172edo - Revision history

Contribution at 22:19, 17 April 2026

2026-04-17T22:19:35Z

← Older revision		Revision as of 22:19, 17 April 2026
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	Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and [[4125/4096]] in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.		Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and [[4125/4096]] in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

	Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 15-limit.		Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

Neutraldown at 02:14, 28 November 2025

2025-11-28T02:14:41Z

← Older revision		Revision as of 02:14, 28 November 2025
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	Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], [[832/825]], [[1001/1000]], and 2197/2187 in the 13-limit.		Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], [[832/825]], [[1001/1000]], and 2197/2187 in the 13-limit.

	Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.		Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and [[4125/4096]] in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

	Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 15-limit.		Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 15-limit.

Contribution at 21:12, 7 June 2025

2025-06-07T21:12:18Z

← Older revision		Revision as of 21:12, 7 June 2025
Line 7:		Line 7:

	Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.		Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

			Using the 172f val, every 7 steps is an excellent approximation of the ninth no-2 zeta peak - associated with [[39edt]] - in the 15-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 16:38, 20 February 2025

2025-02-20T16:38:18Z

← Older revision		Revision as of 16:38, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 '''272''' 399 }} (172b), and {{val\| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.		172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 '''272''' 399 }} (172b), and {{val\| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.

Fredg999: Internal links

2024-07-06T16:59:19Z

Internal links

← Older revision		Revision as of 16:59, 6 July 2024
Line 4:		Line 4:
	172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 '''272''' 399 }} (172b), and {{val\| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.		172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 '''272''' 399 }} (172b), and {{val\| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.

	Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], 832/825, [[1001/1000]], and 2197/2187 in the 13-limit.		Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], [[832/825]], [[1001/1000]], and 2197/2187 in the 13-limit.

	Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.		Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

FloraC: +prime error table; +subsets and supersets

2024-04-26T07:39:55Z

+prime error table; +subsets and supersets

← Older revision		Revision as of 07:39, 26 April 2024
Line 2:		Line 2:
	{{EDO intro}}		{{EDO intro}}

	172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 272 399 }} (172b), and {{val\| 172 273 400 }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.		172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 '''272''' 399 }} (172b), and {{val\| 172 273 '''400''' }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.

	Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], 832/825, [[1001/1000]], and 2197/2187 in the 13-limit.		Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], 832/825, [[1001/1000]], and 2197/2187 in the 13-limit.

	Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.		Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

			=== Odd harmonics ===
			{{Harmonics in equal\|172}}

			=== Subsets and supersets ===
			Since 172 factors into {{factorization\|172}}, 172edo has subset edos {{EDOs\| 2, 4, 43, and 86 }}.

FloraC: This JND information is totally useless when the cited values differ as much as 3.5 to 10 cents

2024-04-26T07:38:22Z

This JND information is totally useless when the cited values differ as much as 3.5 to 10 cents

← Older revision		Revision as of 07:38, 26 April 2024
Line 6:		Line 6:
	Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], 832/825, [[1001/1000]], and 2197/2187 in the 13-limit.		Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], 832/825, [[1001/1000]], and 2197/2187 in the 13-limit.

	Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.		Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

	~~It is the first edo which an approximate all intervals within the smallest commonly cited value of the [[just-noticeable difference]] (3.5 cents)~~.

FloraC: Cleanup

2024-04-26T07:36:27Z

Cleanup

← Older revision		Revision as of 07:36, 26 April 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''172edo''' is the [[~~EDO\|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <172 273 399\| (patent val), <172 272 399\| (172b), and <172 273 400\| (172c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 1220703125/1162261467 in the 5-limit; 245/243, 3125/3087, and 2097152/2066715 in the 7-limit, supporting the 7-limit [[Sensamagic clan\|bohpier temperament]]; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-limit; 169/168, 352/351, 364/363, and 1716/1715 in the 13-limit, supporting the [[Sensamagic clan\|leapweek temperament]]. Using the 172b val, it tempers out the unicorn comma, 1594323/1562500 and 2197265625/2147483648 in the 5-limit; 1728/1715, 3645/3584, and 390625/388962 in the 7-limit; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-limit; 625/624, 975/968, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the alternative 172bdee val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; 351/350, 625/624, 1188/1183, and 1573/1568 in the 13-limit. Using the 172c val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|1 36 -25> in the 5-limit; 4375/4374, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit. Using the alternative 172cef val, it tempers out 441/440, 1344/1331, and 3388/3375 in the 11-limit; 196/195, 352/351, 832/825, 1001/1000, and 2197/2187 in the 13-limit. Using the alternative 172cf val, 196/195, 1716/1715, 2080/2079, 2197/2187, and 2200/2197 are tempered out in the 13-limit. Using the 172f val, 275/273, 640/637, 847/845, and 1575/1573 are tempered out in the 13-limit.		{{EDO intro}}

