Lumatone mapping for 13edo: Difference between revisions

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~~The following mapping for~~ [[13edo]] ~~can be used for every [[MOS]] scale in 13edo with L = 2\13 and s = 1\13~~, ~~such as~~ [[~~5L 3s]] and [[6L 1s~~]].

There are several possible ways to map [[13edo]] onto the onto the Lumatone keyboard. However, none of them even remotely approximate the [[Standard Lumatone mapping for Pythagorean]].

== Archaeotonic (exo-Tetracot) ==

The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap|L {{=}} 2\13}} and {{nowrap|s {{=}} 1\13}}, such as [[5L 3s]] and [[6L 1s]].

[[~~Category~~:Lumatone ~~mappings~~]]

== Fibotonic (compressed) ==

Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing (or more practically, enables division into multiple zones for different instruments) and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.

== Father + Aurora + Variant Orwell ==

[[Bryan Deister]] has demonstrated a [[3L 2s]] (3:2 step ratio) [[aurora]]/[[father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for aurora temperament). Even more simply, this mapping also functions for a [[4L 5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]], or a slightly sharp septendecimal superfifth ~[[26/17]], or a moderately sharp septimal superfifth ~32/21 as in aurora above); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.

== Sephiroth + Variant Orwell + Meansquared ==

It is possible to follow in the footsteps of [[magic]]/[[muggles]] temperament for [[13edo]], but using a much flatter classic major third ~[[5/4]] (as 4\13) as the generator, as [[sephiroth]], producing a [[3L 1s]] scale (4:1 step ratio) going right and up, as used by [[Bryan Deister]] in [https://www.youtube.com/shorts/LOgt_in9SD0 ''a microtonal totentanz in 13edo''] (2023). This also supports scales [[1L 3s]] (4:3 step ratio, going down-right, as in variant [[orwell]], although it would be awkward to play the more familiar [[4L 5s]] scale) and [[5L 2s (4/1-equivalent)]] (4:3 step ratio, going overall straight right through the octave zig-zag, as in [[meansquared]]). Octaves alternate between near/mid/far and mid-near/mid-far, with double octaves being perfectly level (thus enabling dual manuals); the range is 10¼ octaves.

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-The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with L = 2\13 and s = 1\13, such as [[5L 3s]] and [[6L 1s]].
+There are several possible ways to map [[13edo]] onto the onto the Lumatone keyboard. However, none of them even remotely approximate the [[Standard Lumatone mapping for Pythagorean]].
+== Archaeotonic (exo-Tetracot) ==
+The following mapping for [[13edo]] can be used for every [[MOS]] scale in 13edo with {{nowrap|L {{=}} 2\13}} and {{nowrap|s {{=}} 1\13}}, such as [[5L&nbsp;3s]] and [[6L&nbsp;1s]].
 {{Lumatone EDO mapping|n=13|start=0|xstep=2|ystep=-1}}
-[[Category:Lumatone mappings]]
+== Fibotonic (compressed) ==
+Since 13edo is a small edo, you can compress this down to a [[2L 1s]] scale that extends range past human hearing (or more practically, enables division into multiple zones for different instruments) and puts all kinds of intervals within easy reach in different directions while still having a moderate number of repeated notes.
+{{Lumatone EDO mapping|n=13|start=12|xstep=5|ystep=-2}}
+== Father + Aurora + Variant Orwell ==
+[[Bryan Deister]] has demonstrated a [[3L&nbsp;2s]] (3:2 step ratio) [[aurora]]/[[father]] mapping for [[13edo]], in [https://www.youtube.com/shorts/YiIr9l0M67w ''Holding Back My Endless Sigh - 13edo''] (2026). The generator 8\13 (three keys right and one key down-right from the root note) can be taken as a very sharp fifth (~[[3/2]], for father temperament) or a moderately sharp septimal superfifth (~[[32/21]], for aurora temperament). Even more simply, this mapping also functions for a [[4L&nbsp;5s]] (2:1 step ratio) scale for a variant of [[Orwell]] temperament, with the one key right generator being 3\13, which functions as (among other things) a rather sharp septimal minor third ~[[7/6]] (requires the 13d val) or a flat tridecimal minor third ~[[13/11]], of which two make a slightly sharp undecimal major fourth ~[[11/8]]; three of them make a sharp classic minor sixth ~[[8/5]]; four of them make a very flat classic major seventh ~[[15/8]]; and after octave-reduction, seven of them make the super-sharp fifth ~[[3/2]] (better constituted as a near-just vicesimotertial inframinor sixth ~[[23/15]], or a slightly sharp septendecimal superfifth ~[[26/17]], or a moderately sharp septimal superfifth ~32/21 as in aurora above); and eight of them make a very sharp septimal minor seventh ~[[7/4]] (if using the 13d val) or a near-just classic minor seventh ~[[9/5]] (requires constitution of the 9 as 3♯ × 3♭). The range is over seven octaves, with notes repeated multiple times, but unfortunately the downwards slope of the octaves, although mild, would make mapping to multiple manuals tricky.
+{{Lumatone EDO mapping|n=13|start=0|xstep=3|ystep=-1}}
+== Sephiroth + Variant Orwell + Meansquared ==
+It is possible to follow in the footsteps of [[magic]]/[[muggles]] temperament for [[13edo]], but using a much flatter classic major third ~[[5/4]] (as 4\13) as the generator, as [[sephiroth]], producing a [[3L&nbsp;1s]] scale (4:1 step ratio) going right and up, as used by [[Bryan Deister]] in [https://www.youtube.com/shorts/LOgt_in9SD0 ''a microtonal totentanz in 13edo''] (2023). This also supports scales [[1L&nbsp;3s]] (4:3 step ratio, going down-right, as in variant [[orwell]], although it would be awkward to play the more familiar [[4L&nbsp;5s]] scale) and [[5L&nbsp;2s (4/1-equivalent)]] (4:3 step ratio, going overall straight right through the octave zig-zag, as in [[meansquared]]). Octaves alternate between near/mid/far and mid-near/mid-far, with double octaves being perfectly level (thus enabling dual manuals); the range is 10¼ octaves.
+{{Lumatone EDO mapping|n=13|start=11|xstep=4|ystep=-1}}
+{{Navbox Lumatone}}