7777/7776

This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations, or conceptual frameworks.

Interval information

Ratio	7777/7776
Subgroup monzo	2.3.7.11.101 [-5 -5 1 1 1⟩
Size in cents	0.22262381¢
Name	pulsar comma
Color name	101o1oz2, Fifiwolozo comma
FJS name	[math]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19868 bits
Comma size	unnoticeable
open this interval in xen-calc

7777/7776, the pulsar comma or power of six repdigit comma is an unnoticeable comma of 0.223 cents, 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 decimal repdigit number 7777. It is the difference between a stack of five 6/1's 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 stellar remnants collection 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.