Lumatone mapping for 67edo: Difference between revisions

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== Negri ==

The [[1L 8s]] [[Negri]] mapping has a greater octave slope and uses the second best approximation to the 5th harmonic, but still makes familiar intervals easier to play.

The [[1L 8s]] [[Negri]] mapping has a greater octave slope and uses the second best approximation to the 5th harmonic, but still makes familiar intervals easier to play. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/KwnIPUqud0w ''67edo improv''] (2026). The range is a bit over 3⅓ octaves, but each otherwise full octave is missing one note.

== 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).

== Infraorwell (gramitonic) ==

[[Bryan Deister]] has tested forward and reverse chroma [[4L 5s]] (gramitonic, 8:7 step ratio) mappings for [[67edo]]. Both get all notes in each octave and have a range of a bit over 4½ octaves. Apart from straight right (forward chroma version) or straight down-right (reverse chroma version, the most accessible generator is 15\67, which is a near-just septimal minor third ~[[7/6]]. This would suggest [[Orwell]], except that the septimal minor third of 67edo is too close to just for actual Orwell temperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]]. Instead, this yields [[Orwellismic_temperaments#Infraorwell|Infraorwell]].

[[Bryan Deister]] has tested forward and reverse chroma [[4L 5s]] (gramitonic, 8:7 step ratio) mappings for [[67edo]]. Both get all notes in each octave and have a range of a bit over 3½ octaves. Apart from straight right (forward chroma version) or straight down-right (reverse chroma version, the most accessible generator is 15\67, which is a near-just septimal minor third ~[[7/6]]. This would suggest [[Orwell]], except that the septimal minor third of 67edo is too close to just for actual Orwell temperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]]. Instead, this yields [[Orwellismic_temperaments#Infraorwell|Infraorwell]].

=== Forward chroma ===

@@ Line 9: / Line 9: @@
 == Negri ==
-The [[1L 8s]] [[Negri]] mapping has a greater octave slope and uses the second best approximation to the 5th harmonic, but still makes familiar intervals easier to play.
+The [[1L 8s]] [[Negri]] mapping has a greater octave slope and uses the second best approximation to the 5th harmonic, but still makes familiar intervals easier to play. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/KwnIPUqud0w ''67edo improv''] (2026). The range is a bit over 3⅓ octaves, but each otherwise full octave is missing one note.
-{{Lumatone EDO mapping|n=67|start=22|xstep=7|ystep=4}}
+{{Lumatone EDO mapping|n=67|start=8|xstep=7|ystep=4}}
 == 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}}
 == Infraorwell (gramitonic) ==
-[[Bryan Deister]] has tested forward and reverse chroma [[4L&nbsp;5s]] (gramitonic, 8:7 step ratio) mappings for [[67edo]]. Both get all notes in each octave and have a range of a bit over 4½ octaves. Apart from straight right (forward chroma version) or straight down-right (reverse chroma version, the most accessible generator is 15\67, which is a near-just septimal minor third ~[[7/6]]. This would suggest [[Orwell]], except that the septimal minor third of 67edo is too close to just for actual Orwell temperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]]. Instead, this yields [[Orwellismic_temperaments#Infraorwell|Infraorwell]].
+[[Bryan Deister]] has tested forward and reverse chroma [[4L&nbsp;5s]] (gramitonic, 8:7 step ratio) mappings for [[67edo]]. Both get all notes in each octave and have a range of a bit over 3½ octaves. Apart from straight right (forward chroma version) or straight down-right (reverse chroma version, the most accessible generator is 15\67, which is a near-just septimal minor third ~[[7/6]]. This would suggest [[Orwell]], except that the septimal minor third of 67edo is too close to just for actual Orwell temperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]]. Instead, this yields [[Orwellismic_temperaments#Infraorwell|Infraorwell]].
 === Forward chroma ===