Numerological reduction to foundation numbers in the musical overtone series

[Utthavat]

I made a discovery that I wanted to share about the musical overtone series. In addition to musicians, it could be of some interest to people studying mathematical and numerological concepts.
Starting the overtone series from the fundamental tone (and scientifically called the 1st partial) of C(3)(that is one octave lower than the middle C, that is named as C(4), which number in the end of the letter marks the note's octave), we find that the number pattern 246813579 appears and repeats endlessly among the partials of overtone series, if we choose to look at the hertz-values that exist in 432 Hz tuning for a musical instrument (meaning in this case that 432 Hz (432 cycles per second) is the frequency of A(4) and 108 Hz of A(2)). As we can see, all the numbers 2,4,6,8,1,3,5,7,9 are all of the foundation numbers, that all the multi-digit numbers can be reduced to by a numerological reduction method. The pattern gives us first the even foundation numbers then followed the odd foundation numbers.
The operation of reducing these frequencys of overtone series' partials goes as following from first partial to the ninth:

C(3) = 128 Hz = 128 = 11 = 2
= 2
C(4) = 256 Hz = 256 = 13 = 4
= 4
G(4) = 384 Hz = 384 = 15 = 6
= 6
C(5) = 512 Hz = 512 = 8
= 8
E(5) = 640 Hz = 640 = 10 = 1
= 1
G(5) = 768 Hz = 768 = 21 = 3
= 3
Bb(5) = 896 Hz = 896 = 23 = 5
= 5
C(6) = 1024 Hz = 1024 = 7
= 7
D(6) = 1152 Hz = 1152 = 9
= 9

And with the tenth partial the 246813579 pattern starts all over again with certain foundation numbers representing different notes of the harmonic series than on the first round of these nine number reductions. The pattern continues as following:

E(6) = 1280 Hz = 1280 = 11 = 2
= 2
F#(6) = 1408 Hz = 1408 = 13 = 4
= 4
G(6) = 1536 Hz = 1536 = 15 = 6
= 6
Ab(6) = 1664 Hz = 1664 = 17 = 8
= 8
Bb(6) = 1792 Hz = 1792 = 19 = 10 = 1
= 1
B(6) = 1920 Hz = 1920 = 12 = 3
= 3
C(7) = 2048 Hz = 2048 = 14 = 5
= 5
Et Cetera...

Does this pattern or some numbers presented evoke any thoughts on you on numerical symbolism and ideas of correspondences in occult study of numbers?
To my mind first comes at least numbers 432 and 108 as they are of relevant numbers in time cycle division of Hindu tradition and interestingly they both reduce numerologically to the number 9. Ofcourse the theme of number 9 can also be found from SoA:s Hieroglyphical key with 9 planets with the help of a space-diagonal.


[Edited October 25 2022]

[Kavi]

Does this pattern or some numbers presented evoke any thoughts on you on numerical symbolism and ideas of correspondences in occult study of numbers?
To my mind first comes at least numbers 432 and 108 as they are of relevant numbers in time cycle division of Hindu tradition and interestingly they both reduce numerologically to the number 9. Ofcourse the theme of number 9 can also be found from SoA:s Hieroglyphical key with 9 planets with the help of a space-diagonal.


[Edited October 25 2022]

You have done a lot of work here it seems!

World of forms fascinate me, how forms and images are crafted like architecture is amazing.
I should study more numbers.

It seems that on the second chart perfect fifths/fourths have always the nearest numbers with each other?

[Smaragd]

Studying the Book III of Agrippa's Occult Philosophy for the comparative study group on celestial hierarchies, the number nine can be seen jumping out quite significantly. On Chapter X there is an introduction to Kabbalistical concepts (emphasis mine):

But the mecubals of the Hebrews, the most learned in divine things, have received the ten principal names of God, as certain divine powers, or as it were members of God, which by ten numerations which they call Sephiroth, as it were vestiments, instruments or examplars of the Archetype, have an influence on all things created, through the high things, even to the lowest, yet by a certain order: for first and immediately they have influence on the nine orders of angels, and quire of Blessed souls, and by them into the celestial spheres, planets and men, by which Sephiroth everything then receiveth power and virtue.

I will expound on the emphasis below, just making a side note about the part after it where all the universe or manifested side of things is seen coming after the angels and the Blessed souls, "celestial spheres" meaning the zodiac and the planetary orders, not angelic hierarchies.

