Lumatone mapping for 37edo: Difference between revisions

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~~There are many conceivable ways~~ to ~~map~~ [[~~37edo~~]] ~~onto~~ the [[~~Lumatone~~]] ~~keyboard. Only~~ one, ~~however~~, ~~agrees with~~ the [[~~Standard Lumatone mapping for Pythagorean~~]].

== Diatonic ==

The patent fifth ~[[3/2]] is so sharp that attempting to play a standard diatonic scale produces almost exactly a Barbados third ~[[13/10]], so sharp that even though the septimal major third ~[[9/7]] is mapped to the same interval, it is mapped inconsistently; furthermore, the Pythagorean whole tone ~[[9/8]] is itself mapped inconsistently, so if you want to play something sounding traditional diatonic, you have to start your scale moving up one key (instead of right one key) to get a classic-sounding whole tone (rather than the septimal version ~[[8/7]], which is just slightly flat), and then up another key (again instead of right) to get the near-just classic major third ~[[5/4]]; getting further classic intervals likewise requires some unusual movements, which would be awkward in combination. Thus, the diatonic mapping in 37edo is actually a xenharmonic mapping by default.

~~However, as~~ the perfect ~~5th~~ is ~~very~~ sharp, ~~neither~~ this or the ~~b val give easy access~~ to the ~~5th harmonic~~. If you want an arrangement that makes it easy to play the best note combinations together the [[~~porcupine~~]] mapping is considerably superior.

== Antidiatonic ==

Since the perfect fifth is so sharp, you lose little accuracy by using the flat fifth as a generator instead, which can be interpreted as near equalised [[mavila]], or more accurately but complexly as [[undecimation]].

== Aureus Pseudo-Meantone + Mediantone + Roulette + Hemiwürschmidt + Hemiwur ==

[[Bryan Deister]] has demonstrated a [[6L 1s]] (6:1 step ratio) mapping for [[37edo]] in [https://www.youtube.com/shorts/Jt6_r6r3lGY ''37edo improv''] (2026). This mapping functions as an aureus pseudo-meantone mapping; this functions for temperaments [[mediantone]], [[roulette]], [[hemiwürschmidt]], and [[hemiwur]]; it has a generator 6\37 that functions as both a slightly sharp quasi-meantone ~[[19/17]] and a slightly flat septimal middle whole tone ~[[28/25]]. (In contrast to actual [[meantone]] temperament, 37edo represents ~19/17 (or 28/25), ~[[10/9]], and ~[[9/8]] as distinct intervals — the syntonic comma [[81/80]] is not tempered out, but inflated to 2\37, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) The range is a bit under 4½ octaves, and the octaves slope upwards moderately.

== Diatonicized Chromaticism via Rotated Antidiatonic ==

[[Bryan Deister]] has demonstrated a rotated antidiatonic ([[2L 5s]]) mapping in [https://www.youtube.com/shorts/e7dLJTsS3PQ ''37edo''] (2025), using the Mavila (sub-)fifth (21\37) as a generator. This yields a range of over five octaves, although the note 0 positions alternate between middle and near/far. (In the demonstration video, active keys on the Lumatone are cut back at both the left and right edges to yield exactly five octaves.) With this mapping, notes of the [[11L 2s]] scale line up in pairs of row segments (of 6\37 offset from each other by the large MOSstep 3\37, and cut by the small MOSstep 2\37), which may make this mapping attractive for users wishing to play [[Ivan Wyschnegradsky]]'s Diatonicized Chromatic scale in a tuning system different from [[24edo]], while still retaining respectable (though not full piano) range.

== Porcupine ==

However, none of these are the most efficient when it comes to comfortably fingering simple chords. If you want an arrangement that makes it easy to play the best note combinations together, the [[1L 6s]] mapping for [[Porcupine]] is considerably superior. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025).

If you want to ~~maximise your range, the~~ [[~~Chromatic_pairs~~#Gariberttet|Gariberttet]] mapping ~~is probably the clearest arrangement that~~ gives access to the full gamut.

