User:2^67-1/Blackwood-dicot-semaphore equivalence continuum - Revision history

2^67-1 at 22:10, 31 July 2024

2024-07-31T22:10:03Z

← Older revision		Revision as of 22:10, 31 July 2024
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	\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y		\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 2.{{overline\|571428}} = 18/7 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=%5B-128+17+36%3E&submit_comma=submit 5 & 472] \|\| [[342444953666443524469058979480764340963/340282366920938463463374607431768211456\|(39 digits)]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y		\| 0 \|\| 2.{{overline\|571428}} = 18/7 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=%5B-128+17+36%3E&submit_comma=submit 5 & 472] \|\| [[342444953666443524469058979480764340963/340282366920938463463374607431768211456\|(39 digits)]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| n
	\|-		\|-
	\| 0 \|\| 2.6 = 13/5 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] \|\| 70632088586703/70368744177664 (reduced), 4988891938119860195948410209/4951760157141521099596496896 (unreduced) \|\| {{monzo\| -46 6 0 13}} (reduced) {{monzo\| -92 12 0 26 }} (unreduced) \|\| Y		\| 0 \|\| 2.6 = 13/5 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] \|\| 70632088586703/70368744177664 (reduced), 4988891938119860195948410209/4951760157141521099596496896 (unreduced) \|\| {{monzo\| -46 6 0 13}} (reduced) {{monzo\| -92 12 0 26 }} (unreduced) \|\| Y

2^67-1: Added 2.3.7 5&472, therefore completing the semaphore line

2024-07-31T10:48:26Z

Added 2.3.7 5&472, therefore completing the semaphore line

← Older revision		Revision as of 10:48, 31 July 2024
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	\|-		\|-
	\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y		\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y
			\|-
			\| 0 \|\| 2.{{overline\|571428}} = 18/7 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=%5B-128+17+36%3E&submit_comma=submit 5 & 472] \|\| [[342444953666443524469058979480764340963/340282366920938463463374607431768211456\|(39 digits)]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 2.6 = 13/5 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] \|\| 70632088586703/70368744177664 (reduced), 4988891938119860195948410209/4951760157141521099596496896 (unreduced) \|\| {{monzo\| -46 6 0 13}} (reduced) {{monzo\| -92 12 0 26 }} (unreduced) \|\| Y		\| 0 \|\| 2.6 = 13/5 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] \|\| 70632088586703/70368744177664 (reduced), 4988891938119860195948410209/4951760157141521099596496896 (unreduced) \|\| {{monzo\| -46 6 0 13}} (reduced) {{monzo\| -92 12 0 26 }} (unreduced) \|\| Y

2^67-1: Added unreduced and reduced fractions and monzos.

2024-07-28T06:17:41Z

Added unreduced and reduced fractions and monzos.

2^67-1: Squared some fractions

2024-07-28T01:12:30Z

Squared some fractions

← Older revision		Revision as of 01:12, 28 July 2024
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	! Monzo		! Monzo
	\|-		\|-
	\| 0 \|\| -1 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27\|784/729]] \|\| {{monzo\| 2 -3 0 1 }} \|\| n		\| 0 \|\| -1 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27\|784/729]] \|\| {{monzo\| 4 -6 0 2 }} \|\| n
	\|-		\|-
	\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n		\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n
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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
	\|-		\|-
	\| 1.2 = 6/5 \|\| 0.6 = 3/5 \|\| p=1,q=2 Miracle projection (squared) \|\| 1236426679426025390625/~~11805916207174113034249~~ \|\| {{monzo\| -~~35 8~~ 6 3 }} \|\| Y		\| 1.2 = 6/5 \|\| 0.6 = 3/5 \|\| p=1,q=2 Miracle projection (squared) \|\| 1236426679426025390625/1180591620717411303424 \|\| {{monzo\| -70 16 12 6 }} \|\| 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: since 5/3 is present in p=0, q=1, we should include 3/2 for completeness. ive expressed it as 5 & 67d as 67d supports septimal meantone so is potentially notable as a very sharp tuning thereof

