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MusicPhysics

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Obvious physical parameters include average range of human ear and voice, and sonic nature of materials used to build musical instruments. For instance, typical peak resonance of animal gut strings might explain common variations in tuning note for various common instruments. Less obvious physical conditions might also determine peak resonances, things like weather conditions, common building materials, room sizes and echo factors.

Less obvious physical parameters might include average human heart rate at rest or dancing, or sound resonance in bodies of listeners, in addition to obvious resonance of singers' own head and chest register. All of those factors and similar physical attributes might explain much of the background physics of music in ways that tend to limit and guide choosing favorable numbers of cycles per second (cps) for important notes.

However, even given a natural world that might give certain numbers of cps more sonic resonance, the music world still seems to go far beyond obvious resonance in imposing on itself mathematical consistency, for example, in relative tuning.

In choosing substantive tuning note for relative tuning, as well as other "raw" number definitions, a widespread assumption of the importance of mathematical consistency in western music does not seem completely explained by needs for harmony among contemporary musicians and recording and reproducing musical work.

It is a widely-held assumption that the mathematical patterns in Hellenistic music are expressions of meta-musical concepts. Music is used as a medium to express observed mathematical relation. But searching out mathematical patterns similar to relative patterns of the musical scale involves coordinating many variables at once, in order to derive relative relations, and also comparing them in an equally complex process of discerning other patterns of relative relations. Kepler and others have tried complex comparisons of relative patterns whose internal relations are similar to western musical scales. Yet the simple and obvious assumption that musical scales have a physically determined independent reference should more easily be shown by seeking only one simple independent variable.

To begin the search, it seems a reasonable method to choose the most independent variable, the tuning note used to set other notes of the scale. Two major examples are Middle C and A' over Middle C. The cps of Middle C has been discussed as an expression of binary counting, in that the usual Middle C is 260 cps, which is approximately very close to two-to-8th power, 256. However, for our purpose here it is not enough simply to describe a similar mathematical relation, like central number in a counting system. That may be in some ways similar to eight note scales, but it is still not a physical basis for 256 cps as a tuning note.

We might try to find a physical basis for Middle C as trained binary counting by musicians. For instance, maybe there is a one-second clock in the average resting heart rate, (assumed to be around 60 beats a minute,) and the computation process of tuning to Middle C is a quick approximation of counting "One, two, four, eight, sixteen, thirty-two, sixty-four, 128, 256," in one heartbeat. That assumes that the musician can be trained to count the cps of the tuning note by comparing it to the "clock" of the average resting heartbeat. That theory assumes the ability of a human ear to register sound in binary "click" unit of one sound cycle "on-off," and the ability of musician's brain to double that count eight times in one heartbeat. That is, the ear measures the speed of one click cycle, and the brain registers how many times that cycle duration is doubled during an average heartbeat.

That tuning theory for Middle C assumes an internal clock process. I am more interested in an external clock process, in addition. For instance, the observed speed of the sun through the sky, (observable directly and by shadows, etc...) may be a basis to derive tuning A'=440 cps. The length of one cycle of the 440cps sound wave seems to be approximately ground distance covered by the speed of the sun during that duration, one-440th of a second.

At this point I have to check the computations of Earth circumference at the Mediterranean latitude, Earth rotation speed, wave length of 440cps sound-wave. And if it turns out that 440hz is a wave length approximately equal to ground distance covered by observed solar movement during that time duration, we may suspect that speeds registered in other senses may be timed in a musician's brain by musical tone. The mile seems coordinated with Hellenic distance and geographical measurements so I will use it (mile = 1 longitude second.) So far I have solar speed as 900 miles per hour, divided by sixty minutes, divided by sixty seconds, equals a quarter-mile per second. 5,280 feet per mile = 1,320 feet per second. 1320 divided by 440 = 3 feet, that is, using those numbers, the sun apparently moves 3 feet per cycle of the 440cps tone A'. the length of the 440hz sound wave is 2.568 feet according to "www.mcsquared.com/wavelength.htm" applet calculator, which is labelled as based at sea level 20 degrees Celsius. Could 440cps be the result of a similar formula done by ancient mathematicians using different estimates?

It seems that 3 feet sound wavelength is approximately 365cps. (3.095 feet) Is that somehow related to 365 day year and 360 degree/60 mile per degree solar orbit?