User:Overthink/Neutral scale theory - Revision history

Overthink: /* Modes */ filled in table

2025-11-28T21:29:30Z

Modes: filled in table

← Older revision		Revision as of 21:29, 28 November 2025
Line 108:		Line 108:
	=== Modes ===		=== Modes ===

	This scale has 7 modes. They are listed below, with the intervals of the mode and chords on each ~~root~~		This scale has 7 modes. They are listed below, with the intervals of the mode and chords on each note of the scale.

	{\| class="wikitable"		{\| class="wikitable"
	\|+ Modes of mosh (brightest to darkest)		\|+ Modes of mosh (brightest to darkest)
	\|-		\|-
	! Name<ref>[https://en.xen.wiki/w/3L_4s#Proposed_names 3L 4s]</ref>		! Name<ref>[https://en.xen.wiki/w/3L_4s#Proposed_names 3L 4s] on Xenharmonic Wiki</ref>
	! Intervals		! Intervals
	! Chords (from I to VII)		! Chords (from I to VII)
	\|-		\|-
	\| Dalmatian		\| Dalmatian
	\|		\| P1, M2, P3, M4, M5, A6, M7
	\|		\| I, ii, III, IVam, Vsus, VIam, vii
	\|-		\|-
	\| Galatian		\| Galatian
	\|		\| P1, M2, P3, M4, M5, P6, M7
	\|		\| I, IIam, IIIsus, IVam, v, VI, vii
	\|-		\|-
	\| Cilician		\| Cilician
	\|		\| P1, M2, P3, m4, M5, P6, M7
	\|		\| Isus, IIam, iii, IV, v, VI, VIIam
	\|-		\|-
	\| Bithynian		\| Bithynian
	\|		\| P1, m2, P3, m4, M5, P6, M7
	\|		\| i, II, iii, IV, Vam, VIsus, VIIam
	\|-		\|-
	\| Pisidian		\| Pisidian
	\|		\| P1, m2, P3, m4, M5, P6, m7
	\|		\| i, II, IIIam, IVsus, Vam, vi, VII
	\|-		\|-
	\| Illyrian		\| Illyrian
	\|		\| P1, m2, P3, m4, m5, P6, m7
	\|		\| Iam, iisus, IIIam, iv, V, vi, VII
	\|-		\|-
	\| Lycian		\| Lycian
	\|		\| P1, m2, d3, m4, m5, P6, m7
	\|		\| Iam, ii, III, iv, V, VIam, VIIsus
	\|}		\|}

			The Dalmation and Galatian modes on I, Bithynian and Pisidian have minor on I, Illyrian and Lycian have ambi on I, and Cicilian has sus on I.

	== References ==		== References ==
	<references/>		<references/>

Overthink: started modes section

2025-11-28T20:47:18Z

started modes section

@@ Line 75: / Line 75: @@
 In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral (P1-P3-M5) chords on C, E, F, G, and A, a P1-d3-m5 chord on D, and a P1-P3-m5 chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant.
-This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. Of course, this is only one possible construction. Note that chords can also be constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11), with the chain being 4th-Root-5th-2nd for fifths and the reverse for fourths.
+This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 chord on C, and a P1-m2-m4-m5 chord on B and D. Of course, this is only one possible construction. Note that chords can also be constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11), with the chain being 4th-Root-5th-2nd for fifths and the reverse for fourths.
-We need names for these chords, and once again we can borrow some from diatonic:
+We need names for these chords, and once again we can borrow some from diatonic. The major and minor chords are otonal and utonal respectively. The suspended chord is [[3-limit]], like the suspended chord in diatonic, with a [[32/27]] dissonance here compared to a [[9/8]] dissonance (which we consider a consonance here) in diatonic. The '''Ambi''' chord is named for being ambitonal, and is notably an [[anomalous saturated suspension]].
 {| class="wikitable"
@@ Line 89: / Line 89: @@
 | P1-M2-M4-M5
 | M4-P1-M5-M2
-| '''Major / M'''
+| '''Major / M''' (or no symbol)
 |-
 | P1-m2-m4-M5
@@ Line 101: / Line 101: @@
 | P1-m2-m4-m5
 | m4-P1-m5-m2
-| '''Ambi / a''' (Placeholder)
+| '''Ambi / am'''
 |}

Overthink: table stuff

2025-11-28T02:12:47Z

table stuff

← Older revision		Revision as of 02:12, 28 November 2025
Line 75:		Line 75:
	In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral (P1-P3-M5) chords on C, E, F, G, and A, a P1-d3-m5 chord on D, and a P1-P3-m5 chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant.		In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral (P1-P3-M5) chords on C, E, F, G, and A, a P1-d3-m5 chord on D, and a P1-P3-m5 chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant.

