289/288

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Revision as of 10:41, 23 February 2023 by FloraC (talk | contribs) (Consolidate the name)
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Interval information
Ratio 289/288
Subgroup monzo 2.3.17 [-5 -2 2
Size in cents 6.000817¢
Name semitonisma
Color name 17oo2, soso 2nd,
Soso comma
FJS name [math]\displaystyle{ \text{d2}^{17,17} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 16.3449
Weil height (log2 max(n, d)) 16.3499
Wilson height (sopfr(nd)) 50
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.

Temperaments

Tempering it out 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 so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

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.

See also