Stearnsmic clan - Revision history

Xenllium at 05:57, 7 March 2026

2026-03-07T05:57:38Z

Overthink: /* No-five stearnsmic */ slightly expand on 11-limit extension

2026-01-10T21:09:24Z

No-five stearnsmic: slightly expand on 11-limit extension

← Older revision		Revision as of 21:09, 10 January 2026
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	=== Overview to extensions ===		=== Overview to extensions ===
	The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1\|5]]. Pogo adds [[32805/32768]], supers [[5120/5103]], echidna [[1728/1715]], and hedgehog [[50/49]]. Those are strong extensions. The others are weak. Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Septisuperfourth adds [[6144/6125]] and splits the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five. They all have neat extensions to the 11-limit via tempering out both [[540/539]] and [[4000/3993]].		The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1\|5]]. Pogo adds [[32805/32768]], supers [[5120/5103]], echidna [[1728/1715]], and hedgehog [[50/49]]. Those are strong extensions. The others are weak. Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Septisuperfourth adds [[6144/6125]] and splits the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five. They all have neat extensions to the 11-limit via tempering out both [[540/539]] and [[4000/3993]], as well as [[9801/9800]], so that [[11/10]] and [[9/7]] add up to the semioctave.

	Stearnsmic temperaments not listed include:		Stearnsmic temperaments not listed include:
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	* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth\|Escapade family]]		* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth\|Escapade family]]

	Considered below are pogo, supers, stearnscape, garistearn and decistearn.		Considered below are pogo, supers, stearnscape, garistearn and decistearn.

	== Pogo ==		== Pogo ==

FloraC: /* Pogo */ update

2025-12-28T07:09:52Z

Pogo: update

← Older revision		Revision as of 07:09, 28 December 2025
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	{{See also\| Schismatic family #Pogo }}		{{See also\| Schismatic family #Pogo }}

	The pogo temperament (94 &~~amp;~~ 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma.		The pogo temperament (94 & 130) tempers out the [[schisma]], whose amount of tempering of the fifth is just about right for the stearnsma and vice versa. It is also the temperament that reconciles the difference between [[tertiaschis]] and [[countertertiaschis]], using its semi-octave period.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	{{Mapping\|legend=1\| 2 1 22 2 \| 0 3 -24 5 }}		{{Mapping\|legend=1\| 2 1 22 2 \| 0 3 -24 5 }}
			: mapping generators: ~343/243, ~9/7

	[[Optimal tuning]] ([[POTE]]): ~343/243 = ~~1\2~~, ~9/7 = 433.901		[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{c}}

	{{Optimal ET sequence\|legend=1\| 36, 94, 130, 224, 354 }}		{{Optimal ET sequence\|legend=1\| 36, 94, 130, 224, 354 }}

	[[Badness]]: 0.079635		[[Badness]] (Smith): 0.079635

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 2 1 22 2 25 \| 0 3 -24 5 -25 }}		Mapping: {{mapping\| 2 1 22 2 25 \| 0 3 -24 5 -25 }}

	Optimal tuning (POTE): ~99/70 = ~~1\2~~, ~9/7 = 433.911		Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}

	{{Optimal ET sequence\|legend=1\| 36, 94, 130, 224, 354, 578 }}		{{Optimal ET sequence\|legend=0\| 36, 94, 130, 224, 354, 578 }}

	Badness: 0.031857		Badness (Smith): 0.031857

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 2 1 22 2 25 -2 \| 0 3 -24 5 -25 13 }}		Mapping: {{mapping\| 2 1 22 2 25 -2 \| 0 3 -24 5 -25 13 }}

	Optimal tuning (POTE): ~99/70 = ~~1\2~~, ~9/7 = 433.911		Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}

	{{Optimal ET sequence\|legend=1\| 36, 94, 130, 224, 354, 578 }}		{{Optimal ET sequence\|legend=0\| 36, 94, 130, 224, 354, 578 }}

	Badness: 0.017514		Badness (Smith): 0.017514

	== Supers ==		== Supers ==

FloraC: Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

2025-11-27T12:31:49Z

Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

← Older revision		Revision as of 12:31, 27 November 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Stearnsmic clan\| ]] <!-- main article -->		[[Category:Stearnsmic clan\| ]] <!-- main article -->
	[[Category:Hades]] <!-- key article -->		[[Category:Hades]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content"

2025-06-24T00:40:19Z

Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:40, 24 June 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Stearnsmic clan\| ]] <!-- main article -->		[[Category:Stearnsmic clan\| ]] <!-- main article -->
	[[Category:Hades]] <!-- key article -->		[[Category:Hades]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 04:47, 12 June 2025