And as the text goes on describing the Sephiroth, it also names the angelic order through which each Sephiroth influences the lower worlds:

Malchuth [the 10th Sephiroth] hath his influence through the order of Animastic, viz. of Blessed Souls, which by the Hebrews is called Issim, that is Nobles, Lords and Princes; they are inferior to the hierarchies, and have their influence on the sons of men, and give knowledge and the wonderful understanding of things, also the industry and prophecy; and the soul of Messiah is president amongst them...

By the notion that the Blessed Souls of the 10th Sephiroth does not belong to the hierarchies per se, could be interpret to mean they are the incarnated human Masters, the Adepts, the Arhats who embody all the hierachies in the perfection of the number ten (cf. the double pentagram on the SoA symbol). Number nine on the other hand, away from the all-gathering vessel-like meaning of Malkuth - Kingdom, hold the meaning of the "perfectly" serving angelic hierarchies through which everything descends in to form as is, lacking the human ascending impulse of ethics, which has its place only in Malkuth.

We can also remind ourselves how Logos, under which all the Sephiroth and their respective angelic orders and everything else categorically belong, means word or voice. An how in the Secret Doctrine, amongst other sources, there are written about the four Vâc to classify the different metaphysical stages of the divine voice, the last of which being a sensible, audible sound. It would then make sense that the geometric laws of the angels are repeating visibly even in the most coarse - audible, manifested - stages of the voice. But these laws only form a hollow shell of formal existence if the human impulse remains from utilising them as fits the human balance of its principles. With the example of music, attaching meaning of the hierarchies to these repeating laws could freeze the human ability to make truly creative work with music, freeze the human being from having all the different human tools of creativity present with a great balance as the focus limits too narrowly on such technical aspects. But ofcourse there is a possibility that someone could use the information lightly enough to incorporate it just as a small notion to the greater ability to make great music with great purposes.

I don't think this techincal limitation is wholly descriptive of the Nine, although it draws fittingly the real difference between the place of Man and the place of the Hierarchies in the grand perspective of things. The Nine are the hollow Ringwraiths in Tolkien's legendarium, which offers tasty Satanic interpretation possibilites to also see the inspirational side of them, if Christian and other traditions could get alot out of the virtues connected to the angelic hierarchies.

[Kavi]

I don't think this techincal limitation is wholly descriptive of the Nine, although it draws fittingly the real difference between the place of Man and the place of the Hierarchies in the grand perspective of things. The Nine are the hollow Ringwraiths in Tolkien's legendarium, which offers tasty Satanic interpretation possibilites to also see the inspirational side of them, if Christian and other traditions could get alot out of the virtues connected to the angelic hierarchies.

How in Pythagorean worldview the top dot or "invisible monad" in tetractys could be interpreted as Nous, which then in some interpretations could be viewed as "the eye of the soul".

[Smaragd]

The Nine are the hollow Ringwraiths in Tolkien's legendarium, which offers tasty Satanic interpretation possibilites

Pythagorean worldview the top dot or "invisible monad" in tetractys could be interpreted as Nous, which then in some interpretations could be viewed as "the eye of the soul".

Yes, I think the Eye of Sauron with the nine Ringwraiths is a plausible interpretation of the tetractys. But in this very interpretation where the Monad is likened to the Nous may hide the fall of Sauron and Morgoth. In the Lucifer lodge meeting of October frater Nefastos presented this view of four pairs of lower and higher selves, the last two having Lucifer as the higher self, and the higher self of Lucifer as Monad. If the intellect, perhaps even in its manasic state, is the last point which one is able to assume above oneself, it will shadow the heights above it and cause problems that leads oneself to the role of the accuser-adversary, rather than having the adversary as a sacred pair through which perfection is reached.

One way to gain some nuance to the Tetractys is interpreting the peras-apeiron Dyad as the Ruling Intelligence and Spirit (according to the nomenclature of Agrippa amongst others) of any given Monad. For example, in our Hymn to the Master of Death there are present the names Agiel and Zazel. The first is the Intelligence of Saturn, which orders things harmoniously according to the nature of the inner entity behind the name Saturn. The Spirit of Saturn, that is Zazel, is the hindering or adversary powers of Saturn. Perhaps the latter could be thought as the blind substance following the mechanisms of Saturn, yet working blindly out of context, out of the balance which the Intelligence of Saturn presents in its balanced relation to the other archetypal seven. I have often used the word 'Spirit' to mean the Intelligence, and I think it could be seen right in certain contexts, but when speaking of the Intelligence and Spirit pair, it's meaning sort of flips to its opposite side, similarly as Lucifer can be seen as the lower self when the dualistic division is made between the Lucifer-Monad pair.

Interestingly the magic table of Saturn has nine numbers.