7777/7776: Difference between revisions
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'''7777/7776''', the '''power of 6 repdigit comma''' is an unnoticeable comma of 223 millicents, and it is a part of 101-limit just intonation. | '''7777/7776''', the '''power of 6 repdigit comma''' is an unnoticeable comma of 223 millicents, and it is a part of 101-limit just intonation. | ||
The comma derives from the resemblance of a perfect power of 6, 7776, to a repdigit number 7777. It is the difference between a stack of 5 [[6/1|hexataves]] and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, [[243/128]]. | The comma derives from the resemblance of a perfect power of 6, 7776, to a repdigit number 7777. It is the difference between a stack of 5 [[6/1|hexataves]] and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, [[243/128]]. It is also the difference between 404/243 and 128/77. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 20:22, 5 April 2022
| Interval information |
reduced
7777/7776, the power of 6 repdigit comma is an unnoticeable comma of 223 millicents, and it is a part of 101-limit just intonation.
The comma derives from the resemblance of a perfect power of 6, 7776, to a repdigit number 7777. It is the difference between a stack of 5 hexataves and 7, 11, and 101 harmonics stacked, or when octave-reduced, between 7/4, 11/8, and 101/64 and the Pythagorean major seventh, 243/128. It is also the difference between 404/243 and 128/77.
Temperaments
135edo supports a large amount of temperaments when it comes to this comma. Other EDOs which temper it out are 342, 207, 1012, 477, 1147, 971, 270, 836, 877. Note that 270edo is a multiple of 135edo.
135 & 836
Subgroup: 2.3.7.11.101
Mapping: ⟨⟨1 -4 3 5 -23]], ⟨⟨0 29 -1 -8 154]]
POTE Generator: 231.1022c ~8/7