Macrodiatonic and microdiatonic scales: Difference between revisions

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* [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).

* [[5L 2s (3/1-equivalent)|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]].

* [[5L 2s (4/1-equivalent)|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]2). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]2) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]2) in 4.9.49 for the archy equivalent. This ~~sclae~~ is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)|5L 7s<4/1>]] instead.

* [[5L 2s (4/1-equivalent)|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]2). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]2) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]2) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)|5L 7s<4/1>]] instead.

== In broader sense ==

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 * [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).
 * [[5L 2s (3/1-equivalent)|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]].
-* [[5L 2s (4/1-equivalent)|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]<sup>2</sup>). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]<sup>2</sup>) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]<sup>2</sup>) in 4.9.49 for the archy equivalent. This sclae is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)|5L 7s<4/1>]] instead.
+* [[5L 2s (4/1-equivalent)|5L 2s<4/1>]]: This is precisely a 200% stretched diatonic scale. Generator is approximately [[9/4]] ([[3/2]]<sup>2</sup>). This can very clearly be interpreted as a temperament tempering out [[6561/6400]] ([[81/80]]<sup>2</sup>) in 4.9.25 for the meantone equivalent or 4096/3969 ([[64/63]]<sup>2</sup>) in 4.9.49 for the archy equivalent. This scale is extremely widely spaced, so it may preferable to use the macrochromatic scales [[7L 5s (4/1-equivalent)|7L 5s<4/1>]] and [[5L 7s (4/1-equivalent)|5L 7s<4/1>]] instead.
 == In broader sense ==