23edo and octave stretching: Difference between revisions
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[[Octave shrinking]] may also be used instead of octave stretching, which results in a scale with very different properties. 23edo’s approximations of harmonics are still improved upon, but by shifting them in the opposite direction. This is a less-studied option with fertile ground to explore. | [[Octave shrinking]] may also be used instead of octave stretching, which results in a scale with very different properties. 23edo’s approximations of harmonics are still improved upon, but by shifting them in the opposite direction. This is a less-studied option with fertile ground to explore. | ||
== Comparison of | == Comparison of tunings == | ||
What follows is a comparison of compressed- and stretched-octave 23edo tunings. | What follows is a comparison of compressed- and stretched-octave 23edo tunings. | ||
=== Compressed === | |||
; [[zpi|86zpi]] | ; [[zpi|86zpi]] | ||
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{{Harmonics in cet|52.114|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 85zpi}} | {{Harmonics in cet|52.114|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 85zpi}} | ||
{{Harmonics in cet|52.114|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 85zpi (continued)}} | {{Harmonics in cet|52.114|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 85zpi (continued)}} | ||
=== Pure octaves === | |||
; 23edo | ; 23edo | ||
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{{Harmonics in equal|23|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 23edo}} | {{Harmonics in equal|23|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 23edo}} | ||
{{Harmonics in equal|23|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 23edo (continued)}} | {{Harmonics in equal|23|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 23edo (continued)}} | ||
=== Stretched === | |||
; [[WE|23et, 13-limit WE tuning]] | ; [[WE|23et, 13-limit WE tuning]] | ||