Lumatone mapping for 15edo: Difference between revisions

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{{Lumatone mapping intro}} ~~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~~]] ==

== 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]] is a popular temperament that 15edo supports, although the semi-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. [[Bryan Deister]] demonstrates this mapping (but shifted right to avoid missing the upper note 1) in [https://www.youtube.com/shorts/uYlLryh1BbI ''March in 15edo''] (2026).

== [[Blackwood]] ==

=== Fully Expanded (add Augmented/Triforce) ===

The fully expanded [[7L 1s]] mapping reduces the range (now just under four octaves) and increases the octave slope even further, but may be more intuitive to play, including having a forward chroma (rather than reverse as above); also, the slope is now enough upwards to permit reframing as a slight downwards slope with a [[6L 3s]] scale (as in [[augmented]]/[[Augmented_family#Triforce|triforce]], and gentle enough to provide the potential splitting the mapping into multiple manuals (three complete in the middle, and one partial each above and below). [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/O0FCuzMLX9E ''15edo''] (2023), although with the color scheme set for porcupine and not augmented/triforce.

== Blackwood + Augmented (Augene) + Kleismic (Hanson/Keemun/Superkleismic) ==

[[Blackwood]] avoids the [[contorsion]] problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L 3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in [[augmented (temperament)|augmented]], specifically [[augene]]. This also functions as a [[kleismic]] ([[hanson]]/[[keemun]]/[[superkleismic]]) [[4L 3s]] (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.

=== 3L 3s (right, down-right) and 4L 3s (right, up) ===

This version is optimized for playing the [[3L 3s]] scale; it makes the [[4L 3s]] scale slope upwards, although with care it is possible to use the vertically repeated notes to avoid a vertical wraparound. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=CNZbkoqbBwo ''GHOST – Rotary Dial (microtonal cover in 15edo)''] (2023).

== [[Hanson]] ==

=== 3L 3s (right, up) and 4L 3s (right, down-right) ===

This version is optimized for playing the [[4L 3s]] scale; it makes the [[3L 3s]] scale slope upwards, although with care it is possible to use the vertically repeated notes to avoid a vertical wraparound. [[Bryan Deister]] demonstrates this version in [https://www.youtube.com/shorts/n4552NepqZ8 ''Waltz in 15edo''] (2025).

== Hanson ==

If hanson is most of what is needed and augmented and blackwood are not a priority, it is possible to compress the layout to a [[3L 1s]] scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level (even supporting the possibility for dual manuals). [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=8PaoIqPkIWc ''<nowiki>Radiohead – Subterranean Homesick Alien [microtonal 15edo]</nowiki>''] (2024).

@@ Line 1: / Line 1: @@
-{{Lumatone mapping intro}} 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.
+{{Lumatone mapping intro}}
-== [[Porcupine]] ==
+== 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]] is a popular temperament that 15edo supports, although the semi-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. [[Bryan Deister]] demonstrates this mapping (but shifted right to avoid missing the upper note 1) in [https://www.youtube.com/shorts/uYlLryh1BbI ''March in 15edo''] (2026).
 {{Lumatone EDO mapping|n=15|start=0|xstep=2|ystep=1}}
-== [[Blackwood]] ==
+=== Fully Expanded (add Augmented/Triforce) ===
+The fully expanded [[7L&nbsp;1s]] mapping reduces the range (now just under four octaves) and increases the octave slope even further, but may be more intuitive to play, including having a forward chroma (rather than reverse as above); also, the slope is now enough upwards to permit reframing as a slight downwards slope with a [[6L&nbsp;3s]] scale (as in [[augmented]]/[[Augmented_family#Triforce|triforce]], and gentle enough to provide the potential splitting the mapping into multiple manuals (three complete in the middle, and one partial each above and below). [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/O0FCuzMLX9E ''15edo''] (2023), although with the color scheme set for porcupine and not augmented/triforce.
+{{Lumatone EDO mapping|n=15|start=0|xstep=2|ystep=-1}}
+== Blackwood + Augmented (Augene) + Kleismic (Hanson/Keemun/Superkleismic) ==
+[[Blackwood]] avoids the [[contorsion]] problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L&nbsp;3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in [[augmented (temperament)|augmented]], specifically [[augene]]. This also functions as a [[kleismic]] ([[hanson]]/[[keemun]]/[[superkleismic]]) [[4L&nbsp;3s]] (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.
+=== 3L&nbsp;3s (right, down-right) and 4L&nbsp;3s (right, up) ===
+This version is optimized for playing the [[3L&nbsp;3s]] scale; it makes the [[4L&nbsp;3s]] scale slope upwards, although with care it is possible to use the vertically repeated notes to avoid a vertical wraparound. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=CNZbkoqbBwo ''GHOST – Rotary Dial (microtonal cover in 15edo)''] (2023).
 {{Lumatone EDO mapping|n=15|start=13|xstep=3|ystep=-1}}
-== [[Hanson]] ==
+=== 3L&nbsp;3s (right, up) and 4L&nbsp;3s (right, down-right) ===
+This version is optimized for playing the [[4L&nbsp;3s]] scale; it makes the [[3L&nbsp;3s]] scale slope upwards, although with care it is possible to use the vertically repeated notes to avoid a vertical wraparound. [[Bryan Deister]] demonstrates this version in [https://www.youtube.com/shorts/n4552NepqZ8 ''Waltz in 15edo''] (2025).
+{{Lumatone EDO mapping|n=15|start=4|xstep=3|ystep=-2}}
+== Hanson ==
+If hanson is most of what is needed and augmented and blackwood are not a priority, it is possible to compress the layout to a [[3L&nbsp;1s]] scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level (even supporting the possibility for dual manuals). [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=8PaoIqPkIWc ''<nowiki>Radiohead – Subterranean Homesick Alien [microtonal 15edo]</nowiki>''] (2024).
 {{Lumatone EDO mapping|n=15|start=9|xstep=4|ystep=-1}}
 {{Navbox Lumatone}}