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Miracle 10 MODMOS: Difference between revisions

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We can build similar scales in rank-3 using a 16/15 generator, adding a generator of 3/2 to the 2/1 and 16/15 generators, resulting in many more 3/2s and consonant triads being made available. In such scales 1029/1024 is not tempered out, nor the ampersand comma of 5-limit Miracle (the amount by which 3/2 exceeds 6 16/15s). The two such decatonic scales are [[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]]]. They can be interpreted as MODMOS of Miracle[10] (but without 1029/1024 tempered out), and the Miracle MODMOS can be interpreted as the rank-3 scales with an extra comma tempered out, without a change of structure. We explore the Miracle[10] MODMOS that map the path from Miracle[10] to these 3-SNS, and MODMOS that are similar to those.
We can build similar scales in rank-3 using a 16/15 generator, adding a generator of 3/2 to the 2/1 and 16/15 generators, resulting in many more 3/2s and consonant triads being made available. In such scales 1029/1024 is not tempered out, nor the ampersand comma of 5-limit Miracle (the amount by which 3/2 exceeds 6 16/15s). The two such decatonic scales are [[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]]]. They can be interpreted as MODMOS of Miracle[10] (but without 1029/1024 tempered out), and the Miracle MODMOS can be interpreted as the rank-3 scales with an extra comma tempered out, without a change of structure. 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] ==
== MODMOS to SNS (2/1, 3/2, 5/4: 225/224)[10] (and similar) ==
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.
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.


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using the 3-step stacked triads, we get neutral triads on I and VI, major on II; minor on V; and wolf triads on III, IV, VII, VIII, IX, and X.
using the 3-step stacked triads, we get neutral triads on I and VI, major on II; minor on V; and wolf triads on III, IV, VII, VIII, IX, and X.
Going further than Miracle[10] 2|7 ♯3 ♯4 ♯5
=== Miracle[10] 2|7 ♯2 ♯3 ♯4 ♯5 ===
Now try going further, to Miracle[10] 2|7 ♯2 ♯3 ♯4 ♯5 LsssdssLss. On the generator chain this MODMOS is ###....###...####.
12/11 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
using the 3-step stacked triads, we get major on I and X; major-diminished triad (11/9, 6/5) on II; minor on III, IV, and V; wolf triads IX, and augmented triads on VI, VII and VIII.
=== Miracle[10] 1|8 ♯3 ♯4 ♯5 / Miracle[10] 2|7 ♯2 ♯3 ♯4 ===
It's inverse is sLssdsssLs, Miracle[10] 1|8 ♯3 ♯4 ♯5. On the generator chain this MODMOS is ####...###....###
16/15 7/6 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1
using the 3-step stacked thirds, we get major on I, II, and X; minor-diminished triad (6/5,11/9) on III; minor on IV, and V, wolf triad on VI, and augmented triads on VII, VIII, and IX.
=== Miracle[10] 1|8 ♯3 ♯4 ===
sLsdssssLs. #####..###.....##
16/15 7/6 5/4 21/16 7/5 3/2 8/5 12/7 15/8 2/1
using the 3-step stacked thirds, we get major on I and X; a neutral triad on II; minor-diminished triad on III; minor on IV; wolf triads on IV, VI, and IX; and augmented triads on VII and VIII
=== Miracle[10] 2|7 ♯2 ♯3 ♯4 ♯5 ♯6 ===
LssssdsLss. ##.....###..#####
12/11 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 2/1
using the 3-step stacked triads, we get major on I; a major-diminished triad on II; neutral triad on III; minor on IV and V; wolf triads on VI, IX, and X, and augmented triads on VII and VIII.
=== Miracle[10] 1|8 ♯2 ♯3 ♯4 ♯5 ===
LsssdsssLs. ####....##....####
12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1
using the 3-step stacked thirds, we get major on I and X; minor on IV, and V; major-diminished triad on II; minor-diminished triad on III; wolf triad IX; and augmented triads on VI, VII, and VIII.
=== Miracle[10] 1|8 ♯2 ♯3 ♯4 ===
LssdssssLs. #####...##.....###
12/11 7/6 5/4 21/16 7/5 3/2 8/5 12/7 15/8 2/1
using the 3-step stacked thirds, we get major on I and X; minor-diminished triads on II and III; minor on IV; wolf triads on V, VI, and IX; and augmented triads on VII, and VIII.
=== Miracle[10] 1|8 ♯2 ♯3 ♯4 ♯5 ♯6 ===
LssssdssLs. ###.....##...#####
12/11 7/6 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
using the 3-step stacked thirds, we get major on I; major-diminished triads on II and III; minor on IV and V; wolf triads on VI, IX, and X; and augmented triads on VII, and VIII.
== Tonal modes: ==
== Tonal modes: ==
A tonal mode is a mode with major or minor triads on 1/1 and 4/3 and/or 3/2, (and with at least 2 major triads and 2 minor triads)
A tonal mode, here, is a mode with major or minor triads on 1/1 and 4/3 and/or 3/2, and with at least two major triads, and two minor triads.


