1156/1155

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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 septendecimal quartertones comma
Color name 17oo1urg2, sosolurugu 2nd,
Sosolurugu comma
FJS name [math]\text{d2}^{17,17}_{5,7,11}[/math]
Special properties square superparticular,
reduced
Tenney height (log2 n⋅d) 20.3486
Weil height (max(n, d)) 1156
Benedetti height (n⋅d) 1335180
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 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.

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

It factors into the following pairs:

Temperaments

Tempering out this comma results in 35/33 being split into two equal parts, each representing 34/33~35/34, and enables the related essentially tempered chords. If 9801/9800 is also added to the comma list, the quartertone above becomes literally a quarter of 9/8 and is located right between 33/32, the undecimal quartertone, and 36/35, the septimal quartertone.

See also