2024-07-27T18:37:41Z

since 5/3 is present in p=0, q=1, we should include 3/2 for completeness. ive expressed it as 5 & 67d as 67d supports septimal meantone so is potentially notable as a very sharp tuning thereof

← Older revision		Revision as of 18:37, 27 July 2024
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	\|-		\|-
	\| 0 \|\| 1 \|\| [[Archytas]] (squared) \|\| [[64/63\|4096/3969]] \|\| {{monzo\| 12 -4 0 -2 }} \|\| n		\| 0 \|\| 1 \|\| [[Archytas]] (squared) \|\| [[64/63\|4096/3969]] \|\| {{monzo\| 12 -4 0 -2 }} \|\| n
			\|-
			\| 0 \|\| 1.5 = 3/2 \|\| 2.3.7 5 & 97d \|\| 268435456/257298363 \|\| {{monzo\| 28 -7 -6 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 1.{{overline\|6}} = 5/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=5+70&submit_edo=submit&commas= 5 & 70] (squared) \|\| 17592186044416/16679880978201 \|\| {{monzo\| -56 7 0 16 }} \|\| n		\| 0 \|\| 1.{{overline\|6}} = 5/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=5+70&submit_edo=submit&commas= 5 & 70] (squared) \|\| 17592186044416/16679880978201 \|\| {{monzo\| -56 7 0 16 }} \|\| n

2^67-1: Fixed a small error

2024-07-27T01:53:38Z

Fixed a small error

← Older revision		Revision as of 01:53, 27 July 2024
Line 33:		Line 33:
	! Monzo		! Monzo
	\|-		\|-
	\| 0 \|\| 0 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27\|784/729]] \|\| {{monzo\| 2 -3 0 1 }} \|\| n		\| 0 \|\| -1 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27\|784/729]] \|\| {{monzo\| 2 -3 0 1 }} \|\| n
	\|-		\|-
	\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n		\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n

2^67-1: Changed a fraction

2024-07-27T01:35:35Z

Changed a fraction

← Older revision		Revision as of 01:35, 27 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
	\|-		\|-
	\| 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		\| 1.2 = 6/5 \|\| 0.6 = 3/5 \|\| p=1,q=2 Miracle projection (squared) \|\| 1236426679426025390625/11805916207174113034249 \|\| {{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

2^67-1: Added stuff from https://en.xen.wiki/w/Archytas-diatonic_equivalence_continuum, replaced the old x31eq link with the new Sintel link

2024-07-27T00:54:18Z

Added stuff from https://en.xen.wiki/w/Archytas-diatonic_equivalence_continuum, replaced the old x31eq link with the new Sintel link

