Lumatone mapping for 75edo - Revision history

Yourmusic Productions: Elaboration.

2025-10-28T18:20:57Z

Elaboration.

← Older revision		Revision as of 18:20, 28 October 2025
Line 32:		Line 32:
	{{Lumatone EDO mapping\|n=76\|\|start=68\|xstep=12\|ystep=-4}}		{{Lumatone EDO mapping\|n=76\|\|start=68\|xstep=12\|ystep=-4}}

			Removing the octave correction turns this into an approximation of [[Carlos Beta]].
			{{Lumatone EDO mapping\|n=75\|\|start=67\|xstep=12\|ystep=-4}}
	{{Navbox Lumatone}}		{{Navbox Lumatone}}

Lucius Chiaraviglio: /* Neutral Thirds */ Insert Bryan Deister's 18L 1s MOS subset pseudo-diatonic mapping after this

2025-10-28T06:49:58Z

Neutral Thirds: Insert Bryan Deister's 18L 1s MOS subset pseudo-diatonic mapping after this

← Older revision		Revision as of 06:49, 28 October 2025
Line 27:		Line 27:
	The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves (just over 3½) even closer to horizontal, with scale [[7L 3s]] (step size ratio 9:4). [[Bryan Deister]] has demonstrated this mapping, in [https://www.youtube.com/shorts/QflMtKRmlSI ''microtonal improvisation in 75edo''] (2025-06-24). Like [[97edo]], 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~[[25/23]] (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~[[625/529]] (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~[[9/7]] (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~[[34/19]] (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~[[27/26]] and ~[[28/27]]; down-right 2 keys = ~[[14/13]] (errors largely cancel), 3 keys = ~[[19/17]] (errors largely cancel), and 5 keys = ~[[5/4]] (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~[[23/22]] (errors only partially canceling, so somewhat sharp).		The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves (just over 3½) even closer to horizontal, with scale [[7L 3s]] (step size ratio 9:4). [[Bryan Deister]] has demonstrated this mapping, in [https://www.youtube.com/shorts/QflMtKRmlSI ''microtonal improvisation in 75edo''] (2025-06-24). Like [[97edo]], 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~[[25/23]] (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~[[625/529]] (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~[[9/7]] (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~[[34/19]] (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~[[27/26]] and ~[[28/27]]; down-right 2 keys = ~[[14/13]] (errors largely cancel), 3 keys = ~[[19/17]] (errors largely cancel), and 5 keys = ~[[5/4]] (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~[[23/22]] (errors only partially canceling, so somewhat sharp).
	{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}

			== 18L 1s MOS subset pseudo-diatonic ==
			[[Bryan Deister]] has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for [[75edo]] in [https://www.youtube.com/shorts/nlurS-3VYkA ''75edo improv''] (2025) that deliberately uses non-coprime generators on all axes with the numbering of [[76edo]] to use a subset of 75edo to make 19 non-equal divisions of the octave in the form of a [[18L 1s]] MOS scale with a 4:3 step ratio. Note 75 is actually a duplicate of note 0; due to missing notes, it does not actually appear here.
			{{Lumatone EDO mapping\|n=76\|\|start=68\|xstep=12\|ystep=-4}}

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

Lucius Chiaraviglio: /* Compressed (Reversed-Chroma 1L 5s) Tetracot */ 6L 1s; is also supported but requires backtracking.

2025-06-30T00:13:43Z

Compressed (Reversed-Chroma 1L 5s) Tetracot: 6L&nbsp1s; is also supported but requires backtracking.

