Lumatone mapping for 92edo - Revision history

Yourmusic Productions: Fix math error.

2026-02-18T17:39:53Z

Fix math error.

← Older revision		Revision as of 17:39, 18 February 2026
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	There are many conceivable ways to map [[~~95edo~~]] onto the onto the Lumatone keyboard, but the [[Standard Lumatone mapping for Pythagorean]] does not work for the [[patent val]], because the patent fifth is shared with [[46edo]], making two mutually-exclusive rings of fifths. It only works for the very flat (92b val) and very sharp (92bb val) alternate fifths. Also, the large number of notes means the standard diatonic mapping and many others will fail to cover the entire gamut.		There are many conceivable ways to map [[92edo]] onto the onto the Lumatone keyboard, but the [[Standard Lumatone mapping for Pythagorean]] does not work for the [[patent val]], because the patent fifth is shared with [[46edo]], making two mutually-exclusive rings of fifths. It only works for the very flat (92b val) and very sharp (92bb val) alternate fifths. Also, the large number of notes means the standard diatonic mapping and many others will fail to cover the entire gamut.

	== Diatonic ==		== Diatonic ==

Lucius Chiaraviglio: /* 30L 1s subset pseudo-diatonic */ Fix title

2025-10-30T08:08:20Z

30L 1s subset pseudo-diatonic: Fix title

← Older revision		Revision as of 08:08, 30 October 2025
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	{{Lumatone EDO mapping\|n=92\|start=76\|xstep=14\|ystep=-3}}		{{Lumatone EDO mapping\|n=92\|start=76\|xstep=14\|ystep=-3}}

	=== 30L 1s subset pseudo-diatonic ===		=== 30L 1s MOS subset pseudo-diatonic ===

	[[Bryan Deister]] has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for [[92edo]] in [https://www.youtube.com/watch?v=qWAinBYHwtE ''92edo waltz''] (2025) that deliberately uses non-coprime generators on all axes to use a subset of 92edo to make 31 non-equal divisions of the octave in the form of a [[30L 1s]] MOS scale with a 3:2 step ratio. This layout is numbered as for [[93edo]], but note 92 is actually a duplicate of note 0; due to missing notes, it does not actually appear here.		[[Bryan Deister]] has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for [[92edo]] in [https://www.youtube.com/watch?v=qWAinBYHwtE ''92edo waltz''] (2025) that deliberately uses non-coprime generators on all axes to use a subset of 92edo to make 31 non-equal divisions of the octave in the form of a [[30L 1s]] MOS scale with a 3:2 step ratio. This layout is numbered as for [[93edo]], but note 92 is actually a duplicate of note 0; due to missing notes, it does not actually appear here.

Lucius Chiaraviglio: Fix section headings; add Bryan Deister's Lumatone mapping for 30L 1s subset of 92edo

2025-09-30T05:53:07Z

Fix section headings; add Bryan Deister's Lumatone mapping for 30L 1s subset of 92edo

← Older revision		Revision as of 05:53, 30 September 2025
Line 1:		Line 1:
	There are many conceivable ways to map [[95edo]] onto the onto the Lumatone keyboard, but the [[Standard Lumatone mapping for Pythagorean]] does not work for the [[patent val]], because the patent fifth is shared with [[46edo]], making two mutually-exclusive rings of fifths. It only works for the very flat (92b val) and very sharp (92bb val) alternate fifths. Also, the large number of notes means the standard diatonic mapping and many others will fail to cover the entire gamut.		There are many conceivable ways to map [[95edo]] onto the onto the Lumatone keyboard, but the [[Standard Lumatone mapping for Pythagorean]] does not work for the [[patent val]], because the patent fifth is shared with [[46edo]], making two mutually-exclusive rings of fifths. It only works for the very flat (92b val) and very sharp (92bb val) alternate fifths. Also, the large number of notes means the standard diatonic mapping and many others will fail to cover the entire gamut.

	==== ~~Diatonic (sharp~~ fifth~~) =~~===		== Diatonic ==
			=== Sharp fifth ===
	The 92bb val has a very sharp fifth. On a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes (460 required in the space of five octaves), this diatonic mapping would be a good mapping for a very sharp temperament of the [[Archytas clan]].		The 92bb val has a very sharp fifth. On a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes (460 required in the space of five octaves), this diatonic mapping would be a good mapping for a very sharp temperament of the [[Archytas clan]].
	{{Lumatone EDO mapping\|n=92\|start=32\|xstep=18\|ystep=-17}}		{{Lumatone EDO mapping\|n=92\|start=32\|xstep=18\|ystep=-17}}

	===~~= Diatonic (flat~~ fifth~~) =~~===		=== Flat fifth ===
	The 92b val has a very flat fifth, just 0.102{{c}} sharp of [[1/2-comma meantone]]. On a hypothetical XL-sized Lumatone (as above), this diatonic mapping would be a good mapping for [[flattone]] (as 92bcccd) or [[flattertone]] (as 92bcccdd).		The 92b val has a very flat fifth, just 0.102{{c}} sharp of [[1/2-comma meantone]]. On a hypothetical XL-sized Lumatone (as above), this diatonic mapping would be a good mapping for [[flattone]] (as 92bcccd) or [[flattertone]] (as 92bcccdd).
	{{Lumatone EDO mapping\|n=92\|start=76\|xstep=14\|ystep=-3}}		{{Lumatone EDO mapping\|n=92\|start=76\|xstep=14\|ystep=-3}}

	==== Unidentified rank-3 temperament mapping ====		=== 30L 1s subset pseudo-diatonic ===

			[[Bryan Deister]] has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for [[92edo]] in [https://www.youtube.com/watch?v=qWAinBYHwtE ''92edo waltz''] (2025) that deliberately uses non-coprime generators on all axes to use a subset of 92edo to make 31 non-equal divisions of the octave in the form of a [[30L 1s]] MOS scale with a 3:2 step ratio. This layout is numbered as for [[93edo]], but note 92 is actually a duplicate of note 0; due to missing notes, it does not actually appear here.

