1375/1372: Difference between revisions

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{{Infobox interval

| Name = ~~moctdel~~ comma

| Name = moctdelisma, moctdelic comma

| 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 '''moctdelisma''' or '''moctdelic comma''' is a [[small comma|small]] no-3's [[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]], the undecimal semi-augmented eleventh (one octave above [[11/8]]).

In terms of other commas, it is the difference between [[50/49]] and [[56/55]], between [[99/98]] and [[126/125]], and between [[225/224]] and [[441/440]]. In the [[13-limit]], it factors into [[superparticular]] commas as ([[625/624]])⋅([[1716/1715]]), and in the [[17-limit]], ([[715/714]])⋅([[1275/1274]]).

== 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 in the full [[11-limit]] leads to the rank-4 [[moctdelismic]] temperament, and in its minimal prime [[subgroup]] of 2.5.7.11, the [[moctdelic]] temperament. Some rank-2 temperaments such as [[miracle]], [[octoid]] and [[grendel]] temper out this comma, and from this it derives its name.

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~~.

~~=== 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~~

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 generator steps find 5/4, four find [[11/7]]~[[25/16]] and seven find [[11/5]], which is the (no-3's) 11-limit version of [[didacus]], a very strong temperament of the 2.5.7.11 subgroup.

== See ~~also ==~~

See [[Moctdelismic clan]] for the [[clan of temperaments]] where it is tempered out.

* [[~~Small comma~~]]

* [[~~Moctdel~~ clan]]

[[Category:~~Moctdel~~]]

[[Category:Moctdelismic]]

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

@@ Line 1: / Line 1: @@
 {{Infobox interval
-| Name = moctdel comma
+| Name = moctdelisma, moctdelic comma
 | 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 '''moctdelisma''' or '''moctdelic comma''' is a [[small comma|small]] no-3's [[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]], the undecimal semi-augmented eleventh (one octave above [[11/8]]).
+In terms of other commas, it is the difference between [[50/49]] and [[56/55]], between [[99/98]] and [[126/125]], and between [[225/224]] and [[441/440]]. In the [[13-limit]], it factors into [[superparticular]] commas as ([[625/624]])⋅([[1716/1715]]), and in the [[17-limit]], ([[715/714]])⋅([[1275/1274]]).
 == 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 in the full [[11-limit]] leads to the rank-4 [[moctdelismic]] temperament, and in its minimal prime [[subgroup]] of 2.5.7.11, the [[moctdelic]] temperament. Some rank-2 temperaments such as [[miracle]], [[octoid]] and [[grendel]] temper out this comma, and from this it derives its name.
-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.
-=== 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
+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 generator steps find 5/4, four find [[11/7]]~[[25/16]] and seven find [[11/5]], which is the (no-3's) 11-limit version of [[didacus]], a very strong temperament of the 2.5.7.11 subgroup.
-== See also ==
+See [[Moctdelismic clan]] for the [[clan of temperaments]] where it is tempered out.
-* [[Small comma]]
-* [[Moctdel clan]]
-[[Category:Moctdel]]
+[[Category:Moctdelismic]]
 [[Category:Commas named by combining multiple temperament names]]

1375/1372: Difference between revisions

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