Lumatone mapping for 55edo: Difference between revisions

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== Diatonic ==

The [[Standard Lumatone mapping for Pythagorean]] already produces a very efficient mapping for 55edo, so any alternative mapping would have to offer a compelling advantage in making certain intervals or scales easier to play. This mapping is shown in action in [[Bryan Deister]]'s [https://www.youtube.com/shorts/l62rb8ULCXs ''55edo improv''] (2025).

== Tetracot ==

The [[6L 1s]] ([[Tetracot]]~~, 55c val)~~ mapping also provides a heptatonic scale that gives you access to all the notes in the gamut in an intuitive way without any backtracking. ~~However,~~ the [[7L 6s]] ~~MOS has~~ a 7:~~1 step ratio, making it quite lopsided~~.

The [[6L 1s]] [[Tetracot]] mapping also provides a heptatonic scale that gives you access to all the notes in the gamut in an intuitive way without any backtracking. Actual tetracot temperament uses a flat ptolemaic whole tone ~[[10/9]] (tempered together with a flat undecimal submajor second ~[[11/10]] in the [[11-limit]]), requiring use of the 55c val to get 8\55; but it is possible to bypass the need for this wart by instead using the slightly flat tricesimoprimal whole tone ~[[31/28]] to get 8\55, thereby creating a tetracot analog which works with the [[patent val]] of 55edo. This mapping is shown in action in [[Bryan Deister]]'s [https://www.youtube.com/shorts/eQHpMFLrjjQ ''55edo prelude''] (2025).

== Fibonaccic ==

As 55 is a fibonacci number, using the fibonacci numbers one or two steps lower in the sequence as a generator will generate a [[5L 3s]] scale that is only slightly less efficient than the diatonic one, but makes playing xenharmonic combinations of notes together much easier.

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 == Diatonic ==
+The [[Standard Lumatone mapping for Pythagorean]] already produces a very efficient mapping for 55edo, so any alternative mapping would have to offer a compelling advantage in making certain intervals or scales easier to play. This mapping is shown in action in [[Bryan Deister]]'s [https://www.youtube.com/shorts/l62rb8ULCXs ''55edo improv''] (2025).
 {{Lumatone EDO mapping|n=55|start=53|xstep=9|ystep=-4}}
 == Tetracot ==
-The [[6L&nbsp;1s]] ([[Tetracot]], 55c&nbsp;val) mapping also provides a heptatonic scale that gives you access to all the notes in the gamut in an intuitive way without any backtracking. However, the [[7L&nbsp;6s]] MOS has a 7:1 step ratio, making it quite lopsided.
+The [[6L&nbsp;1s]] [[Tetracot]] mapping also provides a heptatonic scale that gives you access to all the notes in the gamut in an intuitive way without any backtracking. Actual tetracot temperament uses a flat ptolemaic whole tone ~[[10/9]] (tempered together with a flat undecimal submajor second ~[[11/10]] in the [[11-limit]]), requiring use of the 55c&nbsp;val to get 8\55; but it is possible to bypass the need for this wart by instead using the slightly flat tricesimoprimal whole tone ~[[31/28]] to get 8\55, thereby creating a tetracot analog which works with the [[patent val]] of 55edo. This mapping is shown in action in [[Bryan Deister]]'s [https://www.youtube.com/shorts/eQHpMFLrjjQ ''55edo prelude''] (2025).
 {{Lumatone EDO mapping|n=55|start=37|xstep=8|ystep=-1}}
+== Fibonaccic ==
+As 55 is a fibonacci number, using the fibonacci numbers one or two steps lower in the sequence as a generator will generate a [[5L 3s]] scale that is only slightly less efficient than the diatonic one, but makes playing xenharmonic combinations of notes together much easier.
+{{Lumatone EDO mapping|n=55|start=53|xstep=8|ystep=-3}}
 {{Navbox Lumatone}}