Stearnsmic clan - Revision history

FloraC: + link to gamelstearn

2026-10-03T08:28:37Z

+ link to gamelstearn

← Older revision		Revision as of 08:28, 3 October 2026
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	* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth\|Escapade family]]		* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth\|Escapade family]]
	* ''[[Decistearn]]'' (+3136/3125) → [[Trisedodge family #Decistearn\|Trisedodge family]]		* ''[[Decistearn]]'' (+3136/3125) → [[Trisedodge family #Decistearn\|Trisedodge family]]
			* ''[[Gamelstearn]]'' (+1029/1024) → [[Compton family #Gamelstearn\|Compton family]]
	* ''[[Garistearn]]'' (+33554432/33480783) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]		* ''[[Garistearn]]'' (+33554432/33480783) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]

FloraC: /* Hedgehog */ missing parenthesis

2026-10-02T16:27:09Z

Hedgehog: missing parenthesis

← Older revision		Revision as of 16:27, 2 October 2026
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	{{See also\| Sensamagic clan }}		{{See also\| Sensamagic clan }}

	Hedgehog is a relatively low-accuracy temperament which tempers out 50/49 ([[jubilisma]], 245/243 ([[sensamagic comma]]), 250/243 ([[porcupine comma]]), and 2430/2401 ([[nuwell comma]]). It is also a strong extension of [[BPS]].		Hedgehog is a relatively low-accuracy temperament which tempers out 50/49 ([[jubilisma]]), 245/243 ([[sensamagic comma]]), 250/243 ([[porcupine comma]]), and 2430/2401 ([[nuwell comma]]). It is also a strong extension of [[BPS]].

	22edo provides an obvious tuning, which happens to be the only [[patent val\|patent-val]] edo tuning, but if you are looking for an alternative you could try the {{val\| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note [[mos]] gives scope for harmony while stopping well short of 22. A related temperament is [[#Echidna\|echidna]], which offers much more accuracy. They merge on 22edo.		22edo provides an obvious tuning, which happens to be the only [[patent val\|patent-val]] edo tuning, but if you are looking for an alternative you could try the {{val\| 146 232 338 411 }} (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note [[mos]] gives scope for harmony while stopping well short of 22. A related temperament is [[#Echidna\|echidna]], which offers much more accuracy. They merge on 22edo.

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:43Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:38, 30 September 2026
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	[[Comma list]]: 118098/117649		[[Comma list]]: 118098/117649

	{{Mapping\|legend=2\| 2 1 2 \| 0 3 5 }}		{{Mapping\|legend=3\| 2 1 2 \| 0 3 5 }}

	{{Mapping\|legend=5\| 2 1 0 2 \| 0 3 0 5 }}		{{Mapping\|legend=5\| 2 1 0 2 \| 0 3 0 5 }}

FloraC: Text replacement - "{{Mapping|legend=3| " to "{{Mapping|legend=5| "

2026-09-30T17:34:06Z

Text replacement - "{{Mapping|legend=3| " to "{{Mapping|legend=5| "

← Older revision		Revision as of 17:34, 30 September 2026
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	{{Mapping\|legend=2\| 2 1 2 \| 0 3 5 }}		{{Mapping\|legend=2\| 2 1 2 \| 0 3 5 }}

	{{Mapping\|legend=3\| 2 1 0 2 \| 0 3 0 5 }}		{{Mapping\|legend=5\| 2 1 0 2 \| 0 3 0 5 }}
	: mapping generators: ~343/243, ~9/7		: mapping generators: ~343/243, ~9/7

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

2026-09-24T12:33:21Z

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

Show changes

FloraC: Sorting (stearnscape is more complex than I thought)

2026-09-20T03:19:37Z

Sorting (stearnscape is more complex than I thought)

@@ Line 27: / Line 27: @@
 The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo (94 & 130) adds [[32805/32768]], supers (58 & 94) adds [[5120/5103]], echidna (22 & 58) adds [[1728/1715]], and hedgehog (14c & 22) adds [[50/49]]. Those are the [[strong extension]]s.
-Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Bisemidim adds [[126/125]]. Septisuperfourth adds [[6144/6125]]. Those split 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.
+Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Bisemidim adds [[126/125]]. Septisuperfourth adds [[6144/6125]]. Those split the generator in three. Stearnscape adds [[250047/250000]] and splits the period in three as well as the generator in two. Octoid adds [[4375/4374]] and splits the period in four. Decistearn adds [[3136/3125]] splits the period in five.
 All of them extend naturally 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 semi-octave period. For strong extensions, the generator can be taken to be ~11/10, and three ~11/10's then make a ~4/3 as a result of tempering out 4000/3993, making [[10/9]] and [[12/11]] equidistant from 11/10.
@@ Line 458: / Line 458: @@
 Badness (Sintel): 1.91
 == Stearnscape ==
@@ Line 523: / Line 573: @@
 Badness (Sintel): 0.782
 == Octoid ==

