9edo: Difference between revisions
→Approximation to JI: -zeta peak index |
octave stretch |
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[http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird] | [http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird] | ||
== Octave stretch and compression == | |||
9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]]. | |||
; 9edo | |||
* Step size: 133.333{{c}}, octave size: 1200.0{{c}} | |||
Pure-octaves 9edo makes a decent 2.5.11 tuning, approximating all those three primes within 18{{c}}. | |||
{{Harmonics in equal|9|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 9edo}} | |||
{{Harmonics in equal|9|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 9edo (continued)}} | |||
; [[zpi|22zpi]] | |||
* Step size: 134.078{{c}}, octave size: 1206.7{{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}}. | |||
{{Harmonics in cet|134.078|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 22zpi}} | |||
{{Harmonics in cet|134.078|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 22zpi (continued)}} | |||
; [[32ed12]] | |||
* Step size: 134.436{{c}}, octave size: 1209.9{{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}}. | |||
{{Harmonics in equal|32|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 32ed12}} | |||
{{Harmonics in equal|32|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 32ed12 (continued)}} | |||
== Diagrams == | == Diagrams == | ||