7176/7175
| Interval information |
fowutwethothorugugu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
7176/7175, the kunijisma, is a 41-limit superparticular comma of about 0.24 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 276/275 and 287/286
- 288/287 and 300/299
- 351/350 and 369/368
- 575/574 and 625/624
- 780/779 and 875/874
- 897/896 and 1025/1024
- 1026/1025 and 1197/1196
It can be factored into the following superparticular ratios:
- 7866/7865 and 81796/81795
- 8464/8463 and 47151/47150
- 8671/8670 and 41616/41615
- 10374/10373 and 23276/23275
- 10626/10625 and 22100/22099
- 11440/11439 and 19251/19250
- 12006/12005 and 17836/17835
- 12636/12635 and 16606/16605
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament kunijismic. Using the 2.3.5.7.13.23.41 subgroup leads to the rank-6 temperament kunijic.
Kunijic
Subgroup: 2.3.5.7.13.23.41
Comma list: 7176/7175
| [⟨ | 1 | 1 | 2 | 2 | 3 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning: ~2 = 1\1, ~3/2 = 701.949, ~5/4 = 386.341, ~7/4 = 968.846, ~13/8 = 840.493, ~23/16 = 628.222
Optimal ET sequence: 5, 7dfim, 7, 8di, 9, 10, 12fim, 15m, 19im, 19, 26i, 27i, 31, 46, 53, 68m, 72im, 84, 121im, 130, 140, 193, 198, 224, 282, 289, 342f, 373, 441, 764, 814, 954, 1007, 1012, 1065, 1205, 1578, 2019, 3255, 4460, 6479, 10228m
Etymology
This comma was named by Francium in 2025. It refers to 7176 Kuniji, the asteroid, which in turn was named after Kuniji Saito, a Japanese astronomer.