Subgroup temperaments: Difference between revisions

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=== Daemotertiaschis ===

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

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: 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:

* 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

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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

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=== 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

@@ Line 88: / Line 88: @@
 === Daemotertiaschis ===
 {{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
@@ Line 1,738: / Line 1,738: @@
 {{Mapping|legend=2| 1 1 1 | 0 17 11 }}
 : 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:
-* 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
@@ Line 1,761: / Line 1,759: @@
 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
@@ Line 1,825: / Line 1,823: @@
 === 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