Lumatone mapping for 67edo - Revision history

Lucius Chiaraviglio: /* Lesser Tendoneutralic */ Convert monzo to use template

2025-11-23T23:56:56Z

Lesser Tendoneutralic: Convert monzo to use template

← Older revision		Revision as of 23:56, 23 November 2025
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	== Lesser Tendoneutralic ==		== 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).
	{{Lumatone EDO mapping\|n=67\|start=50\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=67\|start=50\|xstep=7\|ystep=-1}}

Lucius Chiaraviglio: /* Infraorwell (gramitonic) */ Fix typo

2025-11-08T20:01:24Z

Infraorwell (gramitonic): Fix typo

← Older revision		Revision as of 20:01, 8 November 2025
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	== Infraorwell (gramitonic) ==		== 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 ===		=== Forward chroma ===

Lucius Chiaraviglio: /* Lesser Tendoneutralic */ Insert Infraorwell (2 mappings) after this

2025-11-06T07:58:42Z

Lesser Tendoneutralic: Insert Infraorwell (2 mappings) after this

@@ Line 15: / Line 15: @@
 [[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).
 {{Lumatone EDO mapping|n=67|start=50|xstep=7|ystep=-1}}
 {{Navbox Lumatone}}

Lucius Chiaraviglio: /* Lesser tendoneutralic */ Title capitalization

2025-07-30T06:52:50Z

Lesser tendoneutralic: Title capitalization

← Older revision		Revision as of 06:52, 30 July 2025
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	{{Lumatone EDO mapping\|n=67\|start=22\|xstep=7\|ystep=4}}		{{Lumatone EDO mapping\|n=67\|start=22\|xstep=7\|ystep=4}}

	== Lesser ~~tendoneutralic~~ ==		== 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 {{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).
	{{Lumatone EDO mapping\|n=67\|start=50\|xstep=7\|ystep=-1}}		{{Lumatone EDO mapping\|n=67\|start=50\|xstep=7\|ystep=-1}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

Lucius Chiaraviglio: Add Bryan Deister's Lesser tendoneutralic mapping

2025-07-30T06:52:03Z

Add Bryan Deister's Lesser tendoneutralic mapping

← Older revision		Revision as of 06:52, 30 July 2025
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	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.
	{{Lumatone EDO mapping\|n=67\|start=22\|xstep=7\|ystep=4}}		{{Lumatone EDO mapping\|n=67\|start=22\|xstep=7\|ystep=4}}

			== 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).
			{{Lumatone EDO mapping\|n=67\|start=50\|xstep=7\|ystep=-1}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

Yourmusic Productions: Add Negri, since there's already music using that temperament here.

2025-07-29T09:19:33Z

Add Negri, since there's already music using that temperament here.

← Older revision		Revision as of 09:19, 29 July 2025
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	The smallest mapping that does cover all the notes in a clear fashion with octaves kept near horizontal and a minimum of repetition is the [[2L 7s]] one generated by 30/67.		The smallest mapping that does cover all the notes in a clear fashion with octaves kept near horizontal and a minimum of repetition is the [[2L 7s]] one generated by 30/67.
	{{Lumatone EDO mapping\|n=67\|start=34\|xstep=7\|ystep=2}}		{{Lumatone EDO mapping\|n=67\|start=34\|xstep=7\|ystep=2}}

			== 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.
			{{Lumatone EDO mapping\|n=67\|start=22\|xstep=7\|ystep=4}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

Lucius Chiaraviglio: /* Antidiatonic */ --> Balzano (antidiatonic would be 2L 5s)

2025-07-21T09:48:24Z

Antidiatonic: --> Balzano (antidiatonic would be 2L 5s)

← Older revision		Revision as of 09:48, 21 July 2025
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	{{Lumatone EDO mapping\|n=67\|start=65\|xstep=11\|ystep=-5}}		{{Lumatone EDO mapping\|n=67\|start=65\|xstep=11\|ystep=-5}}

	== ~~Antidiatonic~~ ==		== Balzano ==
	The smallest mapping that does cover all the notes in a clear fashion with octaves kept near horizontal and a minimum of repetition is the [[2L 7s]] one generated by 30/67.		The smallest mapping that does cover all the notes in a clear fashion with octaves kept near horizontal and a minimum of repetition is the [[2L 7s]] one generated by 30/67.
	{{Lumatone EDO mapping\|n=67\|start=34\|xstep=7\|ystep=2}}		{{Lumatone EDO mapping\|n=67\|start=34\|xstep=7\|ystep=2}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

Yourmusic Productions: Create Page.

2025-07-20T13:59:37Z

Create Page.

New page

{{Lumatone mapping intro}} However, due to the size of the edo, this mapping does not quite cover all the notes.

== Diatonic ==
{{Lumatone EDO mapping|n=67|start=65|xstep=11|ystep=-5}}

== Antidiatonic ==
The smallest mapping that does cover all the notes in a clear fashion with octaves kept near horizontal and a minimum of repetition is the [[2L 7s]] one generated by 30/67.
{{Lumatone EDO mapping|n=67|start=34|xstep=7|ystep=2}}

{{Navbox Lumatone}}