Miracle 10 MODMOS - Revision history

BudjarnLambeth: /* MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] */ {{Navbox scale gallery}}

2025-09-28T03:11:37Z

MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10]: {{Navbox scale gallery}}

← Older revision		Revision as of 03:11, 28 September 2025
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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)

			{{Navbox scale gallery}}
	[[Category:Miracle]]		[[Category:Miracle]]
	[[Category:MODMOS]]		[[Category:MODMOS]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:10-tone scales]]		[[Category:10-tone scales]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-23T21:04:02Z

Categorised this uncategorised page

← Older revision		Revision as of 21:04, 23 April 2023
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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)
			[[Category:Miracle]]
			[[Category:MODMOS]]
			[[Category:Lists of scales]]
			[[Category:10-tone scales]]

Lhearne: /* Tonal modes: */ same as previous edit but in this section - added reference to major-diminished and minor-diminished triads (will add links when I have them)

2022-04-13T11:22:14Z

Tonal modes:: same as previous edit but in this section - added reference to major-diminished and minor-diminished triads (will add links when I have them)

Lhearne: /* MODMOS to SNS (2/1, 3/2, 5/4: 225/224)[10] (and similar) */

2022-04-13T11:13:37Z

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

Lhearne: /* Tonal modes: */ took out the ones that only had one major or minor triad

2022-04-10T15:01:46Z

Tonal modes:: took out the ones that only had one major or minor triad

@@ Line 197: / Line 197: @@
 |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, 3 wolves) ====
@@ Line 208: / Line 202: @@
 |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) ===
@@ Line 243: / Line 231: @@
 |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, 3 wolves) ====

Lhearne: added modmos

2022-04-10T14:59:59Z

added modmos

← Older revision		Revision as of 14:59, 10 April 2022
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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. ~~On the generator chain this MODMOS is~~ ####....##....####		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) ===

Lhearne: Added a couple more MODMOS

2022-04-10T13:35:57Z

Added a couple more MODMOS

← Older revision		Revision as of 13:35, 10 April 2022
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	using the 3-step stacked triads, we get major on I and X; minor on III, IV, and V; wolf triads on II and IX, and augmented triads on VI, VII and VIII.		using the 3-step stacked triads, we get major on I and X; minor on III, IV, and V; wolf triads on II and IX, and augmented triads on VI, VII and VIII.

	=== Miracle[10] 1\|8 ♯3 ♯4 ♯5 ===		=== 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 ####...###....###		It's inverse is sLssdsssLs, Miracle[10] 1\|8 ♯3 ♯4 ♯5. On the generator chain this MODMOS is ####...###....###

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

	=== Miracle[10] 1\|8 ♯2 ♯3 ♯4 ♯5 ===		=== Miracle[10] 1\|8 ♯2 ♯3 ♯4 ♯5 ===
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	== 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

	Of all above scales, only the following modes are tonal:		Of all above scales, only the following modes are tonal:
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	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		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, 1 minor, 2 augmented, 1 neutral, 4 wolves) ====
			0\|9 ♯4 ♯5 ssLsdssssL 16/15 8/7 5/4 21/16 10/7 3/2 8/5 12/7 11/6 2/1

			==== ##.....###..##### (1 major, 2 minor, 2 augmented, 1 neutral, 4 wolves) ====
			9\|0 ♭7 ♭8 LssssdsLss 12/11 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 2/1

	==== ####....##....#### (2 major, 2 minor, 3 augmented, 3 wolves) ====		==== ####....##....#### (2 major, 2 minor, 3 augmented, 3 wolves) ====
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	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		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, 1 minor, 2 augmented, 1 neutral, 4 wolves) ====
			1\|8 ♭2 ♭3 ♭4 ♭5 ♭6 dssssLssLs 21/20 9/8 6/5 9/7 11/8 3/2 8/5 12/7 15/8 2/1

			==== ##.....###..##### (1 major, 2 minor, 2 augmented, 1 neutral, 4 wolves) ====
			3\|6 ♭3 ♭4 sdsLssLsss 16/15 9/8 6/5 21/16 7/5 3/2 18/11 7/4 15/8 2/1 (4:5:6:7 on dominant)

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

Lhearne: Added another MODMOS

2022-04-09T15:25:36Z

Added another MODMOS

@@ Line 128: / Line 128: @@
 using the 3-step stacked thirds, we get major on I, II, and X; minor on IV, and V; wolf triads on III and VI, and augmented triads on VII, VIII, and IX.
 == 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)
@@ Line 161: / Line 169: @@
 |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
 === Minor with major dominant (modes starting on V of the above modes) ===
@@ Line 190: / Line 203: @@
 |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
 == MODMOS to SNS ((2/1, 3/2)[5], 16/15: 225/224)[10] ==

Lhearne: Added MODMOS extended from (2/1, 3/2, 5/4)[10]

2022-04-09T15:03:00Z

Added MODMOS extended from (2/1, 3/2, 5/4)[10]

@@ Line 112: / Line 112: @@
 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.
 == 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)
@@ Line 135: / Line 151: @@
 |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) ===
@@ Line 154: / Line 180: @@
 |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] ==

Lhearne: added headings, edited first paragraph

2022-04-09T07:08:47Z

added headings, edited first paragraph

← Older revision		Revision as of 07:08, 9 April 2022
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	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.		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.

