Octaphore: Difference between revisions
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{{Infobox Interval|Name= | {{Infobox Interval | ||
| Name = octaphore comma, enneagari comma | |||
| Ratio = 94450499584/94143178827 | |||
| Monzo = 14 -23 0 8 | |||
}} | |||
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 | The '''octaphore comma''', also known as the '''enneagari comma''', is a [[small comma|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 5.64 [[cent]]s. 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|garischisma (33554432/33480783)]] and the [[septimal ennealimma|septimal ennealimma (40353607/40310784)]]. | ||
== Temperaments == | == Temperaments == | ||
Tempering out the | 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 | [[Subgroup]]: 2.3.5.7 | ||
Comma | [[Comma list]]: 94450499584/94143178827 | ||
Mapping | {{Mapping|legend=1| 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|legend=1| 19, 39d, 58, 77, 96d, 135 }} | |||
=== Actinide === | === Actinide === | ||
Subgroup: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
Comma | [[Comma list]]: 94450499584/94143178827 | ||
Mapping | {{Mapping|legend=1| 1 2 4 | 0 -8 -23 }} | ||
: mapping generators: ~2, ~28/27 | |||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 62.233 | |||
= | {{Optimal ET sequence|legend=1| 19, 20d, 39d, 58, 77, 96d, 135 }} | ||
Revision as of 03:30, 2 October 2024
| Interval information |
enneagari comma
The octaphore comma, 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 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 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
Actinide
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