User:Lucius Chiaraviglio/Keyboard Layout Lab/Marvel and Miracle Lumatone mappings: Difference between revisions

=== 84edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[10L 4s]] (8:1 step ratio) mapping for [[84edo]] in [https://www.youtube.com/shorts/Sqkxrmwggr0 ''microtonal improvisation in 84edo''] (2025). The rightward generator 8\84 (shared with the [[Orwell]] mapping) functions as both ~[[15/14]] and ~[[16/15]], making this a [[Marvel]] temperament; two of these make a slightly flat septimal supermajor second (~[[8/7]]); four of these make a slightly flat Barbados third (~[[13/10]]). However, by itself this generator would produce a [[contorted]] mapping even with the [[semioctave]] [[period]] implied by 10L 4s, so a second generator is required. The chroma of the scale (7\84, the upwards generator) is not very convenient as a secondary generator, and also produces a contorted mapping if used alone, so it makes sense to use the down-right generator 1\84 (the small step of the scale) as the secondary generator.  This functions as a near-just version of the starling chroma (~[[126/125]]), but also functions as a narrow version of the syntonic chroma (~[[81/80]]), a slightly narrow version of the animist chroma (~[[105/104]]), and as a wide version of the buzurgismic/dhanvantarismic chroma (~[[169/168]]) or the mycunumic chroma (~[[196/195]]); two of these make a near-just septimal chroma (~[[64/63]]); and adding three of these to the aforementioned Barbados third (reached with the rightward generator) yields the very accurate fourth (~[[4/3]]) at 35\84 (shared with [[12edo]] as 5\12). (Nevertheless, sheer distance may be a problem for people who do not have long fingers — a problem hard to avoid with large EDO sizes, that force octaves to be long to avoid missing notes.) Near-just versions of common intervals are reachable using both generators in combination: three rightward generators minus two down-right generators to get the classic major third ~[[6/5]] at 22\84, and three of each generator to get the classic major third ~[[5/4]] at 27\84. The range would be 2½ octaves with no missed notes if note for a missed note 36 in the highest semioctave; some notes are repeated for ease in vertical transitions; and the octaves are perfectly level.

Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:39, 17 July 2025 (UTC)<br>

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:09, 18 July 2025 (UTC)