Lumatone mapping for 62edo - Revision history

Lucius Chiaraviglio: /* Ekic Mappings */ More fixes, and add Nusecond temperament; also add back Mohajira as a split-generator version

2026-03-25T19:13:20Z

Ekic Mappings: More fixes, and add Nusecond temperament; also add back Mohajira as a split-generator version

← Older revision		Revision as of 19:13, 25 March 2026
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	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic") scale mappings created by slicing the period in half for a [[myna]]/[[orwell]]-related temperament and a [[hemimeantone]] temperament. Both give a range of a bit over four octaves that are close to level.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic") scale mappings created by slicing the period in half for a [[myna]]/[[orwell]]-related temperament and a [[hemimeantone]] temperament. Both give a range of a bit over four octaves that are close to level.

	=== Myna/Orwell-related 6L 2s (8:7 step ratio) ===		=== Myna/Orwell-related or Nusecond-related 6L 2s (8:7 step ratio) ===
	The first of these mappings is related to orwell, which uses as sharp septimal minor third ~[[7/6]] as its generator, and myna, which uses a flat classic minor third ~[[6/5]] as its generator; the temperament for this mapping splits the difference and uses a septimal neutral second ~[[35/32]] as its generator, represented as 8\62, ~~and also splits~~ the octave in half.		The first of these mappings is related to orwell, which uses as sharp septimal minor third ~[[7/6]] as its generator, and myna, which uses a flat classic minor third ~[[6/5]] as its generator; the temperament for this mapping splits the difference and uses a near-just tridecimal minor third ~[[13/11]] as its generator, represented as 15\62 (one key right plus one key down-right), and splits the octave in half. It can also be interpreted as using a near-just septimal neutral second ~[[35/32]] or a somewhat sharp undecimal neutral second ~[[12/11]] as its generator, represented as 8\62 (one key right), related to [[nusecond]], but again splitting the octave in half.
	{{Lumatone EDO mapping\|n=62\|start=43\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=62\|start=43\|xstep=8\|ystep=-1}}

	=== Hemimeantone-related 6L 2s (9:4 step ratio) ===		=== Hemimeantone/Mohajira-related 6L 2s (9:4 step ratio) ===
	The second is related to [[hemimeantone]], using a slightly sharp tridecimal semifourth ~[[15/13]] (represented as 13\62) as a its generator, making half of the (~~flat~~) fourth ~[[4/3]], but also splitting the octave in half. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].		The second is related to [[hemimeantone]], using a slightly sharp tridecimal semifourth ~[[15/13]] (represented as 13\62, one key right plus one key down-right) as its generator, making half of the (sharp) fourth ~[[4/3]], but also splitting the octave in half. Alternatively, it can be interpreted as using a near-just undevicesimal submajor/supraneutral second ~[[21/19]] as its generator, represented as 9\62 (one key right), related to [[mohajira]] by splitting the near-just undecimal neutral third ~[[11/9]] in half (thus splitting the fifth ~[[3/2]] into quarters), as well as splitting the octave in half. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].
	{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}

Yourmusic Productions: Tidy up math & formatting

2026-03-25T08:21:36Z

Tidy up math & formatting

← Older revision		Revision as of 08:21, 25 March 2026
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	=== Myna/Orwell-related 6L 2s (8:7 step ratio) ===		=== Myna/Orwell-related 6L 2s (8:7 step ratio) ===
	The first of these mappings is related to orwell, which uses as sharp septimal minor third ~[[7/6]] as its generator, and myna, which uses a flat classic minor third ~[[6/5]] as its generator; the temperament for this mapping splits the difference and uses a ~~near-just tridecimal minor third~~ ~[[13/11]] as its generator, represented as 15\62, and also splits the octave in half.		The first of these mappings is related to orwell, which uses as sharp septimal minor third ~[[7/6]] as its generator, and myna, which uses a flat classic minor third ~[[6/5]] as its generator; the temperament for this mapping splits the difference and uses a septimal neutral second ~[[35/32]] as its generator, represented as 8\62, and also splits the octave in half.
	{{Lumatone EDO mapping\|n=62\|start=43\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=62\|start=43\|xstep=8\|ystep=-1}}

