Lumatone mapping for 62edo: Difference between revisions

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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.

=== 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.

=== 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''].

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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&nbsp;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&nbsp;2s (8:7 step ratio) ===
+=== Myna/Orwell-related or Nusecond-related 6L&nbsp;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}}
-=== Hemimeantone-related 6L&nbsp;2s (9:4 step ratio) ===
+=== Hemimeantone/Mohajira-related 6L&nbsp;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}}