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Interval information
Ratio 1156/1155
Factorization 22 × 3-1 × 5-1 × 7-1 × 11-1 × 172
Monzo [2 -1 -1 -1 -1 0 2
Size in cents 1.4982554¢
Name quadrantonisma
Color name 17oo1urg2, sosolurugu 2nd,
Sosolurugu comma
FJS name [math]\text{d2}^{17,17}_{5,7,11}[/math]
Special properties square superparticular,
Tenney height (log2 nd) 20.3486
Weil height (log2 max(n, d)) 20.3499
Wilson height (sopfr (nd)) 64
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.4085 bits
Comma size unnoticeable
S-expression S34
open this interval in xen-calc

1156/1155, the quadrantonisma, is a 17-limit no-13 superparticular comma measuring about 1.41 cents. It may be properly described as the septendecimal quartertones comma, since it is the difference between 34/33 and 35/34, the two 17-limit quartertones.

Commatic relations

In terms of commas, it is the difference between the following pairs:

It factors into the following pairs:


Tempering out this comma in the 17-limit results in the rank-6 quadrantonismic temperament, or in the subgroup, the rank-5 quadrantonic temperament. In either case 35/33 is split into two equal parts, each representing 34/33~35/34, and enables quadrantonismic chords. If 9801/9800 is also added to the comma list, the quartertone above becomes literally a quarter of 9/8 and is tuned exactly middle of 33/32, the undecimal quartertone, and 36/35, the septimal quartertone.


The quadrantonisma was named by Flora Canou in 2023. It is a contraction of septendecimal quartertones comma into a single word consisting of Latin quadrans ("fourth") and tonus ("tone").

See also