Lumatone mapping for 67edo: Difference between revisions

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== Lesser Tendoneutralic ==

[[Bryan Deister]] has demonstrated a [[7L 3s]] (7:6 step ratio) layout for [[67edo]] that uses the tempering out of the [[Lesser tendoneutralisma]] (70368744177664/69894255367443, more conveniently described as {{~~nowrap~~|~~{{!}}~~46 -1 0 0 0 -~~12⟩~~}}), in [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~[[16/13]] (octave-reduced 13th subharmonic). Twelve of these are tempered together to make ~[[12/1]], which is then octave-reduced to the twelfth ~[[3/1]], and thence to the fifth ~[[3/2]]. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo — the notes of a complete [[meantone]] diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).

[[Bryan Deister]] has demonstrated a [[7L 3s]] (7:6 step ratio) layout for [[67edo]] that uses the tempering out of the [[Lesser tendoneutralisma]] (70368744177664/69894255367443, more conveniently described as {{monzo|46 -1 0 0 0 -12}}), in [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~[[16/13]] (octave-reduced 13th subharmonic). Twelve of these are tempered together to make ~[[12/1]], which is then octave-reduced to the twelfth ~[[3/1]], and thence to the fifth ~[[3/2]]. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo — the notes of a complete [[meantone]] diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).

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 == Lesser Tendoneutralic ==
-[[Bryan Deister]] has demonstrated a [[7L&nbsp;3s]] (7:6 step ratio) layout for [[67edo]] that uses the tempering out of the [[Lesser tendoneutralisma]] (70368744177664/69894255367443, more conveniently described as {{nowrap|{{!}}46 -1 0 0 0 -12⟩}}), in [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~[[16/13]] (octave-reduced 13th subharmonic).  Twelve of these are tempered together to make ~[[12/1]], which is then octave-reduced to the twelfth ~[[3/1]], and thence to the fifth ~[[3/2]]. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo &mdash; the notes of a complete [[meantone]] diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).
+[[Bryan Deister]] has demonstrated a [[7L&nbsp;3s]] (7:6 step ratio) layout for [[67edo]] that uses the tempering out of the [[Lesser tendoneutralisma]] (70368744177664/69894255367443, more conveniently described as {{monzo|46 -1 0 0 0 -12}}), in [https://www.youtube.com/shorts/uwxey9_jINA ''microtonal improvisation in 67edo''] (2025). The underlying generator of the temperament is two steps right and one step down-right on the keyboard, which is 20\67, which is a near-just ~[[16/13]] (octave-reduced 13th subharmonic).  Twelve of these are tempered together to make ~[[12/1]], which is then octave-reduced to the twelfth ~[[3/1]], and thence to the fifth ~[[3/2]]. The range is a bit under 3⅓ octaves, and the octaves are almost level, having a barely perceptible downward slant. Although very efficient, this mapping takes a very xenharmonic approach 67edo &mdash; the notes of a complete [[meantone]] diatonic scale are not situated for easy access (being widely spaced vertically and always requiring a vertical wraparound to play the complete diatonic scale).
 {{Lumatone EDO mapping|n=67|start=50|xstep=7|ystep=-1}}