reply to post by ErroneousDylan
I said the RATIO between VenusDay/EarthYear can be written either as 2:3 or 3:2 depending on how you word it. It is completely irrelevant to the fact
that a perfect is 3:2 in just intonation.
O.K. again -- it's only 3/2 as the Perfect Fifth -- that's why 2/3x has to be doubled to 4/3 as the Perfect Fourth. So if you want to say the ratio
is 2:3 then it can't be the Perfect Fifth.
If you want to say it's 3/2 as the Perfect Fifth then that assumes a logarithmic measurement for both the music ratio and the planet ratio -- which
means your Fibonacci Series is also the Golden Ratio.
I hope that's clear for you -- apparently you want me to give you some information or something?
What are you not clear about?
Ah here is your question.
Yet you did not answer me about the Music of the Spheres. Did it exist long before Merrick? The answer is yes.
According to Pliny, Pythagoras devised a literal “music of the spheres” by using musical intervals to describe the distances between the moon
and the known planets. In his Timaeus, Plato took up the idea of a universal philosophy thorough numbers and their musical associations and devised a
series that he termed the World Soul: 1, 2, 3, 9, 8, and 27. By using these as musical ratios (1:2, 2:3, 3:9, etc.) he created a series of musical
notes that gave a default mathematical ratio for the half-step. By mathematical derivation, one can arrive at theoretical proportions for the
non-Pythagorean intervals of seconds, thirds, sixths and sevenths. These intervals are inherently subjective and context-sensitive, however, and have
led to epic battles over “desirable” tuning temperaments, in part due to the fact that fixed-pitch instruments like pianos have one pitch to
represent at least two distinct notes.
That's from Musicofthespheres.org
I hope you're not playing the "willful ignorance" game but not looking up anything yourself.
O.K. Plato based on Timeaus Music of the Spheres on the system Archytas used -- it's not real Pythagorean harmonics -- it already assumes an
irrational solution for the music scale.
My book goes into this in great detail -- based on my correspondence with math professors Luigi Borzacchini and Joe Mazur.
Do you really want to go into all the details? haha. I don't think so. My Devil's Chord thread does.
O.K. so you're saying the ratio of the planets can be 2:3 or 3:2 and it doesn't matter -- but again that's not true for the Perfect Fifth music
interval -- it has to be 3:2 or else it's not commutative and this goes back to Plato and his collaborator Archytas because they used a "divide and
average" or means system -- adding the geometric mean to derive the irrational number.
You don't have to believe me though -- musciologist Ernest McClain has a whole book proving that Plato was using a system already based on
equal-tempered irrational numbers --
The Pythagorean Plato pdf is his book online
So he quotes Plato using the harmonic mean and arithmetic mean and then the geometric mean -- this is the system created by Archytas.
Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the
consequent or second term, should consult Archytas DK 47 B 2. This Fragment requires that the ratios be of this form if the assertions about the three
means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1,
3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them. Indeed, there is early proof deriving from
the Pythagorean school that intervals, such as the fifths, which are represented by superparticular [n + 1 : n] ratios cannot be partitioned into any
number of equal subintervals because the terms of these ratios admit no number of geometric means….There is reason to believe that these were
supplied by Archytas in the early fourth century B.C.233
233 Alan C. Bowen, "The Minor Sixth (8:5) in Early Greek Harmonic Science," The American Journal of
Philology, 1978.
O.K. the Orthodox Pythagoreans
only used the Tetrad as 1:2:3:4.
So whether it's you or Richard Merrick -- your Harmony of the Spheres concept is based on Plato and Archytas using the geometric mean -- it's Western
math and does not apply to nonwestern music harmonics.
edit on 26-5-2012 by fulllotusqigong because: (no reason given)
Orthodox Pythagorean theory recognizes five consonances: fourth, fifth, octave, twelfth, and double octave; and these are represented by the
multiple and superparticular ratios [n + 1 : n] from the tetrad. The number 8 obviously does not belong to the tetrad.235
235 André Barbera, "The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of
Ancient Pythagoreanism," Journal of Music Theory, 1984.
O.K. so 13:8 is not any ancient Music of the Spheres -- it's not Pythagorean -- it already assumes an irrational geometric mean division.
edit
on 26-5-2012 by fulllotusqigong because: (no reason given)