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| == Cantonismic-Werckismic rank-3 temperament Lumatone mappings == | | == Cantonismic-Werckismic rank-3 temperament Lumatone mappings == |
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| === 74edo (demonstrated to work but awaiting approval) ===
| | Due to this page getting too large, moved these to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various rank-3 temperament Lumatone mappings|Various rank-3 temperament Lumatone mappings]]. |
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| [[Bryan Deister]] has demonstrated the [[7L 6s]] mapping of [[74edo]] in [https://www.youtube.com/shorts/ylOGUb395Gg ''microtonal improvisation in 74edo''] (2025). The rightward generator (8\74) functions as ~[[14/13]]; three of them make a classic major third ~[[5/4]] (the [[cantonisma]] 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~[[16/11]]; and eight of them make a highly accurate undecimal supraminor seventh ~[[20/11]]. The upward generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The range is about just over 3 octaves with no missing notes, and the octaves slope downward moderately, resulting in a vertical wraparound.
| | Contents of this section moved to separate page: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 June 2025 (UTC) |
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| {{Lumatone EDO mapping|n=74|start=4|xstep=8|ystep=-5}}
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| Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:02, 12 June 2025 (UTC)
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| Last Modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:17, 12 June 2025 (UTC)
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| == Compton-related rank 3 temperament Lumatone mappings == | | == Compton-related rank 3 temperament Lumatone mappings == |
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| === 96edo (demonstrated to work) ===
| | Due to this page getting too large, moved these to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various rank-3 temperament Lumatone mappings|Various rank-3 temperament Lumatone mappings]]. |
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| [[Bryan Deister]] has demonstrated a mapping for [[96edo]] in which the rightward generator is 8\96 (~[[18/17]]) as in [[12edo]], while the upward generator is 7\96 (~[[20/19]]), in [https://www.youtube.com/shorts/8xqjUkuZFaI ''microtonal improvisation in 96edo''] (2025). The range is just over two octaves, with octaves sloping away and then wrapping around; on the other hand, it is easy to play eight 12edo subsets of 96edo that are displaced slightly from each other, as if one had eight pianos (even if of rather short compass) somehow all in reach at once. (Here, note 0 is in the middle of the left edge instead of Bryan Deister's usual lower left corner, to avoid skipping some of the bottom notes in the lowest note 0 to note 0 octave.) Although not shown in the video, this mapping also enables easy glissandos diagonally up-left or down-right.
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| {{Lumatone EDO mapping|n=96|start=12|xstep=8|ystep=-7}}
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| Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:40, 24 May 2025 (UTC)<br>
| | Contents of this section moved to separate page: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 June 2025 (UTC) |
| Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:33, 26 May 2025 (UTC)
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| == Devichromic Lumatone mappings == | | == Devichromic Lumatone mappings == |
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| == Meantone-related rank-3 Lumatone mappings == | | == Meantone-related rank-3 Lumatone mappings == |
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| === 74edo (proposed and untested) ===
| | Due to this page getting too large, moved these to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various rank-3 temperament Lumatone mappings|Various rank-3 temperament Lumatone mappings]]. |
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| An alternate [[9L 4s]] mapping of [[74edo]] is worthy of consideration. The rightward generator (6\74) functions as ~[[17/16]] and ~[[18/17]] (the semitonisma [[289/288]] is tempered out); two of them make a meantone whole tone (which functions as ~[[10/9]], ~[[9/8]], and ~[[19/17]] — the syntonic comma [[81/80]], the ganassisma [[153/152]], and the malcolmisma [[171/170]] are all tempered out); three of them make the neogothic minor third ~[[13/11]]; four of them make the classic major third ~[[5/4]]; and six of them make the lesser septimal tritone ~[[7/5]]. The down-right generator (5\74) functions as ~[[21/20]] and ~[[22/21]] (the Werckisma ([[441/440]] is tempered out); two of these make ~[[11/10]]; five of these make ~[[24/19]] (which is distinguished from ~5/4); and eight of these make ~[[16/11]]. The stacking of two or four instances of ~[[3/2]] (43\74) and octave-reducing also yields the same results as two or four instances (respectively) of the rightward generator, making this a meantone mapping as expected for the [[patent val]] of 74edo; yet the usefulness of the down-right generator for reaching higher-limit intervals is undeniable, making this a mapping for a [[Meantone]]-related rank-3 temperament in the [[19-limit]] that is different from [[Didymus]]. The range is about 2⅔ octaves with no missing notes, less than [[Bryan Deister]]'s Cantonismic-Werckismic detailed above, but the octaves slope downward only very gently, and include a few more duplicate notes which partially alleviate vertical wraparounds (in addition to the useful temperament properties detailed above).
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| {{Lumatone EDO mapping|n=74|start=66|xstep=6|ystep=-1}}
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| Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 12 June 2025 (UTC)<br>
| | Contents of this section moved to separate page: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 June 2025 (UTC) |
| Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:17, 12 June 2025 (UTC)
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| == Miracle and Miracle-related Lumatone mappings == | | == Miracle and Miracle-related Lumatone mappings == |