Lumatone mapping for 89edo: Difference between revisions
The 8L 3s scale has a generator of 33\89, not 23\89, which makes it a sharp sensi variant that uses the second best fifth, not a myna one. |
→Other Mappings: I misread the 8L 3s scale tree, but Sensoid is neither the correct scale name nor a temperament name found in the Sensi/Sensipent pages; also restore Myna temperament quick description text and text about notes chopped off at the left and right edges; will have to fix this up some more later |
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The smallest mapping that covers the whole gamut is the [[4L 7s]] one. Interestingly, there are two different mappings that fit that criteria, both good. | The smallest mapping that covers the whole gamut is the [[4L 7s]] one. Interestingly, there are two different mappings that fit that criteria, both good. | ||
=== Myna === | === Myna === | ||
The [[myna]] mapping is quite lopsided, but is the optimal patent val for the temperament and efficiently gives access to the full 11-limit. | The [[myna]] mapping is quite lopsided, but is the optimal patent val for the temperament and efficiently gives access to the full 11-limit. The generator is a mildly flat classic minor third ~[[6/5]] (23\89). Two generators make a slightly sharp greater septimal tritone ~[[10/7]]; three of them make a slightly flat septimal major sixth ~[[12/7]]; after octave-reduction, five of them make a mildly sharp undecimal neutral third ~[[11/9]] (however, not ~[[13/16]] unless 89f is used); seven of them make a slightly sharp septimal minor seventh ~[[7/4]]; nine of them make a mildly sharp classic major third ~[[5/4]]; ten of them make a near-just fifth ~[[3/2]]. The overall range is a bit over three octaves, with a gentle downwards slope, but the bass and treble octaves lose many notes at the left and right edges (although the middle of the range does cover the whole gamut, even having a few repeated notes). | ||
{{Lumatone EDO mapping|n=89|start=58|xstep=3|ystep=14}} | {{Lumatone EDO mapping|n=89|start=58|xstep=3|ystep=14}} | ||
=== Orgone === | === Orgone === | ||
The [[Orgone]] mapping | The [[Orgone]] mapping focuses on making the 2.7.11 subgroup easy to play, but is extremely efficient at covering that and only a tenth of a cent off the minimax tuning, plus it skips or repeats fewer notes at the edges. The overall range is a bit over three octaves, with a gentle downwards slope, but the bass and treble octaves lose many notes at the left and right edges. | ||
{{Lumatone EDO mapping|n=89|start=76|xstep=7|ystep=3}} | {{Lumatone EDO mapping|n=89|start=76|xstep=7|ystep=3}} | ||
=== | === 8L 3s === | ||
A much less lopsided [[8L 3s]] (10:3 step ratio) scale minimizes note loss at the left and right edges. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=Rjx1zr3HIE0 ''89edo improv''] (2026-10-28). This mapping is maximally efficient, with a range of just over three octaves (which slope upwards very gently), with no missed notes (even in the bass and treble note 0 to note 0 octaves) and no repeated notes. However, this does not put simple ratios as close together as the previous two. | A much less lopsided [[8L 3s]] (10:3 step ratio) scale minimizes note loss at the left and right edges. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=Rjx1zr3HIE0 ''89edo improv''] (2026-10-28). This mapping is maximally efficient, with a range of just over three octaves (which slope upwards very gently), with no missed notes (even in the bass and treble note 0 to note 0 octaves) and no repeated notes. However, this does not put simple ratios as close together as the previous two. | ||
{{Lumatone EDO mapping|n=89|start=5|xstep=10|ystep=-7}} | {{Lumatone EDO mapping|n=89|start=5|xstep=10|ystep=-7}} | ||