9edo: Difference between revisions
→Ear training: Reorganize to Ear training (existing subsection) + (new subsection) Werntz Nocturne Scale |
→Rank-2 temperaments: use backslashes for edo steps |
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
9edo contains a pentatonic [[mos scale]] produced by stacking 4 | 9edo contains a pentatonic [[mos scale]] produced by stacking 4\9 of [[2L 3s]] (1 3 1 3 1), which has a heptatonic extension, [[2L 5s]] (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic"). | ||
You can also use | You can also use 2\9, which generates mos scales of [[1L 3s]] (3 2 2 2) and [[4L 1s]] (2 2 2 2 1) and can be interpreted as either an extremely sharp [[bug]] scale or an extremely flat [[orwell]] one. | ||
== Historical (and other) relevance == | == Historical (and other) relevance == | ||
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9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]]. | 9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]]. | ||
Pure-octaves 9edo makes a decent 2.5.11 tuning, approximating all those three primes within 18{{c}}. | Pure-octaves 9edo makes a decent 2.5.11 tuning, approximating all those three primes within 18{{c}}. | ||
9edo with octaves stretched about 5{{c}}, as in [[zpi|22zpi]], makes a decent 2.7.11.13 tuning, approximating all those four primes within 17{{c}}. | 9edo with octaves stretched about 5{{c}}, as in [[zpi|22zpi]], makes a decent 2.7.11.13 tuning, approximating all those four primes within 17{{c}}. | ||
9edo with octaves stretched about 10{{c}}, as in [[ed12|32ed12]], makes a decent 2.3.7.11.13 tuning, approximating all those five primes within 20{{c}}. | 9edo with octaves stretched about 10{{c}}, as in [[ed12|32ed12]], makes a decent 2.3.7.11.13 tuning, approximating all those five primes within 20{{c}}. | ||
== Diagrams == | == Diagrams == | ||
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* [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]]. | * [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]]. | ||
=== Werntz | === Werntz Nocturne scale === | ||
{{main|Werntz Nocturne scale}} | |||
== Notes == | == Notes == | ||