and Plato’s ‘citizens of the higher property class’ were generated, musically defining 2:3 and 3:4. From the demiurge 3, and the female 2, the human male number 5 was born who fathered ‘citizens of the second higher property class’, which define the musical 4:5, the major third and 5:6, the minor third.33This is the La Monte Young inspired pdf I was thinking of
Jung Hee Choi:
When I claimed that Adam Neely was relying on a lie from Just Tuning claiming 5/4 is from the natural overtones. here and https://elixirfield.blogspot.com/2020/04/adam-neely-finally-responds-to-me.html
However, he [Archytas] noted that the product of the arithmetic mean and the harmonic mean is equal to the square of the geometric mean, so this gave a way of dividing the fifth of 3:2 into the product of 5:4 and 6:5.A Truman State University review on Scriba, Christoph J. “Mathematics and music.” (Danish)
Normat 38 (1990), no. 1, 3–17, 52.
https://ecoechoinvasives.blogspot.com/2018/03/noncommutative-phase-or-why-wikipedia.html
http://ecoechoinvasives.blogspot.com/2018/02/pythagorean-central-fire-is-number-one.html
So who is the source? This person (Prof. Emeritus) is now 90 years old? yeah he's three years older than my dad would have been (if still alive)....
Antonio T. de Nicolas quoted in Ernest G. McClain, The Myth of Invariance, p. 2
So this is the secret irrational magnitude source for the supposed Just Tuning that Adam Neely is supposedly presenting as based on natural overtones of 1:2:3:4:5.
But we now know that Archytas got this from Philolaus CHANGING the root tonic from 0 to 12 to 0 to 8 - so that the subcontrary mean of Philolaus is now the Harmonic Mean of Archytas - as 8.
Meditations through the Rg Veda Ashok Malhotra & Antonio T. de Nicolas Philosophy East and West 28 (2):230-231 (1978)
That is the source cited...
oops that's just a review....
https://www.infinityfoundation.com/mandala/i_es/i_es_denic_retrospective_frameset.htm
OK so that link is an update from "antonio t. de nicolas" - So now - let's first review Richard McKirahan's expose on Philolaus.
https://sci-hub.tw/10.1163/22134417-90000137
We begin by taking the length corresponding to the ratio 3:2, namely the length 12 to 8. In other words, we start at 12 and take 2/3 of its length. Then we add a length corresponding to the ratio 4:3, but this time we are starting not at [meaning changing the root tonic of the "one" that we listen to as the home pitch of infinity]12 but at 8 and we want to take 3/4 of that. So instead of taking 12:9, which is 3/4 of 12, we take 8:6, which is 3/4 of 8. And so by adding the length 12 to 8 and the length 8 to 6, we get the length 12 to 6, which corresponds to the ratio 2:1. This is the correct result and further, it turns out that these procedures are correct and generalizable.oops. That is the bait and switch that is covered up by Archytas.
Colloquium 7: Philolaus on number
· January 2012google book overview of Antonio T. de Nicolas
De Nicolás explained to McClain the underlying musical structures of the Ṛg Veda.OK still can't find the details.
I've read McClain citing De Nicolas. I've corresponded with McClain. I have also corresponded with Professor John Curtis Franklin - an expert on ancient music theory - and he said he could find NO corroboration of the claims of McClain - and I cite that in my 2012 free pdf book.
Meditations Through the Ṛg Veda: Four-dimensional Man is citing McClain and McClain is citing De Nicolas!
The ratios of the first six integers defined the primary building blocks: the octave 1:2, the fifth 2:3, the fourth 3:4, the major third 4:5, and the minor third 5:6. From these first six intergers, functioning as multiples and sub-multiples of any reference unit ('1') of length or frequency, a numerological cosmology was developed throughout the Near and Far East [Fig. 1(b)].https://www.medhajournal.com/audial-and-literary-cultures-the-bhagavad-gita-as-a-case-study/?doing_wp_cron=1587849426.3850090503692626953125
OK finally I found it.
Tones recur cyclically at every doubling or halving of frequency or wavelength which are reciprocal: vrtra-agni; prakrti-purusa; Arjuna-Krsna; samsara-nirvana: thus the 'basic miracle of music' [Fig. 2(a)]. From this acoustical phenomenon, the number 2 acquires its 'female' status; it defines invariantly the octave matrix within which all tones come to birth [Fig. 2(b)]. Here, in this initial identification of the octave with the ratio 1:2, is the root of all the problems which haunt the acoustical theorist, problems which the ancient theorist conceived as symbolizing the imperfection and disorder of the universe, and also its renewal through new tones, new births, new songs, new gods. The octave refuses to be subdivided into subordinate cycles by the only language ancient man knew – the language of natural number, or integers, and the rational numbers derived from them [Fig. 3(a)]. It is a simple arithmetical fact that the higher powers of three and five which define subordinate intervals of music never agree with higher powers of two which define octave cycles [Fig. 3(b)]. It is a man's yearning for this impossible agreement which introduced a hierarchy of values into the number field. For our ancestors, the essence of the world and of the numbers which interpreted that world was sound, not substance, and that world was rife with disagreement among an endless number of possible structures and possible worlds. The epistemological field of sound, however, remained invariant.So by including 5 - he is covering up the fact that 2 and 3 are noncommutative phase - another FACT that is the true secret of nondualism - from the "three gunas." Oops - instead he is using his "simple fact" to promote hierarchical social relations or a "hierarchy of values."
Oops - this article is a REPRINT on the SAME website that publishes the "Dwai" b.s. on thedaobums - the SAME Dwai who refused to acknowledge the noncommutative phase nondualism truth. haha. Now we know why!!
http://www.antoniotdenicolas.com/works.html
So let's see if we can find the images that go with that article.
Yeah - fascinating.
https://www.infinityfoundation.com/mandala/i_es/i_es_denic_audial_frameset.htm
So he admits that in INDIAN music they "remain faithful"
So when he says "Within the Perfect Fifth" is 5/4 - he really means the Platonic mathematics. Funny.
Nicolas Slonimsky once pointed out, in an effort to dissuade readers from the idea that Western tonality is the inevitable result of how we hear (as opposed to a largely artificial invention), that no matter how high one goes in the harmonic series, a fundamental pitch will not produce a perfect fourth above the fundamental.https://nmbx.newmusicusa.org/IV-The-Phantom-Tonic/
https://ecoechoinvasives.blogspot.com/2018/03/stephen-e-robbins-on-bergson-memory-and.html
The Rāgs of North Indian Music: Their Structure and Evolution By Nazir Ali Jairazbhoy (google book)
OK so now reading the Indian music theory book it says how you do get the overtone as the major third just by plucking the 1 string - as a harmonic to itself but you do NOT get the Perfect Fourth. And so it emphasizes we do not need to refer to Western music theory to derive the major third.
But on the Perfect Fourth it notes this irony:
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 as Sa 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.http://ecoechoinvasives.blogspot.com/2018/03/how-real-pythagorean-harmonics-solves.html
https://ecoechoinvasives.blogspot.com/2018/03/mathematical-physicist-walter-van.html
https://ecoechoinvasives.blogspot.com/2018/03/microcosmic-orbit-as-music-harmonics-of.html
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