7777/7776: Difference between revisions
named the comma and I'll create a separate temperament page |
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| Name = power of 6 repdigit comma | | Name = power of 6 repdigit comma | ||
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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''' or '''pulsar 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]]. It is also the difference between 404/243 and 128/77. | 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. | ||
The name origin is the following: '''p'''ower of '''s'''ix '''r'''epdigit - '''psr''', which is the astronomical shortening for pulsars. | |||
== Temperaments == | == Temperaments == | ||
Tempering it out leads to the pulsar clan of temperaments, the core of which is the 2.3.7.11.101 subgroup. Some of the EDOs which support pulsar temperaments are [[135edo|135]], {{EDOs|342, 207, 1012, 477, 1147, 971, 270, 836, 877}}. Note that 270edo is a multiple of 135edo. | |||
=== 135 & 836 === | === 135 & 836 === | ||
Revision as of 11:32, 30 May 2022
| Interval information |
reduced
7777/7776, the power of 6 repdigit comma or pulsar 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.
The name origin is the following: power of six repdigit - psr, which is the astronomical shortening for pulsars.
Temperaments
Tempering it out leads to the pulsar clan of temperaments, the core of which is the 2.3.7.11.101 subgroup. Some of the EDOs which support pulsar temperaments are 135, 342, 207, 1012, 477, 1147, 971, 270, 836, 877. Note that 270edo is a multiple of 135edo.
135 & 836
Proposed name: White dwarf
Subgroup: 2.3.7.11.101
Mapping: ⟨⟨1 -4 3 5 -23]], ⟨⟨0 29 -1 -8 154]]
POTE Generator: 231.1022c ~8/7