← Older revision		Revision as of 00:54, 27 July 2024
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	! Ratio		! Ratio
	! Monzo		! Monzo
			\|-
			\| 0 \|\| 0 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27\|784/729]] \|\| {{monzo\| 2 -3 0 1 }} \|\| n
	\|-		\|-
	\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n		\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n
	\|-		\|-
	\| 0 \|\| 1 \|\| [[Archytas]] (squared) \|\| [[64/63\|4096/3969]] \|\| {{monzo\| 12 -4 0 -2 }} \|\| n		\| 0 \|\| 1 \|\| [[Archytas]] (squared) \|\| [[64/63\|4096/3969]] \|\| {{monzo\| 12 -4 0 -2 }} \|\| n
			\|-
			\| 0 \|\| 1.{{overline\|6}} = 5/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=5+70&submit_edo=submit&commas= 5 & 70] (squared) \|\| 17592186044416/16679880978201 \|\| {{monzo\| -56 7 0 16 }} \|\| n
	\|-		\|-
	\| 0 \|\| 2 \|\| [[Buzzard]] \|\| [[65536/64827]] \|\| {{monzo\| 16 -3 0 -4 }} \|\| n		\| 0 \|\| 2 \|\| [[Buzzard]] \|\| [[65536/64827]] \|\| {{monzo\| 16 -3 0 -4 }} \|\| n
			\|-
			\| 0 \|\| 2.{{overline\|3}} = 7/3 \|\| [[Septiness]] (squared) \|\| [[67108864/66706983\|4503599627370496/4449821580962289]] \|\| {{monzo\| 52 -8 0 -14 }} \|\| n
	\|-		\|-
	\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y		\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y
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	\| 0 \|\| 3 \|\| [[Slendric]] (squared) \|\| [[1029/1024\|1058841/1048576]] \|\| {{monzo\| -20 2 0 6 }} \|\| n		\| 0 \|\| 3 \|\| [[Slendric]] (squared) \|\| [[1029/1024\|1058841/1048576]] \|\| {{monzo\| -20 2 0 6 }} \|\| n
	\|-		\|-
	\| 0 \|\| 4 \|\| [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=off&weights=weil&target=&edos=&commas=17294403%2F16777216&submit_comma=submit 5 & 81] \|\| 17294403/16777216 \|\| {{monzo\| -24 1 8 }} \|\| Y		\| 0 \|\| 4 \|\| [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=off&weights=weil&target=&edos=&commas=17294403%2F16777216&submit_comma=submit 5 & 81] \|\| 17294403/16777216 \|\| {{monzo\| -24 1 0 8 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 5 \|\| [[Cloudy]] (squared) \|\| [[16807/16384\|282475249/268435456]] \|\| {{monzo\| -28 0 0 10 }} \|\| Y		\| 0 \|\| 5 \|\| [[Cloudy]] (squared) \|\| [[16807/16384\|282475249/268435456]] \|\| {{monzo\| -28 0 0 10 }} \|\| Y

2^67-1: Moved for now!

2024-07-27T00:44:50Z

Moved for now!

New page

The '''blackwood-dicot-semaphore''' equivalence continuum is a continuum of 7-limit rank-3 temperaments describing the set of all 7-limit rank-3 temperaments supported by [[10edo]]. Any rank-2 temperament supported by [[10edo]] can thus be represented by a line between two points in this continuum.

All temperaments in the continuum satisfy (25/24)''p''(49/48)''q'' ~ 256/243, equating a stack of [[25/24|dicot commas (25/24)]] and [[49/48|semaphore commas (49/48)]] with the [[256/243|blackwood comma (256/243)]].

The blackwood comma is the characteristic [[3-limit]] comma tempered out in 10edo.

[[User:Godtone]] notes the following JIP's, each one corresponding to a 1D continua contained therein, for which increasingly efficient approximations generally represents increasingly efficient [[7-limit]] temperaments:

* log2(256/243) / log2(25/24) = 1.2766647429 ; this is the JIP of p=1, q=0 (equiv. to p=-1, q=0)
* log2(256/243) / log2(49/48) = 2.5275365063 ; this is the JIP of p=0, q=1 (equiv. to p=0, q=-1)
* log2(256/243) / log2(1225/1152) = 0.8482245109 ; this is the JIP of p=1, q=1 (equiv. to p=-1, q=-1)
* log2(256/243) / log2(50/49) = 2.5796543166 ; this is the JIP of p=1, q=-1 (equiv. to p=-1, q=1)
* log2(256/243) / log2(60025/55296) = 0.6350918818 ; this is the JIP of p=1, q=2 (equiv. to p=-1, q=-2)
* log2(256/243) / log2(2401/2400) = 125.1044589 ; this is the JIP of p=1, q=-2 (equiv. to p=-1, q=2)
* log2(256/243) / log2(30625/27648) = 0.5096257724 ; this is the JIP of p=2, q=1 (equiv. to p=-2, q=-1)
* log2(256/243) / log2(625/588) = 0.8540148427 ; this is the JIP of p=2, q=-1 (equiv. to p=-2, q=1)

Importantly, each JIP corresponds to a ''rational'', so that, for example, (''p'', ''q'') = (1, -2) is equivalent to (''p'', ''q'') = (2, -4) and to (''p'', ''q'') = (-1, 2) '''but not to (1, 2)'''. Note that all these JIPs lie on the JIL (just intonation line).

