Lumatone mapping for 53edo: Difference between revisions

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== Hemikleismic + Semaja ==

[[Bryan Deister]] has demonstrated ~~a mapping~~ for [[53edo]] ~~in [https://www.youtube.com/shorts/WtSaDQCyfVc ''Waltz in 53edo''] (2026)~~ that functions for [[Kleismic_family#Hemikleismic|hemikleismic]] ([[7L 1s]] scale with a 7:4 step ratio ~~right and right-up~~ with the small step stretched) and [[~~Porwell_temperaments~~#Semaja|semaja]] (rotated [[5L 1s]] with a 10:3 step ratio down-right and down); a [[5L 8s (4/1-equivalent)]] scale with a 10:7 step ratio is also available moving right and down-right. The range is a bit over 4⅓ octaves, with no missed notes and just one repeated note in each octave, but the upper left and lower right corners have many additional non-contiguous notes, and the octaves are not in consistent places; on the other hand, classic thirds both minor (two steps right) and major (one step right plus one step down-right) are in very easy reach as long as they do not pass through a vertical wraparound (it may be necessary to adjust note 0 position to avoid this for a particular performance, such as in the linked video which has note 0 where note 3 is here).

[[Bryan Deister]] has demonstrated two mappings for [[53edo]] that functions for [[Kleismic_family#Hemikleismic|hemikleismic]] ([[7L 1s]] (pine) scale with a 7:4 step ratio with the small step stretched) and [[Gariboh_clan#Semaja|semaja]] (rotated [[5L 1s]] scale with a 10:3 step ratio); both versions favor hemikleismic over semaja. For hemikleismic, the generator 7\53 is half of a near-just classic minor third ~[[6/5]], which functions as a flat undecimal submajor second ~[[11/10]], a sharp undecimal neutral second ~[[12/11]], a slightly sharp septimal neutral second ~[[35/32]], and a near-just large vicesimotertial neutral second ~[[23/21]]. Four of these make a slightly flat tridecimal diminished fifth ~[[13/9]]; five of them make a somewhat flat Boethius' minor sixth ~[[12/9]]; after octave-reduction, ten of them make a flat flat septimal major second ~[[8/7]], which at 10\53 is the generator for semaja; several undevicesimal ratios are also available. Two of the semaja generator make a slightly flat Barbados third ~[[13/10]]; after octave-reduction, eight of them make a near-just classic major third ~[[5/4]]; several tridecimal ratios are also available.

=== Reverse chroma ===

In the reverse-chroma version demonstrated in [https://www.youtube.com/shorts/WtSaDQCyfVc ''Waltz in 53edo''] (2026), the hemikleismic 7L 1s scale is played by moving right and right-up with the small step stretched, and the semaja rotated [[5L 1s]] scale is played by moving down-right and down; a [[5L 8s (4/1-equivalent)]] scale with a 10:7 step ratio is also available moving right and down-right. The range is a bit over 4⅓ octaves, with no missed notes and just one repeated note in each octave, but the upper left and lower right corners have many additional non-contiguous notes, and the octaves are not in consistent places; on the other hand, classic thirds both minor (two steps right) and major (one step right plus one step down-right) are in very easy reach as long as they do not pass through a vertical wraparound (it may be necessary to adjust note 0 position to avoid this for a particular performance, such as in the linked video which has note 0 where note 3 is here).

=== Forward oversize chroma ===

In the forward oversize chroma version (very similar to the [[Lumatone_mapping_for_porcupine#Expanded|expanded Lumatone mapping for porcupine]]), demonstrated in [https://www.youtube.com/shorts/7YfZZ7aMvH8 ''53edo groove''] (2026), the hemikleismic 7L 1s scale is played by moving right and right-down-right with the small step stretched, and the semaja rotated [[5L 1s]] scale is played by moving up and up-left; the 5L 8s (4/1-equivalent) scale is not practical in this version. The range is less than that of the reverse chroma version, at somewhat under three complete octaves, but in exchange, more repeated notes are available to mitigate vertical wraparounds, and the upwards slope of the octaves is less.

