Lucius Chiaraviglio: /* 6L 3s */ Add demo video

2025-07-26T08:36:05Z

6L 3s: Add demo video

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	=== 6L 3s ===		=== 6L 3s ===
	Using the porcupine generator with a third octave period is both quite harmonically efficient and maximises your range without any skipped notes.		Using the porcupine generator with a third octave period is both quite harmonically efficient and maximises your range without any skipped notes. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/Cn28RJSSgQ0 ''microtonal improvisation in 66edo''] (2025).
	{{Lumatone EDO mapping\|n=66\|start=1\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=66\|start=1\|xstep=9\|ystep=-5}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

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2025-07-25T07:37:46Z

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There are many conceivable ways to map [[66edo]] onto the onto the Lumatone keyboard. However, since it has three mutually-exclusive rings of [[22edo]] fifths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. The second best 5th produces two mutually-exclusive rings of [[33edo]] 5ths, so that doesn't work either, the third best is outside the diatonic tuning range and also contorted, which means the antidiatonic scale generated by 29/66 is the closest thing to a diatonic scale that can reach all the notes. Due to the size of the edo, this needs to be expanded to [[7L 2s]] to give access to the full gamut.

== Antidiatonic ==
=== 2L 5s ===
{{Lumatone EDO mapping|n=66|start=30|xstep=8|ystep=5}}
=== 7L 2s ===
{{Lumatone EDO mapping|n=66|start=60|xstep=8|ystep=-3}}

== Other Mappings ==
Due to the composite nature of the edo, less than a third of the generators cover all the notes and most of those do not have named temperaments. Those that do exist are mostly derived by dividing the period and/or generator from a 22edo temperament by 3. The [[ammonite]] mapping does this for [[porcupine]] and is probably the best temperament supported by the edo, although the [[5L 3s]] mapping skips an occasional step and the [[8L 5s]] one is quite inefficient on the lumatone.
=== 5L 3s ===
{{Lumatone EDO mapping|n=66|start=61|xstep=9|ystep=-2}}
=== 8L 5s ===
{{Lumatone EDO mapping|n=66|start=0|xstep=7|ystep=-5}}

=== 6L 3s ===
Using the porcupine generator with a third octave period is both quite harmonically efficient and maximises your range without any skipped notes.
{{Lumatone EDO mapping|n=66|start=1|xstep=9|ystep=-5}}

{{Navbox Lumatone}}

Lumatone mapping for 66edo - Revision history

Lucius Chiaraviglio: /* 6L 3s */ Add demo video

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