No-twos subgroup temperaments: Difference between revisions

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=== Alhena ===

~~{{Todo|inline=1|complete section|comment= Catalog~~ the ~~intermediate extension (~~3.5.7.11/2). }}

Alhena is a strong extension of BPS to the 3.5.7.11/2.13/4 subgroup that equates the "semitone" of [[27/25]]~[[49/45]] to [[13/12]], and then three of these intervals to [[14/11]].

~~This is a strong extension of BPS to the subgroup~~ 3.5.7.11/2.13/~~4 that equates the "semitone" of~~ [[~~27/25~~]]~[[~~49/45~~]] to [[~~13/12~~]], ~~and then three of these intervals to~~ [[14/11]].

Subgroup: 3.5.7.11/2

Comma list: 245/243 ({{monzo| -5 1 2 0 }}), 3773/3750 ({{monzo| -1 -4 3 1 }})

Optimal tunings:

* Subgroup WE: ~3 = 1903.6644{{c}}, ~9/7 = 441.3233{{c}}

* Subgroup CWE: ~3 = 1901.9550{{c}}, ~9/7 = 440.9989{{c}}

: <nowiki/>* é is used as the wart for 11/2.

==== 3.5.7.11/2.13/4 subgroup ====

Subgroup: 3.5.7.11/2.13/4

Comma list: 196/195, 325/324, 1001/1000

Comma list: 196/195 ({{monzo| -1 -1 2 0 -1 }}), 325/324 ({{monzo| -4 2 0 0 1 }}), 1001/1000 ({{monzo| 0 -3 1 1 1 }})

~~: mapping generators: ~3, ~9/7~~

Optimal tunings:

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This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of [[17/15]]. The name was suggested by [[MidnightBlue]] after ~~dubhe~~, a bright double star (the ninth brightest) and similarities to the word ''double''.

This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of [[17/15]]. The name was suggested by [[MidnightBlue]] after Dubhe, a bright double star (the ninth brightest) and similarities to the word ''double''.

Subgroup: 3.5.7.17

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== Antipyth ==

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== Juggernaut ==

{{Todo|inline=1|possibly rename juggernaut (Cole suggested the name "Macrodec", not sure about it yet though)}}

{{Todo|inline=1|rename|comment=CompactStar: possibly rename juggernaut (Cole suggested the name "Macrodec", not sure about it yet though)}}

@@ Line 82: / Line 82: @@
 === Alhena ===
-{{Todo|inline=1|complete section|comment= Catalog the intermediate extension (3.5.7.11/2). }}
+Alhena is a strong extension of BPS to the 3.5.7.11/2.13/4 subgroup that equates the "semitone" of [[27/25]]~[[49/45]] to [[13/12]], and then three of these intervals to [[14/11]].
-This is a strong extension of BPS to the subgroup 3.5.7.11/2.13/4 that equates the "semitone" of [[27/25]]~[[49/45]] to [[13/12]], and then three of these intervals to [[14/11]].
+Subgroup: 3.5.7.11/2
+Comma list: 245/243 ({{monzo| -5 1 2 0 }}), 3773/3750 ({{monzo| -1 -4 3 1 }})
+{{Mapping|legend=2| 1 1 2 -1 | 0 2 -1 11 }}
+Optimal tunings:
+* Subgroup WE: ~3 = 1903.6644{{c}}, ~9/7 = 441.3233{{c}}
+* Subgroup CWE: ~3 = 1901.9550{{c}}, ~9/7 = 440.9989{{c}}
+Optimal ET sequence: [[13edt|b13]], [[43edt|b43]], [[56edt|b56]], [[69edt|b69]], [[151edt|b151]], [[220edt|b220d]], [[289edt|b289dé]] *
+: <nowiki/>* é is used as the wart for 11/2.
 ==== 3.5.7.11/2.13/4 subgroup ====
 Subgroup: 3.5.7.11/2.13/4
-Comma list: 196/195, 325/324, 1001/1000
+Comma list: 196/195 ({{monzo| -1 -1 2 0 -1 }}), 325/324 ({{monzo| -4 2 0 0 1 }}), 1001/1000 ({{monzo| 0 -3 1 1 1 }})
 {{Mapping|legend=2| 1 1 2 -1 2 | 0 2 -1 11 -4 }}
-: mapping generators: ~3, ~9/7
 Optimal tunings:
@@ Line 142: / Line 153: @@
 {{Main| Dubhe }}
-This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of [[17/15]]. The name was suggested by [[MidnightBlue]] after dubhe, a bright double star (the ninth brightest) and similarities to the word ''double''.
+This temperament is a simple 3.5.7.17 weak extension of BPS that splits the generator of 9/7 into two intervals of [[17/15]]. The name was suggested by [[MidnightBlue]] after Dubhe, a bright double star (the ninth brightest) and similarities to the word ''double''.
 Subgroup: 3.5.7.17
@@ Line 832: / Line 843: @@
 == Antipyth ==
-{{Todo|inline=1|rename antipyth}}
+{{Todo|inline=1|rename}}
 {{Main| Antipyth }}
@@ Line 853: / Line 864: @@
 == Juggernaut ==
-{{Todo|inline=1|possibly rename juggernaut (Cole suggested the name "Macrodec", not sure about it yet though)}}
+{{Todo|inline=1|rename|comment=CompactStar: possibly rename juggernaut (Cole suggested the name "Macrodec", not sure about it yet though)}}
 {{Main| Juggernaut }}