User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed temperament Lumatone mappings: Difference between revisions
→81edo (demonstrated to work but awaiting approval): Got approval, and moved down to proper place; filled in description |
→81edo (demonstrated to work): Fix incomplete description of meantone generator |
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=== 81edo (demonstrated to work) === | === 81edo (demonstrated to work) === | ||
[[Bryan Deister]] has demonstrated a [[5L 9s]] (9:4 step ratio) layout for [[81edo]], in [https://www.youtube.com/shorts/yY0TzTiNeB8 ''81edo improv''] (2025). Both the rightward generator (4\81) and the down-right generator (9\81) map to high-limit intervals: 4\81 maps to ~[[29/28]], ~[[30/29]], and ~[[31/30]]; while 9\81 maps to ~[[40/37]]. The down-right generator is [[Saturation, torsion, and contorsion|contorted]] by itself; in principle, the first generator could be used by itself for an unnamed rank-2 temperament, but it is so small that the second generator is needed for convenience. Alternatively, one could make a rank-2 temperament using the combination of these generators, which is 13\81, which maps to the quasi-meantone ~[[19/17]] and to both sizes of classic whole tone ~[[9/8]] and ~[[10/9]], as befits 81edo being a [[meantone]] tuning, | [[Bryan Deister]] has demonstrated a [[5L 9s]] (9:4 step ratio) layout for [[81edo]], in [https://www.youtube.com/shorts/yY0TzTiNeB8 ''81edo improv''] (2025). Both the rightward generator (4\81) and the down-right generator (9\81) map to high-limit intervals: 4\81 maps to ~[[29/28]], ~[[30/29]], and ~[[31/30]]; while 9\81 maps to ~[[40/37]]. The down-right generator is [[Saturation, torsion, and contorsion|contorted]] by itself; in principle, the first generator could be used by itself for an unnamed rank-2 temperament, but it is so small that the second generator is needed for convenience. Alternatively, one could make a rank-2 temperament using the combination of these generators, which is 13\81, which maps to the quasi-meantone ~[[19/17]] and to both sizes of classic whole tone ~[[9/8]] and ~[[10/9]], as befits 81edo being a [[meantone]] tuning; the last step in arriving at meantone is to add an octave to this generator and split it in half to get 47\81, which is the closest approximation to the perfect fifth in 81edo. This produces a interleaved and rotated diatonic layout yielding a range close to 2½ octaves (with some repeated notes to mitigate vertical wraparounds) having a slight downward slant. | ||
{{Lumatone EDO mapping|n=81|start=44|xstep=4|ystep=5}} | {{Lumatone EDO mapping|n=81|start=44|xstep=4|ystep=5}} | ||
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:01, 3 December 2025 (UTC) | Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:01, 3 December 2025 (UTC)<br> | ||
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) | Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:06, 6 December 2025 (UTC) | ||
=== 91edo pseudo-isomorphic (demonstrated to work) === | === 91edo pseudo-isomorphic (demonstrated to work) === | ||