# yantgen / yantra-genus

[Gene Ward Smith, Yahoo tuning-math, message 11469 (Thu Sep 2, 2004 7:25 am)]

Following McClain, we have a definition of yantra_p(n) in terms of all the p-limit integers less than or equal to n. Following Euler, we have a definition of genus(n) in terms of the divisors of n. Following me, we can put the two together and define the yantra-genus for the pair of integers n and m, in terms of the divisors of n less than or equal to m.

Yantgen(n, m) is, by this, the reduction to the octave of all of the divisors of n less than or equal to m. If n has a monzo <e2 e3 ... ep| with the prime q exponent, eq, greater than log base q of n for each odd prime q, then the yantra-genus is just the p-limit yantra yantra_p(m). On the other hand, yantgen(n, n) = genus(n). In between we find things intermediate between a yantra and a genus.

###### REFERENCES

McClain, Ernest. 1976.

The Myth of Invariance:
The Origin of the Gods, Mathematics, and Music, From the Rg Veda to Plato.
Nicolas-Hays, York Beach, Maine.
ISBN: 0-89254-012-5

McClain, Ernest. 1978.

The Pythagorean Plato: Prelude to the Song Itself.
Nicolas-Hays, York Beach, Maine.
ISBN: 0-89254-010-9
. . . . . . . . .
[Gene Ward Smith, Yahoo tuning-math, message 11470 (Thu Sep 2, 2004 8:43 am)]

Here are some instances of this:

yantgen(375, 75) <6 9 14|
[1 6/5 5/4 3/2 8/5 15/8]

yantgen(135, 45) <7 11 16]
[1 9/8 5/4 4/3 3/2 5/3 15/8]

yantgen(9375, 1875) <10 15 23|
[1 75/64 6/5 5/4 32/25 3/2 25/16 8/5 15/8 48/25]

yantgen(1171875, 234375) <16 24 37|
[1 128/125 25/24 16/15 625/512 5/4 32/25 125/96 4/3 512/375 25/16 8/5 625/384 5/3 128/75 125/64]

yantgen(32805, 10935) <17 27 39|
[1 135/128 10/9 9/8 32/27 5/4 81/64 4/3 45/32 40/27 3/2 128/81 5/3 27/16 16/9 15/8 160/81]

yantgen(16875, 5625) <19 30 44|
[1 25/24 16/15 9/8 75/64 6/5 5/4 32/25 4/3 45/32 36/25 3/2 25/16 8/5 5/3 128/75 9/5 15/8 48/25]

yantgen(2109375, 703125) <31 49 72|
[1 128/125 135/128 27/25 1125/1024 9/8 144/125 75/64 6/5 768/625 5/4 32/25 675/512 27/20 864/625 45/32 36/25 375/256 3/2 192/125 25/16 8/5 1024/625 27/16 216/125 225/128 9/5 1152/625 15/8 48/25 125/64]

. . . . . . . . .

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