289/288: Difference between revisions

Phlub (talk | contribs)
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 it out 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.  
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
: 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


[[Sval]] [[mapping]]: [{{val| 2 0 5 }} {{val| 0 1 1 }}]
{{Mapping|legend=2| 2 0 5 | 0 1 1 }}


Sval mapping generators: ~17/12, ~3
: 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)