← Older revision		Revision as of 00:13, 30 June 2025
Line 13:		Line 13:

	=== Compressed (Reversed-Chroma 1L 5s) Tetracot ===		=== Compressed (Reversed-Chroma 1L 5s) Tetracot ===
	[[Bryan Deister]] has demonstrated a compressed [[1L 5s]] mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).		[[Bryan Deister]] has demonstrated a compressed [[1L 5s]] mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. (This also contains the Tetracot [[6L 1s]] scale, but playing that scale in this layout requires backtracking.) This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
	{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}		{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}

Yourmusic Productions at 15:19, 29 June 2025

2025-06-29T15:19:06Z

← Older revision		Revision as of 15:19, 29 June 2025
Line 12:		Line 12:
	{{Lumatone EDO mapping\|n=75\|start=45\|xstep=11\|ystep=-2}}		{{Lumatone EDO mapping\|n=75\|start=45\|xstep=11\|ystep=-2}}

	=== Compressed (Reversed-Chroma 6L 1s) Tetracot ===		=== Compressed (Reversed-Chroma 1L 5s) Tetracot ===
	[[Bryan Deister]] has demonstrated a compressed [[1L 5s]] mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).		[[Bryan Deister]] has demonstrated a compressed [[1L 5s]] mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
	{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}		{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}

Yourmusic Productions: Fix math & formatting.

2025-06-29T15:18:39Z

Fix math & formatting.

← Older revision		Revision as of 15:18, 29 June 2025
Line 13:		Line 13:

	=== Compressed (Reversed-Chroma 6L 1s) Tetracot ===		=== Compressed (Reversed-Chroma 6L 1s) Tetracot ===
	[[Bryan Deister]] has demonstrated a compressed [[6L 1s mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).		[[Bryan Deister]] has demonstrated a compressed [[1L 5s]] mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
	{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}		{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}

Lucius Chiaraviglio: /* Tetracot */ Add Bryan Deister's Reversed-Chroma Compressed Tetracot mapping for 75edo; reorganize section to accommodate this

2025-06-29T06:28:56Z

Tetracot: Add Bryan Deister's Reversed-Chroma Compressed Tetracot mapping for 75edo; reorganize section to accommodate this

← Older revision		Revision as of 06:28, 29 June 2025
Line 6:		Line 6:

	== Tetracot ==		== Tetracot ==
	The [[Tetracot]] mapping is considerably more efficient at putting harmonics close together~~, although it also needs to be expanded from [[~~6L 1s~~]] to~~ [[~~7L 6s~~]] to ~~hit every single note, which puts octaves~~ all ~~over~~ the ~~place~~		The [[Tetracot]] mapping is considerably more efficient at putting harmonics close together.

			=== Standard (6L 1s) Tetracot ===
			However, 75edo is too large for the standard [[Lumatone mapping for Tetracot]] to include all of the notes.
	{{Lumatone EDO mapping\|n=75\|start=45\|xstep=11\|ystep=-2}}		{{Lumatone EDO mapping\|n=75\|start=45\|xstep=11\|ystep=-2}}

			=== Compressed (Reversed-Chroma 6L 1s) Tetracot ===
			[[Bryan Deister]] has demonstrated a compressed [[6L 1s mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
			{{Lumatone EDO mapping\|n=75\|start=17\|xstep=11\|ystep=9}}

			=== Expanded (7L 6s) Tetracot ===
			To cover all of the notes in 75edo, Tetracot needs to be expanded from [[6L 1s]] to [[7L 6s]], which puts octaves all over the place
	{{Lumatone EDO mapping\|n=75\|start=0\|xstep=9\|ystep=-7}}		{{Lumatone EDO mapping\|n=75\|start=0\|xstep=9\|ystep=-7}}

Lucius Chiaraviglio: /* Neutral Thirds */ Put exact date on demo video because another demonstration video is coming that has the same exact name

2025-06-29T05:47:29Z

Neutral Thirds: Put exact date on demo video because another demonstration video is coming that has the same exact name

← Older revision		Revision as of 05:47, 29 June 2025
Line 17:		Line 17:

