User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings: Difference between revisions
→Infraorwell Lumatone mappings: →49edo: (Temporarily moved to near top for visibility.) |
→Archipelago + Catalan Lumatone mappings: →49edo: →Reverse chroma version: Got approval |
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== Archipelago + Catalan Lumatone mappings == | == Archipelago + Catalan Lumatone mappings == | ||
=== 49edo (demonstrated to work) === | === 49edo (2 mappings demonstrated to work) === | ||
The most efficient mapping for [[49edo]], having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is [[Bryan Deister]]'s [[4L 3s]] (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 [[archipelago]]-related temperament and [[catalan]] temperament, demonstrated in [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~[[15/13]] (in the 49f val) for its generator; two of them make the fairly flat fourth ~[[4/3]]; four of them make the sharp septimal minor seventh ~[[7/4]]; six of them (after octave reduction) make a slightly sharp septimal minor third ~[[7/6]]; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~[[11/7]]; and fourteen of them make a sharp classic minor seventh ~[[9/5]]. Although this is a respectable list of intervals, the unmodified rank-2 version of the temperament does not make a very good [[MOS]] scale — instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L 3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out [[364/363]], [[540/539]], and [[847/845]]); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~[[25/24]], which 49edo uses here more like a diatonic semitone (although the actual 49edo diatonic semitone is only 2\49). Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~[[16/11]]; four of them (after octave reduction) make a slightly sharp classic chromatic semitone ~[[25/24]]; five of them make a mildly sharp classic major third ~[[5/4]]; six of them make a sharp fifth ~[[3/2]]; seven of them make a sharp classic minor seventh ~[[9/5]]; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~[[12/11]]; and ten of them make a near-just undecimal minor sixth ~[[11/7]]. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L 3s. | The most efficient mapping for [[49edo]], having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is [[Bryan Deister]]'s [[4L 3s]] (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 [[archipelago]]-related temperament and [[catalan]] temperament, demonstrated in [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~[[15/13]] (in the 49f val) for its generator; two of them make the fairly flat fourth ~[[4/3]]; four of them make the sharp septimal minor seventh ~[[7/4]]; six of them (after octave reduction) make a slightly sharp septimal minor third ~[[7/6]]; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~[[11/7]]; and fourteen of them make a sharp classic minor seventh ~[[9/5]]. Although this is a respectable list of intervals, the unmodified rank-2 version of the temperament does not make a very good [[MOS]] scale — instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L 3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out [[364/363]], [[540/539]], and [[847/845]]); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~[[25/24]], which 49edo uses here more like a diatonic semitone (although the actual 49edo diatonic semitone is only 2\49). Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~[[16/11]]; four of them (after octave reduction) make a slightly sharp classic chromatic semitone ~[[25/24]]; five of them make a mildly sharp classic major third ~[[5/4]]; six of them make a sharp fifth ~[[3/2]]; seven of them make a sharp classic minor seventh ~[[9/5]]; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~[[12/11]]; and ten of them make a near-just undecimal minor sixth ~[[11/7]]. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L 3s. | ||
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Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:57, 10 April 2026 (UTC) | Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:57, 10 April 2026 (UTC) | ||
==== Reverse chroma | ==== Reverse chroma version ==== | ||
It is possible to make a reverse chroma version of the above mapping. The range is considerably less, at a bit over 3⅓ octaves, with considerable regions of non-contiguous notes in the upper left and lower right corners, and the octaves slope down, incurring a vertical wraparound; on the other hand, a considerable number of repeated notes are available in each complete octave to mitigate vertical wraparounds. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026), although with note 0 set to | It is possible to make a reverse chroma version of the above mapping. The range is considerably less, at a bit over 3⅓ octaves, with considerable regions of non-contiguous notes in the upper left and lower right corners, and the octaves slope down, incurring a vertical wraparound; on the other hand, a considerable number of repeated notes are available in each complete octave to mitigate vertical wraparounds. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026), although with note 0 set to where note 38 is here. | ||
{{Lumatone EDO mapping|n=49|start=6|xstep=3|ystep=7}} | {{Lumatone EDO mapping|n=49|start=6|xstep=3|ystep=7}} | ||
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:38, 18 April 2026 (UTC) | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:38, 18 April 2026 (UTC)<br> | ||
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:12, 21 April 2026 (UTC) | |||
== Aureus Pseudo-Meantone Lumatone mappings == | == Aureus Pseudo-Meantone Lumatone mappings == | ||