Lumatone mapping for 20edo - Revision history

Lucius Chiaraviglio: /* Tetracot (+ diminished + blackwood + skwares/squares) */ Add demo video

2025-12-31T20:54:01Z

Tetracot (+ diminished + blackwood + skwares/squares): Add demo video

← Older revision		Revision as of 20:54, 31 December 2025
Line 20:		Line 20:

	== Tetracot (+ diminished + blackwood + skwares/squares) ==		== Tetracot (+ diminished + blackwood + skwares/squares) ==
	[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.		[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/GxElRqwqz-o ''Nocturne in 20edo''] (2025).
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: /* Tetracot (+ diminished + blackwood + skwares/squares) */ Fix wording to avoid potential confusion

2025-12-28T00:55:29Z

Tetracot (+ diminished + blackwood + skwares/squares): Fix wording to avoid potential confusion

← Older revision		Revision as of 00:55, 28 December 2025
Line 20:		Line 20:

	== Tetracot (+ diminished + blackwood + skwares/squares) ==		== Tetracot (+ diminished + blackwood + skwares/squares) ==
	[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a ~~fourth~~ of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.		[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a quarter of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: /* Blackwood + skwares */ Add demo video

2025-11-06T05:52:03Z

Blackwood + skwares: Add demo video

← Older revision		Revision as of 05:52, 6 November 2025
Line 12:		Line 12:

	== Blackwood + skwares ==		== Blackwood + skwares ==
	Combining blackwood with [[skwares]] is another possibility. In the version of skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20 as one move right and one move down-right) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the blackwood sharp fifth at 720{{c}}).		Combining blackwood with [[skwares]] is another possibility. In the version of skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20 as one move right and one move down-right) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the blackwood sharp fifth at 720{{c}}). [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/qS4fpB_uIyo ''20edo''] (2023).
	{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}

Lucius Chiaraviglio: /* Tetracot (+ diminished + blackwood + skwares/squares) */ Add link to Tetracot

2025-09-11T22:05:42Z

Tetracot (+ diminished + blackwood + skwares/squares): Add link to Tetracot

← Older revision		Revision as of 22:05, 11 September 2025
Line 20:		Line 20:

	== Tetracot (+ diminished + blackwood + skwares/squares) ==		== Tetracot (+ diminished + blackwood + skwares/squares) ==
	Tetracot tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.		[[Tetracot]] tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

FloraC: Cleanup +1

2025-09-11T12:22:02Z

Cleanup +1

← Older revision		Revision as of 12:22, 11 September 2025
Line 15:		Line 15:
	{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}

	== Compressed skwares (~~Fibotonic~~ scale) without blackwood ==		== Compressed skwares (fibotonic scale) without blackwood ==
	[[Bryan Deister]] has used a compressed skwares [[2L 1s]] (7:6 step ratio) mapping for 20edo, as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025), which leaves out the blackwood division of the octave in favor of maximizing range. Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.		[[Bryan Deister]] has used a compressed skwares [[2L 1s]] (7:6 step ratio) mapping for 20edo, as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025), which leaves out the blackwood division of the octave in favor of maximizing range. Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.
	{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}

FloraC: Cleanup

2025-09-11T12:21:19Z

Cleanup

Lucius Chiaraviglio: /* Tetracot (+ Diminished + Blackwood + Skwares) */ --> Skwares/Squares, since Tetracot uses the 5th harmonic

2025-08-13T09:11:26Z

Tetracot (+ Diminished + Blackwood + Skwares): --> Skwares/Squares, since Tetracot uses the 5th harmonic

← Older revision		Revision as of 09:11, 13 August 2025
Line 19:		Line 19:
	{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}

	== Tetracot (+ Diminished + Blackwood + Skwares) ==		== Tetracot (+ Diminished + Blackwood + Skwares/Squares) ==
	Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp Blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The Tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) Diminished scale available by alternating right and down-right motions; it has embedded Blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for Skwares, thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.		Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp Blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The Tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) Diminished scale available by alternating right and down-right motions; it has embedded Blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for Skwares/Squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: /* Tetracot (+ Diminished + Blackwood) */ --> + Skwares

2025-08-13T07:55:34Z

Tetracot (+ Diminished + Blackwood): --> + Skwares

← Older revision		Revision as of 07:55, 13 August 2025
Line 19:		Line 19:
	{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}

	== Tetracot (+ Diminished + Blackwood) ==		== Tetracot (+ Diminished + Blackwood + Skwares) ==
	Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp Blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The Tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) Diminished scale available by alternating right and down-right motions; ~~and~~ it has embedded Blackwood rings by way of moving two keys at a time down-right, thus making these temperaments also accessible if one needs to switch temperaments frequently.		Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp Blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The Tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) Diminished scale available by alternating right and down-right motions; it has embedded Blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for Skwares, thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

Lucius Chiaraviglio: Fix Balzano --> Antidiatonic; reorganize Other mappings, and add Bryan Deister's '''2''' Lumatone mappings for 20edo

2025-08-13T07:00:24Z

Fix Balzano --> Antidiatonic; reorganize Other mappings, and add Bryan Deister's '''2''' Lumatone mappings for 20edo

← Older revision		Revision as of 07:00, 13 August 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}} You can use the b val, which creates the [[2L 5s]] ~~Balzano~~ mapping.		{{Lumatone mapping intro}} You can use the b val, which creates the [[2L 5s]] Antidiatonic mapping.