Also note that continua separated by 2401/2400 are meaningfully different, but due to the efficiency of 2401/2400, one may want to examine the continuum of all 7-limit temperaments supported by [[10edo]] for which [[2401/2400]] is tempered.

{| class="wikitable center-1 center-2"
|+ Selected temperaments with integer ''p'' and ''q''

|-
! rowspan="2" | ''p''
! rowspan="2" | ''q''
! rowspan="2" | Temperament
! colspan="2" | Comma
! rowspan="2" | Added by someone else?
|-
! Ratio
! Monzo
|-
| 0 || 0 || [[Blackwood]] || [[256/243]] || {{monzo| 8 -5 0 0 }} || n
|-
| 0 || 1 || [[Archytas]] (squared) || [[64/63|4096/3969]] || {{monzo| 12 -4 0 -2 }} || n
|-
| 0 || 2 || [[Buzzard]] || [[65536/64827]] || {{monzo| 16 -3 0 -4 }} || n
|-
| 0 || 2.5 = 5/2 || [[Slendric schisma|Slendrismic]] || [[Slendric schisma|68719476736/68641485507]] || {{monzo| 36 -5 0 -10 }} || Y
|-
| 0 || 2.6 = 13/5 || 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] || [[4988891938119860195948410209/4951760157141521099596496896|(28 digits)]] || {{monzo| -92 12 0 26 }} || Y
|-
| 0 || 2.{{overline|6}} = 8/3 || 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=72680419155717387%2F72057594037927936&submit_comma=submit 5 & 212] || 72680419155717387/72057594037927936 || {{monzo| -56 7 0 16 }} || n
|-
| 0 || 3 || [[Slendric]] (squared) || [[1029/1024|1058841/1048576]] || {{monzo| -20 2 0 6 }} || n
|-
| 0 || 4 || [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=off&weights=weil&target=&edos=&commas=17294403%2F16777216&submit_comma=submit 5 & 81] || 17294403/16777216 || {{monzo| -24 1 8 }} || Y
|-
| 0 || 5 || [[Cloudy]] (squared) || [[16807/16384|282475249/268435456]] || {{monzo| -28 0 0 10 }} || Y
|-
| 0 || ∞ || [[Semaphore]] || [[49/48]] || {{monzo| -4 -1 0 2 }} || n
|-
| 1 || 0 || [[Srutal]] || [[2048/2025]] || {{monzo| 11 -4 -2 0 }} || n
|-
| 1.25 = 5/4 || 0 || [[Quintosec]] || 140737488355328/140126044921875 || {{monzo| 47 -15 -10 0 }} || n
|-
| 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.{{overline|3}} = 4/3 || 0 || [[Marvel temperaments#Submajor|Submajor]] || 69198046875/68719476736 || {{monzo| -36 11 8 }} || Y
|-
| 1.5 = 3/2 || 0 || 2.3.5 [[Miracle]] || [[34171875/33554432]] || {{monzo| -25 7 6 }} || Y
|-
| 2 || 0 || [[Negri]] || [[16875/16384]] || {{monzo| -14 3 4 0 }} || n
|-
| ∞ || 0 || [[Dicot]] || [[25/24]] || {{monzo| -3 -1 2 0 }} || 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
|-
| 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
|-
| 1 || 1 || [[Mirwomo temperaments|Mirwomo]] || [[33075/32768]] || {{monzo| -15 3 2 2 }} || n
|-
| 0.{{overline|857142}} = 6/7 || 0.{{overline|857142}} = 6/7 || [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=off&weights=weil&target=&edos=&commas=318130560585842112604248046875%2F316912650057057350374175801344&submit_comma=submit 10 & 77 & 308] || [[318130560585842112604248046875/31691265005705735037417580134|(30 digits)]] || {{monzo| -98 23 12 12 }} || 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 || -1 || [https://sintel.pythonanywhere.com/result?subgroup=2.3.5.7&reduce=on&weights=weil&target=&edos=&commas=6272%2F6075&submit_comma=submit 10 & 14 & 27] || 6272/6075 || {{monzo| 7 -5 -2 2 }} || n
|-
| 2 || -2 || [https://sintel.pythonanywhere.com/result?subgroup=2.3.5.7&reduce=on&weights=weil&target=&edos=&commas=153664%2F151875&submit_comma=submit 10 & 19 & 58] || 153664/151875 || {{monzo| 6 -5 -4 4 }} || n
|-
| 2.5 = 5/2 || -2.5 = -5/2 || [[Linus]] || 578509309952/576650390625 || {{monzo| 11 -10 -10 10 }} || n
|-
| 2.6 = 13/5 || -2.6 = -13/5 || [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=%5B-27+25+26+-26%3E&submit_comma=submit 10 & 171 & 20cd] || [[1262558414702117443084716796875/1259966282563754447206426345472|(31 digits)]] || {{monzo| -27 25 26 -26 }} || n
|-
| 2.{{overline|6}} = 8/3 || -2.{{overline|6}} = -8/3 || [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=%5B16+-15+-16+16%3E&submit_comma=submit 10 & 111 & 91] || 2189469451904296875/2177953337809371136 || {{monzo| -16 15 16 -16 }} || n
|-
| 3 || -3 || [https://sintel.pythonanywhere.com/result?subgroup=7&reduce=on&weights=weil&target=&edos=&commas=3796875%2F3764768&submit_comma=submit 10 & 41 & 133d] || 3796875/3764768 || {{monzo| -5 5 6 -6 }} || n
|-
| ∞ || 1 || [[Jubilic]] || [[50/49]] || {{monzo| 1 0 2 -2 }} || n
|-
| ∞ || 2 || [[Breedsmic temperaments|Breedsmic]] || [[2401/2400]] || {{monzo| -5 -1 -2 4 }} || n
|}

