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.

~~Due~~ to the ~~size~~ of the ~~edo~~, this mapping does not ~~quite cover all~~ the notes.

== 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.

== Aureus Pseudo-Meantone + Orwell-related rank-3 temperament + Semisept ==

The slightly sharp quasi-meantone ~[[19/17]] as 13\80 (one key down-right) stacks to a mildly sharp classic major third ~[[5/4]] (the aureusma [[1445/1444]] is tempered out), although by itself this generator does not make very well-space [[MOS]] scales. At the same time, as seen in [[Orwell]] temperament, a mildly sharp septimal minor third ~[[7/6]] is an attractive generator for producing well-spaced [[MOS]] scales, but being 18\80 (one key right + one key down-right), it is not co-prime, thereby suffering [[contorsion]]. One way to get around the contorsion problem to use both generators to make a rank-3 temperament. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/lWuqrdSr8pU ''80edo improv''] (2026), with the Lumatone rotated so as to make progression by 13\80 approximately horizontal. Another way to get MOS scales with reasonable spacing is to take the [[octave complement]] of ~[[7/6]] as ~[[12/7]], which is 62\80, and then split it in half to get 31\80 (one key right + two keys down-right), which is the septendecimal subfourth ~[[17/13]], which is the bright generator for an oneirotonic [[5L 3s]] scale having a 13:5 step ratio; the downside of this rank-2 temperament is that many generator steps are needed to reach some common consonant intervals. Either way, the range is somewhat under 2½ complete octaves (which slope downwards rather severely, and have only a few repeated notes), with considerable partial octaves in the base and treble chopped off by the upper left and lower right corners, respectively.

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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}}
-Due to the size of the edo, this mapping does not quite cover all the notes.
+== 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}}
+== Aureus Pseudo-Meantone + Orwell-related rank-3 temperament + Semisept ==
+The slightly sharp quasi-meantone ~[[19/17]] as 13\80 (one key down-right) stacks to a mildly sharp classic major third ~[[5/4]] (the aureusma [[1445/1444]] is tempered out), although by itself this generator does not make very well-space [[MOS]] scales. At the same time, as seen in [[Orwell]] temperament, a mildly sharp septimal minor third ~[[7/6]] is an attractive generator for producing well-spaced [[MOS]] scales, but being 18\80 (one key right + one key down-right), it is not co-prime, thereby suffering [[contorsion]]. One way to get around the contorsion problem to use both generators to make a rank-3 temperament. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/lWuqrdSr8pU ''80edo improv''] (2026), with the Lumatone rotated so as to make progression by 13\80 approximately horizontal. Another way to get MOS scales with reasonable spacing is to take the [[octave complement]] of ~[[7/6]] as ~[[12/7]], which is 62\80, and then split it in half to get 31\80 (one key right + two keys down-right), which is the septendecimal subfourth ~[[17/13]], which is the bright generator for an oneirotonic [[5L&nbsp;3s]] scale having a 13:5 step ratio; the downside of this rank-2 temperament is that many generator steps are needed to reach some common consonant intervals. Either way, the range is somewhat under 2½ complete octaves (which slope downwards rather severely, and have only a few repeated notes), with considerable partial octaves in the base and treble chopped off by the upper left and lower right corners, respectively.
+{{Lumatone EDO mapping|n=80|start=6|xstep=5|ystep=8}}
 {{Navbox Lumatone}}