FloraC: Bisemidim belongs to this page

2026-09-20T03:13:17Z

Bisemidim belongs to this page

@@ Line 27: / Line 27: @@
 The second comma in the comma list determines how we extend it to include the [[harmonic]] [[5/1|5]]. Pogo (94 & 130) adds [[32805/32768]], supers (58 & 94) adds [[5120/5103]], echidna (22 & 58) adds [[1728/1715]], and hedgehog (14c & 22) adds [[50/49]]. Those are the [[strong extension]]s.
-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.
+Wizard adds [[225/224]]. Harry adds [[2401/2400]]. Those split the generator in two. Bisemidim adds [[126/125]]. Septisuperfourth adds [[6144/6125]]. Those split 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.
 All of them extend naturally 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 semi-octave period. For strong extensions, the generator can be taken to be ~11/10, and three ~11/10's then make a ~4/3 as a result of tempering out 4000/3993, making [[10/9]] and [[12/11]] equidistant from 11/10.
@@ Line 523: / Line 523: @@
 Badness (Sintel): 0.782
 == Octoid ==
-: {{Main| Octoid }}
+{{Main| Octoid }}
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Octoid]].''

FloraC: I deem it not worth noting, thanks!

2026-09-17T06:21:10Z

I deem it not worth noting, thanks!

← Older revision		Revision as of 06:21, 17 September 2026
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	==== Octopus ====		==== Octopus ====
	A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4.		A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4.

	(It is perhaps worth noting, for the purpose of the 56-note MOS scale (the smallest to reach [[9/8]], thus going one generator further than required to reach every prime), that if we were to use [[56edo]] to support it, we would have to use the val 56bccddeffg (using [[wart notation]]), corresponding to flattening every prime in the 19-limit from its [[patent val]] mapping (closest [[direct approximation]]) except for 2 and 19, corresponding to these only using periods to reach.)

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Godtone: /* Octopus */ link

2026-09-16T13:32:49Z

Octopus: link

← Older revision		Revision as of 13:32, 16 September 2026
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	A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4.		A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4.

	(It is perhaps worth noting, for the purpose of the 56-note MOS scale (the smallest to reach 9/8, thus going one generator further than required to reach every prime), that if we were to use [[56edo]] to support it, we would have to use the val 56bccddeffg (using [[wart notation]]), corresponding to flattening every prime in the 19-limit from its [[patent val]] mapping (closest [[direct approximation]]) except for 2 and 19, corresponding to these only using periods to reach.)		(It is perhaps worth noting, for the purpose of the 56-note MOS scale (the smallest to reach [[9/8]], thus going one generator further than required to reach every prime), that if we were to use [[56edo]] to support it, we would have to use the val 56bccddeffg (using [[wart notation]]), corresponding to flattening every prime in the 19-limit from its [[patent val]] mapping (closest [[direct approximation]]) except for 2 and 19, corresponding to these only using periods to reach.)

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Godtone: /* Octopus */ not sure how interesting this factoid is but 56-form is relevant

2026-09-16T13:31:52Z

Octopus: not sure how interesting this factoid is but 56-form is relevant

← Older revision		Revision as of 13:31, 16 September 2026
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	==== Octopus ====		==== Octopus ====
	A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4.		A reasonable alternative tuning of octopus not shown here which works well for 23-limit harmony (and beyond) is [[80edo]], which has a strong sharp tendency that can be thought of as matching the sharpness of mapping [[19/16]] to 1\4.

			(It is perhaps worth noting, for the purpose of the 56-note MOS scale (the smallest to reach 9/8, thus going one generator further than required to reach every prime), that if we were to use [[56edo]] to support it, we would have to use the val 56bccddeffg (using [[wart notation]]), corresponding to flattening every prime in the 19-limit from its [[patent val]] mapping (closest [[direct approximation]]) except for 2 and 19, corresponding to these only using periods to reach.)

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

← Older revision		Revision as of 08:28, 3 October 2026
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	* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth\|Escapade family]]		* ''[[Septisuperfourth]]'' (+6144/6125) → [[Escapade family #Septisuperfourth\|Escapade family]]
	* ''[[Decistearn]]'' (+3136/3125) → [[Trisedodge family #Decistearn\|Trisedodge family]]		* ''[[Decistearn]]'' (+3136/3125) → [[Trisedodge family #Decistearn\|Trisedodge family]]
			* ''[[Gamelstearn]]'' (+1029/1024) → [[Compton family #Gamelstearn\|Compton family]]
	* ''[[Garistearn]]'' (+33554432/33480783) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]		* ''[[Garistearn]]'' (+33554432/33480783) → [[94th-octave temperaments #Garistearn\|94th-octave temperaments]]