1375/1372: Difference between revisions
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The use of *moctdelismic* implies the comma name *moctdelisma* |
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{{Infobox | {{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 | | Color name = 1or<sup>3</sup>y<sup>3</sup>-3, lotriruyo negative 3rd, <br>Lotriruyo comma | ||
| Comma = yes | | 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. | ||
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 | == 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 == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[Moctdelismic clan]] | |||
[[Category: | [[Category:Moctdelismic]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 10:48, 10 January 2026
| Interval information |
moctdelisma
Lotriruyo comma
1375/1372, the moctdel comma or moctdelisma 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
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: [⟨1 0 0 0 2], ⟨0 1 0 0 0], ⟨0 0 1 0 -3], ⟨0 0 0 1 3]]
- 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: 12, 19e, 29, 31, 41, 72, 152, 224
Badness (Sintel): 0.723
Moctdelic
Comma list: 1375/1372
Subgroup: 2.5.7.11
Mapping: [⟨1 0 0 2], ⟨0 1 0 -3], ⟨0 0 1 3]]
- WE: ~2 = 1200.056¢, ~5 = 2785.862¢, ~7 = 3369.486¢
- CWE: ~2 = 1200.000¢, ~5 = 2785.789¢, ~7 = 3369.416¢
Optimal ET sequence: 25, 29, 31, 37
Badness (Sintel): 0.110