Macrodiatonic and microdiatonic scales: Difference between revisions

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* [[Ed7/4|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).

* [[Ed9/5|5L 2s<9/5>]]: Generator is approximately 7/5.

* [[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 (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). This is made by cutting off the 5/3 interval range of the tetratave scale of [[tetrahanson]] [[8L 3s (4/1-equivalent)|8L 3s<4/1>]].

* [[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 (or rather more like macroarchy, with the 17/9 being stretched) [[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]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.

* [[5L 2s (13/4-equivalent)|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.

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 * [[Ed7/4|5L 2s<7/4>]]: Generator is approximately 7/5 (dark generator is approximately 5/4).
 * [[Ed9/5|5L 2s<9/5>]]: Generator is approximately 7/5.
-* [[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 (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). This is made by cutting off the 5/3 interval range of the tetratave scale of [[tetrahanson]] [[8L 3s (4/1-equivalent)|8L 3s<4/1>]].
 * [[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 (or rather more like macroarchy, with the 17/9 being stretched) [[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]]. Harder varieties of the scale can instead be interpreted where the generator is a sharp [[21/11]], and 3 generators is equivalent to [[7/3]], tempering out [[1331/1323]] and producing [[Mintaka]] temperament.
 * [[5L 2s (13/4-equivalent)|5L 2s<13/4>]]: Generator is approximately [[2/1]]. This may be suitable for stretching 4:5:6 into 2:3:4, but the "[[3/2]]" in this chord is not very accurate and [[mavila]]-like in size.