th—I

Bmin7—G7—Cmaj7

12)
Viim7—bII7th—I

Bmin7—Db7—Cmaj7

Key of C = Eb = F# = A
Key of C# = E = G = Bb
Key of D = F = Ab = B

Resolution Movements for Dominants:

Dom to fourth up G7—C(root)

Dom to major third down G7—Eb(root)

Dom to a whole step up G7—A(root)

Dom to half step down G7—F#(root)

Inclusive of the primary II-V-I(or Im), we obtain 12 possible perfect cadences, all resolving to the same root (or root-group). You will find this chart to be of absolute importance as you pursue a deeper analysis of music you already thought you knew.

Basic Assumptions:

It matters not if our root is a major chord or a minor, dominant or other. It matters not if we refer to our practice as functional or modal. Chord types act independently of chord function. I.e. a dominant chord may act as a dominant, or it may act as a Imaj, or IVmaj substitution. This yields an infinite array of harmonic color to our palette.

General Guideline:

One may use the GUFT system to reharmonize a given set of harmonic changes, but it is primarily used as a diagnostic and generative tool. It can be used to remake an existent piece of music, acted upon with good judgment, but its function is to analyze, and also to create new music.

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