Semaphore and godzilla - Revision history

Fitzgerald Lee: nvm

2026-07-16T02:24:47Z

nvm

← Older revision		Revision as of 02:24, 16 July 2026
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	\|-		\|-
	\|		\|
	\| 21/16		\| 9/7
	\| 945.028		\| 945.028
	\| ~~2/3-comma~~		\|
	\|-		\|-
	\|		\|
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	\| 3/2		\| 3/2
	\| 950.978		\| 950.978
	\| ~~1/2-comma~~		\|
	\|-		\|-
	\|		\|

Fitzgerald Lee: /* Tuning spectrum */(7/6)^3/(49/48)^2 = 32/21, thus the eigenmonzo for it is 21/16, not 9/7.

2026-07-16T02:23:56Z

Tuning spectrum: (7/6)^3/(49/48)^2 = 32/21, thus the eigenmonzo for it is 21/16, not 9/7.

← Older revision		Revision as of 02:23, 16 July 2026
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	\|-		\|-
	\|		\|
	\| 9/7		\| 21/16
	\| 945.028		\| 945.028
	\|		\| 2/3-comma
	\|-		\|-
	\|		\|
Line 305:		Line 305:
	\| 3/2		\| 3/2
	\| 950.978		\| 950.978
	\|		\| 1/2-comma
	\|-		\|-
	\|		\|

FloraC: Small improvements in infobox and intro

2026-07-14T13:53:49Z

Small improvements in infobox and intro

← Older revision		Revision as of 13:53, 14 July 2026
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	{{~~interwiki~~		{{Interwiki
	\| en = Semaphore and godzilla		\| en = Semaphore and godzilla
	\| de = Semiphor, Semaphor, Godzilla		\| de = Semiphor, Semaphor, Godzilla
Line 12:		Line 12:
	\| Mapping = 1; 2 8 1 11		\| Mapping = 1; 2 8 1 11
	\| Generators = 7/4		\| Generators = 7/4
	\| Generators tuning = ~~947~~.8		\| Generators tuning = 948.0
	\| Optimization method = CWE		\| Optimization method = CWE
	\| Pergen = (P8, P4/2)		\| Pergen = (P8, P4/2)
Line 20:		Line 20:
	\| Odd limit 2 = 2.3.5.7.13 15 \| Mistuning 2 = 20.5 \| Complexity 2 = 14		\| Odd limit 2 = 2.3.5.7.13 15 \| Mistuning 2 = 20.5 \| Complexity 2 = 14
	}}		}}
	'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out\|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] 2.3.7-[[subgroup]] [[regular temperament\|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".		'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out\|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] [[2.3.7 subgroup\|2.3.7-subgroup]] [[regular temperament\|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".

	If the [[5/1\|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[~~Meantone~~ family #Extensions\|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.		If the [[5/1\|5th harmonic]]'s intervals are desired, [[5/4]] can be sensibly mapped to +8 generators by tempering out [[81/80]], making it a [[meantone family #Extensions\|meantone temperament]]. This temperament is '''godzilla'''. Moreover, the generator can be taken to be [[26/15]], which maps [[13/8]] to +11 generators by tempering out [[91/90]] and [[105/104]]. This extends the temperament to the 2.3.5.7.13 subgroup, with an abundance of harmonic resource and little additional damage.

	A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].		A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].

Fitzgerald Lee at 04:56, 14 July 2026

2026-07-14T04:56:04Z

← Older revision		Revision as of 04:56, 14 July 2026
Line 255:		Line 255:
	\| 9/7		\| 9/7
	\| 945.028		\| 945.028
	\| ~~2/3-comma~~		\|
	\|-		\|-
	\|		\|
Line 305:		Line 305:
	\| 3/2		\| 3/2
	\| 950.978		\| 950.978
	\| ~~1/2-comma~~		\|
	\|-		\|-
	\|		\|
Line 311:		Line 311:
	\| 951.405		\| 951.405
	\|		\|
	\|-
	~~\| [[29edo\|23\29]]~~
	\|
	~~\| 951.724~~
	\|
	\|-
	~~\| [[34edo\|27\34]]~~
	\|
	~~\| 952.941~~
	\|
	\|-		\|-
	\| [[5edo\|4\5]]		\| [[5edo\|4\5]]
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	\| 968.826		\| 968.826
	\|		\|
	\|-
	~~\| [[6edo\|5\6]]~~
	\|
	~~\| 1000.000~~
	\|
	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

