Lumatone mapping for 6edo

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There are several conceivable ways to map 6edo onto the onto the Lumatone keyboard. However, none of them even remotely approximate the Standard Lumatone mapping for Pythagorean and all generators except the single step fail to cover the whole gamut. Setting the 1, 2 & 3 steps to different axes will let you smoothly play any interval in an intuitive way with a range of 15 octaves.

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5edoLumatone mapping for 6edo7edo8edo9edo