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.

Beneath the Waves

"It's worthless - ten dollars from a vendor in the street. But I take it, I bury it in the sand for a thousand years, it becomes priceless."
So said Dr. Rene Belloq in Raiders of the Lost Ark. Well, time after all is relative and about ninety years at the bottom of the north Atlantic is probably roughly equivalent.
Yesterday day I went to see the Titanic exhibit at DMNS and was struck by a rather curious irony. You see Molly Brown was bringing some artifacts to the Denver Museum on board the Titanic when she sank. Now the most common items from that ship, many costing a good deal less then ten dollars at the time, are an exhibit in the very same museum* and have become priceless.
There are of course a number of things that make one think, a pair of spectacles, a gage from the engine room where the firemen stayed behind to keep the generators running. But for me the most sublime was the two ton piece of Titanic’s hull, perhaps because it was not sequestered in an antiseptic case, but merely hung there as a monument to man’s arrogance. As a musician I was somewhat disappointed that there were no musical instruments among the artifacts. The brass and woodwinds I would think might have survived. But upon reflection it is most likely best that they stay where they are, with the musicians who played on…perhaps to the very end, and perhaps on a clear moonlight night on the north Atlantic you hear them playing still. 
But what I found to be the most thought provoking part of the exhibit was the replica mailbags. Though the ship carried over a thousand passengers and no small amount of cargo, it was these bags of Dears and Sincerelys that gave it its designation, RMS Titanic. In a way they represented something almost mystical, the union of democracy and majesty. It might be a letter from some East End charwoman to her wayward son seeking his fortune in America, but once in the bag it became, along with letters from Dukes and doctors, princes and millionaires, the Royal Mail. These letters, or rather their spectral implication, speak to us of a lost time and humanity in a way even more than the artifacts. Written with quill and ink the letters in such bags contained much more than sentences and paragraphs. Indeed Sherlock Holmes once solved a mystery partly do to an unsigned letter being written in a lady’s hand…try doing that with an E-mail. Back in Perry Mason’s day the handwriting expert was indispensable, now they are all but extinct. The world now has more people but less character, as communication is now filtered through a one size fits all keyboard and spell checkers stamp out any remnant of personality. Regardless of class or station, letters are the communiqués of ladies and gentleman, not as clumsy or random as a text message; they are an elegant form of communication, for a more civilized age.

*Yes, I know it is a new wing and would have been a botanical garden at the time but still.

The Rise and Fall of the Universe, or Who Put the Cause in Cosmos?

The last episode of The Universe premiered on the History Channel last Tuesday and after two hours of following the thread of thought through human history we find that despite some new discoveries and CGI graphics, Carl Sagan’s Cosmos is still by far the best film series on the subject.
Sagan’s series is much more dynamic, delving deeper into the subject matter than the simplistic; “this guy discovered this so that guy could discover that” of The Universe. Although Sagan is always trying to shove his materialistic worldview down our throats, at least he gives you enough nice pictures and pretty music to make it go down easer.
The Universe does not seem to have a particular worldview. It does pause to give homage to the fact that the universe having a beginning indicates some sort of creation,* but then wisely observes that science is not equipped to handle metaphysical matters. The real problem with The Universe is that it spends precious little time on real science.
Take relativity for example. Without getting too technical or going into unnecessary details Sagan demonstrates the fundamental principles and why they must be the case. While The Universe on the other hand, literally turns it into a circus, a fairly incoherent circus.
The last episode of Cosmos ironically begins with a quote from Deuteronomy. Of course Sagan would have accepted any source that agreed with his basic premise that we should avoid wiping ourselves out. He apparently thought that it was much better to let our local star or some other natural phenomena do it instead. Perhaps in the meantime we could putter around some tiny percentage of our galaxy, and maybe even feel so much less lonely by discovering bacteria on Europa or perhaps even Alpha Centauri!
But The Universe has no cold war to worry about, and with general stagnation in space exploration on most fronts, there is not much room for propaganda there either. So The Universe takes a more sublime approach. It leaves us with the thought that no matter what we do all humans and human endeavor, all terrestrial life, even the microbes on Europa and untold alien civilizations scattered across the galaxies, even all the constituent particles will ultimately come to naught and be dissolved.
There. Wasn’t that worth waiting for generations of geniuses to build relentlessly on each other’s knowledge to find out?


*Carl Sagan, in his effort to avoid the implications of the cosmos having a definite beginning, dabbled in some rather strange and exotic hypotheses, particularly the “oscillating universe”. The oscillating universe requires an infinite chain of Omega over one universes. Now pretty much all observable data points to our universe not being an Omega over one universe. So either we are the last link in an infinite chain, which is a philosophically difficult position to maintain or there is some other explanation for our universe’s beginning.

