9edo: Difference between revisions

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=== Rank-2 temperaments ===

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").

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 ~~the~~ 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.

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 ==

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[http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird]

== Octave stretch or compression ==

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}}.

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}}.

== Diagrams ==

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== Ear training ==

== See also ==

=== Ear training ===

* [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]].

=== Werntz Nocturne scale ===

== Notes ==

@@ Line 382: / Line 382: @@
 === Rank-2 temperaments ===
-edo contains a pentatonic [[mos scale]] produced by stacking 4/9 of [[2L&nbsp;3s]] (1 3 1 3 1), which has a heptatonic extension, [[2L&nbsp;5s]] (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic").
+edo contains a pentatonic [[mos scale]] produced by stacking 4\9 of [[2L&nbsp;3s]] (1 3 1 3 1), which has a heptatonic extension, [[2L&nbsp;5s]] (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic").
-You can also use the 2/9, which generates mos scales of [[1L&nbsp;3s]] (3 2 2 2) and [[4L&nbsp;1s]] (2 2 2 2 1) and can be interpreted as either an extremely sharp [[bug]] scale or an extremely flat [[orwell]] one.
+You can also use 2\9, which generates mos scales of [[1L&nbsp;3s]] (3 2 2 2) and [[4L&nbsp;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 ==
@@ Line 393: / Line 393: @@
 [http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird]
+== Octave stretch or compression ==
+edo'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}}.
+edo 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}}.
+edo 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 ==
@@ Line 405: / Line 414: @@
 {{Main|Music in 9edo}}
-== Ear training ==
+== See also ==
+=== Ear training ===
 * [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list 9edo ear-training exercises] by [[Alex Ness]].
+=== Werntz Nocturne scale ===
+{{main|Werntz Nocturne scale}}
 == Notes ==