Lumatone mapping for 15edo - Revision history

Lucius Chiaraviglio: /* Porcupine */ Add demo video for semi-expanded version

2026-06-04T03:47:08Z

Porcupine: Add demo video for semi-expanded version

← Older revision		Revision as of 03:47, 4 June 2026
Line 8:		Line 8:

	== Porcupine ==		== 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).
	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}		{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}

Lucius Chiaraviglio: /* Fully Expanded (add Augmented/Triforce) */ Fix word order

2026-05-30T03:23:58Z

Fully Expanded (add Augmented/Triforce): Fix word order

← Older revision		Revision as of 03:23, 30 May 2026
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	=== Fully Expanded (add Augmented/Triforce) ===		=== 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.
	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=-1}}

Lucius Chiaraviglio: /* Blackwood + Augmented (Augene) + Kleismic (Hanson/Keemun/Superkleismic) / add demo video; also fix title case of section heading; / Hanson*/ Add demo video

2026-03-08T22:54:42Z

Blackwood + Augmented (Augene) + Kleismic (Hanson/Keemun/Superkleismic): add demo video; also fix title case of section heading; Hanson: Add demo video

Lucius Chiaraviglio: /* Hanson */ Possibility for dual manuals

2026-03-07T09:45:43Z

Hanson: Possibility for dual manuals

← Older revision		Revision as of 09:45, 7 March 2026
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	== Hanson ==		== 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).
	{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}

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

Lucius Chiaraviglio: /* Blackwood + augmented (augene) + kleismic (hanson/keemun/superkleismic) */ Add links to scales

2026-03-07T09:09:58Z

Blackwood + augmented (augene) + kleismic (hanson/keemun/superkleismic): Add links to scales

← Older revision		Revision as of 09:09, 7 March 2026
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	=== 3L 3s (right, down-right) and 4L 3s (right, up) ===		=== 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.
	{{Lumatone EDO mapping\|n=15\|start=13\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=13\|xstep=3\|ystep=-1}}

	=== 3L 3s (right, up) and 4L 3s (right, down-right) ===		=== 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]] has demonstrated this version in [https://www.youtube.com/shorts/n4552NepqZ8 ''Waltz in 15edo''] (2025).
	{{Lumatone EDO mapping\|n=15\|start=4\|xstep=3\|ystep=-2}}		{{Lumatone EDO mapping\|n=15\|start=4\|xstep=3\|ystep=-2}}

Lucius Chiaraviglio: /* Fully Expanded (add Augmented/Triforce) */ Fix wording

2026-01-22T07:41:32Z

Fully Expanded (add Augmented/Triforce): Fix wording

← Older revision		Revision as of 07:41, 22 January 2026
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	=== Fully Expanded (add Augmented/Triforce) ===		=== 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 ~~two~~ partial 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 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.
	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=-1}}

Lucius Chiaraviglio: /* Porcupine */ Add the fully expanded mapping (also adds Augmented/Triforce), with demo video by Bryan Deister

2026-01-22T07:40:23Z

Porcupine: Add the fully expanded mapping (also adds Augmented/Triforce), with demo video by Bryan Deister

← Older revision		Revision as of 07:40, 22 January 2026
Line 8:		Line 8:

	== 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.		[[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.
	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}		{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}

			=== 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 two partial 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) ==

FloraC: Cleanup

2025-09-11T06:16:59Z

Cleanup

← Older revision		Revision as of 06:16, 11 September 2025
Line 5:		Line 5:
	{{Lumatone EDO mapping\|n=15\|start=12\|xstep=1\|ystep=4}}		{{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.		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 ==
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	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}		{{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 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#family~~\|~~Augmented~~]], specifically [[~~Augmented_family#Augene\|Augene~~]]. This also functions as a [[~~Kleismic~~]] ([[~~Kleismic_family#Kleismic_a.k.a._hanson\|Hanson~~]]/[[~~Kleismic_family#Keemun\|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.		[[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) ===		=== 3L 3s (right, down-right) and 4L 3s (right, up) ===
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	== Hanson ==		== 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.
	{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}

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

Yourmusic Productions: Fix math error.

2025-09-08T22:24:34Z

Fix math error.

← Older revision		Revision as of 22:24, 8 September 2025
Line 23:		Line 23:

	== Hanson ==		== 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 [[4L 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.
	{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}

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

Lucius Chiaraviglio: Reorganization and more elaboration of description

2025-08-29T07:48:56Z

Reorganization and more elaboration of description

← Older revision		Revision as of 07:48, 29 August 2025
Line 1:		Line 1:
	{{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 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).
	{{Lumatone EDO mapping\|n=15\|start=12\|xstep=1\|ystep=4}}		{{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.		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.
	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}		{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=1}}

← Older revision		Revision as of 22:54, 8 March 2026
Line 15:		Line 15:
	{{Lumatone EDO mapping\|n=15\|start=0\|xstep=2\|ystep=-1}}		{{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 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.		[[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) ===		=== 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).
	{{Lumatone EDO mapping\|n=15\|start=13\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=13\|xstep=3\|ystep=-1}}

	=== 3L 3s (right, up) and 4L 3s (right, down-right) ===		=== 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).
	{{Lumatone EDO mapping\|n=15\|start=4\|xstep=3\|ystep=-2}}		{{Lumatone EDO mapping\|n=15\|start=4\|xstep=3\|ystep=-2}}

	== Hanson ==		== 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).		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).
	{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=15\|start=9\|xstep=4\|ystep=-1}}

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