The Dawkins Talk Crisis

Richard Dawkins was on television the other night and as usual he was jawing about God again. I suppose this is because he wrote a book recently that has “God” in the title. I read somewhere that Professor Dawkins is a biologist. I must say, why does he not write a book about biology? Then perhaps he could get on the telly and talk about something he might actually know something about. I am sure he could tell us all sorts of fascinating things about amino acids and helixes and chromosomes, and not come anywhere near all the nonsense he becomes entangled in when he talks about God.
To begin with, he says that science is very close to explaining questions of ultimate reality, without the “God hypothesis”. Now even as a scientist Dawkins should know that we are as close to this as we were a hundred years ago or five hundred years ago or three thousand years ago. The fact is, we are living in a bubble which we, for want of a better name, call “the big bang” and there is simply no way for us to scientifically study what is outside this bubble. But even if we could somehow penetrate this finite but unbounded world we find our selves in, we would probably be left with the same dilemma we have had since antiquity, either an infinite regress of finite propositions or a finite regress to an infinite One.
But ontology aside, Dawkins’ bigger problem is ethical. He keeps acting as if there were some objective morality; but (like every atheist I have ever known) he gives no indication as to where this might come from. Naturally the root of any moral paradigm must be its creation myth, since teleology is central to any ethical principle. But Dawkins’ creation myth (if you can call it that) is apparently evolution by natural selection. Now this is not really a creation myth but rather an epic story, which is not to say one cannot draw moral principles from it, it is just that those principles would be somewhat borrowed capital. However, the real problem with the moral principles one might glean from the proposition of evolution through natural selection is, they have very little to do with what Dawkins apparently thinks is rite or wrong.
For example Dawkins apparently thinks there is something wrong with slavery. Now I would like to know how exactly he gets this idea out of natural selection, whose primary ethical principle is, “live long* and procreate”? How is it fundamentally different for me to use a member of my own species** to achieve longevity and progeny than for me to use a member of another species, or an inanimate object for that matter?
He also fusses about proper treatment of the female. Now proper care of the female is important, indeed critical for the fundamental ethic of evolution. But this does not seem to be what Dawkins is referring to. In fact he seems to want to take an evolutionary step backwards, and make our female more like our male.
Finally, just what is Dawkins point? I can understand the theist’s urge to evangelize; after all, if there really is a God, then it follows that we should all strive to be pleasing to Him. But if there is no God, then who really cares?



*Actually living long is wholly relative to procreating.

**Since nature’s sole means of sorting living things is the species, it may seem as though there may be a difference here. But since according to evolution, one species can become many over time, and thus my progeny and my slaves may be of a different species in the future, my chauvinism would still be appropriate.

Socialist or Progressive?

Among a certain political sect it is fashionable to call oneself a progressive. Of course the term “progressive” like the term improvement or advancement is, of itself, rather meaningless. One cannot make abstract progress, there must be a specific proposition, not currently realized, that one is progressing toward.
Now most would identify the position most progressives are progressing toward, as socialism, and I would have to agree with that, but that does not mean that one should identify progressives with socialists.
True socialists are actually rather rare, in fact there are a great many people who claim to be socialist, who in fact are not. A true socialist is some one who follows the principles of socialism to their logical conclusion, and desires that conclusion. Now the fundamental principle of socialism is that an elite (the government) should control and manage all resources, and thus naturally also the life of the individual, including, or rather primarily regarding, procreation (since obviously in any sound economic system involving humans, who ever controls the recesses must control procreation).
The progressive on the other hand, though he likes the socialist’s principle, gets squeamish when it is carried to its logical conclusion.
Of course many who call themselves progressive would probably not balk too much at the idea of a general restriction on the number of children a woman can have. But such would hardly be adequate for responsible socialism, and would really be no better and probably worse than letting women procreate willy-nilly. It could function as somewhat of a clumsy emergency shutoff mechanism, but one could hardly call an automobile operator a good driver, if his sole ability were to hit the breaks.
Making the restriction disproportionate, so that the prime females could have more children than the culls might appear to be progress, but this could still leave the society inadequately, and inappropriately populated if the prime females did not choose to procreate enough.
If the elite (the government) is to be truly responsible it must not merely restrict procreation for the culls, it must compel it for the primes, so that an appropriate population can be achieved. But it is pointless for the prime females to have more children if their mates are culls. So a responsible government must not only dictate how many children a woman has, but also who she marries.
It is this, the logical conclusion of socialism, which the progressive does not like. And that is why he calls himself a progressive. If he were a socialist, he would desire its fullness and nothing less. But where the socialist desires a sound (if fairly abominable) economic system. The progressive desires neither soundness nor stability but merely an endless Zenonean progress towards socialism.
Or perhaps more close to reality, the progressive is looking for a free lunch. He wants resources, but he does not want to pay for them, either by being responsible for them himself, or surrendering that responsibility to another. There is, of course, a way to get a free lunch, and that is to steal it. This is what the progressive truly is, not a respectable advisory like the socialist, but merely a despicable thief. He wishes to steal from both sides and escape before he is caught. If there are any true socialists, they should despise the progressive as much as we do.