User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings: Difference between revisions

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 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:44, 23 July 2025 (UTC)
+== Aureus Pseudo-Meantone Lumatone mappings ==
+=== 63edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\63 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals &mdash; for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.
+{{Lumatone EDO mapping|n=63|start=6|xstep=10|ystep=-7}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:52, 23 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:39, 15 November 2025 (UTC)
+=== 87edo (demonstrated to work but awaiting approval) ===
+[[Bryan Deister]] has demonstrated a [[11L&nbsp;5s]] (7:2 step ratio) mapping for [[87edo]] in [[https://www.youtube.com/shorts/rINJKiMQE78 ''Circuit Bent - Stomach Book (microtonal cover in 87edo)''] (2025). The generator 14\87, which is two keys right from the root note, is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it near-just; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 87edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Since this interval is two keys right instead of just one (as needed to avoid missing notes), this version of the temperament can be viewed as a split generator version, in which each ~19/17 is split into two equal intervals that function as both a small septendecimal semitone ~[[18/17]] and a large undevicesimal semitone ~[[19/18]], both being close to just (and the photisma [[324/323]] is tempered out). Although no second generator is needed to reach all of the notes, for convenience, down-right by one key (2\87) can be used for convenienbce as a second generator that functions as ~[[49/48]] (inconsistently mapped), ~[[55/54]], ~[[64/63]], ~[[65/64]], and ~[[81/80]], of which the septimal chroma ~64/63 is near-just, and four of these make a near-just classic diatonic semitone ~[[16/15]] (the currently unnamed unnoticeable comma [[5250987/5242880]] is tempered out). The range is somewhat over two octaves (which slant very slightly downwards) with no missed notes and some repeated notes to mitigate vertical wraparounds.
+{{Lumatone EDO mapping|n=87|start=0|xstep=7|ystep=-5}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:39, 15 November 2025 (UTC)
 == Compressed Neutral Thirds Lumatone mappings ==
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 Moved here from [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Unnamed_Temperament_Lumatone_mappings|Unnamed Temperament Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:49, 6 November 2025 (UTC)<br>
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:58, 8 November 2025 (UTC)
+== Lesser Tendoneutralic Lumatone mappings ==
+=== 67edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[7L&nbsp;3s]] (7:6 step ratio) layout for [[67edo]] that uses the tempering out of the [[Lesser tendoneutralisma]] (70368744177664/69894255367443, more conveniently described as {{nowrap|{{!}}46 -1 0 0 0 -12⟩}}), in [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~[[16/13]] (octave-reduced 13th subharmonic).  Twelve of these are tempered together to make ~[[12/1]], which is then octave-reduced to the twelfth ~[[3/1]], and thence to the fifth ~[[3/2]]. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo &mdash; the notes of a complete [[meantone]] diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).
+{{Lumatone EDO mapping|n=67|start=50|xstep=7|ystep=-1}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:56, 29 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:52, 30 July 2025 (UTC)
 == Machine Lumatone mappings ==
@@ Line 114: / Line 144: @@
 Last Modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:39, 29 March 2025 (UTC)
 Moved here from Various Kit-Bashed Lumatone mappings:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:35, 23 July 2025 (UTC)
-== Lesser Tendoneutralic Lumatone mappings ==
-=== 67edo (demonstrated to work) ===
-[[Bryan Deister]] has demonstrated a [[7L&nbsp;3s]] (7:6 step ratio) layout for [[67edo]] that uses the tempering out of the [[Lesser tendoneutralisma]] (70368744177664/69894255367443, more conveniently described as {{nowrap|{{!}}46 -1 0 0 0 -12⟩}}), in [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~[[16/13]] (octave-reduced 13th subharmonic).  Twelve of these are tempered together to make ~[[12/1]], which is then octave-reduced to the twelfth ~[[3/1]], and thence to the fifth ~[[3/2]]. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo &mdash; the notes of a complete [[meantone]] diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).
-{{Lumatone EDO mapping|n=67|start=50|xstep=7|ystep=-1}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:56, 29 July 2025 (UTC)<br>
-Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:52, 30 July 2025 (UTC)
 == Neutral Thirds + Opossum + Hemisensi + Ptolemy Lumatone mappings ==
@@ Line 136: / Line 155: @@
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:17, 8 October 2025 (UTC)<br>
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:59, 9 October 2025 (UTC)
-== Pseudo-Meantone Lumatone mappings ==
-=== 63edo (demonstrated to work) ===
-[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals &mdash; for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.
-{{Lumatone EDO mapping|n=63|start=6|xstep=10|ystep=-7}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:52, 23 July 2025 (UTC)<br>
-Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:44, 27 July 2025 (UTC)
 == Semaphore/Semiquartal Lumatone mappings ==