# 1156/1155

 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 $\text{d2}^{17,17}_{5,7,11}$ Special properties square superparticular,reduced Tenney height (log2 nd) 20.3486 Weil height (log2 max(n, d)) 20.3499 Wilson height (sopfr (nd)) 64 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.22077 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:

## Temperaments

Tempering out this comma in the 17-limit results in the rank-6 quadrantonismic temperament, or in the 2.3.5.7.11.17 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.

Subgroup: 2.3.5.7.11.17

 [⟨ 1 0 0 0 0 -1 ], ⟨ 0 1 0 0 1 1 ], ⟨ 0 0 1 0 1 1 ], ⟨ 0 0 0 1 1 1 ], ⟨ 0 0 0 0 -2 -1 ]]
sval mapping generators: ~2, ~3, ~5, ~7, ~34/11

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186

Optimal ET sequence17cg, 19eg, 22, 27eg, 39dg, 43, 46, 65d, 68, 72, 118, 171, 183, 239, 282, 301, 311, 400, 422, 472, 494, 894, 1012g, 1205, 1388

Subgroup: 2.3.5.7.11.13.17

 [⟨ 1 0 0 0 0 0 -1 ], ⟨ 0 1 0 0 1 0 1 ], ⟨ 0 0 1 0 1 0 1 ], ⟨ 0 0 0 1 1 0 1 ], ⟨ 0 0 0 0 -2 0 -1 ], ⟨ 0 0 0 0 0 1 0 ]]
mapping generators: ~2, ~3, ~5, ~7, ~34/11, ~13

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186, ~13/8

Optimal ET sequence17cg, 19eg, 22, 26, 27eg, 29g, 39dfg, 43, 46, 65d, 68, 72, 111, 121, 140, 171, 183, 217, 282, 301, 311, 354, 400, 422, 494, 894, 1012g, 1133, 1205, 1506g, 1627e

## Etymology

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").