# 289/288

(Redirected from Semitonic)
 Ratio 289/288 Subgroup monzo 2.3.17 [-5 -2 2⟩ Size in cents 6.0008173¢ Name semitonisma Color name 17oo2, soso 2nd,Soso comma FJS name $\text{d2}^{17,17}$ Special properties square superparticular,reduced Tenney height (log2 nd) 16.3449 Weil height (log2 max(n, d)) 16.3499 Wilson height (sopfr (nd)) 50 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.52958 bits Comma size small S-expression S17 open this interval in xen-calc

289/288, the semitonisma, also described as the septendecimal semitones comma and septendecimal 6-cent comma, is a 17-limit (also 2.3.17 subgroup) superparticular comma of about 6 cents. It is the difference between 17/16 and 18/17, the two septendecimal semitones, as well as between 17/12 and 24/17, the two septendecimal tritones. It is also the difference between two stacked 17/16 and 9/8.

## Commatic relations

This comma identifies itself as the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

## Temperaments

Tempering out this comma in the full 17-limit results in the rank-6 semitonismic temperament, or in the 2.3.17 subgroup, the rank-2 semitonic temperament. In either case the octave is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

### Semitonic

Subgroup: 2.3.17

Sval mapping[2 0 5], 0 1 1]]

sval mapping generators: ~17/12, ~3

Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)

### Semitonismic

Subgroup: 2.3.5.7.11.13.17

 [⟨ 2 0 0 0 0 0 5 ], ⟨ 0 1 0 0 0 0 1 ], ⟨ 0 0 1 0 0 0 0 ], ⟨ 0 0 0 1 0 0 0 ], ⟨ 0 0 0 0 1 0 0 ], ⟨ 0 0 0 0 0 1 0 ]]
mapping generators: ~17/12, ~3, ~5, ~7, ~11, ~13

Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8

## Etymology

The semitonisma was named by Flora Canou in 2023. It is a contraction of septendecimal semitones comma into a single word consisting of Latin semi ("half") and tonus ("tone"). However, septendecimal semitones comma and septendecimal 6-cent comma were attested much earlier.