Subgroup temperaments - Revision history

Eliora: /* Daemotertiaschis */

2026-08-07T21:53:45Z

Daemotertiaschis

← Older revision		Revision as of 21:53, 7 August 2026
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	=== Daemotertiaschis ===		=== Daemotertiaschis ===
	{{See also\|Schismatic family#Tertiaschis}}		{{See also\|Schismatic family#Tertiaschis}}
	Daemotertiaschis is produced by taking every other generator of tertiaschis, and the subgroup is chosen so it tempers out exactly the same commas. It is notable due to offering a [[7L 4s\|daemotonic 7L 4s]] scale of reasonable hardness, which is notoriously difficult to approximate with simple JI or RTT methods.		Daemotertiaschis is produced by taking every other generator of tertiaschis, and the subgroup is chosen so it tempers out exactly the same commas. It is notable due to offering a [[7L 4s\|daemotonic 7L 4s]] scale of reasonable hardness (hence the name ― daemo- + tertiaschis), which is notoriously difficult to approximate with simple JI or RTT methods.

	Subgroup: 2.9.5.7.33.13.17		Subgroup: 2.9.5.7.33.13.17

FilterNashi: /* 2.3.11/5.13/5 subgroup */

2026-08-03T13:54:33Z

2.3.11/5.13/5 subgroup

← Older revision		Revision as of 13:54, 3 August 2026
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1199.~~993~~{{c}}, ~169/165 = 41.~~292~~{{c}}		* WE: ~2 = 1199.9934923{{c}}, ~169/165 = 41.2918271{{c}}
	: error map: {{val\| -0.~~007~~ -0.~~000~~ +0.~~157~~ -0.~~010~~}}		: error map: {{val\| -0.0065077 -0.0004485 +0.1565720 -0.0103579}}
	* CWE: ~2 = ~~1200.000{{c}}~~, ~169/165 = 41.~~292~~{{c}}		* CWE: ~2 = 2/1, ~169/165 = 41.2917463{{c}}
	: error map: {{val\| +0.~~000~~ +0.~~005~~ +0.~~163~~ -0.~~005~~}}		: error map: {{val\| 0.0000000 +0.0046870 +0.1627569 -0.0043781}}

	edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233		edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233

FilterNashi: /* 2.3.13/5 subgroup */convincing precision

2026-08-03T13:50:16Z

2.3.13/5 subgroup: convincing precision

← Older revision		Revision as of 13:50, 3 August 2026
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	{{Mapping\|legend=2\| 1 1 1 \| 0 17 11 }}		{{Mapping\|legend=2\| 1 1 1 \| 0 17 11 }}
	: mapping generators: ~2, ~2250/2197		: mapping generators: ~2, ~2250/2197

	~~{{Todo\|inline=1\|correct maths\|comment=Optimal tunings and error maps showed below is not yet precise enough.}}~~

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.~~000~~{{c}}, ~2250/2197 = 41.~~291~~{{c}}		* WE: ~2 = 1200.0001354{{c}}, ~2250/2197 = 41.2914993{{c}}
	: error map: {{val\| +0.~~000~~ +0.~~001~~ -0.~~007~~}}		: error map: {{val\| +0.0001354 +0.0006234 -0.0073197}}
	* CWE: ~2 = ~~1200.000{{c}}~~, ~2250/2197 = 41.~~292~~{{c}}		* CWE: ~2 = 2/1, ~2250/2197 = 41.2915011{{c}}
	: error map: {{val\| +0.~~000~~ +0.~~001~~ -0.~~007~~}}		: error map: {{val\| 0.0000000 +0.0005177 -0.0074359}}

	edos: 29, 465, 494, 436, 523, 407, 378, 349, 30[-3], 28[+3], 320, 291, 59[-3], 262		edos: 29, 465, 494, 436, 523, 407, 378, 349, 30[-3], 28[+3], 320, 291, 59[-3], 262

Overthink: /* Supramin */ add note

2026-07-30T15:48:12Z

Supramin: add note

← Older revision		Revision as of 15:48, 30 July 2026
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	=== Supramin ===		=== Supramin ===
	This is a remarkable low-complexity microtemperament that contains the 14:17:19 triad within just four generator steps. An excellent tuning is [[25edo]], which provides an accurate yet tone-efficient tuning of this temperament. It was named by [[User:Overthink\|Overthink]] in 2026 after the fact that the generator is a [[17/14]] supraminor third, two of which reach [[28/19]].		This is a remarkable low-complexity microtemperament that contains the 14:17:19 triad within just four generator steps. An excellent tuning is [[25edo]], which provides an accurate yet tone-efficient tuning of this temperament. It was named by [[User:Overthink\|Overthink]] in 2026 after the fact that the generator is a [[17/14]] supraminor third, two of which reach [[28/19]]. It is related to [[cohemimabila]].

