2058/2057
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| Ratio | 2058/2057 |
| Factorization | 2 × 3 × 73 × 11-2 × 17-1 |
| Monzo | [1 1 0 3 -2 0 -1⟩ |
| Size in cents | 0.84142604¢ |
| Name | xenisma |
| Color name | 17u1uuz32, sululutrizo 2nd |
| FJS name | [math]\text{M2}^{7,7,7}_{11,11,17}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 22.0134 |
| Weil height (log2 max(n, d)) | 22.0141 |
| Wilson height (sopfr (nd)) | 65 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40051 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
2058/2057, the xenisma, is a 17-limit (also 2.3.7.11.17 subgroup) comma measuring about 0.84 cents. It is the amount by which a stack of two 14/11's exceed 34/21.
Commatic relations
This comma is the difference between the following superparticular pairs:
- 364/363 and 442/441
- 441/440 and 561/560
- 936/935 and 1716/1715
- 1225/1224 and 3025/3024
- 1701/1700 and 9801/9800
Not to mention some nonsuperparticular but useful relations:
It factors into the following superparticular pairs:
- 2401/2400 and 14400/14399
- 2080/2079 and 194481/194480
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 xenismic temperament, or in the 2.3.7.11.17 subgroup, the rank-4 xenic temperament. In either case it enables xenismic chords.
Etymology
The xenisma was named by Margo Schulter in 2000[1].