Fitzgerald Lee: /* Tunings */

2026-07-14T04:52:51Z

Tunings

← Older revision		Revision as of 04:52, 14 July 2026
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	\| 9/7		\| 9/7
	\| 945.028		\| 945.028
	\|		\| 2/3-comma
	\|-		\|-
	\|		\|
Line 305:		Line 305:
	\| 3/2		\| 3/2
	\| 950.978		\| 950.978
	\|		\| 1/2-comma
	\|-		\|-
	\|		\|
Line 311:		Line 311:
	\| 951.405		\| 951.405
	\|		\|
			\|-
			\| [[29edo\|23\29]]
			\|
			\| 951.724
			\|
			\|-
			\| [[34edo\|27\34]]
			\|
			\| 952.941
			\|
	\|-		\|-
	\| [[5edo\|4\5]]		\| [[5edo\|4\5]]
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	\| 968.826		\| 968.826
	\|		\|
			\|-
			\| [[6edo\|5\6]]
			\|
			\| 1000.000
			\|
	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

Xenllium at 00:10, 23 May 2026

2026-05-23T00:10:52Z

← Older revision		Revision as of 00:10, 23 May 2026
Line 26:		Line 26:
	A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].		A more accurate but complex mapping of 5 can be found in [[immunity]], or 5/4 itself can be made the period by tempering out [[128/125]], resulting in [[triforce]].

	~~See~~ [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla\|#Godzilla]] ~~for technical data~~.		For technical information, see [[Semaphoresmic clan #Semaphore]] and [[Semaphoresmic clan #Godzilla\|#Godzilla]]. For a discussion on 11- and 13-limit extensions, see [[Godzilla extensions]].

	== Interval chains ==		== Interval chains ==

FloraC: Undo revision 229963 by MisterShafXen (talk)

2026-05-10T17:59:05Z

Undo revision 229963 by MisterShafXen (talk)

← Older revision		Revision as of 17:59, 10 May 2026
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	\|		\|
	\| 933.333		\| 933.333
	\| 9cff~~/9[-5, -13]~~ val		\| 9cff val
	\|-		\|-
	\| [[14edo\|11\14]]		\| [[14edo\|11\14]]
	\|		\|
	\| 942.857		\| 942.857
	\| 14cf~~/14[-5, -13]~~ val, lower bound of 7- and 9-odd-limit diamond monotone		\| 14cf val, lower bound of 7- and 9-odd-limit diamond monotone
	\|-		\|-
	\|		\|

MisterShafXen: added alternative wart notation as seen on sintel temperament calculator

2026-05-10T12:16:49Z

added alternative wart notation as seen on sintel temperament calculator

← Older revision		Revision as of 12:16, 10 May 2026
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	\|		\|
	\| 933.333		\| 933.333
	\| 9cff val		\| 9cff/9[-5, -13] val
	\|-		\|-
	\| [[14edo\|11\14]]		\| [[14edo\|11\14]]
	\|		\|
	\| 942.857		\| 942.857
	\| 14cf val, lower bound of 7- and 9-odd-limit diamond monotone		\| 14cf/14[-5, -13] val, lower bound of 7- and 9-odd-limit diamond monotone
	\|-		\|-
	\|		\|

Xenllium at 02:28, 18 April 2026

2026-04-18T02:28:17Z

← Older revision		Revision as of 02:28, 18 April 2026
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	\| CWE: ~7/4 = 947.8216{{c}}		\| CWE: ~7/4 = 947.8216{{c}}
	\| POTE: ~7/4 = 947.3650{{c}}		\| POTE: ~7/4 = 947.3650{{c}}
			\|}

