Lumatone mapping for 13edo: Difference between revisions

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== 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]]); 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.

[[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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 == 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]]); 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.
+[[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}}