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There are simple, ideal ratios as expressed in a harmonic series, and then there is the more complex reality of equal temperament, in which the frequency ratios are not so simple and are best written as roots or decimals. Here is one more exercise before we go on to discussions of music.
Originally posted by fulllotusqigong
reply to post by Morpheas
Here's the book pdf link
read the book online here
Or whatever other format you want the book in hereedit on 26-5-2012 by fulllotusqigong because: (no reason given)
Originally posted by fulllotusqigong
O.K. so you're claiming that the Just Tuning "ratios" work as either 2:3 or 3:2 right? Nope.
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.
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.
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
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
Originally posted by fulllotusqigong
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?
Originally posted by fulllotusqigong
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.
It should also be noted that the frequency wave created by the orbit around the Sun by Earth and the frequency wave of the rotation of Venus's day create a harmonic interval ratio of 3:2 (a Fibonacci sequnce). This pure harmonic interval creates a perfect fifth in the musical scale.
He thought that the 8:5 triangle could have been a simple and practical device to approximate the convergence of the Fibonacci Series to, thus implying that the Egyptian knew and performed this calculation. However, he did not go far enough as to prove it.
Originally posted by fulllotusqigong
Again no golden ratio in Egypt.
Originally posted by ErroneousDylan
Originally posted by fulllotusqigong
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.
Which I have said over and over again... and you just some to completely ignore it... Stop being delusional.
Yes I claimed that a RATIO can be expressed in any order, be it 2:3 or 3:2. And yes I claim that the Perfect Fifth ratio is 3:2. Those two statements are completely unrelated to each other in the context that I used them. You completely misunderstood it and just can't seem to let it go...
What exactly are you trying to convey OTHER than the fact that the ratio of 2:3 is not a Perfect Fifth? That is all you have said in the past few pages..
I'm glad you acknowledge the fact that harmonic orbital resonance has been explained much earlier than Merrick though. Meaning Merrick can not take credit for it.
The law of Pythagoras, an example of the inverse-square law so fundamental to science, can also be approached geometrically through another Pythagorean law, the law of growth-fundamental to chaos and complexity or open systems science, as we'll also see. It's represented by the 4:3 or 3:2 proportioned five-pointed star, "thought to have been a sign of the Pythagorean brotherhood," comments Edward Rothstein, music critic for The New York Times. (43) The profound simple principle is thus: "As the whole line is to the greater segment, so is the greater to the lesser." Rothstein notes that the power of the principle is "to contain itself within itself in the simplest possible fashion." (called the golden mean, the golden section or the Divine Proportion) Rothstein, also a mathematician, explains that the law of growth can be stated as "each number being the sum of the two previous numbers."(44) Or as the music analyst Erno Lendvai puts it: "If every branch of a tree, in one year shoots a new branch, and these new branches double after two years, the number of the branches shows the following yearly increase: 2, 3, 5, 8, 21, 34." (also known as the Fibonacci number series).(45) The mathematical analysis Spirals: From Theodorus to Chaos by Phillip J. Davis (1993) attempts to demystify the law by giving it further credence at the same time: It simply grows its stalks or florets in succession around the apex of the stem so that each fits the gaps of the others. The plant is not in love with the Fibonacci series; it does not even count its stalks; it just puts out stalks were they will have the most room. All the beauty and all the mathematics are a natural by-product of a simple system of growth interacting with its spatial environment.(46) This law of growth has been so important to human civilization that Egyptian, Mayan, Asian, Greek, Gothic, Renaissance and modern architecture and art have all been created by its precise measurements.(47) The growth pattern can be applied to music analysis in at least three manners. The ratios can be attributed to the number series (i.e. 1:1, 1:2, 3:2, 5: 3, 8:5, 21:13 equals the intervals of unison, octave, perfect fifth, major sixth, minor sixth and minor sixth again).(48) Dover publications, known for their prestigious music texts, published the book The Divine Proportion that investigates how the ratio of the major sixth and the major third approximate the golden mean proportion. Lendvai applies the number series to the intervals with each number represented each step of the scale (i.e. 1=minor second, 2=major second, 3=minor third, 5=perfect fourth and 8=minor sixth).(49)
He described the NeoPlatonic Harmony of the Spheres that, as elaborated by Reiser, includes artificial intelligence, zero-point energy, techno-samadhi, biological holograms, plasma and lasers, galatic manipulation of higher dimensions. Dr. Reiser explictly describes the evolution of the Matrix by stating that the Earth is an egg and in the egg is an embryo. The embryo feeds off the humans, animals and plants, as the ectoderm and entoderm of the egg, in order to create the new World Mother or the Matrix, the Sub-Stance or Psi-Plasma of Nondualism. Again unfortunately, according to this plan, most of humanity and the environment are seen as necessary costs to developing the next level of evolution.
Originally posted by fulllotusqigong
reply to post by PurpleChiten
I wish I could say math is an opinion.
Also it's not just the OP -- as I've pointed out there's a new book out based on this premise.
My critique of this has been censored.
The New Age lies are thick and so must be exposed.
Claims about the Fibonacci Series and the Perfect Fifth music ratio are half-baked theories.
I wrote my masters thesis on this topic at the University of Minnesota in 2000.