Lumatone mapping for 38edo: Difference between revisions

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~~[[38edo]] is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard~~ Lumatone mapping ~~for Pythagorean]] only reaches [[19edo]] intervals.~~ Even the b val does not generate a diatonic or antidiatonic scale~~, and the~~ bb val is very flat indeed.

{{Lumatone mapping intro}} Even the b val does not generate a diatonic or antidiatonic scale.

== Antidiatonic/Balzano ==

The bb val fifth is very flat indeed, generating a very lopsided [[2L 5s]] scale having a 9:4 step ratio or a [[2L 7s]] scale (with backtracking) having a 5:4 step ratio.

Instead, as slicing the perfect ~~5th~~ in two results in an essentially perfect [[11/9]], it makes a lot of sense to use ~~the~~ [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]].

== Neutral thirds ==

Instead, as slicing the perfect fifth in two results in an essentially perfect [[11/9]], it makes a lot of sense to use a [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]]. The versions below present a tradeoff familiar for Neutral Thirds mappings, between rotating the notes of the diatonic scale or incurring a considerable slope of the octaves that causes vertical wraparounds.

=== Rotated (Opossum + Ptolemy) ===

A rotated version yields a range of five octaves but for a few missing notes in the bottom octave (or top octave, depending upon the placement of note 0), with octaves sloping down mildly. This version lends itself to [[Porcupine_family#Opossum|Opossum]] and [[Rastmic_clan#Ptolemy|Ptolemy]].

Or if you want greater range while still reaching a lot of good intervals in few steps the [[~~astrology~~]] mapping works well.

=== Non-Rotated (Opossum + Hemisensi + Ptolemy) ===

[[Bryan Deister]] has demonstrated a [[3L 4s]] (6:5 step ratio) layout for [[38edo]] in [https://www.youtube.com/shorts/rewy-32BfRs ''Spirit of the Night - Secret of Mana (microtonal cover in 38edo)''] (2025). The range is a bit over five octaves, although at the cost of octaves sloping down severely enough to incur two vertical wraparounds. This mapping lends itself to [[Porcupine_family#Opossum|Opossum]], [[Sensipent_family#Hemisensi|Hemisensi]], and [[Rastmic_clan#Ptolemy|Ptolemy]].

== Astrology ==

Or if you want greater range while still reaching a lot of good intervals in few steps while only incurring a gentle downward slope of octaves, the [[Astrology]] mapping works well.

== Bison + Hemisensi + Hemikleismic ==

It is possible to map [[38edo|38df]] to support scales [[4L 2s]] (7:5 step ratio, and proceeding overall down-right) and [[7L 1s]] (5:3 step ratio, with the small step proceeding right + up-right), supporting temperaments [[Sensipent_family#Bison|bison]], [[Kleismic_family#Hemisensi|hemisensi]], and [[Kleismic_family#Hemikleismic|hemikleismic]]. [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/Gdx4hk7FKU0 ''<nowiki>waltz in 38edo [short]</nowiki>''] (2026), motivated by the wish to reverse major and minor thirds but without needing a super-flat fifth. This yields a range of a bit over 4¾ octaves, but with a severe downwards slope that incurs vertical wraparounds.

== Bison + Hemikleismic + Divination + Hocus ==

[[Bryan Deister]] has demonstrated a [[2L 4s]] (step ratio 7:6) mapping for [[38edo]] in [https://www.youtube.com/shorts/QcFEW45uxHY ''38edo improv''] (2025) that functions for [[Sensipent_family#Bison|Bison]], [[Kleismic_family#Hemikleismic|Hemikleismic]], [[Magic_family#Divination|Divination]], and [[Magic_family#Hocus|Hocus]] temperaments. The range is just under 5½ octaves, and the octaves slope down only slightly.