			{{Lumatone EDO mapping\|n=93\|start=87\|xstep=15\|ystep=-6}}

			== Unidentified rank-3 temperament mapping ==
	[[Bryan Deister]] has demonstrated an [[8L 5s]] (step ratio 9:4) mapping for [[92edo]] in [https://www.youtube.com/shorts/5XFOALAzLiA ''microtonal improvisation in 92edo''] (2025). As 9\92, the rightward generator maps to a slightly flat ~[[31/29]], and five of these make the slightly sharp patent fifth ~[[3/2]]. The upward generator 5\92 yields ~[[14/13]] by stacking two of these. The down-right generator 4\92 functions as ~[[33/32]], ~[[34/33]], and ~[[35/34]]; stacking two of these (8\92) yields ~[[17/16]]; stacking six of these (24\92) yields ~[[6/5]]; stacking eight of these (32\92) yields ~[[14/11]]. The first note 0 can be placed in the lower left corner (as actually used in the demonstration video) to avoid having a little piece of an octave before it, but this results in a vertical wraparound of the octaves, which slant down moderately (over the range of slightly over 2¼ octaves).		[[Bryan Deister]] has demonstrated an [[8L 5s]] (step ratio 9:4) mapping for [[92edo]] in [https://www.youtube.com/shorts/5XFOALAzLiA ''microtonal improvisation in 92edo''] (2025). As 9\92, the rightward generator maps to a slightly flat ~[[31/29]], and five of these make the slightly sharp patent fifth ~[[3/2]]. The upward generator 5\92 yields ~[[14/13]] by stacking two of these. The down-right generator 4\92 functions as ~[[33/32]], ~[[34/33]], and ~[[35/34]]; stacking two of these (8\92) yields ~[[17/16]]; stacking six of these (24\92) yields ~[[6/5]]; stacking eight of these (32\92) yields ~[[14/11]]. The first note 0 can be placed in the lower left corner (as actually used in the demonstration video) to avoid having a little piece of an octave before it, but this results in a vertical wraparound of the octaves, which slant down moderately (over the range of slightly over 2¼ octaves).
	{{Lumatone EDO mapping\|n=92\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=92\|start=2\|xstep=9\|ystep=-5}}

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

Lucius Chiaraviglio: Create Lumatone mapping for 92edo, starting with Bryan Deister's Lumatone mapping for 92edo and the obligatory diatonic mappings

2025-06-04T15:23:34Z

Create Lumatone mapping for 92edo, starting with Bryan Deister's Lumatone mapping for 92edo and the obligatory diatonic mappings

New page

There are many conceivable ways to map [[95edo]] onto the onto the Lumatone keyboard, but the [[Standard Lumatone mapping for Pythagorean]] does not work for the [[patent val]], because the patent fifth is shared with [[46edo]], making two mutually-exclusive rings of fifths. It only works for the very flat (92b val) and very sharp (92bb val) alternate fifths. Also, the large number of notes means the standard diatonic mapping and many others will fail to cover the entire gamut.

==== Diatonic (sharp fifth) ====
The 92bb val has a very sharp fifth. On a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes (460 required in the space of five octaves), this diatonic mapping would be a good mapping for a very sharp temperament of the [[Archytas clan]].
{{Lumatone EDO mapping|n=92|start=32|xstep=18|ystep=-17}}

==== Diatonic (flat fifth) ====
The 92b val has a very flat fifth, just 0.102{{c}} sharp of [[1/2-comma meantone]]. On a hypothetical XL-sized Lumatone (as above), this diatonic mapping would be a good mapping for [[flattone]] (as 92bcccd) or [[flattertone]] (as 92bcccdd).
{{Lumatone EDO mapping|n=92|start=76|xstep=14|ystep=-3}}

==== Unidentified rank-3 temperament mapping ====
[[Bryan Deister]] has demonstrated an [[8L 5s]] (step ratio 9:4) mapping for [[92edo]] in [https://www.youtube.com/shorts/5XFOALAzLiA ''microtonal improvisation in 92edo''] (2025). As 9\92, the rightward generator maps to a slightly flat ~[[31/29]], and five of these make the slightly sharp patent fifth ~[[3/2]]. The upward generator 5\92 yields ~[[14/13]] by stacking two of these. The down-right generator 4\92 functions as ~[[33/32]], ~[[34/33]], and ~[[35/34]]; stacking two of these (8\92) yields ~[[17/16]]; stacking six of these (24\92) yields ~[[6/5]]; stacking eight of these (32\92) yields ~[[14/11]]. The first note 0 can be placed in the lower left corner (as actually used in the demonstration video) to avoid having a little piece of an octave before it, but this results in a vertical wraparound of the octaves, which slant down moderately (over the range of slightly over 2¼ octaves).
{{Lumatone EDO mapping|n=92|start=2|xstep=9|ystep=-5}}

{{Navbox Lumatone}}