4301/4300
| Interval information |
fothutwethosologugu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
4301/4300, the boydenisma, is a 43-limit superparticular comma of about 0.40 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 345/344 and 375/374
- 391/390 and 430/429
- 646/645 and 760/759
- 1377/1376 and 2025/2024
- 1936/1935 and 3520/3519
It can be factored into the following superparticular intervals:
- 4641/4640 and 58696/58695
- 4761/4760 and 44506/44505
- 5083/5082 and 27951/27950
- 5376/5375 and 21505/21504
- 7225/7224 and 10626/10625
- 7956/7955 and 9361/9360
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament boydenismic. Using the 2.5.11.17.23.43 subgroup leads to the rank-5 temperament boydenic.
Boydenic
Subgroup: 2.5.11.17.23.43
Comma list: 4301/4300
| [⟨ | 1 | 2 | 3 | 4 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.357, ~11/8 = 551.270, ~17/16 = 104.888, ~23/16 = 628.192
Optimal ET sequence: 4, 5egn, 6gn, 6, 8in, 9, 15, 16n, 21, 22i, 29g, 30, 31, 34n, 43n, 50, 59, 115, 124, 298, 422, 516, 640, 699, 814, 938, 1637, 2575, 3355i, 3479, 3777, 4417i, 5116i, 5414gi
Badness (Sintel): 0.019
Etymology
This comma was named by Francium in 2025. It refers to 4301 Boyden, the asteroid, which in turn was named after Uriah A. Boyden, an American mechanical engineer.