			172edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 172 273 399 }} ([[patent val]]), {{val\| 172 272 399 }} (172b), and {{val\| 172 273 400 }} (172c). Using the patent val, it [[tempering out\|tempers out]] the [[semicomma]], 2109375/2097152 and 1220703125/1162261467 in the 5-limit; [[245/243]], [[3125/3087]], and 2097152/2066715 in the 7-limit, [[support]]ing the 7-limit [[bohpier]] temperament; [[385/384]], [[896/891]], 1331/1323, and 9375/9317 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1716/1715]] in the 13-limit, supporting the [[leapweek]] temperament. Using the 172f val, [[275/273]], [[640/637]], [[847/845]], and [[1575/1573]] are tempered out in the 13-limit.

	It is the first ~~EDO~~ which an approximate all intervals within the smallest commonly cited value of the [[just-noticeable difference]] (3.5 cents).		Using the 172c val, it tempers out the [[diaschisma]], 2048/2025 and {{monzo\| 1 36 -25 }} in the 5-limit; [[4375/4374]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit. Using the alternative 172cf val, [[196/195]], 1716/1715, [[2080/2079]], [[2197/2187]], and [[2200/2197]] are tempered out in the 13-limit. Using the alternative 172cef val, it tempers out [[441/440]], 1344/1331, and [[3388/3375]] in the 11-limit; 196/195, [[352/351]], 832/825, [[1001/1000]], and 2197/2187 in the 13-limit.
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
			Using the 172b val, it tempers out the [[unicorn comma]], 1594323/1562500 and 2197265625/2147483648 in the 5-limit; [[1728/1715]], [[3645/3584]], and [[390625/388962]] in the 7-limit; [[441/440]], 1944/1925, [[4000/3993]], and 4125/4096 in the 11-limit; [[625/624]], 975/968, [[1188/1183]], [[1287/1280]], and [[1573/1568]] in the 13-limit. Using the alternative 172bdee val, it tempers out [[225/224]], 118098/117649, and 3176523/3125000 in the 7-limit; [[243/242]], 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; [[351/350]], 625/624, 1188/1183, and 1573/1568 in the 13-limit.

			It is the first edo which an approximate all intervals within the smallest commonly cited value of the [[just-noticeable difference]] (3.5 cents).

CompactStar at 22:27, 13 March 2024

2024-03-13T22:27:45Z

← Older revision		Revision as of 22:27, 13 March 2024
Line 2:		Line 2:
	'''172edo''' is the [[EDO\|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <172 273 399\| (patent val), <172 272 399\| (172b), and <172 273 400\| (172c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 1220703125/1162261467 in the 5-limit; 245/243, 3125/3087, and 2097152/2066715 in the 7-limit, supporting the 7-limit [[Sensamagic clan\|bohpier temperament]]; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-limit; 169/168, 352/351, 364/363, and 1716/1715 in the 13-limit, supporting the [[Sensamagic clan\|leapweek temperament]]. Using the 172b val, it tempers out the unicorn comma, 1594323/1562500 and 2197265625/2147483648 in the 5-limit; 1728/1715, 3645/3584, and 390625/388962 in the 7-limit; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-limit; 625/624, 975/968, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the alternative 172bdee val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; 351/350, 625/624, 1188/1183, and 1573/1568 in the 13-limit. Using the 172c val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|1 36 -25> in the 5-limit; 4375/4374, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit. Using the alternative 172cef val, it tempers out 441/440, 1344/1331, and 3388/3375 in the 11-limit; 196/195, 352/351, 832/825, 1001/1000, and 2197/2187 in the 13-limit. Using the alternative 172cf val, 196/195, 1716/1715, 2080/2079, 2197/2187, and 2200/2197 are tempered out in the 13-limit. Using the 172f val, 275/273, 640/637, 847/845, and 1575/1573 are tempered out in the 13-limit.		'''172edo''' is the [[EDO\|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <172 273 399\| (patent val), <172 272 399\| (172b), and <172 273 400\| (172c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 1220703125/1162261467 in the 5-limit; 245/243, 3125/3087, and 2097152/2066715 in the 7-limit, supporting the 7-limit [[Sensamagic clan\|bohpier temperament]]; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-limit; 169/168, 352/351, 364/363, and 1716/1715 in the 13-limit, supporting the [[Sensamagic clan\|leapweek temperament]]. Using the 172b val, it tempers out the unicorn comma, 1594323/1562500 and 2197265625/2147483648 in the 5-limit; 1728/1715, 3645/3584, and 390625/388962 in the 7-limit; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-limit; 625/624, 975/968, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the alternative 172bdee val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; 351/350, 625/624, 1188/1183, and 1573/1568 in the 13-limit. Using the 172c val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|1 36 -25> in the 5-limit; 4375/4374, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit. Using the alternative 172cef val, it tempers out 441/440, 1344/1331, and 3388/3375 in the 11-limit; 196/195, 352/351, 832/825, 1001/1000, and 2197/2187 in the 13-limit. Using the alternative 172cf val, 196/195, 1716/1715, 2080/2079, 2197/2187, and 2200/2197 are tempered out in the 13-limit. Using the 172f val, 275/273, 640/637, 847/845, and 1575/1573 are tempered out in the 13-limit.