	== Balzano ==		== Antidiatonic (and Balzano) ==
			Antidiatonic is [[2L 5s]], in this case with a 5:2 step ratio, and can be played in this mapping without backtracking. Balzano is [[2L 7s]], in this case with a 3:2 step ratio, and can be played in this mapping by slightly backtracking at the large steps.
	{{Lumatone EDO mapping\|n=20\|start=4\|xstep=2\|ystep=3}}		{{Lumatone EDO mapping\|n=20\|start=4\|xstep=2\|ystep=3}}

	~~== Other mappings ==~~		The Antidiatonic/Balzano mapping is not particularly optimal for making the best tuned intervals easily playable, however, which the [[Blackwood]] and [[Tetracot]] mappings solve.
	The Balzano mapping is not particularly optimal for making the best tuned intervals easily playable, however, which the [[Blackwood]] and [[Tetracot]] mappings solve.

	=== Blackwood ===		== Blackwood + Diminished ==
			[[Bryan Deister]] has used a [[Diminished]] [[4L 4s]] (4:1 step ratio) mapping for 20edo that also functions as a [[Blackwood]] mapping, as demonstrated in [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025). In this mapping, the octave can be interpreted as being divided into five parts (Blackwood temperament) or 4\20 or four parts of 5\20 (Diminished temperament). Octaves slope, as expected for a Blackwood mapping, but with plenty of repeated vertical notes, and the range is a bit over 5½ octaves.
			{{Lumatone EDO mapping\|n=20\|start=6\|xstep=4\|ystep=-3}}

			== Blackwood + Skwares ==
			Combining Blackwood with [[Skwares]] is another possibility. In the version of Skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20 as one move right and one move down-right) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the Blackwood sharp fifth at 720{{c}}).
	{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}

	=== Tetracot ===		== Compressed Skwares (Fibotonic scale) without Blackwood ==
			[[Bryan Deister]] has used a compressed Skwares) [[2L 1s]] (7:6 step ratio) mapping for 20edo, as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025), which leaves out the Blackwood division of the octave in favor of maximizing range. Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.
			{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}

			== Tetracot (+ Diminished + Blackwood) ==
			Tetracot tempers together the Ptolmeic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmeic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp Blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The Tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) Diminished scale available by alternating right and down-right motions; and it has embedded Blackwood rings by way of moving two keys at a time down-right, thus making these temperaments also accessible if one needs to switch temperaments frequently.
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

ArrowHead294 at 14:38, 23 March 2025

2025-03-23T14:38:10Z

← Older revision		Revision as of 14:38, 23 March 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}} You can use the b val, which creates the [[2L 5s]] Balzano mapping.		{{Lumatone mapping intro}} You can use the b val, which creates the [[2L 5s]] Balzano mapping.

			== Balzano ==
	{{Lumatone EDO mapping\|n=20\|start=4\|xstep=2\|ystep=3}}		{{Lumatone EDO mapping\|n=20\|start=4\|xstep=2\|ystep=3}}

			== Other mappings ==
			The Balzano mapping is not particularly optimal for making the best tuned intervals easily playable, however, which the [[Blackwood]] and [[Tetracot]] mappings solve.

	~~This is not particularly optimal for making the best tuned intervals easily playable, however. Better options are the [[~~Blackwood~~]] mapping.~~		=== Blackwood ===
	{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}

			=== Tetracot ===
	~~Or the [[~~Tetracot~~]] mapping.~~
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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

← Older revision		Revision as of 12:21, 11 September 2025
Line 1:		Line 1:
	{{Lumatone mapping intro}} You can use the b val, which creates the [[2L 5s]] Antidiatonic mapping.		{{Lumatone mapping intro}} You can use the b val, which creates the [[2L 5s]] Antidiatonic mapping.

