289/288
| Interval information |
Soso comma
reduced
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 results in the rank-2 semitonic temperament in the 2.3.17 subgroup, or the rank-6 semitonismic temperament in the full 17-limit. 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
Optimal ET sequence: 12, 58, 70, 82, 94, 106, 118, 224g
Sval mapping: [⟨2 2 7], ⟨0 1 1]]
[CTE]] generators: ~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
Optimal ET sequence: 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg
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.