Semaphoresmic clan: Difference between revisions

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Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes.

Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]] and [[105/104]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes.

=== 7-limit ===

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: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Negri (5-limit)]].''

Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.

Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 and/or 105/104 to the comma list; this will be discussed below under the title of negra.

=== 7-limit ===

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=== Wilsec ===

Wilsec splits the fifthward generator of negri in half for 11/8~15/11, tempering out [[121/120]]. Its ploidacot is gamma-octacot.

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 225/224

Mapping: {{mapping| 1 6 -1 ~~5 4~~ | 0 -8 6 -4 -1 }}

Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }}

: mapping generators: ~2, ~16/11

: mapping generators: ~2, ~11/8

Optimal tunings:

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Comma list: 49/48, 65/64, 91/90, 121/120

Mapping: {{mapping| 1 6 -1 ~~5 4 7~~ | 0 -8 6 -4 -1 -6 }}

Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}

Optimal tunings:

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Comma list: 49/48, 65/64, 91/90, 121/120, 154/153

Mapping: {{mapping| 1 6 -1 ~~5 4 7 -2~~ | 0 -8 6 -4 -1 -6 11 }}

Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}

Optimal tunings:

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Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153

Mapping: {{mapping| 1 6 -1 ~~5 4 7 -~~2 7 | 0 -8 6 -4 -1 -6 11 -5 }}

Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}

Optimal tunings:

@@ Line 68: / Line 68: @@
 {{Main| Semaphore and godzilla }}
-Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes.
+Godzilla tempers out [[81/80]], equating [[9/8]] and [[10/9]], so it finds the prime 5 at a stack of four fifths, as does any temperament in the [[meantone family]]. Like many entries of this clan, godzilla can be extended naturally to the 2.3.5.7.13 subgroup by identifying the hemifourth as ~15/13, tempering out [[91/90]] and [[105/104]]. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. [[Mos scale]]s are of 5, 9, or 14 notes.
 === 7-limit ===
@@ Line 335: / Line 335: @@
 : ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Negri (5-limit)]].''
-Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding [[91/90]] to the comma list; this will be discussed below under the title of negra.
+Negri tempers out the [[negri comma]] in the 5-limit, 49/48 and [[225/224]] in the 7-limit. It may be described as {{nowrap| 9 & 10 }}; its ploidacot is omega-tetracot. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 and/or 105/104 to the comma list; this will be discussed below under the title of negra.
 === 7-limit ===
@@ Line 494: / Line 494: @@
 === Wilsec ===
+Wilsec splits the fifthward generator of negri in half for 11/8~15/11, tempering out [[121/120]]. Its ploidacot is gamma-octacot.
 Subgroup: 2.3.5.7.11
 Comma list: 49/48, 121/120, 225/224
-Mapping: {{mapping| 1 6 -1 5 4 | 0 -8 6 -4 -1 }}
+Mapping: {{mapping| 1 -2 5 1 3 | 0 8 -6 4 1 }}
-: mapping generators: ~2, ~16/11
+: mapping generators: ~2, ~11/8
 Optimal tunings:
@@ Line 515: / Line 517: @@
 Comma list: 49/48, 65/64, 91/90, 121/120
-Mapping: {{mapping| 1 6 -1 5 4 7 | 0 -8 6 -4 -1 -6 }}
+Mapping: {{mapping| 1 -2 5 1 3 1 | 0 8 -6 4 1 6 }}
 Optimal tunings:
@@ Line 530: / Line 532: @@
 Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
-Mapping: {{mapping| 1 6 -1 5 4 7 -2 | 0 -8 6 -4 -1 -6 11 }}
+Mapping: {{mapping| 1 -2 5 1 3 1 9 | 0 8 -6 4 1 6 -11 }}
 Optimal tunings:
@@ Line 545: / Line 547: @@
 Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153
-Mapping: {{mapping| 1 6 -1 5 4 7 -2 7 | 0 -8 6 -4 -1 -6 11 -5 }}
+Mapping: {{mapping| 1 -2 5 1 3 1 9 2 | 0 8 -6 4 1 6 -11 5 }}
 Optimal tunings: