Miracle 10 MODMOS

First, Miracle[10]:

In the mode 2|7, sssssssLss it approximates

16/15~15/14 8/7 11/9 21/16 7/5 3/2 8/5 7/4 15/8 2/1

using 3-step stacked triads, we get neutral triads on I, II, IX and X; and wolf triads on III, IV, V, VI, VI, and VIII.

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

Miracle[10] 2|7 ♯3 sLdssssLss. On the generator chain this MODMOS is #####.####.....#

16/15~15/14 7/6 11/9 21/16 7/5 3/2 8/5 7/4 15/8 2/1

using the 3-step stacked triads, we get major on X; neutral on I, II, VII, and IX; minor on III; wolf triads on IV and V; and augmented triads on VI and VII.

Let's try Miracle[10] 2|7 ♯3 ♯4 sLsdsssLss. On the generator chain this MODMOS is ####..####....##

16/15~15/14 7/6 5/4 21/16 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; neutral on II and IX; minor on III, and IV; wolf triads on V and VI, and augmented triads on VII and VIII.

Now go to Miracle[10] 2|7 ♯3 ♯4 ♯5 sLssdssLss, which is also the 3-SN scale mLmmsmmLmm, but with 243/242 tempered out to make 11/9 and 27/22 equivalent.

On the generator chain this MODMOS is ###...####...###

16/15~15/14 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, II, and X; minor on III, IV, and V; wolf triads on VI, and IX, and augmented triads on VII and VIII.

And back a different way:

Miracle[10] 2|7 ♯4 ♯5 ssLsdssLss. On the generator chain this MODMOS is ###..#####...##

16/15~15/14 8/7 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, II; minor on IV, and V; wolf triads on III, VI, VII, and IX, an augmented triad on VIII; and a neutral triad on X.

Miracle[10] 2|7 ♯5 sssLdssLss. On the generator chain this MODMOS is ###.######...#

16/15~15/14 8/7 11/9 4/3 7/5 3/2 8/5 7/4 15/8 2/1

using the 3-step stacked triads, we get neutral triads on I and X, major on II; minor on V; and wolf triads on III, IV, VI, VII, VIII, and IX.

And we'll also try Miracle[10] 2|7 ♯4 ssLdsssLss. On the generator chain this MODMOS is ####.#####....#

16/15~15/14 8/7 5/4 21/16 7/5 3/2 8/5 7/4 15/8 2/1

using the 3-step stacked triads, we get major on I; neutral triads on II, IX, and X; minor on IV; wolf triads on III, V, VI, and VII; and an augmented triad on VIII.

If we want to minimize the number of wolf triads, out of these scales, ♯3, ♯3 ♯4, and ♯3 ♯4 ♯5 are best.

If we want to maximize the number of major and minor triads, ♯3 ♯4 ♯5 is best.

#3 #4 is cool because you get 2 major, 2 minor, 2 neutral, 2 augmented, and 2 wolf triads.

No major or minor triads can be found in MODMOS of Miracle[10] with a span of less than 14 generators, since 5/4 is found at 13 generators.

We get to 11/8 with MODMOS that span 16 generators, which include Miracle[10] 2|7 ♯3, ♯3 ♯4, and ♯3 ♯4 ♯5, which have an 11/8 above III.

♯3 ♯4 ♯5 is symmetric.

♯3, ♯3 ♯4, ♯4, ♯5, and ♯4 ♯5 all have inverses that are different MODMOS.

Of these, the inverse of ♯3 ♯4 is of particular interest. ##....####..#### on the generator chain:

From Miracle[10] 7|2 ssLsssssss: 16/15~15/14 8/7 5/4 4/3 10/7 32/21 18/11 7/4 15/8 2/1

It is Miracle[10] 7|2 ♭8 ♭9 ssLsssdsLs: 16/15~15/14 8/7 5/4 4/3 10/7 32/21 8/5 12/7 15/8 2/1

Let's put it in a minor mode:

Miracle[10] 1|8 ♭4 ♭5 ssdsLsssLs: 16/15~15/14 8/7 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1.

using the 3-step stacked triads, we get minor on I, II; neutral on III and X; augmented on IV, and V; wolf triads on VI and VII, and major on VIII, and IX.

Same triads as it's inverse, just ordered differently.

Let's try ##..######..##:

Miracle[10] 2|7 ♯5 ♯6 sssLsdsLss.

16/15~15/14 8/7 11/9 4/3 10/7 3/2 8/5 7/4 15/8 2/1.

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.

The generator chain sequences ###...####...###, ####..####....##, and ##....####..#### give the best scales in the opinion of the author.

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)

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

Major with minor subdominant

###..#####...## (2 major, 2 minor, 1 augmented, 1 neutral, 4 wolves)

2|7 ♯4 ♯5 ssLsdssLss 16/15 8/7 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1

##..#####...### (2 major, 2 minor, 1 augmented, 1 neutral, 4 wolves)

7|2 ♭7 ♭8 ssLssdsLss 16/15 8/7 5/4 4/3 10/7 3/2 8/5 7/4 15/8 2/1

####..####....## (2 major, 2 minor, 2 augmented, 2 neutral, 2 wolves)

1|8 ♯4 ♯5 ssLsdsssLs 16/15 8/7 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1

##....####..#### (2 major, 2 minor, 2 augmented, 2 neutral, 2 wolves)

8|1 ♭7 ♭8 sLsssdsLss 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 2/1

###...####...### (3 major, 3 minor, 2 augmented, 2 wolves)

2|7 ♯3 ♯4 ♯5 or 8|1 ♭6 ♭7 ♭8 sLssdssLss 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 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

Minor with major dominant (modes starting on V of the above modes)

###..#####...## (2 major, 2 minor, 1 augmented, 1 neutral, 4 wolves)

1|8 ♭2 ♭3 ♭4 dssLssssLs 21/20 9/8 6/5 21/16 7/5 3/2 8/5 12/7 15/8 2/1 (4:5:6:7 on dominant)

##..#####...### (2 major, 2 minor, 1 augmented, 1 neutral, 4 wolves)

1|8 ♭3 ♭4 sdsLssssLs 16/15 9/8 6/5 21/16 7/5 3/2 8/5 12/7 15/8 2/1 (4:5:6:7 on dominant)

####..####....## (2 major, 2 minor, 2 augmented, 2 neutral, 2 wolves)

1|8 ♭2 ♭3 ♭4 ♭5 dsssLsssLs 21/20 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1

##....####..#### (2 major, 2 minor, 2 augmented, 2 neutral, 2 wolves)

2|7 ♭3 ♭4 sdsLsssLss: 16/15 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 (4:5:6:7 on dominant)

###...####...### (3 major, 3 minor, 2 augmented, 2 wolves)

2|7 ♭2 ♭3 ♭4 dssLsssLss 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 (4:5:6:7 on dominant)

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