Miracle 10 MODMOS: Difference between revisions

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First, Miracle[10]:

== Miracle[10] ==

First, [[Miracle]][10]:

In the mode 2|7, sssssssLss it approximates

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We ~~will interpolate~~ from ~~here~~ to the 3-~~SN scale~~ mLmmsmmLmm, and back:

7-limit Miracle[10] can be described as a [[step-nested scale]] as SNS (2/1, 16/15: 225/224, 1029/1024)[10].

We can build similar rank-3 scales using a 16/15 generator, including [[SNS (2/1, 3/2, 5/4: 225/224)-10|SNS (2/1, 3/2, 5/4: 225/224)[10]]], and [[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|SNS ((2/1, 3/2)[5], 16/15: 225/224)[10]]]. Such scales can be interpreted as MODMOS of Miracle[10] (but without 1029/1024 tempered out). We explore the Miracle[10] MODMOS that map the path from Miracle[10] to these 3-SNS, and MODMOS that are similar to those.

== MODMOS to SNS (2/1, 3/2, 5/4: 225/224)[10] ==

SNS (2/1, 3/2, 5/4: 225/224)[10] in mode 1 has step pattern mLmmsmmLmm, and step signature and mapping 2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20). m is the small step of Miracle[10], 16/15~15/14; L is the large step of Miracle[10], 35/23 (12/11 in the 11-limit); and s is the diminished step of Miracle[10], 21/20.

Accordingly, mLmmsmmLmm can be written as sLssdssLss.

It approximates the JI intervals 16/15~15/14 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1

We can write it as Miracle[10] 2|7 ♯3 ♯4 ♯5 or Miracle[10] 8|1 ♭6 ♭7 ♭8.

We will interpolate from Miracle[10] 2|7 to Miracle[10] 2|7 ♯3 ♯4 ♯5, and back a different way.

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1|8 ♭3 ♭4 ♭5 sdssLsssLs 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1

== MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] ==

SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] in mode 1 has step pattern smLmsmLmsm, and step signature and mapping 2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20). m is the small step of Miracle[10], 16/15~15/14; s is the diminished step of Miracle[10], 21/20; and L is the augmented step of Miracle[10], 10/9.

Accordingly, smLmsmLmsm can be written as dsAsdsAsds. This is clearly a much more complex MODMOS than those above.

It approximates the JI intervals 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1

We can write it as Miracle[10] 7|2 ♭2 ♭3 ♭6 ♭7 ♯8 ♯9, or as Miracle[10] 6|3 ♭2 ♭3 ♯4 ♯5 ♯8 ♯9.

using the 3-step stacked triads, we get major on I, V, and VII; augmented on II (14/11, 5/4) and III (5/4, 14/11), minor on IV, VIII, and X, large major (14/11, 33/28) on VI, small minor (33/28, 14/11) on IX.

So here we get 3 major, 3 minor, 2 augmented, and instead of 2 wolves, we get a large major and a small minor!

Now let's consider a path from Miracle[10] to this MODMOS. (tbc)

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-First, Miracle[10]:
+== Miracle[10] ==
+First, [[Miracle]][10]:
 In the mode 2|7, sssssssLss it approximates
@@ Line 8: / Line 9: @@
-We will interpolate from here to the 3-SN scale mLmmsmmLmm, and back:
+-limit Miracle[10] can be described as a [[step-nested scale]] as SNS (2/1, 16/15: 225/224, 1029/1024)[10].
+We can build similar rank-3 scales using a 16/15 generator, including [[SNS (2/1, 3/2, 5/4: 225/224)-10|SNS (2/1, 3/2, 5/4: 225/224)[10]]], and [[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|SNS ((2/1, 3/2)[5], 16/15: 225/224)[10]]]. Such scales can be interpreted as MODMOS of Miracle[10] (but without 1029/1024 tempered out). We explore the Miracle[10] MODMOS that map the path from Miracle[10] to these 3-SNS, and MODMOS that are similar to those.
+== MODMOS to SNS (2/1, 3/2, 5/4: 225/224)[10] ==
+SNS (2/1, 3/2, 5/4: 225/224)[10] in mode 1 has step pattern mLmmsmmLmm, and step signature and mapping 2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20). m is the small step of Miracle[10], 16/15~15/14; L is the large step of Miracle[10], 35/23 (12/11 in the 11-limit); and s is the diminished step of Miracle[10], 21/20.
+Accordingly, mLmmsmmLmm can be written as sLssdssLss.
+It approximates the JI intervals 16/15~15/14 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
+We can write it as Miracle[10] 2|7 ♯3 ♯4 ♯5 or Miracle[10] 8|1 ♭6 ♭7 ♭8.
+We will interpolate from Miracle[10] 2|7 to Miracle[10] 2|7 ♯3 ♯4 ♯5, and back a different way.
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 |8 ♭3 ♭4 ♭5 sdssLsssLs 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
+== MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] ==
+SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] in mode 1 has step pattern smLmsmLmsm, and step signature and mapping 2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20). m is the small step of Miracle[10], 16/15~15/14; s is the diminished step of Miracle[10], 21/20; and L is the augmented step of Miracle[10], 10/9.
+Accordingly, smLmsmLmsm can be written as dsAsdsAsds. This is clearly a much more complex MODMOS than those above.
+It approximates the JI intervals 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
+We can write it as Miracle[10] 7|2 ♭2 ♭3 ♭6 ♭7 ♯8 ♯9, or as Miracle[10] 6|3 ♭2 ♭3 ♯4 ♯5 ♯8 ♯9.
+using the 3-step stacked triads, we get major on I, V, and VII; augmented on II (14/11, 5/4) and III (5/4, 14/11), minor on IV, VIII, and X, large major (14/11, 33/28) on VI, small minor (33/28, 14/11) on IX.
+So here we get 3 major, 3 minor, 2 augmented, and instead of 2 wolves, we get a large major and a small minor!
+Now let's consider a path from Miracle[10] to this MODMOS. (tbc)