123edo - Revision history

ArrowHead294 at 18:41, 13 March 2025

2025-03-13T18:41:16Z

← Older revision		Revision as of 18:41, 13 March 2025
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	Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.		Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.

	Whereas 5 steps of 41edo can be used as a generator for the [[~~Bohlen-Pierce~~]] scale, 5 steps of 123edo with the 123ce val can be used as a generator for the [[triple BP]] scale.		Whereas 5 steps of 41edo can be used as a generator for the [[Bohlen–Pierce]] scale, 5 steps of 123edo with the 123ce val can be used as a generator for the [[triple BP]] scale.

	=== Prime harmonics ===		=== Prime harmonics ===

Fredg999: Fix internal link

2025-02-20T20:24:46Z

Fix internal link

← Older revision		Revision as of 20:24, 20 February 2025
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	Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.		Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.

	Whereas 5 steps of 41edo can be used as a generator for the [[Bohlen-Pierce ~~scale~~]], 5 steps of 123edo with the 123ce val can be used as a generator for the [[triple BP]] scale.		Whereas 5 steps of 41edo can be used as a generator for the [[Bohlen-Pierce]] scale, 5 steps of 123edo with the 123ce val can be used as a generator for the [[triple BP]] scale.

	=== Prime harmonics ===		=== Prime harmonics ===

Fredg999: Fix typo, clarify relation between 123edo and triple BP (with 41edo and BP)

2025-02-20T20:24:31Z

Fix typo, clarify relation between 123edo and triple BP (with 41edo and BP)

← Older revision		Revision as of 20:24, 20 February 2025
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	{{ED intro}}		{{ED intro}}

	Since {{nowrap\| 123 {{=}} 3 × 41 }}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. As an ~~equl~~ temperament, it [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		Since {{nowrap\| 123 {{=}} 3 × 41 }}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. As an equal temperament, it [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.
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	Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.		Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.

	5 steps of the 123ce val can be used as a generator for the [[triple BP]] scale.		Whereas 5 steps of 41edo can be used as a generator for the [[Bohlen-Pierce scale]], 5 steps of 123edo with the 123ce val can be used as a generator for the [[triple BP]] scale.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: 39edt is a concrete tuning of triple BP, generated by 1\39edt, not 5\123

2025-02-20T20:09:33Z

39edt is a concrete tuning of triple BP, generated by 1\39edt, not 5\123

← Older revision		Revision as of 20:09, 20 February 2025
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	{{ED intro}}		{{ED intro}}

	Since {{nowrap\|123 {{=}} 3 × 41}}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. It [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		Since {{nowrap\| 123 {{=}} 3 × 41 }}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. As an equl temperament, it [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.
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	Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.		Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.

	5 steps of the 123ce val can be used as a generator for [[~~39EDT~~]]~~, the triple Bohlen–Pierce~~ scale.		5 steps of the 123ce val can be used as a generator for the [[triple BP]] scale.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 123 factors into {{~~factorization~~\|~~123~~}}, 123edo contains [[3edo]] and [[41edo]] as its subsets.		Since 123 factors into {{nowrap\| 3 × 41 }}, 123edo contains [[3edo]] and [[41edo]] as its subsets.

	[[Category:Gravid]]		[[Category:Gravid]]

ArrowHead294 at 19:09, 20 February 2025

2025-02-20T19:09:52Z

← Older revision		Revision as of 19:09, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|123~~}}		{{ED intro}}

	Since {{nowrap\|123 {{=}} 3 × 41}}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. It [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		Since {{nowrap\|123 {{=}} 3 × 41}}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. It [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

ArrowHead294 at 19:09, 20 February 2025

2025-02-20T19:09:39Z

← Older revision		Revision as of 19:09, 20 February 2025
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	{{EDO intro\|123}}		{{EDO intro\|123}}

	123 = 3 × 41, ~~and~~ 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. ~~The equal temperament~~ [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		Since {{nowrap\|123 {{=}} 3 × 41}}, 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. It [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.
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	Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.		Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.

	5 steps of the 123ce val ~~is related to~~ [[~~Triple BP~~]].		5 steps of the 123ce val can be used as a generator for [[39EDT]], the triple Bohlen–Pierce scale.

