2601/2600

Interval information

Ratio	2601/2600
Factorization	2-3 × 32 × 5-2 × 13-1 × 172
Monzo	[-3 2 -2 0 0 -1 2⟩
Size in cents	0.6657312 ¢
Name	sextantonisma
Color name	17oo3ugg2, sosothugugu 2nd, Sosothugugu comma
FJS name	[math]\displaystyle{ \text{d2}^{17,17}_{5,5,13} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	22.6891
Weil norm (log2 max(n, d))	22.6897
Wilson norm (sopfr(nd))	69
Comma size	unnoticeable
S-expression	S51
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2601/2600, the sextantonisma, is an unnoticeable 17-limit (also 2.3.5.13.17-subgroup) superparticular comma measuring about 0.666 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. It also represents 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 *
• 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

* relation within the 2.3.5.13.17 subgroup

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 sextantonismic chords are enabled.

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

Subgroup-val mapping: [⟨1 0 0 2 1], ⟨0 1 0 0 -1], ⟨0 0 0 0 1], ⟨0 0 0 2 1]]

mapping generators: ~2, ~3, ~5, ~51/20

Optimal tunings:

• WE: ~2 = 1200.0165 ¢, ~3/2 = 701.9109 ¢, ~5/4 = 386.3400 ¢, ~51/40 = 420.2767 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9128 ¢, ~5/4 = 386.3554 ¢, ~51/40 = 420.2871 ¢

Optimal ET sequence: 22f, 26, 31, 34, 72, 106, 137, 171, 183, 217, 277, 354, 388, 460, 494, 677, 814, 848, 3609g, 4069g, 4457g, 4917gg

Badness (Sintel): 0.0654

Sextantonismic

Subgroup: 2.3.5.7.11.13.17

Mapping:

[⟨	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 tunings:

• WE: ~2 = 1200.0165 ¢, ~3/2 = 701.9109 ¢, ~5/4 = 386.3400 ¢, ~7/4 = 968.7969 ¢, ~11/8 = 551.2685 ¢, ~51/40 = 420.2767 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9128 ¢, ~5/4 = 386.3554 ¢, ~7/4 = 968.8019 ¢, ~11/8 = 551.2883 ¢, ~51/40 = 420.2871 ¢

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*

* optimal patent val: 2932

Badness (Sintel): 0.689

Etymology

The sextantonisma was named by Flora Canou in 2023. It is a contraction of sixth-tones comma into a single word consisting of Latin sextans ("sixth") and tonus ("tone"). This comma was chosen as the sixth-tones comma because the sixth-tones it separates lie in the middle of the harmonic series segment of sixth-tones, 48::54.

See also

• List of superparticular intervals