Ultrapyth - Revision history

FloraC: Cleanup on infobox

2026-02-09T10:08:04Z

Cleanup on infobox

← Older revision		Revision as of 10:08, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Ultrapyth		\| Title = Ultrapyth
	\| Subgroups = 2.3.5.7, 2.3.5.7.13		\| Subgroups = 2.3.5.7, 2.3.5.7.13
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	\| Edo join 1 = 5 \| Edo join 2 = 32		\| Edo join 1 = 5 \| Edo join 2 = 32
	\| Mapping = 1; 1 14 -2 18		\| Mapping = 1; 1 14 -2 18
	\| ~~Generator~~ = 3/2		\| Generators = 3/2
	\| ~~Generator~~ tuning = 713.6		\| Generators tuning = 713.6
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[5L 7s]], [[5L 12s]], [[5L 17s]], [[5L 22s]]		\| MOS scales = [[5L 7s]], [[5L 12s]], [[5L 17s]], [[5L 22s]]
	\| Pergen = (P8, P5)		\| Pergen = (P8, P5)
	\| Odd limit 1 = 7 \| Mistuning 1 = 11.4 \| Complexity 1 = 17		\| Odd limit 1 = 7 \| Mistuning 1 = 11.4 \| Complexity 1 = 17
	\| Odd limit 2 = (2.3.5.7.13) 21 \| Mistuning 2 = 22.8 \| Complexity 2 = 22		\| Odd limit 2 = 2.3.5.7.13 21 \| Mistuning 2 = 22.8 \| Complexity 2 = 22
	}}		}}
	'''Ultrapyth''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], tempering out [[64/63]]. The difference is that instead of extending to 2.3.5.7 by mapping 5 to +9 generators, it extends to the 2.3.7.13/5 subgroup (known as '''oceanfront''') by mapping the ultramajor third [[13/10]] to +4 generators (which is also the diatonic major third), tempering out [[91/90]]. This makes sense because the tunings of 2.3.7 archy that optimize for the simplest 2.3.7 intervals (8/7 and [[7/6]]) are sharp of the optimal tuning for 9/7, making that third more ultramajor than supermajor. If intervals of 5 and 13 independently are desired (i.e. [[5/4]], [[13/8]]), then oceanfront may be extended to ultrapyth by mapping 5 to +14 fifths (a double-augmented unison) and 13 to +18 fifths (a double-augmented third). The best tunings for ultrapyth are between 712 and 714 cents.		'''Ultrapyth''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], tempering out [[64/63]]. The difference is that instead of extending to 2.3.5.7 by mapping 5 to +9 generators, it extends to the 2.3.7.13/5 subgroup (known as '''oceanfront''') by mapping the ultramajor third [[13/10]] to +4 generators (which is also the diatonic major third), tempering out [[91/90]]. This makes sense because the tunings of 2.3.7 archy that optimize for the simplest 2.3.7 intervals (8/7 and [[7/6]]) are sharp of the optimal tuning for 9/7, making that third more ultramajor than supermajor. If intervals of 5 and 13 independently are desired (i.e. [[5/4]], [[13/8]]), then oceanfront may be extended to ultrapyth by mapping 5 to +14 fifths (a double-augmented unison) and 13 to +18 fifths (a double-augmented third). The best tunings for ultrapyth are between 712 and 714 cents.

Overthink: + missing subgroup

2026-01-03T01:05:24Z

+ missing subgroup

← Older revision		Revision as of 01:05, 3 January 2026
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	\| Title = Ultrapyth		\| Title = Ultrapyth
	\| Subgroups = 2.3.5.7, 2.3.5.7.13		\| Subgroups = 2.3.5.7, 2.3.5.7.13
	\| Comma basis = [[64/63]], [[6860/6561]] (2.3.5.7)<br>[[64/63]], [[91/90]], [[6125/6084]]		\| Comma basis = [[64/63]], [[6860/6561]] (2.3.5.7)<br>[[64/63]], [[91/90]], [[6125/6084]] (2.3.5.7.13)
	\| Edo join 1 = 5 \| Edo join 2 = 32		\| Edo join 1 = 5 \| Edo join 2 = 32
	\| Mapping = 1; 1 14 -2 18		\| Mapping = 1; 1 14 -2 18

