Octaphore

Interval information

Ratio	94450499584/94143178827
Factorization	214 × 3-23 × 78
Monzo	[14 -23 0 8⟩
Size in cents	5.642232¢
Names	Octaphore comma, Enneagari
FJS name	[math]\displaystyle{ \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
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The octaphore comma 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 Octophore temperament (note the different spelling), and tempering it out in the 2.3.7 subgroup leads to the rank-2 Actinide temperament.

Octophore

Subgroup: 2.3.5.7

Comma List: 94450499584/94143178827

Mapping: [⟨1 2 2 4], ⟨0 -8 0 -23], ⟨0 0 1 0]]

POTE tuning: ~28/27 = 62.233, ~5/4 = 386.314

Optimal ET sequence: 19, 39d, 58, 77, 96d, 135

Actinide

Subgroup: 2.3.7

Comma List: 94450499584/94143178827

Mapping: [⟨1 2 4], ⟨0 -8 -23]]

POTE tuning: ~28/27 = 62.233

Optimal ET sequence: 19, 20d, 39d, 58, 77, 96d, 135

See also

Small comma