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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=== Miracle[10] 1|8 ♯2 ♯3 ♯4 ♯5 === | === Miracle[10] 1|8 ♯2 ♯3 ♯4 ♯5 === | ||
LsssdsssLs. | LsssdsssLs. ####....##....#### | ||
12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1 | 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; wolf triads on II, III, IX; and augmented triads on VI, VII, and VIII. | using the 3-step stacked thirds, we get major on I and X; minor on IV, and V; wolf triads on II, III, and 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 on IV; wolf triads on II, III, 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; minor on IV, and V; wolf triads on II, III, VI, IX, and X; and augmented triads on VII, and VIII. | |||
== Tonal modes: == | == Tonal modes: == | ||
A tonal mode, here, is a mode with major or minor triads on 1/1 and 4/3 and/or 3/2 | 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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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 | 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 | ||
==== #####...##.....### (2 major, 1 minor, 2 augmented, 5 wolves) ==== | |||
0|9 ♯3 ♯4 ♯5 sLssdssssL 12/11 8/7 5/4 21/16 10/7 3/2 8/5 12/7 11/6 2/1 | |||
==== ###.....##...##### (1 major, 2 minor, 2 augmented, 5 wolves) ==== | |||
9|0 ♭6 ♭7 ♭8 LssssdssLs. 12/11 7/6 5/4 4/3 10/7 3/2 8/5 12/7 15/8 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) === | ||