@@ Line 1: / Line 1: @@
-[[38edo]] is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard Lumatone mapping for Pythagorean]] only reaches [[19edo]] intervals. Even the b val does not generate a diatonic or antidiatonic scale, and the bb val is very flat indeed.
+{{Lumatone mapping intro}} Even the b&nbsp;val does not generate a diatonic or antidiatonic scale.
+== Antidiatonic/Balzano ==
+The bb val fifth is very flat indeed, generating a very lopsided [[2L&nbsp;5s]] scale having a 9:4 step ratio or a [[2L&nbsp;7s]] scale (with backtracking) having a 5:4 step ratio.
 {{Lumatone EDO mapping|n=38|start=10|xstep=4|ystep=5}}
-Instead, as slicing the perfect 5th in two results in an essentially perfect [[11/9]], it makes a lot of sense to use the [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]].
+== Neutral thirds ==
+Instead, as slicing the perfect fifth in two results in an essentially perfect [[11/9]], it makes a lot of sense to use a [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]]. The versions below present a tradeoff familiar for Neutral Thirds mappings, between rotating the notes of the diatonic scale or incurring a considerable slope of the octaves that causes vertical wraparounds.
+=== Rotated (Opossum + Ptolemy) ===
+A rotated version yields a range of five octaves but for a few missing notes in the bottom octave (or top octave, depending upon the placement of note 0), with octaves sloping down mildly. This version lends itself to [[Porcupine_family#Opossum|Opossum]] and [[Rastmic_clan#Ptolemy|Ptolemy]].
 {{Lumatone EDO mapping|n=38|start=31|xstep=5|ystep=1}}
-Or if you want greater range while still reaching a lot of good intervals in few steps the [[astrology]] mapping works well.
+=== Non-Rotated (Opossum + Hemisensi + Ptolemy) ===
+[[Bryan Deister]] has demonstrated a [[3L&nbsp;4s]] (6:5 step ratio) layout for [[38edo]] in [https://www.youtube.com/shorts/rewy-32BfRs ''Spirit of the Night - Secret of Mana (microtonal cover in 38edo)''] (2025). The range is a bit over five octaves, although at the cost of octaves sloping down severely enough to incur two vertical wraparounds. This mapping lends itself to [[Porcupine_family#Opossum|Opossum]], [[Sensipent_family#Hemisensi|Hemisensi]], and [[Rastmic_clan#Ptolemy|Ptolemy]].
+{{Lumatone EDO mapping|n=38|start=30|xstep=6|ystep=-1}}
+== Astrology ==
+Or if you want greater range while still reaching a lot of good intervals in few steps while only incurring a gentle downward slope of octaves, the [[Astrology]] mapping works well.
 {{Lumatone EDO mapping|n=38|start=35|xstep=7|ystep=-2}}
-{{Lumatone mapping navigation}}
+== Bison + Hemisensi + Hemikleismic ==
+It is possible to map [[38edo|38df]] to support scales [[4L&nbsp;2s]] (7:5 step ratio, and proceeding overall down-right) and [[7L&nbsp;1s]] (5:3 step ratio, with the small step proceeding right + up-right), supporting temperaments [[Sensipent_family#Bison|bison]], [[Kleismic_family#Hemisensi|hemisensi]], and [[Kleismic_family#Hemikleismic|hemikleismic]]. [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/Gdx4hk7FKU0 ''<nowiki>waltz in 38edo [short]</nowiki>''] (2026), motivated by the wish to reverse major and minor thirds but without needing a super-flat fifth. This yields a range of a bit over 4¾ octaves, but with a severe downwards slope that incurs vertical wraparounds.
+{{Lumatone EDO mapping|n=38|start=17|xstep=5|ystep=2}}
+== Bison + Hemikleismic + Divination + Hocus ==
+[[Bryan Deister]] has demonstrated a [[2L&nbsp;4s]] (step ratio 7:6) mapping for [[38edo]] in [https://www.youtube.com/shorts/QcFEW45uxHY ''38edo improv''] (2025) that functions for [[Sensipent_family#Bison|Bison]], [[Kleismic_family#Hemikleismic|Hemikleismic]], [[Magic_family#Divination|Divination]], and [[Magic_family#Hocus|Hocus]] temperaments. The range is just under 5½ octaves, and the octaves slope down only slightly.
+{{Lumatone EDO mapping|n=38|start=19|xstep=6|ystep=1}}
+{{Navbox Lumatone}}