2601/2600
Ratio | 2601/2600 |
Factorization | 2^{-3} × 3^{2} × 5^{-2} × 13^{-1} × 17^{2} |
Monzo | [-3 2 -2 0 0 -1 2⟩ |
Size in cents | 0.66573123¢ |
Name | sextantonisma |
Color name | 17oo3ugg2, sosothugugu 2nd, Sosothugugu comma |
FJS name | [math]\text{d2}^{17,17}_{5,5,13}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 22.6891 |
Weil height (log_{2} max(n, d)) | 22.6897 |
Wilson height (sopfr (nd)) | 69 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20396 bits |
Comma size | unnoticeable |
S-expression | S51 |
open this interval in xen-calc |
2601/2600, the sextantonisma, is a 17-limit (also 2.3.5.13.17 subgroup) superparticular comma measuring about 0.67 cents. It may be properly described as the septendecimal sixth-tones comma, since it is the difference between 51/50 and 52/51, the two 17-limit sixth-tones. Another prominent identity is the little gap between 18/13 and a stack of two 20/17's.
Commatic relations
In terms of commas, it is the difference between the following pairs:
- 289/288 and 325/324 (both of these commas are also within the 2.3.5.13.17 subgroup, while most others listed here are not)
- 561/560 and 715/714
- 833/832 and 1225/1224
- 1156/1155 and 2080/2079
- 1275/1274 and 2500/2499
- 1701/1700 and 4914/4913
- 2401/2400 and 31213/31212
- 2431/2430 and 37180/37179
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 sextantonismic temperament, or in the 2.3.5.13.17 subgroup, the rank-4 sextantonic temperament. In either case 26/25 is split into two equal parts, each representing 51/50~52/51, and enables the sextantonismic chords. If 140625/140608 is also added to the comma list, the sixth-tone above becomes literally a sixth of 9/8 and is tuned exactly middle of 51/50 and 52/51. This temperament, however, strongly suggests also tempering out 9801/9800 and/or 12376/12375 since 2601/2600 = (9801/9800)(12376/12375)^{2}(140625/140608).
Sextantonic
Subgroup: 2.3.5.13.17
Sval mapping: [⟨1 0 0 2 1], ⟨0 1 0 0 -1], ⟨0 0 0 0 1], ⟨0 0 0 2 1]]
- sval mapping generators: ~2, ~3, ~5, ~51/20
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9252, ~5/4 = 386.3777, ~51/40 = 420.3045
Optimal ET sequence: 12, 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg
Sextantonismic
Subgroup: 2.3.5.7.11.13.17
[⟨ | 1 | 0 | 0 | 0 | 0 | 1 | 2 | ], |
⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
⟨ | 0 | 0 | 0 | 0 | 0 | 2 | 1 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~51/20
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9252, ~5/4 = 386.3777, ~7/4, ~11/8, ~51/40 = 420.3045
Optimal ET sequence: 17cg, 22f, 26, 29g, 31, 38df, 43, 46, 60e, 65d, 68, 72, 103, 111, 140, 171, 183, 217, 243e, 282, 311, 354, 400, 422, 460, 494, 742, 814, 954, 1236, 1696, 2190g, 4069g*
Etymology
The sextantonisma was named by Flora Canou in 2023. It is a contraction of septendecimal sixth-tones comma into a single word consisting of Latin sextans ("sixth") and tonus ("tone").