== Ammonite + Gariberttet + Porcupinefish Lumatone mappings ==

Alternatives to the [[Porcupine]] mapping for [[37edo]] that stay in the same temperament clan are the [[Porcupine_family#Ammonite|ammonite]]/[[Porcupine_family#Porcupinefish|porcupinefish]] [[3L 2s]] (9:5 step ratio) mappings, which also function for [[Subgroup_temperaments#Gariberttet|gariberttet]] (as 37b). The generator for ammonite is 14\37, easily available as one key right plus one key down-right in both versions of this mapping; it functions as a near-just Barbados third (tridecimal semisixth, ~[[13/10]]). The generator for porcupinefish is 5\37, easily available as one key down-right (forward chroma) or one step right (reverse chroma); it functions as an undecimal neutral second (a slightly flat ~[[11/10]] and a sharp ~[[12/11]], tempering out the biyatisma [[121/120]], thus enabling two of these generators to make a sharp classic minor third ~[[6/5]]). The generator for gariberttet is 9\37, easily available as one key right (forward chroma) or one key down-right (reverse chroma); it functions as a near-just tridecimal minor third (~[[13/11]]).

==== Forward chroma (demonstrated to work) ====

The range is a bit under 7½ octaves, which slope down mildly, with no repeated notes and no missed notes. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/mVRbcB2hoBU ''37edo prelude''] (2026).

==== Reverse chroma (proposed and untested) ====

The total range is just short of eight octaves, but while the middle octaves have no missing notes and a few repeated notes to mitigate vertical wraparounds, the first and last octaves have many notes chopped off at the edges, and the octaves slope down enough to incur a vertical wraparound. Currently, no demo video is available for this mapping.

== Gariberttet ==

If you want to concentrate on [[Subgroup temperaments#Gariberttet|Gariberttet]], the mapping for this gives access to the full gamut (apart from some notes chopped off at the left and right edges in the first and last octaves), with a range of 6⅓ octaves, which have only a gentle upwards slope.

[[~~Category~~:~~Lumatone mappings~~]] [[~~Category~~:37edo]]

== Llywelynsmic clan + Semaphore + Gariberttet + Oceanfront/Ultrapyth ==

A [[2L 3s]] mapping for [[37edo]] with an 8:7 step ratio opens easy access to several temperaments. The generator for the [[llywelynsmic clan]] is 7\37 (one key down-right), which functions as a slightly flat septimal whole tone ~[[8/7]], as well as (a sharp and inconsistently mapped Pythagorean whole tone ~[[9/8]] (assuming use of the [[patent val]] for 37edo). Temperaments in this clan include [[Llywelynsmic_clan#Llywelyn_a.k.a._shoe|shoe]], [[Porwell_temperaments#Semaja|semaja]], and [[Syntonic–diatonic_equivalence_continuum#Laconic|laconic]]/[[Gamelismic_clan#Gorgo|gorgo]]. The generator for [[Semaphoresmic_clan#Semaphore|semaphore]] is 8\37 (one key right), which functions as a flat septimal minor third ~[[7/6]], a very sharp tridecimal semifourth ~[[15/13]], and a somewhat sharp undevicesimal semifourth ~[[22/19]]. The generator for [[gariberttet]] is 9\37 (one key right plus one key up); it functions as a near-just tridecimal minor third (~[[13/11]]). The generator for [[The_Biosphere#Oceanfront|oceanfront]] and [[Archytas_clan#Ultrapyth|ultrapyth]] is 15\37 (one key right plus one key down-right); it functions as a very flat fourth ~[[4/3]]. The range is 7¾ octaves, but the octaves slope down enough to incur a vertical wraparound, and while the middle octaves have no missed notes and only a few repeated notes, the first and last octaves have several notes chopped off by the upper left and lower right corners, respectively. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/TEzitpGJvt0 ''37edo''] (2023), although with the range limited by MIDI channel mapping.