== Buzzard ==

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 == Hemikleismic + Semaja ==
-[[Bryan Deister]] has demonstrated a mapping for [[53edo]] in [https://www.youtube.com/shorts/WtSaDQCyfVc ''Waltz in 53edo''] (2026) that functions for [[Kleismic_family#Hemikleismic|hemikleismic]] ([[7L&nbsp;1s]] scale with a 7:4 step ratio right and right-up with the small step stretched) and [[Porwell_temperaments#Semaja|semaja]] (rotated [[5L&nbsp;1s]] with a 10:3 step ratio down-right and down); a [[5L&nbsp;8s (4/1-equivalent)]] scale with a 10:7 step ratio is also available moving right and down-right. The range is a bit over 4⅓ octaves, with no missed notes and just one repeated note in each octave, but the upper left and lower right corners have many additional non-contiguous notes, and the octaves are not in consistent places; on the other hand, classic thirds both minor (two steps right) and major (one step right plus one step down-right) are in very easy reach as long as they do not pass through a vertical wraparound (it may be necessary to adjust note 0 position to avoid this for a particular performance, such as in the linked video which has note 0 where note 3 is here).
+[[Bryan Deister]] has demonstrated two mappings for [[53edo]] that functions for [[Kleismic_family#Hemikleismic|hemikleismic]] ([[7L&nbsp;1s]] (pine) scale with a 7:4 step ratio with the small step stretched) and [[Gariboh_clan#Semaja|semaja]] (rotated [[5L&nbsp;1s]] scale with a 10:3 step ratio); both versions favor hemikleismic over semaja. For hemikleismic, the generator 7\53 is half of a near-just classic minor third ~[[6/5]], which functions as a flat undecimal submajor second ~[[11/10]], a sharp undecimal neutral second ~[[12/11]], a slightly sharp septimal neutral second ~[[35/32]], and a near-just large vicesimotertial neutral second ~[[23/21]]. Four of these make a slightly flat tridecimal diminished fifth ~[[13/9]]; five of them make a somewhat flat Boethius' minor sixth ~[[12/9]]; after octave-reduction, ten of them make a flat flat septimal major second ~[[8/7]], which at 10\53 is the generator for semaja; several undevicesimal ratios are also available. Two of the semaja generator make a slightly flat Barbados third ~[[13/10]]; after octave-reduction, eight of them make a near-just classic major third ~[[5/4]]; several tridecimal ratios are also available.
+=== Reverse chroma ===
+In the reverse-chroma version demonstrated in [https://www.youtube.com/shorts/WtSaDQCyfVc ''Waltz in 53edo''] (2026), the hemikleismic 7L&nbsp;1s scale is played by moving right and right-up with the small step stretched, and the semaja rotated [[5L&nbsp;1s]] scale is played by moving down-right and down; a [[5L&nbsp;8s (4/1-equivalent)]] scale with a 10:7 step ratio is also available moving right and down-right. The range is a bit over 4⅓ octaves, with no missed notes and just one repeated note in each octave, but the upper left and lower right corners have many additional non-contiguous notes, and the octaves are not in consistent places; on the other hand, classic thirds both minor (two steps right) and major (one step right plus one step down-right) are in very easy reach as long as they do not pass through a vertical wraparound (it may be necessary to adjust note 0 position to avoid this for a particular performance, such as in the linked video which has note 0 where note 3 is here).
 {{Lumatone EDO mapping|n=53|start=7|xstep=7|ystep=3}}
+=== Forward oversize chroma ===
+In the forward oversize chroma version (very similar to the [[Lumatone_mapping_for_porcupine#Expanded|expanded Lumatone mapping for porcupine]]), demonstrated in [https://www.youtube.com/shorts/7YfZZ7aMvH8 ''53edo groove''] (2026), the hemikleismic 7L&nbsp;1s scale is played by moving right and right-down-right with the small step stretched, and the semaja rotated [[5L&nbsp;1s]] scale is played by moving up and up-left; the 5L&nbsp;8s (4/1-equivalent) scale is not practical in this version. The range is less than that of the reverse chroma version, at somewhat under three complete octaves, but in exchange, more repeated notes are available to mitigate vertical wraparounds, and the upwards slope of the octaves is less.
+{{Lumatone EDO mapping|n=53|start=32|xstep=7|ystep=-10}}
 == Buzzard ==