Revision as of 05:27, 16 July 2025 by Lucius Chiaraviglio(talk | contribs)(→Bischismic: Insert Bryan Deister's Magic (Divination/Soothsaying) related Lumatone mapping after this)
You can use the b val instead, but this is barely distinguishable from a circulating system of 7edo and only covers about 2/3rds of the notes due to the size of the edo.
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There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since that means all notes are available in at least some of the octaves, this may actually be advantageous.
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Bischismic
The Bischismic mapping can cover the whole gamut, although it needs to be expanded from 2L 8s to 10L 2s to do so.
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Magic (Divination/Soothsaying) related Lumatone mappings
Bryan Deister has demonstrated a 8L 6s mapping of 82edo. Being even 82edo supports a semioctave period, with the diagassormisma (3042/3025) being tempered out in the patent val or the kalisma (9801/9800) being tempered out in the 82e val; this enables it to use the (somewhat sharp) septimal major third ~9/7 (as 30\82) as a generator (which would be contorted down to 41edo with a whole octave period), in a temperament like Soothsaying or Divination, but using the septimal major third as a generator instead of the classic major third ~5/4. (Since 82edo also supports actual Soothsaying in its patent val and actual Divination in its 82e val, it is also possible to use generator 26\82, the somewhat flat ~5/4, although the resulting 6L 4s scale is a bit more tricky to play using this layout.) The range is about 2¾ octaves with no missed notes, and the octaves slant down.
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Other mappings
To maximise your range, you can use the 8L 2s mapping generated by 9/82 and a half octave period, but this is not particularly efficient at putting the best note combinations close to one-another.
