Starling temperaments - Revision history

FloraC: /* Nusecond */ 31 & 39d makes more sense than 31 & 70

2026-10-21T09:09:17Z

Nusecond: 31 & 39d makes more sense than 31 & 70

← Older revision		Revision as of 09:09, 21 October 2026
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Nusecond]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Nusecond]].''

	Nusecond tempers out [[2430/2401]] and [[16875/16807]] in addition to 126/125, and may be described as {{nowrap\| 31 & 70 }}. It has a neutral second generator of [[49/45]], two of which make up a 6/5 minor third since 2430/2401 is tempered out. Note that in the data below, the generator is its [[octave complement]] since eleven such generators [[octave reduction\|octave reduced]] give the [[3/2\|perfect fifth]]; its [[ploidacot]] is thus theta-hendecacot.		Nusecond tempers out [[2430/2401]] and [[16875/16807]] in addition to 126/125, and may be described as the {{nowrap\| 31 & 39d }} temperament. It has a neutral second generator of [[49/45]], two of which make up a 6/5 minor third since 2430/2401 is tempered out. Note that in the data below, the generator is its [[octave complement]] since eleven such generators [[octave reduction\|octave reduced]] give the [[3/2\|perfect fifth]]; its [[ploidacot]] is thus theta-hendecacot.

	[[31edo]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. Mosses of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note mos might also be considered from the melodic point of view.		[[31edo]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. Mosses of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note mos might also be considered from the melodic point of view.

FloraC: + link to brutus

2026-10-19T12:36:39Z

+ link to brutus

← Older revision		Revision as of 12:36, 19 October 2026
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	Temperaments discussed in families and clans are:		Temperaments discussed in families and clans are:
			* ''[[Brutus]]'' (+10/9) → [[Very low accuracy temperaments #Brutus\|Very low accuracy temperaments]]
	* ''[[Pater]]'' (+16/15) → [[Father family #Pater\|Father family]]		* ''[[Pater]]'' (+16/15) → [[Father family #Pater\|Father family]]
	* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone\|Meantone family]]		* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone\|Meantone family]]

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:32Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

Show changes

FloraC: - bisemidim (more properly addressed in stearnsmic clan)

2026-09-20T03:15:05Z

- bisemidim (more properly addressed in stearnsmic clan)

@@ Line 26: / Line 26: @@
 * ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton|Ditonmic family]]
 * ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean|Vishnu family]]
 * ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]]
-Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, supersensi, and cobalt, sorted by increasing [[badness]].
+Considered below are myna, nusecond, oolong, vines, kumonga, cypress, casablanca, amigo, supersensi, and cobalt, sorted by increasing [[badness]].
 Since {{nowrap|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord.
@@ Line 473: / Line 474: @@
 Badness (Sintel): 1.19
 == Cypress ==

FloraC: + link to ripple

2026-09-11T14:26:21Z

+ link to ripple

← Older revision		Revision as of 14:26, 11 September 2026
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	* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]		* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]
	* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate\|Passion family]]		* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate\|Passion family]]
			* ''[[Ripple]]'' (+405/392) → [[Ripple family #Septimal ripple\|Ripple family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
	* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]

FloraC: Recategorize

2026-08-15T08:01:29Z

Recategorize

← Older revision		Revision as of 08:01, 15 August 2026
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	== References ==		== References ==

			[[Category:Starling temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:~~Starling temperaments\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

FloraC: - "paraguay" (addressed in parakleismic family)

2026-08-09T13:49:01Z

- "paraguay" (addressed in parakleismic family)

@@ Line 22: / Line 22: @@
 * ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee|Mabila family]]
 * ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja|Buzzardsmic clan]]
 * ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton|Ditonmic family]]
 * ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean|Vishnu family]]
 * ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]]
-Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].
+Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, supersensi, and cobalt, sorted by increasing [[badness]].
 Since {{nowrap|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord.
@@ Line 471: / Line 472: @@
 Badness (Sintel): 1.19
 == Bisemidim ==

Hkm: /* Uruguay */

2026-07-23T05:17:06Z

Uruguay

← Older revision		Revision as of 05:17, 23 July 2026
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	Badness (Sintel): 1.86		Badness (Sintel): 1.86

	~~==== Uruguay ====~~
	~~Subgroup: 2.3.5.7.11.13~~

	~~Comma list: 56/55, 78/77, 100/99, 1183/1152~~

	~~Mapping: {{mapping\| 1 -8 -8 -9 2 0 \| 0 13 14 16 2 5 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1199.6132{{c}}, ~5/3 = 884.7325{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.0005{{c}}

	~~{{Optimal ET sequence\|legend=0\| 19, 42e }}~~

	~~Badness (Sintel): 2.51~~

	== Bisemidim ==		== Bisemidim ==

Hkm: /* Gilead */

2026-07-22T17:40:42Z

Gilead

← Older revision		Revision as of 17:40, 22 July 2026
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	Badness (Sintel): 1.27		Badness (Sintel): 1.27

	~~== Gilead ==~~
	~~: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].''~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 126/125, 343/324~~

	~~{{Mapping\|legend=1\| 1 -5 -5 -6 \| 0 9 10 12 }}~~
	~~: mapping generators: ~2, ~5/3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1201.4516{{c}}, ~5/3 = 879.6394{{c}}
	~~: [[error map]]: {{val\| +1.452 +7.542 +2.823 -21.862 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 878.7223{{c}}
	~~: error map: {{val\| 0.000 +6.545 +0.909 -24.159 }}~~

	~~{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd }}~~

	~~[[Badness]] (Sintel): 2.92~~

	== Supersensi ==		== Supersensi ==

FloraC: Text replacement - "octave" to "octave"

2026-07-14T14:15:08Z

Text replacement - "octave" to "octave"

← Older revision		Revision as of 14:15, 14 July 2026
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	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''

	Named by [[User:Xenllium\|Xenllium]] in 2026, xenial may be described as the {{nowrap\| 19 & 70 }} temperament, splitting the [[8/3\|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2\|perfect fifth]] above 7 [[~~2/1\|~~octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.		Named by [[User:Xenllium\|Xenllium]] in 2026, xenial may be described as the {{nowrap\| 19 & 70 }} temperament, splitting the [[8/3\|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2\|perfect fifth]] above 7 [[octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

← Older revision		Revision as of 14:26, 11 September 2026
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	* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]		* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]
	* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate\|Passion family]]		* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate\|Passion family]]
			* ''[[Ripple]]'' (+405/392) → [[Ripple family #Septimal ripple\|Ripple family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
	* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]