	[[Subgroup]]: 2.17/7.19/7		[[Subgroup]]: 2.17/7.19/7

FloraC: Move MVP archagall and archagall here

2026-07-22T16:05:06Z

Move MVP archagall and archagall here

← Older revision		Revision as of 16:05, 22 July 2026
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	{{Optimal ET sequence\|legend=1\| 5, 13c, 18, 23, 41, 64, 87, 151 }}		{{Optimal ET sequence\|legend=1\| 5, 13c, 18, 23, 41, 64, 87, 151 }}

			== 2.75.85 subgroup ==
			=== MVP archagall ===
			By tempering out the comma [[24576/24565]] in the 2.75.85 subgroup, we have three [[85/64]]'s up and one octave down as a [[75/64]] and we have two [[128/85]]'s up and one octave down as a [[17/15]] whole tone. It is because of this combination of accuracy, efficiency and mapping-wise simplicity and its corresponding explanatory power in what this comma does that the comma has been named the ''archagallisma''. The ''MVP'' stands for ''minimum viable product'', as this is the core of what the archagall logic achieves, with further extensions adding to the subgroup while avoiding significantly impacting its accuracy. This is a highly accurate temperament that could be considered to be encoding the "high-accuracy logic" of [[superpyth]] and which is inescapably related to the [[17L 5s]] scale form as it is the 17 & 22 temperament (or less accurately, the 5 & 17 temperament) in the 2.75.85 subgroup.

			[[Subgroup]]: 2.75.85

			[[Comma list]]: 24576/24565 ({{monzo\| 13 1 -3 }})

			{{Mapping\|legend=2\| 1 2 5 \| 0 3 1 }}
			: mapping generators: ~2, ~85/32

			[[Optimal tuning]]s:
			* [[Tp tuning\|Subgroup]] [[WE]]: ~2 = 1199.9692{{c}}, ~85/64 = 491.5853{{c}}
			* [[Tp tuning\|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~85/64 = 491.5794{{c}}

			{{Optimal ET sequence\|legend=1\| 5, 12, 17, 22, 61, 83, 310, 393, 476, 1345, 1821, 4118, 5939, 7760* }}

			== 2.75.9/7.85 subgroup ==
			=== Archagall ===
			A fairly natural way to extend [[#MVP archagall\|MVP archagall]] is by tempering out [[2025/2023]] ([[S-expression\|S15/S17]]), which equates a stack of two [[17/15]]'s with [[9/7]] without much damage. As 9/7 was not previously in the subgroup, this does not decrease the rank of the temperament and qualifies a proper and natural extension. We can equally get the same temperament by tempering out S15/S16 instead (equating a stack of three [[16/15]]'s with [[17/14]]); however, [[16/15]] is not in the subgroup, so it is preferred to think of it as adding 2025/2023.

			[[Subgroup]]: 2.75.9/7.85

			[[Comma list]]: 2025/2023 ({{monzo\| 2 -2 1 0 }}), 24576/24565 ({{monzo\| 13 1 0 -3 }})

			{{Mapping\|legend=2\| 1 2 6 5 \| 0 3 -4 1 }}
			: mapping generators: ~2, ~85/32

			[[Optimal tuning]]s:
			* [[Tp tuning\|Subgroup]] [[WE]]: ~2 = 1200.0241{{c}}, ~85/64 = 491.3358{{c}}
			* [[Tp tuning\|Subgroup]] [[CWE]]: ~2 = 1200.0000{{c}}, ~85/64 = 491.3290{{c}}

			{{Optimal ET sequence\|legend=1\| 5, 12, 17, 22, 83, 105, 127, 403, 530, 657, 784, 1441* }}

	== 4.3.5 subgroup ==		== 4.3.5 subgroup ==

Fredg999: /* 2.3.13/5 subgroup */ More specific todo category (not a perfect match, but a good spot to be found by someone who can help)

2026-07-11T05:31:43Z

2.3.13/5 subgroup: More specific todo category (not a perfect match, but a good spot to be found by someone who can help)

← Older revision		Revision as of 05:31, 11 July 2026
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	: mapping generators: ~2, ~2250/2197		: mapping generators: ~2, ~2250/2197

	{{Todo\|inline=1\| comment=Optimal tunings and error maps showed below is not yet precise enough.}}		{{Todo\|inline=1\|correct maths\|comment=Optimal tunings and error maps showed below is not yet precise enough.}}

	Optimal tunings:		Optimal tunings:

FloraC: Move darian calendar here

2026-07-02T12:48:38Z

Move darian calendar here

@@ Line 12: / Line 12: @@
 = Composite subgroup temperaments =
 == 2.9.5.7 subgroup ==
 See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]].

Hkm at 03:42, 30 June 2026

2026-06-30T03:42:02Z

← Older revision		Revision as of 03:42, 30 June 2026
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	[[Category:Subgroup temperaments\| ]] <!-- main article -->		[[Category:Subgroup temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
			[[Category:Rank 2]]
	{{Todo\| review \| cleanup }}		{{Todo\| review \| cleanup }}

FloraC: /* 2.….11/7.… subgroups */ move blackweed here

2026-06-28T10:47:20Z

2.….11/7.… subgroups: move blackweed here

@@ Line 1,551: / Line 1,551: @@
 == 2.….11/7.… subgroups ==
 === Pepperoni ===
 {{Main| Parapyth }}

FilterNashi: /* 2.3.11/5.13/5 subgroup */

2026-06-24T11:04:53Z

2.3.11/5.13/5 subgroup

← Older revision		Revision as of 11:04, 24 June 2026
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	: error map: {{val\| -0.007 -0.000 +0.157 -0.010}}		: error map: {{val\| -0.007 -0.000 +0.157 -0.010}}
	* CWE: ~2 = 1200.000{{c}}, ~169/165 = 41.292{{c}}		* CWE: ~2 = 1200.000{{c}}, ~169/165 = 41.292{{c}}
	: error map: {{val\| -0.000 +0.005 0.163 -0.005}}		: error map: {{val\| +0.000 +0.005 +0.163 -0.005}}

	edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233		edos: 29, 465, 494, 436, 523, 407, 378, 349, 320, 291, 30[-3], 262, 28[+3], 233