Overthink: /* Tuning spectrum */ + 2.3.5.7.13 minimax

2025-12-30T01:42:07Z

Tuning spectrum: + 2.3.5.7.13 minimax

← Older revision		Revision as of 01:42, 30 December 2025
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	\|13/8		\|13/8
	\|713.363		\|713.363
	\|		\| 2.3.5.7.13 13- to 21-odd-limit minimax
	\|-		\|-
	\| '''[[37edo\|22\37]]'''		\| '''[[37edo\|22\37]]'''

Overthink: + Infobox

2025-12-30T01:40:14Z

+ Infobox

← Older revision		Revision as of 01:40, 30 December 2025
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			{{Infobox Regtemp
			\| Title = Ultrapyth
			\| Subgroups = 2.3.5.7, 2.3.5.7.13
			\| Comma basis = [[64/63]], [[6860/6561]] (2.3.5.7)<br>[[64/63]], [[91/90]], [[6125/6084]]
			\| Edo join 1 = 5 \| Edo join 2 = 32
			\| Mapping = 1; 1 14 -2 18
			\| Generator = 3/2
			\| Generator tuning = 713.6
			\| Optimization method = CWE
			\| MOS scales = [[5L 7s]], [[5L 12s]], [[5L 17s]], [[5L 22s]]
			\| Pergen = (P8, P5)
			\| Odd limit 1 = 7 \| Mistuning 1 = 11.4 \| Complexity 1 = 17
			\| Odd limit 2 = (2.3.5.7.13) 21 \| Mistuning 2 = 22.8 \| Complexity 2 = 22
			}}
	'''Ultrapyth''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], tempering out [[64/63]]. The difference is that instead of extending to 2.3.5.7 by mapping 5 to +9 generators, it extends to the 2.3.7.13/5 subgroup (known as '''oceanfront''') by mapping the ultramajor third [[13/10]] to +4 generators (which is also the diatonic major third), tempering out [[91/90]]. This makes sense because the tunings of 2.3.7 archy that optimize for the simplest 2.3.7 intervals (8/7 and [[7/6]]) are sharp of the optimal tuning for 9/7, making that third more ultramajor than supermajor. If intervals of 5 and 13 independently are desired (i.e. [[5/4]], [[13/8]]), then oceanfront may be extended to ultrapyth by mapping 5 to +14 fifths (a double-augmented unison) and 13 to +18 fifths (a double-augmented third). The best tunings for ultrapyth are between 712 and 714 cents.		'''Ultrapyth''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], tempering out [[64/63]]. The difference is that instead of extending to 2.3.5.7 by mapping 5 to +9 generators, it extends to the 2.3.7.13/5 subgroup (known as '''oceanfront''') by mapping the ultramajor third [[13/10]] to +4 generators (which is also the diatonic major third), tempering out [[91/90]]. This makes sense because the tunings of 2.3.7 archy that optimize for the simplest 2.3.7 intervals (8/7 and [[7/6]]) are sharp of the optimal tuning for 9/7, making that third more ultramajor than supermajor. If intervals of 5 and 13 independently are desired (i.e. [[5/4]], [[13/8]]), then oceanfront may be extended to ultrapyth by mapping 5 to +14 fifths (a double-augmented unison) and 13 to +18 fifths (a double-augmented third). The best tunings for ultrapyth are between 712 and 714 cents.

Overthink: /* Tuning spectrum */ note 13-limit vals

2025-12-29T10:22:38Z

Tuning spectrum: note 13-limit vals

← Older revision		Revision as of 10:22, 29 December 2025
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	\|		\|
	\| 709.091		\| 709.091
	\| ~~22cc~~ val		\| 22ccff val
	\|-		\|-
	\|		\|
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	\|		\|
	\| 711.111		\| 711.111
	\| ~~27c~~ val		\| 27cf val
	\|-		\|-
	\| '''[[32edo\|19\32]]'''		\| '''[[32edo\|19\32]]'''
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	\|		\|
	\| 714.286		\| 714.286
	\|		\| 42f val
	\|-		\|-
	\|		\|
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	\|		\|
	\| 714.894		\| 714.894
	\| ~~47bc~~ val		\| 47bcff val
	\|-		\|-
	\|		\|