			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 2.3.5.7.13-subgroup norm-based tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~7/4 = 948.9311{{c}}
			\| CWE: ~7/4 = 948.0037{{c}}
			\| POTE: ~7/4 = 947.5708{{c}}
	\|}		\|}

Line 216:		Line 232:
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! Edo<br>generator		! Edo <br>generator
	! [[Eigenmonzo\|Unchanged interval<br>(eigenmonzo)]]*		! [[Eigenmonzo\|Unchanged interval <br>(eigenmonzo)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
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	\|		\|
	\| 947.368		\| 947.368
	\| Lower bound of no-11 13-odd-limit diamond monotone<br>No-11 15-odd-limit diamond monotone (singleton)		\| Lower bound of {{nowrap\|no-11}} 13-odd-limit diamond monotone <br>{{nowrap\|No-11}} 15-odd-limit diamond monotone (singleton)
	\|-		\|-
	\|		\|
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	\| 5/4		\| 5/4
	\| 948.289		\| 948.289
	\|		\| 7-, 9-odd-limit, {{nowrap\|no-11}} 13- and 15-odd-limit minimax
	\|-		\|-
	\|		\|
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	\|		\|
	\| 960.000		\| 960.000
	\| Upper bound of 7-, 9-odd-limit, ~~<br>~~and no-11 13-odd-limit diamond monotone		\| Upper bound of 7-, 9-odd-limit, and {{nowrap\|no-11}} 13-odd-limit diamond monotone
	\|-		\|-
	\|		\|

FloraC: Cleanup on infobox

2026-02-09T09:38:17Z

Cleanup on infobox

← Older revision		Revision as of 09:38, 9 February 2026
Line 9:		Line 9:
	\| Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.13		\| Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.13
	\| Comma basis = [[49/48]] (2.3.7); <br> [[49/48]], [[81/80]] (2.3.5.7); <br> [[49/48]], [[81/80]], [[91/90]] (L7.13)		\| Comma basis = [[49/48]] (2.3.7); <br> [[49/48]], [[81/80]] (2.3.5.7); <br> [[49/48]], [[81/80]], [[91/90]] (L7.13)
			\| Edo join 1 = 5 \| Edo join 2 = 19
	\| Mapping = 1; 2 8 1 11		\| Mapping = 1; 2 8 1 11
	\| ~~Edo join 1 = 5 \| Edo join 2 = 19~~		\| Generators = 7/4
	~~\| Generator~~ = 7/4		\| Generators tuning = 947.8
	\| ~~Generator~~ tuning = 947.8
	\| Optimization method = CWE		\| Optimization method = CWE
	\| Pergen = (P8, P4/2)		\| Pergen = (P8, P4/2)
Line 18:		Line 18:
	\| MOS scales = [[4L 1s]], [[5L 4s]], [[5L 9s]], [[5L 14s]]		\| MOS scales = [[4L 1s]], [[5L 4s]], [[5L 9s]], [[5L 14s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 20.5 \| Complexity 1 = 9		\| Odd limit 1 = 9 \| Mistuning 1 = 20.5 \| Complexity 1 = 9
	\| Odd limit 2 = (2.3.5.7.13) 15 \| Mistuning 2 = 20.5 \| Complexity 2 = 14		\| Odd limit 2 = 2.3.5.7.13 15 \| Mistuning 2 = 20.5 \| Complexity 2 = 14
	}}		}}
	'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out\|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] 2.3.7-[[subgroup]] [[regular temperament\|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".		'''Semaphore''', of the [[semaphoresmic clan]], is characterized by [[49/48]] being [[tempering out\|tempered out]], so the [[generator]] represents [[7/4]] and [[12/7]] (or [[8/7]] and [[7/6]]) equally. This results in a very low [[complexity]] 2.3.7-[[subgroup]] [[regular temperament\|temperament]], with the drawback that most intervals of 7 must be out of tune by at least half of the comma 49/48, or about 18 [[cent]]s. ''Semaphore'' is a play on the words "semi-" and "fourth".