Lumatone mapping for 15edo: Difference between revisions

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{{Lumatone mapping intro}} ~~You can use the extremely flat 8\15 fifth of 640¢. This layout preserves the location of the octave, and places the down-fifth where the fifth usually is.~~

== Antidiatonic ==

It is possible to use the extremely flat 8\15 fifth of 640{{c}} to get an antidiatonic mapping. This layout preserves the location of the octave, and places the down-fifth where the fifth usually is; however, the resulting [[2L 5s]] scale is extremely hard (5:1 step ratio), as is the [[2L 7s]] scale that one can get by backtracking at each L step (4:1 step ratio).

This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the Porcupine, Blackwood, and Hanson mappings.

== [[Porcupine]] ==

== Porcupine ==

[[Porcupine]] is a popular temperament that 15edo supports, although the expanded mapping here ([[1L 6s]] scale with 3:2 step ratio and no backtracking) spreads the octaves out more than is optimal for such a small tuning system as 15edo, thereby limiting the range to somewhat over four octaves, which slope upwards too much for convenience in splitting the keyboard into multiple manuals.

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-{{Lumatone mapping intro}} You can use the extremely flat 8\15 fifth of 640¢. This layout preserves the location of the octave, and places the down-fifth where the fifth usually is.
+{{Lumatone mapping intro}}
+== Antidiatonic ==
+It is possible to use the extremely flat 8\15 fifth of 640{{c}} to get an antidiatonic mapping. This layout preserves the location of the octave, and places the down-fifth where the fifth usually is; however, the resulting [[2L&nbsp;5s]] scale is extremely hard (5:1 step ratio), as is the [[2L&nbsp;7s]] scale that one can get by backtracking at each L step (4:1 step ratio).
 {{Lumatone EDO mapping|n=15|start=12|xstep=1|ystep=4}}
 This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the Porcupine, Blackwood, and Hanson mappings.
-== [[Porcupine]] ==
+== Porcupine ==
+[[Porcupine]] is a popular temperament that 15edo supports, although the expanded mapping here ([[1L&nbsp;6s]] scale with 3:2 step ratio and no backtracking) spreads the octaves out more than is optimal for such a small tuning system as 15edo, thereby limiting the range to somewhat over four octaves, which slope upwards too much for convenience in splitting the keyboard into multiple manuals.
 {{Lumatone EDO mapping|n=15|start=0|xstep=2|ystep=1}}