2025-06-12T04:47:29Z

← Older revision		Revision as of 04:47, 12 June 2025
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	{{Mapping\|legend=1\| 2 1 22 2 \| 0 3 -24 5 }}		{{Mapping\|legend=1\| 2 1 22 2 \| 0 3 -24 5 }}

	~~{{Multival\|legend=1\| 6 -48 10 -90 -1 158 }}~~

	[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 433.901		[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 433.901
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	{{Mapping\|legend=1\| 2 1 -12 2 \| 0 3 23 5 }}		{{Mapping\|legend=1\| 2 1 -12 2 \| 0 3 23 5 }}

	~~{{Multival\|legend=1\| 6 46 10 59 -1 -106 }}~~

	[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 434.218		[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~9/7 = 434.218
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	: mapping generators: ~2450/2187, ~567/500		: mapping generators: ~2450/2187, ~567/500

	~~{{Multival\|legend=1\| 36 66 60 21 -6 -46 }}~~

	[[Optimal tuning]] ([[CTE]]): ~2450/2187 = 1\6, ~567/500 = 216.9394 (~245/243 = 16.9394)		[[Optimal tuning]] ([[CTE]]): ~2450/2187 = 1\6, ~567/500 = 216.9394 (~245/243 = 16.9394)
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	{{Mapping\|legend=1\| 94 149 0 264 \| 0 0 1 0 }}		{{Mapping\|legend=1\| 94 149 0 264 \| 0 0 1 0 }}

	~~{{Multival\|legend=1\| 0 94 0 149 0 -264 }}~~

	[[Optimal tuning]] ([[POTE]]): ~1029/1024 = 1\94, ~5/4 = 386.7805		[[Optimal tuning]] ([[POTE]]): ~1029/1024 = 1\94, ~5/4 = 386.7805
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	: mapping generators: ~15/14, ~135/98		: mapping generators: ~15/14, ~135/98

	~~{{Multival\|legend=1\| 30 20 50 -38 -5 60 }}~~

	[[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~135/98 = 553.810 (~36/35 = 46.190)		[[Optimal tuning]] ([[CTE]]): ~15/14 = 1\10, ~135/98 = 553.810 (~36/35 = 46.190)

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:44:00Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo\| 1 10 0 -6 }} = 118098/117649.		The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo\| 1 10 0 -6 }} = 118098/117649.

BudjarnLambeth: {{Technical data page}}

2025-04-13T10:06:11Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 10:06, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo\| 1 10 0 -6 }} = 118098/117649.		The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo\| 1 10 0 -6 }} = 118098/117649.

Tristanbay: made link to the newly-created stearnsma page

2024-10-24T18:46:31Z

made link to the newly-created stearnsma page

← Older revision		Revision as of 18:46, 24 October 2024
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	The '''stearnsmic clan''' tempers out the stearnsma, the no-fives comma {{monzo\| 1 10 0 -6 }} = 118098/117649.		The '''stearnsmic clan''' tempers out the [[stearnsma]], the no-fives comma {{monzo\| 1 10 0 -6 }} = 118098/117649.

	== No-five stearnsmic ==		== No-five stearnsmic ==

Godtone: /* Decistearn / add very good 23-limit extension (note: i calculated the 23-limit badness as 19-limit badness 23-limit dirichlet badness / 19-limit dirichlet badness; afaik that should be correct)

2024-07-02T16:14:38Z

Decistearn: add very good 23-limit extension (note: i calculated the 23-limit badness as 19-limit badness * 23-limit dirichlet badness / 19-limit dirichlet badness; afaik that should be correct)

← Older revision		Revision as of 16:14, 2 July 2024
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	Badness: 0.018232		Badness: 0.018232

			=== 23-limit ===
			By equating 16/13 with 69/56 and 85/69 (enabling 56:69:85 chords), we find [[23/16]] at 2 generators underneath 6 periods (which is the [[5edo]] fifth, [[10edo\|6\10]]).

			Subgroup: 2.3.5.7.11.13.17.19.23

			Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475, 897/896

			Mapping: {{mapping\| 10 2 14 5 30 37 27 24 36 \| 0 3 2 5 1 0 3 4 2 }}

			Optimal tuning (CTE): ~161/150 = 1\10, ~11/8 = 553.918 (~36/35 = 46.082)

			{{Optimal ET sequence\|legend=1\| 30dh, 50, 80, 130 }}

			Badness: 0.016719

	[[Category:Temperament clans]]		[[Category:Temperament clans]]