1375/1372: Difference between revisions

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== Temperaments ==

Tempering out this comma leads to the rank-4 '''moctdel temperament''' in the full [[11-limit]], and moctdelic temperament in its minimal prime [[subgroup]] of 2.5.7.11.

Tempering out this comma leads to the rank-4 '''moctdel temperament''' in the full [[11-limit]], and '''moctdelic temperament''' in its minimal prime [[subgroup]] of 2.5.7.11.

In the 2.7/5.11 subgroup it creates a very efficient temperament with a generator of 7/5, two of which equals [[55/28]] and three of which equals [[11/4]] as discussed. If we split the generator in 3, we get [[~]][[28/25]] which is notable as the difference between [[5/4]] and [[7/5]] so that two gens finds 5/4, four gens finds [[25/16]]~[[11/7]] and seven gens finds [[11/5]], which is the (no-3's) 11-limit version of [[didacus]], a very strong temperament of the 2.5.7.11 subgroup.

=== Moctdel ===

[[Comma list]]: 1375/1372

[[Subgroup]]: full 11-limit

{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 0 | 0 0 1 0 -3 | 0 0 0 1 3 }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.056¢, ~3 = 1901.955¢, ~5 = 2785.862¢, ~7 = 3369.486¢

* [[CWE]]: ~2 = 1200.000¢, ~3 = 1901.910¢, ~5 = 2785.789¢, ~7 = 3369.416¢

{{Optimal ET sequence|legend=1| 12, 19e, 29, 31, 41, 72, 152, 224 }}

[[Badness]] (Sintel): 0.723

=== Moctdelic ===

@@ Line 7: / Line 7: @@
 == Temperaments ==
-Tempering out this comma leads to the rank-4 '''moctdel temperament''' in the full [[11-limit]], and moctdelic temperament in its minimal prime [[subgroup]] of 2.5.7.11.
+Tempering out this comma leads to the rank-4 '''moctdel temperament''' in the full [[11-limit]], and '''moctdelic temperament''' in its minimal prime [[subgroup]] of 2.5.7.11.
 In the 2.7/5.11 subgroup it creates a very efficient temperament with a generator of 7/5, two of which equals [[55/28]] and three of which equals [[11/4]] as discussed. If we split the generator in 3, we get [[~]][[28/25]] which is notable as the difference between [[5/4]] and [[7/5]] so that two gens finds 5/4, four gens finds [[25/16]]~[[11/7]] and seven gens finds [[11/5]], which is the (no-3's) 11-limit version of [[didacus]], a very strong temperament of the 2.5.7.11 subgroup.
+=== Moctdel ===
+[[Comma list]]: 1375/1372
+[[Subgroup]]: full 11-limit
+{{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 0 | 0 0 1 0 -3 | 0 0 0 1 3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.056¢, ~3 = 1901.955¢, ~5 = 2785.862¢, ~7 = 3369.486¢
+* [[CWE]]: ~2 = 1200.000¢, ~3 = 1901.910¢, ~5 = 2785.789¢, ~7 = 3369.416¢
+{{Optimal ET sequence|legend=1| 12, 19e, 29, 31, 41, 72, 152, 224 }}
+[[Badness]] (Sintel): 0.723
 === Moctdelic ===