Lumatone mapping for 80edo: Difference between revisions

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== Diatonic ==

Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to [[5/4]] is a ''pentuply-augmented'' sixth or ''hextuply-diminished'' unison, which is impossible to play with the root note of the scale.

== Diaschismic ==

On the other hand, the [[diaschismic]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.

== Bidia ==

Slicing the period into quarters produces the [[Bidia]] mapping, which keeps octaves closer to horizontal and makes the well-tuned 19th harmonic easily accessible. The (rightward) generator 7\80 is the Bidia generator which functions as ~[[16/15]], ~[[17/16]], and ~[[18/17]]; two of these make a somewhat sharp ~[[9/8]]; if allowed to pass the quarter-octave, three of these make a near-just classic minor third ~[[6/5]]; and four of them make a slightly sharp undecimal major third ~[[14/11]].

[[Bryan Deister]] has demonstrated this mapping (except shifted to put the first note 0 where the first note 6 is shown here, to avoid a missed first note 3) in [https://www.youtube.com/shorts/H6DlCHKii-o ''microtonal improvisation in 80edo''] (2025). The range is about 2¾ octaves, and the octaves slope down very gently.

[[Herman Miller]] has created a .ltn file for this mapping that can be downloaded [https://drive.google.com/file/d/13WTaNm7mMF_w3DrW4qh8fcD9WY07BElV here]. (Backup version: [[File:80edo-4x1-3-kbd-7-20-bidia.ltn]]).

== Supermajor ==

The [[3L 8s]] [[Ragismic_microtemperaments#Supermajor|Supermajor]] mapping covers the gamut with slightly greater range while keeping octaves near horizontal, but many of the other harmonics involve awkward vertical stretches.

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 {{Lumatone mapping intro}}
+== Diatonic ==
+Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to [[5/4]] is a ''pentuply-augmented'' sixth or ''hextuply-diminished'' unison, which is impossible to play with the root note of the scale.
 {{Lumatone EDO mapping|n=80|start=8|xstep=14|ystep=-9}}
+== Diaschismic ==
+On the other hand, the [[diaschismic]] mapping can cover the whole gamut and make harmonics easy to play together, although it needs to be expanded from [[2L&nbsp;8s]] to [[10L&nbsp;2s]] to hit every single note.
+{{Lumatone EDO mapping|n=80|start=29|xstep=7|ystep=5}}
+{{Lumatone EDO mapping|n=80|start=71|xstep=7|ystep=-2}}
+== Bidia ==
+Slicing the period into quarters produces the [[Bidia]] mapping, which keeps octaves closer to horizontal and makes the well-tuned 19th harmonic easily accessible. The (rightward) generator 7\80 is the Bidia generator which functions as ~[[16/15]], ~[[17/16]], and ~[[18/17]]; two of these make a somewhat sharp ~[[9/8]]; if allowed to pass the quarter-octave, three of these make a near-just classic minor third ~[[6/5]]; and four of them make a slightly sharp undecimal major third ~[[14/11]].
+[[Bryan Deister]] has demonstrated this mapping (except shifted to put the first note 0 where the first note 6 is shown here, to avoid a missed first note 3) in [https://www.youtube.com/shorts/H6DlCHKii-o ''microtonal improvisation in 80edo''] (2025). The range is about 2¾ octaves, and the octaves slope down very gently.
+[[Herman Miller]] has created a .ltn file for this mapping that can be downloaded [https://drive.google.com/file/d/13WTaNm7mMF_w3DrW4qh8fcD9WY07BElV here]. (Backup version: [[File:80edo-4x1-3-kbd-7-20-bidia.ltn]]).
+{{Lumatone EDO mapping|n=80|start=69|xstep=7|ystep=-1}}
+== Supermajor ==
+The [[3L 8s]] [[Ragismic_microtemperaments#Supermajor|Supermajor]] mapping covers the gamut with slightly greater range while keeping octaves near horizontal, but many of the other harmonics involve awkward vertical stretches.
+{{Lumatone EDO mapping|n=80|start=62|xstep=7|ystep=1}}
 {{Navbox Lumatone}}