1375/1372: Difference between revisions
Created page with "{{Infobox Interval | Name = moctdel comma | Color name = 1or<sup>3</sup>y<sup>3</sup>-3, lotriruyo negative 3rd, <br>Lotriruyo comma | Comma = yes }} '''1375/1372''', the '''m..." |
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'''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''' 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 === | |||
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. | |||
== See also == | == See also == | ||
Revision as of 16:47, 6 October 2024
| Interval information |
Lotriruyo comma
1375/1372, the moctdel comma is a no-threes 11-limit comma with a size of 3.78 cents. It is the amount by which a stack of three 7/5s falls short of 11/4, undecimal eleventh (one octave above 11/8). Some rank-two temperaments such as miracle, octoid and grendel temper out this comma, and from this it derives its name.
Temperaments
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.