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[37edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
+{{Lumatone mapping intro}}
+== Diatonic ==
+The patent fifth ~[[3/2]] is so sharp that attempting to play a standard diatonic scale produces almost exactly a Barbados third ~[[13/10]], so sharp that even though the septimal major third ~[[9/7]] is mapped to the same interval, it is mapped inconsistently; furthermore, the Pythagorean whole tone ~[[9/8]] is itself mapped inconsistently, so if you want to play something sounding traditional diatonic, you have to start your scale moving up one key (instead of right one key) to get a classic-sounding whole tone (rather than the septimal version ~[[8/7]], which is just slightly flat), and then up another key (again instead of right) to get the near-just classic major third ~[[5/4]]; getting further classic intervals likewise requires some unusual movements, which would be awkward in combination. Thus, the diatonic mapping in 37edo is actually a xenharmonic mapping by default.
 {{Lumatone EDO mapping|n=37|start=10|xstep=7|ystep=-6}}
-However, as the perfect 5th is very sharp, neither this or the b val give easy access to the 5th harmonic. If you want an arrangement that makes it easy to play the best note combinations together the [[porcupine]] mapping is considerably superior.
+== Antidiatonic ==
+Since the perfect fifth is so sharp, you lose little accuracy by using the flat fifth as a generator instead, which can be interpreted as near equalised [[mavila]], or more accurately but complexly as [[undecimation]].
+{{Lumatone EDO mapping|n=37|start=23|xstep=5|ystep=1}}
+== Aureus Pseudo-Meantone + Mediantone + Roulette + Hemiwürschmidt + Hemiwur ==
+[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (6:1 step ratio) mapping for [[37edo]] in [https://www.youtube.com/shorts/Jt6_r6r3lGY ''37edo improv''] (2026). This mapping functions as an aureus pseudo-meantone mapping; this functions for temperaments [[mediantone]], [[roulette]], [[hemiwürschmidt]], and [[hemiwur]]; it has a generator 6\37 that functions as both a slightly sharp quasi-meantone ~[[19/17]] and a slightly flat septimal middle whole tone ~[[28/25]]. (In contrast to actual [[meantone]] temperament, 37edo represents ~19/17 (or 28/25), ~[[10/9]], and ~[[9/8]] as distinct intervals &mdash; the syntonic comma [[81/80]] is not tempered out, but inflated to 2\37, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) The range is a bit under 4½ octaves, and the octaves slope upwards moderately.
+{{Lumatone EDO mapping|n=37|start=12|xstep=6|ystep=-5}}
+== Diatonicized Chromaticism via Rotated Antidiatonic ==
+[[Bryan Deister]] has demonstrated a rotated antidiatonic ([[2L&nbsp;5s]]) mapping in [https://www.youtube.com/shorts/e7dLJTsS3PQ ''37edo''] (2025), using the Mavila (sub-)fifth (21\37) as a generator. This yields a range of over five octaves, although the note 0 positions alternate between middle and near/far. (In the demonstration video, active keys on the Lumatone are cut back at both the left and right edges to yield exactly five octaves.) With this mapping, notes of the [[11L&nbsp;2s]] scale line up in pairs of row segments (of 6\37 offset from each other by the large MOSstep 3\37, and cut by the small MOSstep 2\37), which may make this mapping attractive for users wishing to play [[Ivan Wyschnegradsky]]'s Diatonicized Chromatic scale in a tuning system different from [[24edo]], while still retaining respectable (though not full piano) range.
+{{Lumatone EDO mapping|n=37|start=29|xstep=6|ystep=-1}}
+== Porcupine ==
+However, none of these are the most efficient when it comes to comfortably fingering simple chords. If you want an arrangement that makes it easy to play the best note combinations together, the [[1L&nbsp;6s]] mapping for [[Porcupine]] is considerably superior. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/m9hmiH8zong ''37edo jam''] (2025).
 {{Lumatone EDO mapping|n=37|start=10|xstep=5|ystep=2}}
-If you want to maximise your range, the [[Chromatic_pairs#Gariberttet|Gariberttet]] mapping is probably the clearest arrangement that gives access to the full gamut.
