Kaguyisma
| Ratio | 10880/10879 |
| Subgroup monzo | 2.5.11.17.23.43 [7 1 -1 1 -1 -1⟩ |
| Size in cents | 0.15912809¢ |
| Name | kaguyisma |
| Color name | 43u23u17o1uy1 fothutwethusoluyo unison |
| FJS name | [math]\text{m2}^{5,17}_{11,23,43}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 26.8186 |
| Weil height (log2 max(n, d)) | 26.8188 |
| Wilson height (sopfr(nd)) | 113 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19845 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
10880/10879, the kaguyisma, is a 43-limit superparticular comma of about 0.16 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular commas:
- 11271/11270 and 313600/313599
- 11340/11339 and 268192/268191
- 11662/11661 and 162240/162239
- 12376/12375 and 90000/89999
- 14400/14399 and 44506/44505
- 14535/14534 and 43264/43263
- 18792/18791 and 25840/25839
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament kaguyismic. Using the 2.5.11.17.23.43 subgroup leads to the rank-5 temperament kaguyic.
Kayugismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43
Comma list: 10880/10879
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 386.303, ~7/4 = 968.826, ~11/8 = 551.341, ~13/8 = 840.528, ~17/16 = 104.924, ~19/16 = 297.513, ~23/16 = 628.313, ~29/16 = 1029.577, ~31/16 = 1145.036, ~37/32 = 251.344, ~41/32 = 429.062
Kaguyic
Subgroup: 2.5.11.17.23.43
Comma list: 10880/10879
| [⟨ | 1 | 2 | 3 | 4 | 4 | 6 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 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 = 386.303, ~11/8 = 551.341, ~17/16 = 104.924, ~23/16 = 628.313
Optimal ET sequence: 4n, 5eg, 6gn, 6, 9, 13n, 15, 16, 19, 21, 28g, 29g, 30, 35, 37, 44, 46, 50, 59, 115, 124, 298, 422, 516, 640, 699, 814, 938, 1637, 1715, 1839, 2137, 2777, 2836, 4973, 5613, 8449, 8573in
Etymology
The kaguyisma was named by Francium in 2024. It refers to 10880 Kaguya, the asteroid. Which was in turn named after the princess from Japanese folklore.