289/288: Difference between revisions
I noticed that this was a super common comma in 12ed2 when you consider the strength of its 17 limit properties. |
m Cleanup |
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== Temperaments == | == Temperaments == | ||
Tempering | Tempering out this comma results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out. | ||
=== Semitonismic === | === Semitonismic === | ||
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{{val| 0 0 0 0 0 1 0 }}] | {{val| 0 0 0 0 0 1 0 }}] | ||
: mapping generators: ~17/12, ~3, ~5, ~7, ~11, ~13 | |||
[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8 | [[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8 | ||
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[[Subgroup]]: 2.3.17 | [[Subgroup]]: 2.3.17 | ||
{{Mapping|legend=2| 2 0 5 | 0 1 1 }} | |||
: sval mapping generators: ~17/12, ~3 | |||
[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472) | [[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472) |