Overthink: /* Tuning spectrum */ + ratios of 13

2025-12-29T10:20:59Z

Tuning spectrum: + ratios of 13

← Older revision		Revision as of 10:20, 29 December 2025
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	\| 7- and 9-odd-limit minimax		\| 7- and 9-odd-limit minimax
	\|-		\|-
	\| [[37edo\|22\37]]		\|
	\|		\|13/8
	~~\| 713.514~~		\|713.363
			\|
			\|-
			\| '''[[37edo\|22\37]]'''
	\|		\|
			\| '''713.514'''
			\| '''Lower bound of 2.3.5.7.13 13-odd-limit diamond monotone<br>2.3.5.7.13 15- and 21-odd-limit diamond monotone (singleton)
			\|-
			\|
			\|13/10
			\|713.553
			\|
			\|-
			\|
			\|14/13
			\|713.585
			\|
	\|-		\|-
	\|		\|
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	\| 713.593		\| 713.593
	\|		\|
			\|-
			\|
			\|13/12
			\|714.034
			\|
	\|-		\|-
	\|		\|
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	\| 714.181		\| 714.181
	\|		\|
			\|-
			\|
			\|21/13
			\|714.197
			\|
	\|-		\|-
	\| [[42edo\|25\42]]		\| [[42edo\|25\42]]
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	\| 714.369		\| 714.369
	\|		\|
			\|-
			\|
			\|13/9
			\|714.789
			\|
	\|-		\|-
	\| [[47edo\|28\47]]		\| [[47edo\|28\47]]
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	\| 715.587		\| 715.587
	\|		\|
			\|-
			\|
			\|15/13
			\|717.420
			\|
	\|-		\|-
	\| '''[[5edo\|3\5]]'''		\| '''[[5edo\|3\5]]'''
	\|		\|
	\| '''720.000'''		\| '''720.000'''
	\| '''Upper bound of 7- and 9-odd-limit diamond monotone'''		\| '''Upper bound of 7- and 9-odd-limit,<br>2.3.5.7.13 13-odd-limit diamond monotone'''
	\|-		\|-
	\|		\|

FloraC: /* Interval chain */ wrap the latter table cuz the different heights in the head is a pain to look at

2025-12-23T14:25:27Z

Interval chain: wrap the latter table cuz the different heights in the head is a pain to look at

← Older revision		Revision as of 14:25, 23 December 2025
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	\|}		\|}
	<nowiki/>* In 2.3.7.13/5-subgroup [[CWE]] tuning, <br>octave reduced		<nowiki/>* In 2.3.7.13/5-subgroup [[CWE]] tuning, <br>octave reduced
	</div>		</div></div>
	<div style="display: inline-grid;">		<div><div style="display: inline-grid;">
	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	\|+ style="font-size: 105%;" \| Ultrapyth		\|+ style="font-size: 105%;" \| Ultrapyth

Overthink: /* Tuning spectrum */ fix monotone tuning (flatter tunings swap 7/5 and 10/7)

2025-12-22T20:57:52Z

Tuning spectrum: fix monotone tuning (flatter tunings swap 7/5 and 10/7)

← Older revision		Revision as of 20:57, 22 December 2025
Line 133:		Line 133:
	\|		\|
	\| 711.111		\| 711.111
	\| 27c val~~, lower bound of 7- and 9-odd-limit diamond monotone~~		\| 27c val
	\|-		\|-
	\| [[32edo\|19\32]]		\| '''[[32edo\|19\32]]'''
	\|
	~~\| 712.500~~
	\|		\|
			\| '''712.500'''
			\| '''Lower bound of 7- and 9-odd-limit diamond monotone'''
	\|-		\|-
	\|		\|
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	\|		\|
	\|-		\|-
	\| [[5edo\|3\5]]		\| '''[[5edo\|3\5]]'''
	\|		\|
	\| 720.000		\| '''720.000'''
	\| Upper bound of 7- and 9-odd-limit diamond monotone		\| '''Upper bound of 7- and 9-odd-limit diamond monotone'''
	\|-		\|-
	\|		\|

FloraC: /* Tunings */ + tuning spectrum

2025-10-06T15:15:39Z

Tunings: + tuning spectrum

@@ Line 101: / Line 101: @@
 | POTE: ~3/2 = 713.6509{{c}}
 |}
 == See also ==

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:05:48Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:05, 12 September 2025
Line 87:		Line 87:
	== Tunings ==		== Tunings ==
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|