User:2^67-1/Sandbox - Revision history

2^67-1 at 12:00, 4 September 2024

2024-09-04T12:00:12Z

← Older revision		Revision as of 12:00, 4 September 2024
Line 1:		Line 1:
	~~BLANK FOR NOW~~		A program to find increasingly better EDns in a given subgroup with a given equave ('increasingly better' is given by decreasing relative error)

			<syntaxhighlight lang="python">
			import math

			def fracmult(a,b):
			g = math.gcd(a[0]b[0],a[1]b[1])
			return [a[0]b[0]//g,a[1]b[1]//g]

			def reciprocal(a):
			return [a[1],a[0]]

			def equavereduce(a,b):
			while b[0]a[1] > a[0]b[1]:
			b = fracmult(b,reciprocal(a))
			while b[0] < b[1]:
			b = fracmult(b,a)
			return b

			def tonalitydiamond(a,b,c):
			return [equavereduce(a,b),equavereduce(a,reciprocal(b)),equavereduce(a,c),equavereduce(a,reciprocal(c)),equavereduce(a,fracmult(b,reciprocal(c))),equavereduce(a,fracmult(c,reciprocal(b)))]

			def cents(a):
			return 1200*math.log2(a[0]/a[1])

			def centslist(a):
			c = []
			for i in a:
			c.append(cents(i))
			return c

			def ednerror(a,e,equave):
			step = cents(equave)/e
			approx = round(a/step,0)*step
			error = math.fabs(a-approx)
			return error

			def ednerrorlist(a,e,equave):
			error = []
			for i in a:
			error.append(ednerror(cents(i),e,equave))
			return error

			def euc(a):
			total = 0
			for i in a:
			total = total + i**2
			return total**(1/2)

			def avg(a):
			total = 0
			for i in a:
			total = total + i
			return total/len(a)


			best = 10**10

			for i in range(1, 100000):
			if avg(ednerrorlist(tonalitydiamond([3,2],[5,2],[7,4]),i,[3,2]))*i < best:
			best = avg(ednerrorlist(tonalitydiamond([3,2],[5,2],[7,4]),i,[3,2]))*i
			print(i)
			</syntaxhighlight>

2^67-1: This will be moved to a new article.

2024-07-27T00:43:29Z

This will be moved to a new article.

Show changes

Godtone: clarify that it's the 5-limit restriction

2024-07-26T14:16:52Z

clarify that it's the 5-limit restriction

← Older revision		Revision as of 14:16, 26 July 2024
Line 59:		Line 59:
	\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n		\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n
	\|-		\|-
	\| 1.{{overline\|285714}} = 9/7 \|\| 0 \|\| [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 }} \|\| Y		\| 1.{{overline\|285714}} = 9/7 \|\| 0 \|\| 2.3.5 [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 }} \|\| Y
	\|-		\|-
	\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n		\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n

Godtone: add lagaca (very good approximation to JIP); i only found out this was named cuz of projective tuning space

2024-07-26T14:15:03Z

add lagaca (very good approximation to JIP); i only found out this was named cuz of projective tuning space

← Older revision		Revision as of 14:15, 26 July 2024
Line 58:		Line 58:
	\|-		\|-
	\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n		\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n
			\|-
			\| 1.{{overline\|285714}} = 9/7 \|\| 0 \|\| [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 }} \|\| Y
	\|-		\|-
	\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n		\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n

Godtone: fix my comment; this is significantly more accurate than 1.3 * (p=1, q=0)

2024-07-26T14:14:21Z

fix my comment; this is significantly *more* accurate than 1.3 * (p=1, q=0)

← Older revision		Revision as of 14:14, 26 July 2024
Line 58:		Line 58:
	\|-		\|-
	\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n		\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n
	\|-
	~~\| 1.{{overline\|285714}} = 9/7 \|\| 0 \|\| [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 }} \|\| Y~~
	\|-		\|-
	\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n		\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n

Godtone: add the slightly less accurate approximation of the JIP which happens to be named and documented on the wiki already

2024-07-26T14:13:06Z

add the slightly less accurate approximation of the JIP which happens to be named and documented on the wiki already

← Older revision		Revision as of 14:13, 26 July 2024
Line 58:		Line 58:
	\|-		\|-
	\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n		\| 1.25 = 5/4 \|\| 0 \|\| [[Quintosec]] \|\| 140737488355328/140126044921875 \|\| {{monzo\| 47 -15 -10 0 }} \|\| n
			\|-
			\| 1.{{overline\|285714}} = 9/7 \|\| 0 \|\| [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 }} \|\| Y
	\|-		\|-
	\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n		\| 1.3 = 13/10 \|\| 0 \|\| 2.3.5 [https://sintel.pythonanywhere.com/result?subgroup=5&reduce=on&weights=weil&target=&edos=&commas=%5B119+-37+-26%3E&submit_comma=submit 10 & 171] \|\| [[670975306467707996070384979248046875/664613997892457936451903530140172288\|(36 digits)]] \|\| {{monzo\| -119 37 26 0 }} \|\| n

Godtone: add less complex approximations to the JIP for completeness and out of curiosity. at least some of these are interesting, for various reasons.

2024-07-26T14:07:30Z

add less complex approximations to the JIP for completeness and out of curiosity. at least some of these are interesting, for various reasons.