			Miracle can be thought of as a cluster temperament, with 10 clusters in an octave, based around Miracle[10]. The Miracle[10] chroma is very versatile, representing 2048/2025 and 525/512 in the 5-limit; 49/48, 50/49, and 64/63 in the 7-limit; and 45/44, 55/54, and 56/55 in the 11-limit.

			Accordingly, any 11-limit decatonic scale of interest likely to be a MODMOS of Miracle[10]. Since there are an enormous number of possibilities, we will limit our exploration to MODMOS that bridge the gap between Miracle[10], and two rank-3 decatonic scales of interest.

	7-limit Miracle[10] can be described as a [[step-nested scale]] as SNS (2/1, 16/15: 225/224, 1029/1024)[10].		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.		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] ==
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	We will interpolate from Miracle[10] 2\|7 to Miracle[10] 2\|7 ♯3 ♯4 ♯5, and back a different way.		We will interpolate from Miracle[10] 2\|7 to Miracle[10] 2\|7 ♯3 ♯4 ♯5, and back a different way.

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

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

			=== Miracle[10] 2\|7 ♯3 ♯4 ===

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

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	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.		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.

			=== Miracle[10] 2\|7 ♯3 ♯4 ♯5 ===
			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.
	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 ###...####...###		On the generator chain this MODMOS is ###...####...###
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	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.		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:		And back a different way:

			=== Miracle[10] 2\|7 ♯4 ♯5 ===

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

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	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.		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 ===
			Miracle[10] 2\|7 ♯4 ♯5 sssLdssLss. On the generator chain this MODMOS is ###.######...#
	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		16/15~15/14 8/7 11/9 4/3 7/5 3/2 8/5 7/4 15/8 2/1
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	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.		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.

			=== Miracle[10] 2\|7 ♯4 ===

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

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	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.		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.

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

	<nowiki>#</nowiki>3 #4 is cool because you get 2 major, 2 minor, 2 neutral, 2 augmented, and 2 wolf triads.		<nowiki>#</nowiki>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.		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.		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 ♯4 ♯5 is symmetric.

	♯3, ♯3 ♯4, ♯4, ♯5, and ♯4 ♯5 all have inverses that are different MODMOS.		♯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:		Of these, the inverse of ♯3 ♯4 is of particular interest. ##....####..#### on the generator chain:
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	Same triads as it's inverse, just ordered differently.		Same triads as it's inverse, just ordered differently.

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

	Let's try ##..######..##:		=== Miracle[10] 2\|7 ♯5 ♯6 ===
			Let's also try ##..######..##

	Miracle[10] 2\|7 ♯5 ♯6 sssLsdsLss.		Miracle[10] 2\|7 ♯5 ♯6 sssLsdsLss.
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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.



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

	== 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 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)

← Older revision		Revision as of 11:22, 13 April 2022
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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, ~~2 wolves~~) ====		==== ###....###...#### (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		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		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, ~~2 wolves~~) ====		==== ####...###....### (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		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		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, ~~3 wolves~~) ====		==== ####....##....#### (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		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

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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, ~~2 wolves~~) ====		==== ###....###...#### (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		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\|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, ~~2 wolves~~) ====		==== ####...###....### (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		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		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, ~~3 wolves~~) ====		==== ####....##....#### (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		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

← Older revision		Revision as of 11:13, 13 April 2022
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	12/11 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1		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; minor on III, IV, and V; wolf triads ~~on II and~~ IX, and augmented triads on VI, VII and VIII.		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 ===		=== Miracle[10] 1\|8 ♯3 ♯4 ♯5 / Miracle[10] 2\|7 ♯2 ♯3 ♯4 ===
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	16/15 7/6 5/4 4/3 7/5 3/2 8/5 12/7 15/8 2/1		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 on IV, and V; wolf ~~triads~~ on ~~III and~~ VI, and augmented triads on VII, VIII, and IX.		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 ===		=== Miracle[10] 1\|8 ♯3 ♯4 ===
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	16/15 7/6 5/4 21/16 7/5 3/2 8/5 12/7 15/8 2/1		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 on IV; wolf triads on ~~III, V~~, VI, and IX; and augmented triads on VII, and VIII		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 ===		=== Miracle[10] 2\|7 ♯2 ♯3 ♯4 ♯5 ♯6 ===
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	12/11 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 2/1		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 neutral triad on III, minor on IV, and V; wolf triads on II, IX, and X, and augmented triads on ~~VI,~~ VII and VIII.		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 ===		=== Miracle[10] 1\|8 ♯2 ♯3 ♯4 ♯5 ===
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	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~~, and~~ 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; 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 ===		=== Miracle[10] 1\|8 ♯2 ♯3 ♯4 ===
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	12/11 7/6 5/4 21/16 7/5 3/2 8/5 12/7 15/8 2/1		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.		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 ===		=== Miracle[10] 1\|8 ♯2 ♯3 ♯4 ♯5 ♯6 ===
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	12/11 7/6 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1		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.		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: ==