5832/5831
| Interval information |
3rd, Sutriru comma
reduced
5832/5831, the chlorisma, is an exceptionally small 17-limit (also 2.3.7.17-subgroup) unnoticeable comma of about 0.297 cents. It is amount by which a stack of three 9/7's exceeds 17/8, or the amount by which a stack of three 7/6's falls short of 27/17. Equivalently, it is the difference between 18/17 and 343/324, or between 24/17 and 343/243.
In Sagittal notation, this is the default comma represented by two tinas.
Commatic relations
In terms of commas, it is the difference between the following superparticular pairs:
- 540/539 and 595/594
- 729/728 and 833/832
- 1701/1700 and 2401/2400
- 1716/1715 and 2431/2430
- 4914/4913 and 31213/31212
It factors into the following superparticular pair:
- 9801/9800 and 14400/14399
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 chlorismic temperament, or in the 2.3.7.17 subgroup, the rank-3 chloric temperament. In either case it equates a stack of three 9/7 supermajor thirds with 17/8, the 17th harmonic minus three octaves. 80edo represents both 9/7 and 17/8 within 0.1 cents, so it and many 80th-octave temperaments temper out the chlorisma.
Chloric
Subgroup: 2.3.7.17
Subgroup-val mapping: [⟨1 0 0 3], ⟨0 1 0 6], ⟨0 0 1 -3]]
- mapping generators: ~2, ~3, ~7
- WE: ~2 = 1199.9952 ¢, ~3/2 = 701.9358 ¢, ~7/4 = 968.8729 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9344 ¢, ~7/4 = 968.8712 ¢
Optimal ET sequence: 14, 22, 36, 94, 99, 130, 135, 171, 364, 400, 571, 971, 2378, 2549, 2949, 3920
Badness (Sintel): 0.0174
Chlorismic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 1 | 0 | 0 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 6 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | -3 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
- WE: ~2 = 1199.9952 ¢, ~3/2 = 701.9358 ¢, ~5/4 = 386.3232 ¢, ~7/4 = 968.8729 ¢, ~11/8 = 551.3322 ¢, ~13/8 = 840.5419 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9344 ¢, ~5/4 = 386.3194 ¢, ~7/4 = 968.8712 ¢, ~11/8 = 551.3264 ¢, ~13/8 = 840.5367 ¢
Optimal ET sequence: 19, 22, 27eg, 41, 49fg, 50, 58, 72, 121, 149, 166g, 171, 193, 198g, 224g, 243e, 270, 364, 373g, 400, 422, 494, 742, 764, 814, 935, 1084, 1106, 1178, 1236, 1506, 2000, 2414, 2684, 3178, 3920, 4684, 5498, 10182d, 14102dg, 14174d, 15680dg, 19600dg *
Badness (Sintel): 1.13
Etymology
The chlorisma was named by Jerdle in 2021. Despite the similar name, it has no relation to the previously-named chlorine temperament.