7777/7776
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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 (log_{2} nd) | 25.8498 |
Weil height (log_{2} 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.