Lumatone mapping for 62edo: Difference between revisions

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== ~~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.

== 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.

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 {{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&nbsp;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=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&nbsp;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}}