The best way to use any musical system, is to first learn it so well that it becomes intuitive, and then forget about it.  Let the music emerge of its own accord, don’t constrain it with a bunch of logical constructionist thinking.  First learn a system deeply until you no longer have to even think about it, become facile with the system so you “just know it” like you know your own name, so you can mentally run through any permutations easily, but then let go of it and allow the subconscious mind to make music with it.  

So, with that big neon sign firmly positioned above all else … 

Underlying all of this system are the three Octatonic Scales, but they are not used directly as such.  Seven-pitched symmetrical tonalities are the real focus of this whole system.  The Octatonics are only important to understand the crucial inter-relationships between all the seven-pitched symmetrical scales.  The Acoustic Scale is the real key to tonality, as it emerges from everything … everything … from subatomic vibrations to galaxies.

What conventional traditional musical systems have missed is the center of symmetry.

Begin by considering D as the center of a symmetrical keyboard.  Sit at a piano and look at this.  Ascending from D with an F#, and descending from D with a Bb, we have the Acoustic Scale, but in a permutation which is equally balanced between major and minor modalities in a mirror of each other on either side of the tonal center.  This sort of mirroring around a center will show up again and again throughout this system…

Utilizing the full Acoustic Scale centered in this way, but emphasizing more or less one side or the other around that tonal center, allows creation of a range of subtle hues which may be more or less ambiguous or distinct, depending only upon how the pitches are voiced.  Rather than merely “major” or “minor” or any other modalities, there is a continuum, a spectrum of unlimited hues.  Utilizing the balance between ambiguity versus distinctiveness is up to the composer.  It can sound very vague, or it can sound very clearly defined.

Working out all twelve transpositions of this symmetrically centered Acoustic Scale around the cycle of fifths, related keys show up in four triangular axial sets, related by octatonics (as explained in greater detail further on…)

 

   Shifting amongst the tonal centers within one same triangular axis yields such a subtly smooth harmonic motion that it may be barely noticeable, or considered in a way analogous to “chord substitutions” in another idiom.   Rotating the triangular axis through any of these four positions, by smaller or larger turns, brings forth a sense of more or less dramatic harmonic motion.

The overall sound is quite tonal, clearly not atonal, but certain aspects of the “common practice period” of functional harmony are absent here, and it is no accident.   The overbearing gravitational pull of dominant/subdominant trajectories is entirely averted, giving way to a far more flexible sort of harmonic motion.  This is at once a great ease and a greater challenge, as modulation in any direction is quite facile, but establishing any contextual sense of “home” requires rather careful attention.

There are deep symmetries to be found in every dimension via this way of considering the cycle of the Acoustic Scale, and the more one explores those symmetries the more the beauty of natural acoustical harmonic interrelationships reveals itself…

continue reading next section … Tonal Relations