Lumatone mapping for 15edo: Difference between revisions

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== 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.

[[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).

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

The fully expanded [[7L 1s]] mapping reduces the range (now under ~~just~~ 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.

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 + 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.

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).

=== 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]] ~~has demonstrated~~ this version in [https://www.youtube.com/shorts/n4552NepqZ8 ''Waltz in 15edo''] (2025).

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.

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 8: / Line 8: @@
 == 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.
+[[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}}
 === Fully Expanded (add Augmented/Triforce) ===
-The fully expanded [[7L&nbsp;1s]] mapping reduces the range (now under just 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.
+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 + 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.
+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}}
 === 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]] has demonstrated this version in [https://www.youtube.com/shorts/n4552NepqZ8 ''Waltz in 15edo''] (2025).
+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.
+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}}