2080/2079
| Ratio | 2080/2079 |
| Factorization | 25 × 3-3 × 5 × 7-1 × 11-1 × 13 |
| Monzo | [5 -3 1 -1 -1 1⟩ |
| Size in cents | 0.8325242¢ |
| Name | ibnsinma |
| Color name | 3o1ury1, tholuruyo 1sn, Tholuruyo comma |
| FJS name | [math]\text{P1}^{5,13}_{7,11}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 22.044 |
| Weil height (log2 max(n, d)) | 22.0447 |
| Wilson height (sopfr (nd)) | 55 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40044 bits |
| Comma size | unnoticeable |
| S-expressions | S64 × S65, S78 × S79 × S80 |
| open this interval in xen-calc | |
2080/2079, the ibnsinma, is a 13-limit unnoticeable comma measuring about 0.8 cents. It is such a significant comma in the 13-limit being the 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
Mapping:
[⟨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 GPV 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.