Revision as of 10:32, 7 September 2026 by Lucius Chiaraviglio(talk | contribs)(Add Bryan Deister's Bohpier mapping; optimize note 0 position for slendric/rodan + guiron mappings; also fix a couple of section headings)
The magic mapping is particularly efficient at putting good intervals close to each other and dissonant ones far away, as demonstrated in more detail in the writings on the kite guitar.
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Tetracot
The tetracot mapping also puts consonant intervals within easy reach, making major, minor, and neutral triads particularly intuitive to play.
Standard
The standard 6L 1s mapping is less lopsided and offers over 4½ octaves of range, but the octaves slope up. Bryan Deister has demonstrated this mapping (although offset in MIDI note position) in Winds Up The Best - 41edo (2026) ([short 1], [short 2]), from a point a few seconds into [short 1] up to slightly beyond the halfway point of [short 2], before switching on-the-fly to the baldy mapping (see below), which is also used in the first few seconds of [short 1].
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Compressed
This can be compressed down to a 1L 5s mapping that extends range, but makes fingerings for common chords slightly more awkward, although it does slightly reduce the upward slope of octaves.
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Slendric (Rodan) + Guiron
In 41edo, the near-just fifth ~3/2 is 24\41, and dividing this into three parts yields a slightly sharp septimal major second ~8/7, which is the generator for slendric and its extension rodan and for guiron, which meets with slendric/rodan at 41edo. In both versions below, this generator (8\41) is reached very simply by moving one key right from the root note.
Compressed
If you want to maximise your range while having access to all notes in each octave, the compressed rodan mapping is about as good as you can get (at 6¼ octaves); however, it puts octaves all over the place.
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Expanded
The expanded rodan mapping still has a wider range (somewhat over five octaves except for one missing note 38 in the top octave) compared to the diatonic mapping (just under five octaves) and is more ergonomic for play, as is the baldy mapping below this.
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Baldy
Bryan Deister has demonstrated the baldy mapping (although offset in MIDI note position) in Winds Up The Best - 41edo (2026) ([short 1], [short 2]), in the first few seconds of [short 1] and the last slightly less than half of [short 2], with the rest being in the tetracot mapping (see above), again having switched mappings on the fly.
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Miracle (miraculous)
It is possible to map 41edo as a miracle (miraculous) tuning, with a 8L 3s scale (4:3 step ratio), using a secor (~15/14 tempered together with ~16/15) which is in turn tempered together with ~14/13 (as per the miraculous 13-limit extension). In this mapping, the range is only three octaves, but the octaves are perfectly level, each note is repeated at least twice, with a few being repeated three times, thus enabling the use of two manuals if the layout is offset appropriately. Bryan Deister has used this layout in microtonal dance in 41edo (2023), although without a color scheme that would show the layout.
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Superkleismic
Bryan Deister has demonstrated a superkleismic4L 3s (8:3 step ratio) mapping for 41edo, in 41edo groove (2025). Bryan Deister explains that the coloring in this video highlights major triads, where going right and up yields a major third (~5/4, somewhat flat) and going right three times yields the fifth (~3/2, near-just). The range is somewhat over five octaves, which slope down moderately.
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Bohpier
Since 41edo is very close to BPS (Bohlen–Pierce–Stearns) with its generator split into 5 equal parts and the addition of prime 2, it makes sense to map it for bohpier temperament, as demonstrated by Bryan Deister in 41edo improv (2026-09-01). The generator 5\41 (reached very simply by moving one key right from the root note) functions as a flat undecimal neutral second ~12/11 and a sharp lesser tridecimal neutral second ~13/12. The range is somewhat over 4½ octaves, although the octaves slope down severely, incurring vertical wraparounds.