	=== Hemimeantone-related 6L 2s (9:4 step ratio) ===		=== Hemimeantone-related 6L 2s (9:4 step ratio) ===
	The second is related to hemimeantone]], using a slightly ~~flat~~ tridecimal semifourth ~[[15/13]] (represented as 13\62) as a its generator, making half of the (flat) fourth ~[[4/3]], but also splitting the octave in half. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].		The second is related to [[hemimeantone]], using a slightly sharp tridecimal semifourth ~[[15/13]] (represented as 13\62) as a its generator, making half of the (flat) fourth ~[[4/3]], but also splitting the octave in half. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].
	{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}

Lucius Chiaraviglio: /* Ekic Scale Mappings */ --> Ekic Mappings

2026-03-25T07:42:08Z

Ekic Scale Mappings: --> Ekic Mappings

← Older revision		Revision as of 07:42, 25 March 2026
Line 5:		Line 5:
	{{Lumatone EDO mapping\|n=62\|start=20\|xstep=12\|ystep=-11}}		{{Lumatone EDO mapping\|n=62\|start=20\|xstep=12\|ystep=-11}}

	== Ekic ~~Scale~~ Mappings ==		== Ekic Mappings ==
	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing the period in half for a [[myna]]/[[orwell]]-related temperament and a [[hemimeantone]] temperament. Both give a range of a bit over four octaves that are close to level.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic") scale mappings created by slicing the period in half for a [[myna]]/[[orwell]]-related temperament and a [[hemimeantone]] temperament. Both give a range of a bit over four octaves that are close to level.

	=== Myna/Orwell-related 6L 2s (8:7 step ratio) ===		=== Myna/Orwell-related 6L 2s (8:7 step ratio) ===

Lucius Chiaraviglio: /* Myna-related and Mohajira-related (Ekic scale) Mappings */ Fill out description; add sub-section headers; and move 8:7 step ratio version note 0 to get 4 complete note 0 to note 0 octaves; also semi-mohajira --> hemimeantone

2026-03-25T07:40:38Z

Myna-related and Mohajira-related (Ekic scale) Mappings: Fill out description; add sub-section headers; and move 8:7 step ratio version note 0 to get 4 complete note 0 to note 0 octaves; also semi-mohajira --> hemimeantone

← Older revision		Revision as of 07:40, 25 March 2026
Line 5:		Line 5:
	{{Lumatone EDO mapping\|n=62\|start=20\|xstep=12\|ystep=-11}}		{{Lumatone EDO mapping\|n=62\|start=20\|xstep=12\|ystep=-11}}

	== ~~Myna-related and Mohajira-related (~~Ekic ~~scale)~~ Mappings ==		== Ekic Scale Mappings ==
	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing ~~both~~ the ~~generator and~~ period in half for ~~the~~ [[myna]] and [[~~mohajira~~]] mappings.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing the period in half for a [[myna]]/[[orwell]]-related temperament and a [[hemimeantone]] temperament. Both give a range of a bit over four octaves that are close to level.
	{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}
	[[Bryan Deister]] demonstrates ~~the semi-mohajira~~ mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].		=== Myna/Orwell-related 6L 2s (8:7 step ratio) ===
			The first of these mappings is related to orwell, which uses as sharp septimal minor third ~[[7/6]] as its generator, and myna, which uses a flat classic minor third ~[[6/5]] as its generator; the temperament for this mapping splits the difference and uses a near-just tridecimal minor third ~[[13/11]] as its generator, represented as 15\62, and also splits the octave in half.
			{{Lumatone EDO mapping\|n=62\|start=43\|xstep=8\|ystep=-1}}

			=== Hemimeantone-related 6L 2s (9:4 step ratio) ===
			The second is related to hemimeantone]], using a slightly flat tridecimal semifourth ~[[15/13]] (represented as 13\62) as a its generator, making half of the (flat) fourth ~[[4/3]], but also splitting the octave in half. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].
	{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}

Yourmusic Productions: Spelling.

