1375/1372: Difference between revisions

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{{Infobox ~~Interval~~

{{Infobox interval

| Name = moctdel comma

| Name = moctdel comma, moctdelisma

| Color name = 1or3y3-3, lotriruyo negative 3rd, Lotriruyo comma

| Comma = yes

}}

'''1375/1372''', the '''moctdel comma''' is a no-threes [[11-limit]] comma with a size of 3.78 [[cent]]s. It is the amount by which a stack of three [[7/5]]s falls short of [[11/4]], undecimal eleventh (one octave above [[11/8]]). Some rank-two temperaments such as [[Gamelismic clan|miracle]], [[Ragismic microtemperaments|octoid]] and [[Mirkwai clan|grendel]] temper out this comma, and from this it derives its name.

'''1375/1372''', the '''moctdel comma''' or '''moctdelisma''' is a no-threes [[11-limit]] comma with a size of 3.78 [[cent]]s. It is the amount by which a stack of three [[7/5]]s falls short of [[11/4]], undecimal eleventh (one octave above [[11/8]]). Some rank-two temperaments such as [[Gamelismic clan|miracle]], [[Ragismic microtemperaments|octoid]] and [[Mirkwai clan|grendel]] temper out this comma, and from this it derives its name.

== Temperaments ==

Tempering out this comma leads to the rank-4 '''moctdelismic 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.

=== Moctdelismic ===

[[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 ===

[[Comma list]]: 1375/1372

[[Subgroup]]: 2.5.7.11

[[Optimal tuning]]s:

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

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

[[Badness]] (Sintel): 0.110

== See also ==

* [[Small comma]]

* [[Moctdelismic clan]]

[[Category:~~Moctdel~~]]

[[Category:Moctdelismic]]

[[Category:Commas named by combining multiple temperament names]]

@@ Line 1: / Line 1: @@
-{{Infobox Interval
+{{Infobox interval
-| Name = moctdel comma
+| Name = moctdel comma, moctdelisma
 | Color name = 1or<sup>3</sup>y<sup>3</sup>-3, lotriruyo negative 3rd, <br>Lotriruyo comma
 | Comma = yes
 }}
-'''1375/1372''', the '''moctdel comma''' is a no-threes [[11-limit]] comma with a size of 3.78 [[cent]]s. It is the amount by which a stack of three [[7/5]]s falls short of [[11/4]], undecimal eleventh (one octave above [[11/8]]). Some rank-two temperaments such as [[Gamelismic clan|miracle]], [[Ragismic microtemperaments|octoid]] and [[Mirkwai clan|grendel]] temper out this comma, and from this it derives its name.
+'''1375/1372''', the '''moctdel comma''' or '''moctdelisma''' is a no-threes [[11-limit]] comma with a size of 3.78 [[cent]]s. It is the amount by which a stack of three [[7/5]]s falls short of [[11/4]], undecimal eleventh (one octave above [[11/8]]). Some rank-two temperaments such as [[Gamelismic clan|miracle]], [[Ragismic microtemperaments|octoid]] and [[Mirkwai clan|grendel]] temper out this comma, and from this it derives its name.
+== Temperaments ==
+Tempering out this comma leads to the rank-4 '''moctdelismic 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.
+=== Moctdelismic ===
+[[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 ===
+[[Comma list]]: 1375/1372
+[[Subgroup]]: 2.5.7.11
+{{Mapping|legend=1| 1 0 0 2 | 0 1 0 -3 | 0 0 1 3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.056¢, ~5 = 2785.862¢, ~7 = 3369.486¢
+* [[CWE]]: ~2 = 1200.000¢, ~5 = 2785.789¢, ~7 = 3369.416¢
+{{Optimal ET sequence|legend=1| 25, 29, 31, 37 }}
+[[Badness]] (Sintel): 0.110
 == See also ==
 * [[Small comma]]
+* [[Moctdelismic clan]]
-[[Category:Moctdel]]
+[[Category:Moctdelismic]]
+[[Category:Commas named by combining multiple temperament names]]