	== Antidiatonic (and ~~Balzano~~) ==		== Antidiatonic (and balzano) ==
	Antidiatonic is [[2L 5s]], in this case with a 5:2 step ratio, and can be played in this mapping without backtracking. Balzano is [[2L 7s]], in this case with a 3:2 step ratio, and can be played in this mapping by slightly backtracking at the large steps.		Antidiatonic is [[2L 5s]], in this case with a 5:2 step ratio, and can be played in this mapping without backtracking. Balzano is [[2L 7s]], in this case with a 3:2 step ratio, and can be played in this mapping by slightly backtracking at the large steps.
	{{Lumatone EDO mapping\|n=20\|start=4\|xstep=2\|ystep=3}}		{{Lumatone EDO mapping\|n=20\|start=4\|xstep=2\|ystep=3}}

	The ~~Antidiatonic~~/~~Balzano~~ mapping is not particularly optimal for making the best tuned intervals easily playable, however, which the [[~~Blackwood~~]] and [[~~Tetracot~~]] mappings solve.		The antidiatonic/balzano mapping is not particularly optimal for making the best tuned intervals easily playable, however, which the [[blackwood]] and [[tetracot]] mappings solve.

	== Blackwood + ~~Diminished~~ ==		== Blackwood + diminished ==
	[[Bryan Deister]] has used a [[~~Diminished~~]] [[4L 4s]] (4:1 step ratio) mapping for 20edo that also functions as a [[~~Blackwood~~]] mapping, as demonstrated in [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025). In this mapping, the octave can be interpreted as being divided into five parts (~~Blackwood~~ temperament) or 4\20 or four parts of 5\20 (~~Diminished~~ temperament). Octaves slope, as expected for a ~~Blackwood~~ mapping, but with plenty of repeated vertical notes, and the range is a bit over 5½ octaves.		[[Bryan Deister]] has used a [[diminished (temperament)\|diminished]] [[4L 4s]] (4:1 step ratio) mapping for 20edo that also functions as a [[blackwood]] mapping, as demonstrated in [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025). In this mapping, the octave can be interpreted as being divided into five parts (blackwood temperament) or 4\20 or four parts of 5\20 (diminished temperament). Octaves slope, as expected for a blackwood mapping, but with plenty of repeated vertical notes, and the range is a bit over 5½ octaves.
	{{Lumatone EDO mapping\|n=20\|start=6\|xstep=4\|ystep=-3}}		{{Lumatone EDO mapping\|n=20\|start=6\|xstep=4\|ystep=-3}}

	== Blackwood + ~~Skwares~~ ==		== Blackwood + skwares ==
	Combining ~~Blackwood~~ with [[~~Skwares~~]] is another possibility. In the version of ~~Skwares~~ used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20 as one move right and one move down-right) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the ~~Blackwood~~ sharp fifth at 720{{c}}).		Combining blackwood with [[skwares]] is another possibility. In the version of skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20 as one move right and one move down-right) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the blackwood sharp fifth at 720{{c}}).
	{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=12\|xstep=4\|ystep=-1}}

	== Compressed ~~Skwares~~ (Fibotonic scale) without ~~Blackwood~~ ==		== Compressed skwares (Fibotonic scale) without blackwood ==
	[[Bryan Deister]] has used a compressed ~~Skwares)~~ [[2L 1s]] (7:6 step ratio) mapping for 20edo, as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025), which leaves out the ~~Blackwood~~ division of the octave in favor of maximizing range. Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.		[[Bryan Deister]] has used a compressed skwares [[2L 1s]] (7:6 step ratio) mapping for 20edo, as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025), which leaves out the blackwood division of the octave in favor of maximizing range. Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.
	{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=3\|xstep=7\|ystep=-1}}

	== Tetracot (+ ~~Diminished~~ + ~~Blackwood~~ + ~~Skwares~~/~~Squares~~) ==		== Tetracot (+ diminished + blackwood + skwares/squares) ==
	Tetracot tempers together the ~~Ptolmeic~~ whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the ~~Ptolmeic~~ whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp ~~Blackwood~~ fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The ~~Tetracot~~ mapping does have an embedded [[4L 4s]] (3:2 step ratio) ~~Diminished~~ scale available by alternating right and down-right motions; it has embedded ~~Blackwood~~ rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for ~~Skwares~~/~~Squares~~), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.		Tetracot tempers together the Ptolmaic whole tone ~[[10/9]] with the undecimal submajor second ~[[11/10]] to make a fourth of the fifth ~[[3/2]]; however, in the case of 20edo, this requires using the 20c val to make the Ptolmaic whole tone map to its near-just [[direct approximation]] value (instead of its very flat [[patent val]] mapping) (and make the undecimal submajor whole tone fairly sharp) to get the sharp blackwood fifth. Octaves slope up, and the range is 4¾ octaves; notes are abundantly repeated, but unfortunately the upwards slope of the octaves is inconvenient for division into multiple manuals. The tetracot mapping does have an embedded [[4L 4s]] (3:2 step ratio) diminished scale available by alternating right and down-right motions; it has embedded blackwood rings by way of moving two keys at a time down-right; and it even has an embedded 2L 1s (7:6 step ratio) scale for skwares/squares), thus making these temperaments also accessible if one needs to switch temperaments frequently, thus gaining considerable versatility in exchange for the lost range.
	{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}		{{Lumatone EDO mapping\|n=20\|start=17\|xstep=3\|ystep=-1}}

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