Lumatone mapping for 59edo: Difference between revisions

[[Bryan Deister]] has demonstrated a [[3L 4s]] mapping (step ratio 9:8, not 13:5 as appearing on the page for 3L 4s) of 59edo in [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025) as 9 right, 1 up. The rightward generator is a whole tone that maps inconsistently due to the dual fifth nature of 59edo; however, three of these generators give an ~[[11/8]] that is only slightly flat. The down-right generator 8\59 maps to ~[[11/10]], which is not affected by the dual fifth nature of 59edo; four of these stack to yield a ~[[16/11]] that is only slightly sharp. Both fifths are also easily reachable. This mapping gets a range of a bit over five octaves, but at the cost of some skipped notes, especially in the upper left and lower right corners, but also a few in all octaves in between, and the octaves slant down severely.

In the comments to the video linked above, Deister recommends 7 right, 1 up as a complete [[5L 4s]] (7:6 step ratio) mapping. The range is now down to a bit over four octaves, with missing notes in at the ends due to the upper left and lower right corners, but at least no missing notes in the middle octaves, and the octave slope is not so severe.