Octaphore
| Ratio | 94450499584/94143178827 |
| Factorization | 214 × 3-23 × 78 |
| Monzo | [14 -23 0 8⟩ |
| Size in cents | 5.6422318¢ |
| Names | the octaphore, enneagari comma |
| FJS name | [math]\text{5d6}^{7,7,7,7,7,7,7,7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 72.913 |
| Weil height (log2 max(n, d)) | 72.9177 |
| Wilson height (sopfr(nd)) | 153 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.49165 bits |
| open this interval in xen-calc | |
The octaphore, also known as the enneagari comma, is a small 7-limit (also 2.3.7-subgroup) comma measuring about 5.64 cents. It is so named because it is the amount by which eight 28/27 third-tones exceed the 4/3 perfect fourth. It can also be found as the amount by which seven 28/27 third-tones exceed the 9/7 supermajor third, or as the sum of the garischisma (33554432/33480783) and the septimal ennealimma (40353607/40310784).
Temperaments
Tempering out the octaphore comma in the full 7-limit leads to rank-3 octaphore temperament, and excluding prime 5 from the subgroup leads to the 2.3.7 subgroup rank-2 Unicorn temperament.
Octaphore
Subgroup: 2.3.5.7
Comma list: 94450499584/94143178827
Mapping: [⟨1 2 0 4], ⟨0 -8 0 -23], ⟨0 0 1 0]]
- mapping generators: ~2, ~28/27, ~5
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.233, ~5/4 = 386.314
Optimal ET sequence: 19, 39d, 58, 77, 96d, 135
2.3.7 Unicorn
If we temper the octaphore in its minimal prime subgroup of 2.3.7, we get the 2.3.7-subgroup version of unicorn, where it finds prime 5 by interpreting five gens as a flat ~6/5 by tempering 126/125.
Subgroup: 2.3.7
Comma list: 94450499584/94143178827
Mapping: [⟨1 2 4], ⟨0 -8 -23]]
- mapping generators: ~2, ~28/27
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 62.233
Optimal ET sequence: 19, 20d, 39d, 58, 77, 96d, 135