1375/1372: Difference between revisions
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'''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]]). | '''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 == | == Temperaments == | ||
[[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. | [[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 | 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 [[Moctdelismic clan]] for the [[clan of temperaments]] where it is tempered out. | See [[Moctdelismic clan]] for the [[clan of temperaments]] where it is tempered out. | ||
Latest revision as of 16:43, 8 November 2026
| Interval information |
moctdelic comma
Lotriruyo comma
1375/1372, the moctdelisma or moctdelic comma is a small no-3's 11-limit comma with a size of 3.78 cents. 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 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 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 Moctdelismic clan for the clan of temperaments where it is tempered out.