The Grand Unified Theory of Music

Hay! Took a bit of a hiatus this semester to concentrate on music and other things, but here is a sample of some of the stuff I have been working on.

Perfect Tempos

When I set out on this research project my goal was no less then to understand the twelve tone tonic system and the mysterious force within it. Though I have admittedly fallen short of this goal, I believe the research and contemplation has still deepened my understanding of music, and perhaps may be the beginnings of ultimately achieving my goal.
"The two most basic elements of music are sound and time." So said W. Ronald Clemmons in his book Sounds in Time, and I doubt there is much serious disagreement on this fact. We could think of music as a mathematical abstraction on a parchment or “score”, but still what this would be representing is the mathematics of sound in time. Time is of course fundamental to sound it self. It is what unites our musical spectrum as well as forming the distinctions within it.
The distinction of two different tones is fundamentally a distinction in time. It is a distinction of the rhythmic pulse of sound within the tone; a faster pulse gives us a higher frequency or pitch, where as a slower pulse gives lower frequency. The same principle of course is at play in the extreme bass of our musical spectrum, where the rhythmic pulse is slowed to the point that it is no longer called tone but beat. However it is essentially the same phenomena we encounter in the treble region, beat and tone are just different was of looking at the pulse of music.
We often think of beats as having divisions and subdivisions, but any frequency bearing tone played within an underlying rhythmic structure can be seen as a pulse within a pulse.
Although it is easy to think of these elements of music, in a purely analytical fashion, as belonging to a single united spectrum of time and sound, they usually seem quite distinct in music as we actually encounter it. This is because composers generally avoid the dialectical area of the spectrum where the distinction becomes “muddy” (though vibrato can, on occasion, create a sort of flirting between the regions, if not actual meeting). Still there is a single interval that runs throughout the spectrum, let us call it the tonic interval. It manifests the most fundamental mathematical relationship that the human mind can grasp, that of doubling or Halfling (depending on which direction you are going.) We see this principle in the tonal area as the octave. We see it in the rhythm section in the basic form of the notes, whole, half, quarter etc. The adjustment of this interval is made in the tonal section by use the twelve “keys” within the interval (Major, minor or modal dose not really concern us here, as these refer only to how the tonic interval is internally divided.) It is made in the rhythm section by use of the more flexible* concept tempo.
This brings us to the main focus of this paper, the alignment of these two principles, key and tempo. Clearly these two principles can be aligned but for demonstration purposes let us take A4 at 440 Hz. The next tonic down would be 220Hz and the next 110Hz and the next 55Hz and the next 27.5Hz and the next 13.75 Hz (we are now getting below level of human hearing) and the next 6.88Hz and the next 3.44Hz or approximately 206 cycles per minuet. We have passed from the realm of tone through the “muddy” region and have come at long last to the domain of rhythm (that is if you are slightly demented). However, I would prefer to work with 103 or even 52, but this just underscores an important point. We are not talking about there being a perfect tempo for each key but rather there being perfect tempos for each key. It is now important to state that when we say “perfect” we are not meaning to imply that they are the only or even the best tempo for that key, merely that they are the tempos that align perfectly with the tonic interval and thus cause the least pan spectral dissonance. Music though is not meant to be perfectly consonant; indeed if it were perfectly consonant it would not be music.
So how do perfect tempos and pan spectral consonance affect the aesthetic and therapeutic aspects music? I am afraid this is a matter deserving its own paper, a paper I have not yet done enough research to write but hopefully soon I will have.
In the mean time here is a table of perfect tempos for the western twelve tone tonic system.


A = 206, 103, 52
A# = 219, 109, 55
B = 116, 58, 29
C = 123, 61, 31 (tonic)
C# = 130, 65, 32
D = 138, 69, 34
D# = 146, 73, 36
E = 155, 77, 39
F = 164, 82, 41
F# = 173, 87, 44
G = 184, 92, 46 (dominate)
G# = 195, 97, 49


* I am not including microtones in this assessment; theoretically the interval is fully flexible throughout the full spectrum.