# 2601/2600

 Ratio 2601/2600 Factorization 2-3 × 32 × 5-2 × 13-1 × 172 Monzo [-3 2 -2 0 0 -1 2⟩ Size in cents 0.66573123¢ Name sextantonisma Color name 17oo3ugg2, sosothugugu 2nd,Sosothugugu comma FJS name $\text{d2}^{17,17}_{5,5,13}$ Special properties square superparticular,reduced Tenney height (log2 nd) 22.6891 Weil height (log2 max(n, d)) 22.6897 Wilson height (sopfr (nd)) 69 Harmonic entropy(Shannon, $\sqrt{nd}$) ~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:

## 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 sequence12, 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 sequence17cg, 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").