Breedsmic temperaments: Difference between revisions

Line 1,106:

Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224

Mapping: {{mapping|1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}

Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}

Optimal tunings:

Line 1,121:

Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224

Mapping: {{mapping|1 -25 -16 -13 -26 -6 -11 5 | 0 74 51 44 82 27 42 1}}

Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 5 | 0 74 51 44 82 27 42 1 }}

Optimal tunings:

Line 1,128:

== Hemigoldis ==

: ''For the 5-limit version, see [[Diaschismic–gothmic equivalence continuum #Goldis]].''

Though fairly complex in the [[7-limit]], hemigoldis does a lot better in badness metrics than pure 5-limit goldis, and yet again has many possible extensions to other primes. For example, two periods minus six generators yields a "tetracot second" which can be interpreted as ~[[21/19]] to add prime 19 or perhaps more accurately ~[[31/28]] to add prime 7, or even simply as ~[[32/29]] to add prime 29, though the other two have the benefit of clearly connecting to the 7-limit representation. Note that again [[89edo]] is a possible tuning for combining it with flat nestoria and not appearing in the optimal ET sequence.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 2401/2400, 549755813888/533935546875

: mapping generators: ~2, ~7/4

[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000, ~7/4 = 970.690

{{Optimal ET sequence|legend=1| 21, 47b, 68, 157, 382bccd, 529bccd }}

[[Badness]] (Sintel): 4.40

== Surmarvelpyth ==

@@ Line 1,106: / Line 1,106: @@
 Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
-Mapping: {{mapping|1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}
+Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}
 Optimal tunings:
@@ Line 1,121: / Line 1,121: @@
 Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
-Mapping: {{mapping|1 -25 -16 -13 -26 -6 -11 5 | 0 74 51 44 82 27 42 1}}
+Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 5 | 0 74 51 44 82 27 42 1 }}
 Optimal tunings:
@@ Line 1,128: / Line 1,128: @@
 {{Optimal ET sequence|legend=0| 103, 167, 270 }}
+== Hemigoldis ==
+: ''For the 5-limit version, see [[Diaschismic–gothmic equivalence continuum #Goldis]].''
+Though fairly complex in the [[7-limit]], hemigoldis does a lot better in badness metrics than pure 5-limit goldis, and yet again has many possible extensions to other primes. For example, two periods minus six generators yields a "tetracot second" which can be interpreted as ~[[21/19]] to add prime 19 or perhaps more accurately ~[[31/28]] to add prime 7, or even simply as ~[[32/29]] to add prime 29, though the other two have the benefit of clearly connecting to the 7-limit representation. Note that again [[89edo]] is a possible tuning for combining it with flat nestoria and not appearing in the optimal ET sequence.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 549755813888/533935546875
+{{Mapping|legend=1| 1 21 -9 2 | 0 -24 14 1 }}
+: mapping generators: ~2, ~7/4
+[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000, ~7/4 = 970.690
+{{Optimal ET sequence|legend=1| 21, 47b, 68, 157, 382bccd, 529bccd }}
+[[Badness]] (Sintel): 4.40
 == Surmarvelpyth ==