User:Lucius Chiaraviglio/Keyboard Layout Lab: Difference between revisions

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@@ Line 13: / Line 13: @@
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:50, 1 May 2025 (UTC)<br>
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:30, 2 May 2025 (UTC)
+== Cantonismic-Werckismic rank-3 temperament Lumatone mappings ==
+=== 74edo (demonstrated to work but awaiting approval) ===
+[[Bryan Deister]] has demonstrated the [[7L&nbsp;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.
+{{Lumatone EDO mapping|n=74|start=4|xstep=8|ystep=-5}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:02, 12 June 2025 (UTC)
+Last Modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:17, 12 June 2025 (UTC)
 == Compton-related rank 3 temperament Lumatone mappings ==
@@ Line 53: / Line 64: @@
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:56, 30 May 2025 (UTC)
 Moved here from [[User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings|Various other Lumatone mappings]] page:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:15, 31 May 2025 (UTC)
-== Cantonismic-Werckismic rank-3 temperament Lumatone mappings ==
-=== 74edo (demonstrated to work but awaiting approval) ===
-[[Bryan Deister]] has demonstrated the [[7L&nbsp;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 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 just over 3 octaves with no missing notes, and the octaves slope downward moderately, resulting in a vertical wraparound.
-{{Lumatone EDO mapping|n=74|start=4|xstep=8|ystep=-5}}
 == Meantone-related rank-3 Lumatone mappings ==
@@ Line 66: / Line 69: @@
 === 74edo (proposed and untested) ===
-An alternate [[9L&nbsp;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]] &mdash; 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 (indeed, with a few duplicate notes which partially alleviate vertical wraparounds), and the octaves slope downward very gently.
+An alternate [[9L&nbsp;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]] &mdash; 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).
 {{Lumatone EDO mapping|n=74|start=66|xstep=6|ystep=-1}}
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 12 June 2025 (UTC)<br>
-Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:02, 12 June 2025 (UTC)
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:17, 12 June 2025 (UTC)
 == Miracle and Miracle-related Lumatone mappings ==