2025-10-11T06:29:40Z

Spelling.

← Older revision		Revision as of 06:29, 11 October 2025
Line 8:		Line 8:
	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.
	{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}
	[[~~Brian~~ Deister]] demonstrates the semi-mohajira mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].		[[Bryan Deister]] demonstrates the semi-mohajira mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].
	{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}

Yourmusic Productions: Add music.

2025-10-11T06:29:19Z

Add music.

← Older revision		Revision as of 06:29, 11 October 2025
Line 8:		Line 8:
	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.
	{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}
			[[Brian Deister]] demonstrates the semi-mohajira mapping in [https://www.youtube.com/watch?v=ujaUA-uwDvE ''62edo improv''].
	{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}

	== Godzilla-related rank-3 Mappings ==		== Godzilla-related rank-3 Mappings ==

	[[Bryan Deister]] has demonstrated a [[Godzilla]] Lumatone mapping for [[62edo]] in [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025), with scale [[5L 4s]] with 10:3 step ratio, which also has easy provision for dividing the near-just septimal minor seventh ~[[7/4]] (50\62) into five equal parts each functioning as a meantone whole tone (~[[9/8]], ~[[10/9]], and ~[[19/17]]) (10\62 is right by one key), which is naturally useful in its own right for mixing the common practice sound in with the xenharmonic sounds. A logical implication of splitting the ~7/4 into five meantone whole tones is that the near-just classic major third ~[[5/4]] is very easily accessible as two of these divided generators, and the only slightly flat lesser septimal tritone ~[[7/5]] is easily accessible as three of them. As convenient as this rightward generator is, it would produce a contorted mapping if not for a second generator; the upwards generator 7\62 is convenient for this as a a tridecimal neutral second that functions as both ~[[12/13]] and ~[[13/14]] (the buzurgisma/dhanvantarisma [[169/168]] is tempered out); backing off from ~7/4 by two of these generators gives the fifth (the flat ~[[3/2]] shared with [[31edo]]), while backing off from ~7/5 by two of these generators gives a moderately flat classic minor third ~[[6/5]]. Octaves slant down moderately, and the range is just under 4⅓ octaves with no missed notes and no repeated notes.		Bryan Deister has demonstrated a [[Godzilla]] Lumatone mapping for [[62edo]] in [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025), with scale [[5L 4s]] with 10:3 step ratio, which also has easy provision for dividing the near-just septimal minor seventh ~[[7/4]] (50\62) into five equal parts each functioning as a meantone whole tone (~[[9/8]], ~[[10/9]], and ~[[19/17]]) (10\62 is right by one key), which is naturally useful in its own right for mixing the common practice sound in with the xenharmonic sounds. A logical implication of splitting the ~7/4 into five meantone whole tones is that the near-just classic major third ~[[5/4]] is very easily accessible as two of these divided generators, and the only slightly flat lesser septimal tritone ~[[7/5]] is easily accessible as three of them. As convenient as this rightward generator is, it would produce a contorted mapping if not for a second generator; the upwards generator 7\62 is convenient for this as a a tridecimal neutral second that functions as both ~[[12/13]] and ~[[13/14]] (the buzurgisma/dhanvantarisma [[169/168]] is tempered out); backing off from ~7/4 by two of these generators gives the fifth (the flat ~[[3/2]] shared with [[31edo]]), while backing off from ~7/5 by two of these generators gives a moderately flat classic minor third ~[[6/5]]. Octaves slant down moderately, and the range is just under 4⅓ octaves with no missed notes and no repeated notes.
	{{Lumatone EDO mapping\|n=62\|start=4\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=62\|start=4\|xstep=10\|ystep=-7}}

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

Lucius Chiaraviglio: /* Other mappings */ --> Myna-related and Mohajira-related (Ekic scale) Mappings, and add Bryan Deister's Godzilla-related rank-3 Lumatone mapping for 62edo