← Older revision		Revision as of 06:17, 28 July 2024
Line 33:		Line 33:
	! Monzo		! Monzo
	\|-		\|-
	\| 0 \|\| -1 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27\|784/729]] \|\| {{monzo\| 4 -6 0 2 }} \|\| n		\| 0 \|\| -1 \|\| [[Trienstonic clan #No-fives trienstonic\|No-fives trienstonic]] (squared) \|\| [[28/27]] (reduced), 784/729 (unreduced) \|\| {{monzo\| 2 -3 0 1 }} (reduced), {{monzo\| 4 -6 0 2 }} (unreduced) \|\| n
	\|-		\|-
	\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n		\| 0 \|\| 0 \|\| [[Blackwood]] \|\| [[256/243]] \|\| {{monzo\| 8 -5 0 0 }} \|\| n
	\|-		\|-
	\| 0 \|\| 1 \|\| [[Archytas]] ~~(squared)~~ \|\| [[64/63\|4096/3969]] \|\| {{monzo\| 12 -4 0 -2 }} \|\| n		\| 0 \|\| 1 \|\| [[Archytas]] \|\| [[64/63]] (reduced), 4096/3969 (unreduced) \|\| {{monzo\| 6 -2 0 -1 }} (reduced), {{monzo\| 12 -4 0 -2 }} (unreduced) \|\| n
	\|-		\|-
	\| 0 \|\| 1.5 = 3/2 \|\| 2.3.7 5 & 97d \|\| 268435456/257298363 \|\| {{monzo\| 28 -7 -6 }} \|\| Y		\| 0 \|\| 1.5 = 3/2 \|\| 2.3.7 5 & 97d \|\| 268435456/257298363 \|\| {{monzo\| 28 -7 0 -6 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 1.{{overline\|6}} = 5/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=5+70&submit_edo=submit&commas= 5 & 70] (~~squared~~) \|\| 17592186044416/16679880978201 \|\| {{monzo\| -~~56 7~~ 0 16 }} \|\| n		\| 0 \|\| 1.{{overline\|6}} = 5/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=5+70&submit_edo=submit&commas= 5 & 70] \|\| 4194304/4084101 (reduced), 17592186044416/16679880978201 (unreduced) \|\| {{monzo\| 22 -5 0 -5 }} (reduced), {{monzo\| 44 -10 0 -10}} (unreduced) \|\| n
	\|-		\|-
	\| 0 \|\| 2 \|\| [[Buzzard]] \|\| [[65536/64827]] \|\| {{monzo\| 16 -3 0 -4 }} \|\| n		\| 0 \|\| 2 \|\| [[Buzzard]] \|\| [[65536/64827]] \|\| {{monzo\| 16 -3 0 -4 }} \|\| n
	\|-		\|-
	\| 0 \|\| 2.{{overline\|3}} = 7/3 \|\| [[Septiness]] ~~(squared)~~ \|\| [[67108864/66706983\|4503599627370496/4449821580962289]] \|\| {{monzo\| 52 -8 0 -14 }} \|\| n		\| 0 \|\| 2.{{overline\|3}} = 7/3 \|\| [[Septiness]] \|\| [[67108864/66706983]] (reduced), 4503599627370496/4449821580962289 (unreduced) \|\| {{monzo\| 26 -4 0 -7 }} (reduced), {{monzo\| 52 -8 0 -14 }} (unreduced) \|\| n
	\|-		\|-