+== Ammonite + Gariberttet + Porcupinefish Lumatone mappings ==
+Alternatives to the [[Porcupine]] mapping for [[37edo]] that stay in the same temperament clan are the [[Porcupine_family#Ammonite|ammonite]]/[[Porcupine_family#Porcupinefish|porcupinefish]] [[3L&nbsp;2s]] (9:5 step ratio) mappings, which also function for [[Subgroup_temperaments#Gariberttet|gariberttet]] (as 37b). The generator for ammonite is 14\37, easily available as one key right plus one key down-right in both versions of this mapping; it functions as a near-just Barbados third (tridecimal semisixth, ~[[13/10]]). The generator for porcupinefish is 5\37, easily available as one key down-right (forward chroma) or one step right (reverse chroma); it functions as an undecimal neutral second (a slightly flat ~[[11/10]] and a sharp ~[[12/11]], tempering out the biyatisma [[121/120]], thus enabling two of these generators to make a sharp classic minor third ~[[6/5]]). The generator for gariberttet is 9\37, easily available as one key right (forward chroma) or one key down-right (reverse chroma); it functions as a near-just tridecimal minor third (~[[13/11]]).
+==== Forward chroma (demonstrated to work) ====
+The range is a bit under 7½ octaves, which slope down mildly, with no repeated notes and no missed notes.  [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/mVRbcB2hoBU ''37edo prelude''] (2026).
+{{Lumatone EDO mapping|n=37|start=0|xstep=9|ystep=-4}}
+==== Reverse chroma (proposed and untested) ====
+The total range is just short of eight octaves, but while the middle octaves have no missing notes and a few repeated notes to mitigate vertical wraparounds, the first and last octaves have many notes chopped off at the edges, and the octaves slope down enough to incur a vertical wraparound. Currently, no demo video is available for this mapping.
+{{Lumatone EDO mapping|n=37|start=0|xstep=5|ystep=4}}
+== Gariberttet ==
+If you want to concentrate on [[Subgroup temperaments#Gariberttet|Gariberttet]], the mapping for this gives access to the full gamut (apart from some notes chopped off at the left and right edges in the first and last octaves), with a range of 6⅓ octaves, which have only a gentle upwards slope.
 {{Lumatone EDO mapping|n=37|start=21|xstep=9|ystep=-8}}
-[[Category:Lumatone mappings]] [[Category:37edo]]
+== Llywelynsmic clan + Semaphore + Gariberttet + Oceanfront/Ultrapyth ==
+A [[2L&nbsp;3s]] mapping for [[37edo]] with an 8:7 step ratio opens easy access to several temperaments. The generator for the [[llywelynsmic clan]] is 7\37 (one key down-right), which functions as a slightly flat septimal whole tone ~[[8/7]], as well as (a sharp and inconsistently mapped Pythagorean whole tone ~[[9/8]] (assuming use of the [[patent val]] for 37edo). Temperaments in this clan include [[Llywelynsmic_clan#Llywelyn_a.k.a._shoe|shoe]], [[Porwell_temperaments#Semaja|semaja]], and [[Syntonic–diatonic_equivalence_continuum#Laconic|laconic]]/[[Gamelismic_clan#Gorgo|gorgo]]. The generator for [[Semaphoresmic_clan#Semaphore|semaphore]] is 8\37 (one key right), which functions as a flat septimal minor third ~[[7/6]], a very sharp tridecimal semifourth ~[[15/13]], and a somewhat sharp undevicesimal semifourth ~[[22/19]]. The generator for [[gariberttet]] is 9\37 (one key right plus one key up); it functions as a near-just tridecimal minor third (~[[13/11]]). The generator for [[The_Biosphere#Oceanfront|oceanfront]] and [[Archytas_clan#Ultrapyth|ultrapyth]] is 15\37 (one key right plus one key down-right); it functions as a very flat fourth ~[[4/3]]. The range is 7¾ octaves, but the octaves slope down enough to incur a vertical wraparound, and while the middle octaves have no missed notes and only a few repeated notes, the first and last octaves have several notes chopped off by the upper left and lower right corners, respectively. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/TEzitpGJvt0 ''37edo''] (2023), although with the range limited by MIDI channel mapping.
+{{Lumatone EDO mapping|n=37|start=0|xstep=8|ystep=-1}}
+{{Navbox Lumatone}}