			It is the first EDO which an approximate all intervals within the smallest commonly cited value of the [[just-noticeable difference]] (3.5 cents).
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:11:28Z

Infobox ET added

← Older revision		Revision as of 21:11, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''172edo''' is the [[EDO\|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <172 273 399\| (patent val), <172 272 399\| (172b), and <172 273 400\| (172c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 1220703125/1162261467 in the 5-limit; 245/243, 3125/3087, and 2097152/2066715 in the 7-limit, supporting the 7-limit [[Sensamagic clan\|bohpier temperament]]; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-limit; 169/168, 352/351, 364/363, and 1716/1715 in the 13-limit, supporting the [[Sensamagic clan\|leapweek temperament]]. Using the 172b val, it tempers out the unicorn comma, 1594323/1562500 and 2197265625/2147483648 in the 5-limit; 1728/1715, 3645/3584, and 390625/388962 in the 7-limit; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-limit; 625/624, 975/968, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the alternative 172bdee val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; 351/350, 625/624, 1188/1183, and 1573/1568 in the 13-limit. Using the 172c val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|1 36 -25> in the 5-limit; 4375/4374, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit. Using the alternative 172cef val, it tempers out 441/440, 1344/1331, and 3388/3375 in the 11-limit; 196/195, 352/351, 832/825, 1001/1000, and 2197/2187 in the 13-limit. Using the alternative 172cf val, 196/195, 1716/1715, 2080/2079, 2197/2187, and 2200/2197 are tempered out in the 13-limit. Using the 172f val, 275/273, 640/637, 847/845, and 1575/1573 are tempered out in the 13-limit.		'''172edo''' is the [[EDO\|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <172 273 399\| (patent val), <172 272 399\| (172b), and <172 273 400\| (172c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 1220703125/1162261467 in the 5-limit; 245/243, 3125/3087, and 2097152/2066715 in the 7-limit, supporting the 7-limit [[Sensamagic clan\|bohpier temperament]]; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-limit; 169/168, 352/351, 364/363, and 1716/1715 in the 13-limit, supporting the [[Sensamagic clan\|leapweek temperament]]. Using the 172b val, it tempers out the unicorn comma, 1594323/1562500 and 2197265625/2147483648 in the 5-limit; 1728/1715, 3645/3584, and 390625/388962 in the 7-limit; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-limit; 625/624, 975/968, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the alternative 172bdee val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; 351/350, 625/624, 1188/1183, and 1573/1568 in the 13-limit. Using the 172c val, it tempers out the [[Diaschismic family\|diaschisma]], 2048/2025 and \|1 36 -25> in the 5-limit; 4375/4374, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit. Using the alternative 172cef val, it tempers out 441/440, 1344/1331, and 3388/3375 in the 11-limit; 196/195, 352/351, 832/825, 1001/1000, and 2197/2187 in the 13-limit. Using the alternative 172cf val, 196/195, 1716/1715, 2080/2079, 2197/2187, and 2200/2197 are tempered out in the 13-limit. Using the 172f val, 275/273, 640/637, 847/845, and 1575/1573 are tempered out in the 13-limit.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->