	\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y		\| 0 \|\| 2.5 = 5/2 \|\| [[Slendric schisma\|Slendrismic]] \|\| [[Slendric schisma\|68719476736/68641485507]] \|\| {{monzo\| 36 -5 0 -10 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 2.6 = 13/5 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] \|\| [[4988891938119860195948410209/4951760157141521099596496896\|(~~28 digits~~)]] \|\| {{monzo\| -92 12 0 26 }} \|\| Y		\| 0 \|\| 2.6 = 13/5 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=4988891938119860195948410209%2F4951760157141521099596496896&submit_comma=submit 5 & 171] \|\| 70632088586703/70368744177664 (reduced), 4988891938119860195948410209/4951760157141521099596496896 (unreduced) \|\| {{monzo\| -46 6 0 13}} (reduced) {{monzo\| -92 12 0 26 }} (unreduced) \|\| Y
	\|-		\|-
	\| 0 \|\| 2.{{overline\|6}} = 8/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=72680419155717387%2F72057594037927936&submit_comma=submit 5 & 212] \|\| 72680419155717387/72057594037927936 \|\| {{monzo\| -56 7 0 16 }} \|\| n		\| 0 \|\| 2.{{overline\|6}} = 8/3 \|\| 2.3.7 [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=on&weights=weil&target=&edos=&commas=72680419155717387%2F72057594037927936&submit_comma=submit 5 & 212] \|\| 72680419155717387/72057594037927936 \|\| {{monzo\| -56 7 0 16 }} \|\| n
	\|-		\|-
	\| 0 \|\| 3 \|\| [[Slendric]] (squared) \|\| [[1029/1024\|1058841/1048576]] \|\| {{monzo\| -20 2 0 6 }} \|\| n		\| 0 \|\| 3 \|\| [[Slendric]] (squared) \|\| [[1029/1024]] (reduced), 1058841/1048576 (unreduced) \|\| {{monzo\| -10 1 0 3 }} (reduced), {{monzo\| -20 2 0 6 }} (unreduced)\|\| n
	\|-		\|-
	\| 0 \|\| 4 \|\| [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=off&weights=weil&target=&edos=&commas=17294403%2F16777216&submit_comma=submit 5 & 81] \|\| 17294403/16777216 \|\| {{monzo\| -24 1 0 8 }} \|\| Y		\| 0 \|\| 4 \|\| [https://sintel.pythonanywhere.com/result?subgroup=2.3.7&reduce=off&weights=weil&target=&edos=&commas=17294403%2F16777216&submit_comma=submit 5 & 81] \|\| 17294403/16777216 \|\| {{monzo\| -24 1 0 8 }} \|\| Y
	\|-		\|-
	\| 0 \|\| 5 \|\| [[Cloudy]] (squared) \|\| [[16807/16384\|282475249/268435456]] \|\| {{monzo\| -28 0 0 10 }} \|\| Y		\| 0 \|\| 5 \|\| [[Cloudy]] (squared) \|\| [[16807/16384]] (reduced), 282475249/268435456 (unreduced) \|\| {{monzo\| -14 0 0 5 }} (reduced), {{monzo\| -28 0 0 10 }} (unreduced) \|\| Y