Of all above scales, only the following modes are tonal:
Of all above scales, only the following modes are tonal.


=== Major with minor subdominant ===
=== Major with minor subdominant ===
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1|8 ♯4 ♯5 ♯6 or 7|2 ♭7 ♭8 ♭9 and ssLssdssLs 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
1|8 ♯4 ♯5 ♯6 or 7|2 ♭7 ♭8 ♭9 and ssLssdssLs 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
==== ###....###...#### (2 major, 3 minor, 3 augmented, 1 major-diminished, 1 wolf) ====
8|1 ♭7 ♭8 ♭9 sLsssdssLs 16/15 7/6 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
9|0 ♭6 ♭7 ♭8 LsssdssLss 12/11 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
==== ####...###....### (3 major, 2 minor, 3 augmented, 1 minor-diminished, 1 wolf) ====
1|8 ♯3 ♯4 ♯5 sLssdsssLs 16/15 7/6 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1
0|9 ♯4 ♯5 ♯6 ssLssdsssL 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 11/6 2/1
==== ####....##....#### (2 major, 2 minor, 3 augmented, 1 major-diminished, 1 minor-diminished, 1 wolf) ====
1|8 ♯2 ♯3 ♯4 ♯5 or 9|0 ♭6 ♭7 ♭8 ♭9 LsssdsssLs 12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1
0|9 ♯3 ♯4 ♯5 ♯6 or 8|1 ♭7 ♭8 ♭9 ♭10 sLsssdsssL 16/15 7/6 5/4 4/3 10/7 3/2 8/5 12/7 11/6 2/1


=== Minor with major dominant (modes starting on V of the above modes) ===
=== Minor with major dominant (modes starting on V of the above modes) ===
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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
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
==== ###....###...#### (2 major, 3 minor, 3 augmented, 1 major-diminished, 1 wolf) ====
2|7 ♭3 ♭4 ♭5 sdssLssLss 16/15 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1
3|6 ♭2 ♭3 ♭4 dssLssLsss 21/20 9/8 6/5 21/16 7/5 3/2 18/11 7/4 15/8 2/1 (4:5:6:7 on dominant)
==== ####...###....### (3 major, 2 minor, 3 augmented, 1 minor-diminished, 1 wolf) ====
2|7 ♭2 ♭3 ♭4 ♭5 dsssLssLss 21/20 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1
1|8 ♭3 ♭4 ♭5 ♭6 sdsssLssLs 16/15 9/8 6/5 9/7 11/8 3/2 8/5 12/7 15/8 2/1
==== ####....##....#### (2 major, 2 minor, 3 augmented, 1 major-diminished, 1 minor-diminished, 1 wolf) ====
3|6 ♭2 ♭3 ♭4 ♭5 dsssLsLsss 21/20 9/8 6/5 9/7 7/5 3/2 18/11 7/4 15/8 2/1
2|7 ♭3 ♭4 ♭5 ♭6 sdsssLsLss 16/15 9/8 6/5 9/7 11/8 3/2 8/5 7/4 15/8 2/1


== MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] ==
== MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] ==
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Now let's consider a path from Miracle[10] to this MODMOS. (tbc)
Now let's consider a path from Miracle[10] to this MODMOS. (tbc)
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