7777/7776

Interval information

Ratio

7777/7776

Subgroup monzo

2.3.7.11.101 [-5 -5 1 1 1⟩

Size in cents

0.2226238¢

Name

power of 6 repdigit comma

FJS name

[math]\displaystyle{ \text{d2}^{7,11,101} }[/math]

Special properties

superparticular,
reduced

Tenney height (log₂ nd)

25.8498

Weil height (log₂ max(n, d))

25.85

Wilson height (sopfr(nd))

144

Open this interval in xen-calc

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

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