	\|-		\|-
	\| 0 \|\| ∞ \|\| [[Semaphore]] \|\| [[49/48]] \|\| {{monzo\| -4 -1 0 2 }} \|\| n		\| 0 \|\| ∞ \|\| [[Semaphore]] \|\| [[49/48]] \|\| {{monzo\| -4 -1 0 2 }} \|\| n
Line 65:		Line 65:
	\| 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 \|\| 2.3.5 [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 }} \|\| Y		\| 1.{{overline\|285714}} = 9/7 \|\| 0 \|\| 2.3.5 [[Lagaca]] \|\| 9696448624912261962890625/9671406556917033397649408 \|\| {{monzo\| -83 26 18 0 }} \|\| 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
	\|-		\|-
	\| 1.{{overline\|3}} = 4/3 \|\| 0 \|\| [[Marvel temperaments#Submajor\|Submajor]] \|\| 69198046875/68719476736 \|\| {{monzo\| -36 11 8 }} \|\| Y		\| 1.{{overline\|3}} = 4/3 \|\| 0 \|\| [[Marvel temperaments#Submajor\|Submajor]] \|\| 69198046875/68719476736 \|\| {{monzo\| -36 11 8 0 }} \|\| Y
	\|-		\|-
	\| 1.5 = 3/2 \|\| 0 \|\| 2.3.5 [[Miracle]] \|\| [[34171875/33554432]] \|\| {{monzo\| -25 7 6 }} \|\| Y		\| 1.5 = 3/2 \|\| 0 \|\| 2.3.5 [[Miracle]]/[[Ampersand]] \|\| [[34171875/33554432]] \|\| {{monzo\| -25 7 6 0 }} \|\| Y
	\|-		\|-
	\| 2 \|\| 0 \|\| [[Negri]] \|\| [[16875/16384]] \|\| {{monzo\| -14 3 4 0 }} \|\| n		\| 2 \|\| 0 \|\| [[Negri]] \|\| [[16875/16384]] \|\| {{monzo\| -14 3 4 0 }} \|\| n
Line 79:		Line 79:
	\| 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
	\|-		\|-
	\| 1.2 = 6/5 \|\| 0.6 = 3/5 \|\| p=1,q=2 Miracle projection (~~squared~~) \|\| 1236426679426025390625/1180591620717411303424 \|\| {{monzo\| -70 16 12 6 }} \|\| Y		\| 1.2 = 6/5 \|\| 0.6 = 3/5 \|\| p=2, q=1 Miracle projection \|\| 35162859375/34359738368 (reduced), 1236426679426025390625/1180591620717411303424 (unreduced) \|\| {{monzo\|-35 8 6 3 }} (reduced), {{monzo\| -70 16 12 6 }} (unreduced) \|\| Y
	\|-		\|-
	\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512\|275625/262144]] \|\| {{monzo\| -18 2 4 2 }} \|\| Y		\| 2 \|\| 1 \|\| [[Avicennmic temperaments\|Avicennmic]] \|\| [[525/512]] (reduced), 275625/262144 (unreduced) \|\| {{monzo\| -9 1 2 1 }} (reduced), {{monzo\| -18 2 4 2 }} (unreduced) \|\| Y
	\|-		\|-
	\| 1 \|\| 1 \|\| [[Mirwomo temperaments\|Mirwomo]] \|\| [[33075/32768]] \|\| {{monzo\| -15 3 2 2 }} \|\| n		\| 1 \|\| 1 \|\| [[Mirwomo temperaments\|Mirwomo]] \|\| [[33075/32768]] \|\| {{monzo\| -15 3 2 2 }} \|\| n