2080/2079
| Interval information |
Tholuruyo comma
reduced
S78 × S79 × S80
2080/2079, the ibnsinma, is a 13-limit unnoticeable comma measuring about 0.83 cents. It is the amount by which a stack consisting of 11/10 and 14/13 falls short of Pythagorean minor third, 32/27.
Commatic relations
This comma identifies itself as the difference difference between eight pairs of superparticular ratios:
- 64/63 and 66/65
- 78/77 and 81/80
- 100/99 and 105/104
- 325/324 and 385/384
- 364/363 and 441/440
- 540/539 and 729/728
- 676/675 and 1001/1000
- 1716/1715 and 9801/9800
Not to mention some nonsuperparticular but useful ratios:
Or as a relation in the four formal commas defined by Functional Just System:
It factors into the following superparticular intervals:
In Sagittal notation, it is the default comma represented by two minas or six tinas.
Temperaments
By tempering it out is defined the ibnsinmic temperament, which enables the ibnsinmic chords, the essentially tempered chords in the 21-odd-limit. Another consequence is that it makes fifth complements of 13/11 and 80/63, and of 40/33 and 26/21. You may find a list of good equal temperaments that support this temperament below.
Subgroup: 2.3.5.7.11.13
| [⟨ | 1 | 0 | 0 | 0 | 0 | -5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11
Optimal ET sequence: 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde *
Etymology
The ibnsinma was named by Margo Schulter in 2012, when it went by ibn Sina's comma[1]. It was contracted to avicennma and later changed to ibnsinma, all essentially meaning the same thing, but note that avicennma refers to Avicenna's enharmonic diesis (525/512) today.