User:Lucius Chiaraviglio/Keyboard Layout Lab/Marvel and Miracle Lumatone mappings: Difference between revisions
→84edo (demonstrated to work but awaiting approval): Add septimal chroma as easily reachable with the down-right generator |
→84edo (demonstrated to work but awaiting approval): The upwards generator 7\84 is not very convnient |
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=== 84edo (demonstrated to work but awaiting approval) === | === 84edo (demonstrated to work but awaiting approval) === | ||
[[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 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 would produce a [[contorted]] mapping even with the [[semioctave]] [[period]] implied by 10L 4s, so a second generator is required. The down-right generator 1\84 (the small step of the scale) maps 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]]) shared with [[12edo]]. The range would be 3½ 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. | [[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 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 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 itself 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) maps 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]]) shared with [[12edo]]. The range would be 3½ 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. | ||
{{Lumatone EDO mapping|n=84|start=12|xstep=8|ystep=-7}} | {{Lumatone EDO mapping|n=84|start=12|xstep=8|ystep=-7}} | ||
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:39, 17 July 2025 (UTC) | 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]]) 08:54, 17 July 2025 (UTC) | |||
== Harry + Marvolo (Marvel) + Miracle Lumatone mappings == | == Harry + Marvolo (Marvel) + Miracle Lumatone mappings == | ||