	=== Prime harmonics ===		=== Prime harmonics ===

Lériendil at 00:18, 6 October 2024

2024-10-06T00:18:58Z

← Older revision		Revision as of 00:18, 6 October 2024
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	Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.		Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as [[225/224]], [[245/243]], and [[1029/1024]]; [[275/273]], 352/351, 847/845, [[1573/1568]], and 3185/3168 in the 13-limit. Using the 123e val, it tempers out [[121/120]], 176/175, and [[441/440]] in the 11-limit; 196/195, 351/350, 352/351, [[1287/1280]], and [[2197/2187]] in the 13-limit.

	5 steps of the ~~123be~~ val is related to [[Triple BP]].		5 steps of the 123ce val is related to [[Triple BP]].

	=== Prime harmonics ===		=== Prime harmonics ===

Fredg999: Internal link

2024-07-06T16:57:19Z

Internal link

← Older revision		Revision as of 16:57, 6 July 2024
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	{{EDO intro\|123}}		{{EDO intro\|123}}

	123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.

FloraC: Note the gravity comma

2024-05-29T08:23:07Z

Note the gravity comma

← Older revision		Revision as of 08:23, 29 May 2024
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	{{EDO intro\|123}}		{{EDO intro\|123}}

	123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] ~~the~~ [[valentine comma]], ~~1990656~~/~~1953125 and the~~ [[misty comma]], ~~67108864/66430125~~ in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.

FloraC: +subsets and supersets; relation to 41edo

2024-05-29T08:19:26Z

+subsets and supersets; relation to 41edo

← Older revision		Revision as of 08:19, 29 May 2024
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	{{EDO intro\|123}}		{{EDO intro\|123}}

	The equal temperament [[tempering out\|tempers out]] the [[valentine comma]], 1990656/1953125 and the [[misty comma]], 67108864/66430125 in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]~~, providing the [[optimal patent val]] for the [[gravid]] temperament~~; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]].		123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] the [[valentine comma]], 1990656/1953125 and the [[misty comma]], 67108864/66430125 in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|123}}		{{Harmonics in equal\|123}}

			=== Subsets and supersets ===
			Since 123 factors into {{factorization\|123}}, 123edo contains [[3edo]] and [[41edo]] as its subsets.

	[[Category:Gravid]]		[[Category:Gravid]]

← Older revision		Revision as of 16:57, 6 July 2024
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	{{EDO intro\|123}}		{{EDO intro\|123}}

	123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], [[832/825]], [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.

← Older revision		Revision as of 08:23, 29 May 2024
Line 2:		Line 2:
	{{EDO intro\|123}}		{{EDO intro\|123}}

	123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] ~~the~~ [[valentine comma]], ~~1990656~~/~~1953125 and the~~ [[misty comma]], ~~67108864/66430125~~ in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.		123 = 3 × 41, and 123edo shares its [[perfect fifth\|fifth]] with [[41edo]]. The equal temperament [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]), 67108864/66430125 ([[misty comma]]), and {{monzo\| -13 17 -6 }} ([[graviton]]) in the [[5-limit]]; [[126/125]], [[1029/1024]] and 537824/531441 in the [[7-limit]]; [[243/242]], [[896/891]], 2401/2376, and [[3388/3375]] in the [[11-limit]]; [[196/195]], [[351/350]], 832/825, [[1575/1573]], and 2197/2178 in the [[13-limit]]. It provides the [[optimal patent val]] for the [[gravid]] temperament.

	Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.		Given its in[[consistency]] to the [[7-odd-limit]] and higher odd limits, the mapping {{val\| 123 195 286 '''346''' }} (123d) is also possible for the 7-limit. Using the 123d val, it tempers out [[2430/2401]], [[3136/3125]], and [[5120/5103]] in the 7-limit; [[176/175]], 243/242, [[1375/1372]], and 2560/2541 in the 11-limit; [[169/168]], [[364/363]], [[640/637]], [[729/728]], and 832/825 in the 13-limit. Using the 123df val, it tempers out [[144/143]], 351/350, [[352/351]], and [[847/845]] in the 13-limit.