No-twos subgroup temperaments: Difference between revisions

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=== Mintra ===

~~: ''See also: [[No-twos subgroup temperaments #Mintaka|Mintaka]] and [[No-twos subgroup temperaments #Deneb|Deneb]].''~~

This temperament splits 27/7 (the BPS generator up a tritave) into three by means of [[11/7]] or, equivalently, [[7/1]] in three by means of [[21/11]], and is the intersection of BPS, [[#Deneb|deneb]], and [[#Mintaka|mintaka]] temperaments as well as the most natural temperament satisfied in the 3.5.7.11 subgroup in [[39edt]].

This temperament splits 27/7 (the BPS generator up a tritave) into three by means of [[11/7]] or, equivalently, [[7/1]] in three by means of [[21/11]], and is the intersection of BPS, Deneb, and Mintaka temperaments as well as the most natural temperament satisfied in the 3.5.7.11 subgroup in [[39edt]].

Subgroup: 3.5.7.11

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Comma list: 245/243, 1331/1323

Subgroup-val mapping: {{mapping| 1 ~~5 0~~ 1 | 0 -6 3 2 }}

Subgroup-val mapping: {{mapping| 1 -1 3 3 | 0 6 -3 -2 }}

mapping generators: ~3, ~21/11

: mapping generators: ~3, ~11/7

Optimal ~~tuning (~~CWE): ~3 = 1901.~~955~~{{c}}, ~11/7 = 780.~~752~~{{c}}

Optimal tunings:

* WE: ~3 = 1904.1393{{c}}, ~11/7 = 781.6168{{c}}

* CWE: ~3 = 1901.9550{{c}}, ~11/7 = 780.7525{{c}}

~~Supporting ETs~~: 39, 17, 56, 22, ~~5, 95, 12, 61, 73, 134, 27c, 151e, 100, 90~~

Badness (Sintel): 0.302

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Subgroup-val mapping: {{mapping| 1 5 0 1 10 | 0 -6 3 2 -13 }}

~~: mapping generators: ~3, ~21/11~~

Optimal ~~tuning (~~CWE): ~3 = 1901.~~955~~{{c}}, ~11/7 = 780.~~428~~{{c}}

Optimal tunings:

* WE: ~3 = 1903.9326{{c}}, ~11/7 = 781.1856{{c}}

* CWE: ~3 = 1901.9550{{c}}, ~11/7 = 780.4280{{c}}

~~Supporting ETs~~: 39, 17, 22, ~~56, 5f, 61, 95, 100, 134, 73f, 139cf, 83cf, 173e, 178cef~~

Optimal ET sequence: [[17edt|b17]], [[22edt|b22]], [[39edt|b39]], [[290edt|b229cde]]

Badness (Sintel): 0.373

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Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 4 -2 5 }}

: mapping generators: ~3, ~17/15

Optimal ~~tuning (~~CWE): ~3 = 1901.~~955~~{{c}}, ~17/15 = 220.~~142~~{{c}}

Optimal tunings:

* WE: ~3 = 1903.4591{{c}}, ~17/15 = 220.2094{{c}}

* CWE: ~3 = 1901.9550{{c}}, ~17/15 = 220.1420{{c}}

~~Supporting ETs~~: 26, 9, 17, 43, 69, 8, ~~35, 95, 61, 60, 121, 25g, 112, 44~~

Badness (Sintel): 0.177

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Optimal tunings:

* WE: ~13/9 = 634.~~144~~{{c}}, ~65/63 = 49.~~695~~{{c}}

* WE: ~13/9 = 634.1444{{c}}, ~65/63 = 49.6946{{c}}

* CWE: ~13/9 = 633.~~985~~{{c}}, ~65/63 = 49.~~733~~{{c}}

* CWE: ~13/9 = 633.9850{{c}}, ~65/63 = 49.7330{{c}}

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 === Mintra ===
-: ''See also: [[No-twos subgroup temperaments #Mintaka|Mintaka]] and [[No-twos subgroup temperaments #Deneb|Deneb]].''
+This temperament splits 27/7 (the BPS generator up a tritave) into three by means of [[11/7]] or, equivalently, [[7/1]] in three by means of [[21/11]], and is the intersection of BPS, [[#Deneb|deneb]], and [[#Mintaka|mintaka]] temperaments as well as the most natural temperament satisfied in the 3.5.7.11 subgroup in [[39edt]].
-This temperament splits 27/7 (the BPS generator up a tritave) into three by means of [[11/7]] or, equivalently, [[7/1]] in three by means of [[21/11]], and is the intersection of BPS, Deneb, and Mintaka temperaments as well as the most natural temperament satisfied in the 3.5.7.11 subgroup in [[39edt]].
 Subgroup: 3.5.7.11
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 Comma list: 245/243, 1331/1323
-Subgroup-val mapping: {{mapping| 1 5 0 1 | 0 -6 3 2 }}
+Subgroup-val mapping: {{mapping| 1 -1 3 3 | 0 6 -3 -2 }}
-mapping generators: ~3, ~21/11
+: mapping generators: ~3, ~11/7
-Optimal tuning (CWE): ~3 = 1901.955{{c}}, ~11/7 = 780.752{{c}}
+Optimal tunings:
+* WE: ~3 = 1904.1393{{c}}, ~11/7 = 781.6168{{c}}
+* CWE: ~3 = 1901.9550{{c}}, ~11/7 = 780.7525{{c}}
-Supporting ETs: 39, 17, 56, 22, 5, 95, 12, 61, 73, 134, 27c, 151e, 100, 90
+Optimal ET sequence: [[17edt|b17]], [[39edt|b39]], [[95edt|b95]], [[134edt|b134]], [[229edt|b229de]]
 Badness (Sintel): 0.302
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 Subgroup-val mapping: {{mapping| 1 5 0 1 10 | 0 -6 3 2 -13 }}
-: mapping generators: ~3, ~21/11
-Optimal tuning (CWE): ~3 = 1901.955{{c}}, ~11/7 = 780.428{{c}}
+Optimal tunings:
+* WE: ~3 = 1903.9326{{c}}, ~11/7 = 781.1856{{c}}
+* CWE: ~3 = 1901.9550{{c}}, ~11/7 = 780.4280{{c}}
-Supporting ETs: 39, 17, 22, 56, 5f, 61, 95, 100, 134, 73f, 139cf, 83cf, 173e, 178cef
+Optimal ET sequence: [[17edt|b17]], [[22edt|b22]], [[39edt|b39]], [[290edt|b229cde]]
 Badness (Sintel): 0.373
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 Subgroup-val mapping: {{mapping| 1 1 2 2 | 0 4 -2 5 }}
+: mapping generators: ~3, ~17/15
-Optimal tuning (CWE): ~3 = 1901.955{{c}}, ~17/15 = 220.142{{c}}
+Optimal tunings:
+* WE: ~3 = 1903.4591{{c}}, ~17/15 = 220.2094{{c}}
+* CWE: ~3 = 1901.9550{{c}}, ~17/15 = 220.1420{{c}}
-Supporting ETs: 26, 9, 17, 43, 69, 8, 35, 95, 61, 60, 121, 25g, 112, 44
+Optimal ET sequence: [[8edt|b8]], [[9edt|b9]], [[17edt|b17]], [[26edt|b26]], [[69edt|b69]], [[95edt|b95]], [[121edt|b121]]
 Badness (Sintel): 0.177
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 Optimal tunings:
-* WE: ~13/9 = 634.144{{c}}, ~65/63 = 49.695{{c}}
+* WE: ~13/9 = 634.1444{{c}}, ~65/63 = 49.6946{{c}}
-* CWE: ~13/9 = 633.985{{c}}, ~65/63 = 49.733{{c}}
+* CWE: ~13/9 = 633.9850{{c}}, ~65/63 = 49.7330{{c}}
 Optimal ET sequence: [[39edt|b39]], [[114edt|b114]], [[153edt|b153]], [[498edt|b498cf]], [[651edt|b651cf]]