2025-07-24T07:26:53Z

Other mappings: --> Myna-related and Mohajira-related (Ekic scale) Mappings, and add Bryan Deister's Godzilla-related rank-3 Lumatone mapping for 62edo

← Older revision		Revision as of 07:26, 24 July 2025
Line 5:		Line 5:
	{{Lumatone EDO mapping\|n=62\|start=20\|xstep=12\|ystep=-11}}		{{Lumatone EDO mapping\|n=62\|start=20\|xstep=12\|ystep=-11}}

	== ~~Other~~ Mappings ==		== Myna-related and Mohajira-related (Ekic scale) Mappings ==
	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] (TAMNAS "Ekic" scale) mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.
	{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}

	{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}		{{Lumatone EDO mapping\|n=62\|start=2\|xstep=9\|ystep=-5}}

			== Godzilla-related rank-3 Mappings ==

			[[Bryan Deister]] has demonstrated a [[Godzilla]] Lumatone mapping for [[62edo]] in [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025), with scale [[5L 4s]] with 10:3 step ratio, which also has easy provision for dividing the near-just septimal minor seventh ~[[7/4]] (50\62) into five equal parts each functioning as a meantone whole tone (~[[9/8]], ~[[10/9]], and ~[[19/17]]) (10\62 is right by one key), which is naturally useful in its own right for mixing the common practice sound in with the xenharmonic sounds. A logical implication of splitting the ~7/4 into five meantone whole tones is that the near-just classic major third ~[[5/4]] is very easily accessible as two of these divided generators, and the only slightly flat lesser septimal tritone ~[[7/5]] is easily accessible as three of them. As convenient as this rightward generator is, it would produce a contorted mapping if not for a second generator; the upwards generator 7\62 is convenient for this as a a tridecimal neutral second that functions as both ~[[12/13]] and ~[[13/14]] (the buzurgisma/dhanvantarisma [[169/168]] is tempered out); backing off from ~7/4 by two of these generators gives the fifth (the flat ~[[3/2]] shared with [[31edo]]), while backing off from ~7/5 by two of these generators gives a moderately flat classic minor third ~[[6/5]]. Octaves slant down moderately, and the range is just under 4⅓ octaves with no missed notes and no repeated notes.
			{{Lumatone EDO mapping\|n=62\|start=4\|xstep=10\|ystep=-7}}

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

Yourmusic Productions: minor clarification

2025-07-20T13:28:16Z

minor clarification

← Older revision		Revision as of 13:28, 20 July 2025
Line 6:		Line 6:

	== Other Mappings ==		== Other Mappings ==
	Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut. These are the [[6L 2s]] mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.		Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut with maximum range. These are the [[6L 2s]] mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.
	{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}		{{Lumatone EDO mapping\|n=62\|start=50\|xstep=8\|ystep=-1}}

Yourmusic Productions: Create Page.

2025-07-19T21:30:18Z

Create Page.

New page

{{Lumatone mapping intro}} Due to its size, it would not quite cover the whole gamut even if it was.

== Diatonic ==
You can use the b val, but this is extremely sharp, surpassing half comma [[superpyth]] and making major seconds near perfect [[8/7]]'s. This does mean that the better 5th is also fairly easily accessible as an augmented 4th, but the best approximation to [[5/4]] is a triply augmented 6th, while [[11/8]] is a triply diminished seventh, both of which are pretty awkward to play in a chord.
{{Lumatone EDO mapping|n=62|start=20|xstep=12|ystep=-11}}

== Other Mappings ==
Since 31edo is such a well-tuned edo in general, most of the mos scales in 62edo do not improve on it, making it difficult to use the extra notes if concordant harmony is your goal. However, there are two different octatonic mappings of comparable efficiency that are clear winners if you simply want access to the full gamut. These are the [[6L 2s]] mappings created by slicing both the generator and period in half for the [[myna]] and [[mohajira]] mappings.
{{Lumatone EDO mapping|n=62|start=50|xstep=8|ystep=-1}}

{{Lumatone EDO mapping|n=62|start=2|xstep=9|ystep=-5}}

{{Navbox Lumatone}}