Lumatone mapping for 55edo: Difference between revisions

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== Tetracot ==
== 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).
{{Lumatone EDO mapping|n=55|start=37|xstep=8|ystep=-1}}
{{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}}
{{Navbox Lumatone}}

Latest revision as of 03:25, 29 May 2026

There are many conceivable ways to map 55edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

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 55edo improv (2025).

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Tetracot

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 55edo prelude (2025).

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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.

53
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19
27
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