	== Neutral Thirds ==		== Neutral Thirds ==
	The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves (just over 3½) even closer to horizontal, with scale [[7L 3s]] (step size ratio 9:4). [[Bryan Deister]] has demonstrated this mapping, in [https://www.youtube.com/shorts/QflMtKRmlSI ''microtonal improvisation in 75edo''] (2025). Like [[97edo]], 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~[[25/23]] (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~[[625/529]] (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~[[9/7]] (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~[[34/19]] (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~[[27/26]] and ~[[28/27]]; down-right 2 keys = ~[[14/13]] (errors largely cancel), 3 keys = ~[[19/17]] (errors largely cancel), and 5 keys = ~[[5/4]] (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~[[23/22]] (errors only partially canceling, so somewhat sharp).		The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves (just over 3½) even closer to horizontal, with scale [[7L 3s]] (step size ratio 9:4). [[Bryan Deister]] has demonstrated this mapping, in [https://www.youtube.com/shorts/QflMtKRmlSI ''microtonal improvisation in 75edo''] (2025-06-24). Like [[97edo]], 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~[[25/23]] (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~[[625/529]] (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~[[9/7]] (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~[[34/19]] (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~[[27/26]] and ~[[28/27]]; down-right 2 keys = ~[[14/13]] (errors largely cancel), 3 keys = ~[[19/17]] (errors largely cancel), and 5 keys = ~[[5/4]] (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~[[23/22]] (errors only partially canceling, so somewhat sharp).
	{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}

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

Lucius Chiaraviglio: /* Neutral Thirds */ Add demonstration video and scale/temperament-related text

2025-06-26T07:02:30Z

Neutral Thirds: Add demonstration video and scale/temperament-related text

← Older revision		Revision as of 07:02, 26 June 2025
Line 17:		Line 17:

	== Neutral Thirds ==		== Neutral Thirds ==
	The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves even closer to horizontal.		The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves (just over 3½) even closer to horizontal, with scale [[7L 3s]] (step size ratio 9:4). [[Bryan Deister]] has demonstrated this mapping, in [https://www.youtube.com/shorts/QflMtKRmlSI ''microtonal improvisation in 75edo''] (2025). Like [[97edo]], 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~[[25/23]] (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~[[625/529]] (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~[[9/7]] (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~[[34/19]] (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~[[27/26]] and ~[[28/27]]; down-right 2 keys = ~[[14/13]] (errors largely cancel), 3 keys = ~[[19/17]] (errors largely cancel), and 5 keys = ~[[5/4]] (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~[[23/22]] (errors only partially canceling, so somewhat sharp).
	{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}

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

Lucius Chiaraviglio: /* Diatonic */ Add demonstration video

2025-06-23T01:47:43Z

Diatonic: Add demonstration video

← Older revision		Revision as of 01:47, 23 June 2025
Line 2:		Line 2:

	== Diatonic ==		== Diatonic ==
	However, Due to the size of the edo, this mapping does not cover all the notes. In addition, like [[46edo]], 75edo is a [[leapday]] system, so the best approximation to [[5/4]] is a ''triply-augmented'' unison, which makes for awkward fingerings.		However, Due to the size of the edo, this mapping does not cover all the notes. In addition, like [[46edo]], 75edo is a [[leapday]] system, so the best approximation to [[5/4]] is a ''triply-augmented'' unison, which makes for awkward fingerings. Despite the missing notes, [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/watch?v=sdN-5y3jhDY&lc=UgxpTCf_D53IW3ACl1Z4AaABAg ''improv in 75edo''] (2025)
	{{Lumatone EDO mapping\|n=75\|start=6\|xstep=13\|ystep=-8}}		{{Lumatone EDO mapping\|n=75\|start=6\|xstep=13\|ystep=-8}}

Yourmusic Productions: Expansion.

2025-06-13T18:31:07Z

Expansion.

← Older revision		Revision as of 18:31, 13 June 2025
Line 15:		Line 15:
	To maximise range while covering the whole gamut, giving easy access to lower harmonics and keeping octaves near horizontal, slice the period into thirds to produce the [[Fog]] mapping.		To maximise range while covering the whole gamut, giving easy access to lower harmonics and keeping octaves near horizontal, slice the period into thirds to produce the [[Fog]] mapping.
	{{Lumatone EDO mapping\|n=75\|start=42\|xstep=6\|ystep=7}}		{{Lumatone EDO mapping\|n=75\|start=42\|xstep=6\|ystep=7}}

			== Neutral Thirds ==
			The neutral thirds mapping has slightly less range, but skips fewer notes around the edges and keeps octaves even closer to horizontal.
			{{Lumatone EDO mapping\|n=75\|start=2\|xstep=9\|ystep=-5}}

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