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Hmmm! Reasonable ideas randomly cemented together into overall muddle. Or so it seems to me. The first muddle is not recognising that if G to C is 3:2 and octave C is higher than C by a factor 2 then it follows automatically that octave C to G is 4:3, which he seems to think is contradictory. And then we mysteriously jump from musical issues to qigong without so much as blinking ...
Brian
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Brian D. Josephson
Emeritus Professor of Physics, University of Cambridge
Director, Mind–Matter Unification Project
Cavendish Laboratory, JJ Thomson Ave, Cambridge CB3 0HE, UK
WWW: http://www.tcm.phy.cam.ac.uk/~
Tel. +44(0)1223 37260/337254
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"It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative nature of the quotient corresponding to the three places {2, 3,∞}."
And so it is recognized in music theory that there is no Perfect Fourth overtone harmonic and so it is called the "Phantom Tonic" because it requires changing the value of the 1 as the fundamental pitch. But indeed 4/3 is C to F as the Perfect Fourth and so the way it was generated by Philolaus, as Professor Richard McKirahan has detailed recently, by translating the Greek, is a double octave is used based on the root tonic defined by X with a zero node and no longer by 1 as the fundamental pitch. In other words now time is inherently defined by geometric space. So the root tonic is now 0 to 8 as 1 pitch with the wavelength as 3/4 so that the 6/8 wavelength is the frequency 4/3. But this has to be converted to a geometric magnitude so that the Perfect Fifth plus the Perfect Fourth = Octave. So then the root tonic is changed to 0 to 12 and reversed in direction so that 8/12 wavelength is now the 2/3 wavelength with 3/2 as the Perfect Fifth of geometric magnitude plus 8/6 as the 4/3 wavelength but now as geometric magnitude. Therefore 12 to 6 is the Perfect Fifth plus Perfect Fourth equaling 2 as geometric magnitude logarithm. And so then for Archytas the equation used was "arithmetic mean x harmonic mean = geometric mean squared" so that the root tonic is now defined as "X" instead of 1 and so the octave is geometric mean squared and the Perfect Fifth has to be 3/2 as C to G and the Perfect Fourth has to be 4/3 as C to F, created from 2/3 undertone that is doubled to 4/3. Archtas also defined the Perfect Fifth as a geometric mean squared to then derive the 6/5 and 5/4 as harmonic mean and arithmetic mean....
What this process of converting noncommutative time-frequency into symmetric geometric ratios does is cover up the fact of the undertone series as the complementary to the root tonic of C. So then if 3/2 is C to G and then C is 4 that means that C to G is the Perfect Fifth as the 3/2 harmonic but for the next octave the G would be "under" the C as wavelength 4/3 and so the frequency would be 3/4 which means it is a Perfect Fourth since 2/3 is the Perfect Fifth frequency C to F. So your claim only works by ignoring the difference of noncommutative geometry as it affects the pitch in relation to the tonic. And so then this symmetric math of logarithms was extended to relativity but then de Broglie realized that since time slows down as a particle goes towards the speed of light, increasing in frequency this goes again time being inverse to frequency. Therefore there HAS to be a 2nd time as a phase wave from the future that is superluminal. But this is exactly what the ancients already knew since 1 was not a number but instead light.
I will end with an example from East Indian music theory since I know you have acknowledged the important of Indian philosophy.
Ma [Perfect Fourth], although consonant to Sa (root tonic), is alien to the overtone series and is not evoked in the sound of Sa. On the other hand, Sa is evoked in the sound of Ma, since Sa is a fifth above Ma and is its second overtone. For this reason it can be argued that the tendency to view Ma [the Perfect Fourth] as the ground-note has a 'natural' basis. The same cannot be said for Pa [Perfect Fifth] as Sa [fundamental pitch] is not part of its overtone series. ... The thesis can be expressed in the following way: If two drones either a fourth or fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates the overtone series to which the other note (or one of its octaves) belongs. By amplifying a prominent overtone the secondary drone lends support to the primary and intensifies its 'primary' character.
The Rāgs of North Indian Music: Their Structure and Evolution
Nazir Ali Jairazbhoy - 1995 - MusicThe same cannot be said for Pa as Sa is not part of its overtone series. This thesis can be expressed in the following way: If two drones either a fourth or a fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates ...
The question is if 1 is the first note and the octave is the same pitch -
say C then 3 is G as the Overtone but 3 is F as the undertone and
throat singing proves Adam wrong - undertones are real and NOT the "New"
root tonic but rather there is NO root tonic, instead time is infinite
noncommutative phase since G=3=F at the same time. Nobel Physicist Brian
Josephson replied to me about this issue today. His reply and my
response is on my blog http://elixirfield.blogspot.com Math Professor Kauffman Louis H, Amson John C - 2013 - Science "The special synchronization is the algebra of the time shift embodied in ηη = 1 and [a, b]η = η[b, a] that makes the algebra of i = [1,−1]η imply that i squared = −1. "The ancients knew this was true due to noncommutative phase of music, as Alain Connes discovered. So 1 is not a number because 2/3 and 3/2 are noncommutative as infinite two-dimensional time-frequency information that constructs the illusion of 3D space as a "zero point." So Gerard t'Hooft is correct - calling it a moebius strip. It was known as the Tai Chi or the Tetraktys or the three gunas of India. |
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