← Older revision		Revision as of 14:07, 26 July 2024
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	\|-		\|-
	\| 0.8{{overline\|3}} = 5/6 \|\| 0.8{{overline\|3}} = 5/6 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=9671406556917033397649408%2F9618459881658113759765625&submit_comma=submit 80d & 130 & 140] (decoid detemp.) \|\| [[9671406556917033397649408/9618459881658113759765625\|(25 digits)]] \|\| {{monzo\| 83 -20 -10 -10 }} \|\| Y		\| 0.8{{overline\|3}} = 5/6 \|\| 0.8{{overline\|3}} = 5/6 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=9671406556917033397649408%2F9618459881658113759765625&submit_comma=submit 80d & 130 & 140] (decoid detemp.) \|\| [[9671406556917033397649408/9618459881658113759765625\|(25 digits)]] \|\| {{monzo\| 83 -20 -10 -10 }} \|\| Y
			\|-
			\| 0.8 = 4/5 \|\| 0.8 = 4/5 \|\| 10 & 53 & 275 \|\| 295147905179352825856/290807555001001171875 \|\| {{monzo\| 68 -17 -8 -8 }} \|\| Y
			\|-
			\| 0.75 = 3/4 \|\| 0.75 = 3/4 \|\| (10 or 36 or 46 or 56) & 118d & 220 \|\| 9007199254740992/8792367498140625 \|\| {{monzo\| 53 -14 -6 -6}} \|\| Y
			\|-
			\| 0.{{overline\|6}} = 2/3 \|\| 0.{{overline\|6}} = 2/3 \|\| 39 & 58 & 68 \|\| 274877906944/265831216875 \|\| {{monzo\| 38 -11 -4 -4 }} \|\| Y
			\|-
			\| 0.5 = 1/2 \|\| 0.5 = 1/2 \|\| p=1, q=1 Pajara projection \|\| 8388608/8037225 \|\| {{monzo\| 23 -8 -2 -2 }} \|\| Y
	\|-		\|-
	\| 1 \|\| ∞ \|\| [[Jubilic]] \|\| [[50/49]] \|\| {{monzo\| 1 0 2 -2 }} \|\| n		\| 1 \|\| ∞ \|\| [[Jubilic]] \|\| [[50/49]] \|\| {{monzo\| 1 0 2 -2 }} \|\| n

Godtone: wrote the ratio and decimal in wrong order

2024-07-26T13:48:14Z

wrote the ratio and decimal in wrong order

← Older revision		Revision as of 13:48, 26 July 2024
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	\| 1 \|\| 0.5 = 1/2 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=67108864%2F66976875&submit_comma=submit 10 & 53 & 130] \|\| 67108864/66976875 \|\| {{monzo\| 26 -7 -4 -2 }} \|\| n		\| 1 \|\| 0.5 = 1/2 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=67108864%2F66976875&submit_comma=submit 10 & 53 & 130] \|\| 67108864/66976875 \|\| {{monzo\| 26 -7 -4 -2 }} \|\| n
	\|-		\|-
	\| 6/5 ~~= 1.2~~ \|\| 3/5 ~~= 0.6~~ \|\| p=1,q=2 Miracle projection (squared) \|\| 35162859375/34359738368 [[1236426679426025390625/1180591620717411303424\|(squared)]] \|\| {{monzo\| -35 8 6 3 }} \|\| Y		\| 1.2 = 6/5 \|\| 0.6 = 3/5 \|\| p=1,q=2 Miracle projection (squared) \|\| 35162859375/34359738368 [[1236426679426025390625/1180591620717411303424\|(squared)]] \|\| {{monzo\| -35 8 6 3 }} \|\| Y
	\|-		\|-
	\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y		\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y

Godtone: fix my comment lol (p=2, q=1 not p=1, q=2) (also i figured out why the monzo wasnt displaying)

2024-07-26T13:37:44Z

fix my comment lol (p=2, q=1 not p=1, q=2) (also i figured out why the monzo wasnt displaying)

← Older revision		Revision as of 13:37, 26 July 2024
Line 70:		Line 70:
	\|-		\|-
	\| 1 \|\| 0.5 = 1/2 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=67108864%2F66976875&submit_comma=submit 10 & 53 & 130] \|\| 67108864/66976875 \|\| {{monzo\| 26 -7 -4 -2 }} \|\| n		\| 1 \|\| 0.5 = 1/2 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=67108864%2F66976875&submit_comma=submit 10 & 53 & 130] \|\| 67108864/66976875 \|\| {{monzo\| 26 -7 -4 -2 }} \|\| n
			\|-
			\| 6/5 = 1.2 \|\| 3/5 = 0.6 \|\| p=1,q=2 Miracle projection (squared) \|\| 35162859375/34359738368 [[1236426679426025390625/1180591620717411303424\|(squared)]] \|\| {{monzo\| -35 8 6 3 }} \|\| Y
	\|-		\|-
	\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y		\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y

Godtone: fix my comment lol (p=2, q=1 not p=1, q=2)

2024-07-26T13:36:50Z

fix my comment lol (p=2, q=1 not p=1, q=2)

← Older revision		Revision as of 13:36, 26 July 2024
Line 70:		Line 70:
	\|-		\|-
	\| 1 \|\| 0.5 = 1/2 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=67108864%2F66976875&submit_comma=submit 10 & 53 & 130] \|\| 67108864/66976875 \|\| {{monzo\| 26 -7 -4 -2 }} \|\| n		\| 1 \|\| 0.5 = 1/2 \|\| [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=67108864%2F66976875&submit_comma=submit 10 & 53 & 130] \|\| 67108864/66976875 \|\| {{monzo\| 26 -7 -4 -2 }} \|\| n
	\|-
	~~\| 6/5 = 1.2 \|\| 3/5 = 0.6 \|\| p=1,q=2 Miracle projection \|\| 35162859375/34359738368 [[1236426679426025390625/1180591620717411303424\|(squared)]] \|\| {{monzo\|\| -35 8 6 3 }} \|\| Y~~
	\|-		\|-
	\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y		\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y