Lumatone mapping for 21edo: Difference between revisions

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Since the 7th harmonic is the lowest one that is accurately tuned, the [[gorgo]] mapping works well for creating consonant combinations of notes, and also has a wider range.

Or this inverted version of the above, which is based on the [[4L 5s]] scale:

== Augmented (August) ==

It is possible to use [[21edo]] for some types of blues music, taking advantage of its highly accurate [[7/1|7th harmonic]], as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026). The mapping for this uses a sharp septimal minor third ~[[7/6]] as a generator with the octave divided in to three parts as a sharp classic major third ~[[5/4]], making this an [[augmented_(temperament)|augmented temperament]] mapping of the flat fifth ([[august]]) variety, with scales [[3L 3s]] proceeding right and down-right and [[8L 1s (4/1-equivalent)]] proceeding right, with both scales having a 5:2 step ratio. (The ⅓-octave complement of ~[[7/6]] is a mildly-flat septimal diatonic semitone ~[[15/14]], which is one key down-right, a convenient mapping for a diatonic semitone.) The range is about 6¾ octaves, and the octaves slope down considerably (incurring vertical wraparounds mitigated by repeated notes), while the double octaves slope upwards mildly.

@@ Line 8: / Line 8: @@
 Since the 7th harmonic is the lowest one that is accurately tuned, the [[gorgo]] mapping works well for creating consonant combinations of notes, and also has a wider range.
 {{Lumatone EDO mapping|n=21|start=3|xstep=4|ystep=1}}
 Or this inverted version of the above, which is based on the [[4L&nbsp;5s]] scale:
 {{Lumatone EDO mapping|n=21|start=9|xstep=5|ystep=-4}}
+== Augmented (August) ==
+It is possible to use [[21edo]] for some types of blues music, taking advantage of its highly accurate [[7/1|7th harmonic]], as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026). The mapping for this uses a sharp septimal minor third ~[[7/6]] as a generator with the octave divided in to three parts as a sharp classic major third ~[[5/4]], making this an [[augmented_(temperament)|augmented temperament]] mapping of the flat fifth ([[august]]) variety, with scales [[3L&nbsp;3s]] proceeding right and down-right and [[8L&nbsp;1s&nbsp;(4/1-equivalent)]] proceeding right, with both scales having a 5:2 step ratio. (The ⅓-octave complement of ~[[7/6]] is a mildly-flat septimal diatonic semitone ~[[15/14]], which is one key down-right, a convenient mapping for a diatonic semitone.) The range is about 6¾ octaves, and the octaves slope down considerably (incurring vertical wraparounds mitigated by repeated notes), while the double octaves slope upwards mildly.
+{{Lumatone EDO mapping|n=21|start=2|xstep=5|ystep=-3}}
 {{Navbox Lumatone}}