	This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. ~~We need names for these~~ chords, and ~~once again we can borrow from diatonic:~~		This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. Of course, this is only one possible construction. Note that chords can also be constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11), with the chain being 4th-Root-5th-2nd for fifths and the reverse for fourths.

	~~''Rewrite~~: ~~This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''~~		We need names for these chords, and once again we can borrow some from diatonic:

	{\| class="wikitable"		{\| class="wikitable"
	\|+ Mosh chord names		\|+ Mosh chord names
	! Chord		! colspan=2 \|Chord
	! Name		! rowspan=2 \|Name
			\|-
			! Root up
			! Chain of 5ths
	\|-		\|-
	\| P1-M2-M4-M5		\| P1-M2-M4-M5
			\| M4-P1-M5-M2
	\| '''Major / M'''		\| '''Major / M'''
	\|-		\|-
	\| P1-m2-m4-M5		\| P1-m2-m4-M5
			\| m4-P1-M5-m2
	\| '''Minor / m'''		\| '''Minor / m'''
	\|-		\|-
	\| P1-M2-m4-M5		\| P1-M2-m4-M5
			\| m4-P1-M5-M2
	\| '''Suspended / sus'''		\| '''Suspended / sus'''
	\|-		\|-
	\| P1-m2-m4-m5		\| P1-m2-m4-m5
	\| ''~~Placeholder~~''		\| m4-P1-m5-m2
			\| '''Ambi / a''' (Placeholder)
	\|}		\|}

Overthink: + another note

2025-11-28T01:27:01Z

+ another note

← Older revision		Revision as of 01:27, 28 November 2025
Line 1:		Line 1:
	Neutral scales are generated by a neutral third of around 350 cents, which exists in 17edo, 24edo, and many other tunings. The generator can be taken to represent [[11/9]], and two generators reach [[3/2]], tempering out the comma [[243/242]]. This generator leads to [[MOS]]es of size 4, 7, 10, 17, etc. Here we will mainly be considering the 7-note [[3L 4s]] and 10-note [[7L 3s]] MOSes.		Neutral scales are generated by a neutral third of around 350 cents, which exists in 17edo, 24edo, and many other tunings. The generator can be taken to represent [[11/9]], and two generators reach [[3/2]], tempering out the comma [[243/242]]. This generator leads to [[MOS]]es of size 4, 7, 10, 17, etc. Here we will mainly be considering the 7-note [[3L 4s]] and 10-note [[7L 3s]] MOSes.

			''Note: Similar theory can be used in the 2.3.13 temperament tempering out 512/507.''

	== 3L 4s (mosh) ==		== 3L 4s (mosh) ==
Line 75:		Line 77:
	This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. We need names for these chords, and once again we can borrow from diatonic:		This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. We need names for these chords, and once again we can borrow from diatonic:

	''~~Note~~: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''		''Rewrite: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''

	{\| class="wikitable"		{\| class="wikitable"

Overthink: /* 3L 4s (mosh) */ made interval tables collapsed by default

2025-11-28T01:24:38Z

3L 4s (mosh): made interval tables collapsed by default

← Older revision		Revision as of 01:24, 28 November 2025
Line 7:		Line 7:
	The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap\|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.		The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap\|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.

	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ 24edo mosh scale		\|+ 24edo mosh scale
	\|-		\|-
Line 31:		Line 31:
	Just like diatonic, this scale has major and minor intervals, which are found on different notes of the scale. A table of such intervals is below.		Just like diatonic, this scale has major and minor intervals, which are found on different notes of the scale. A table of such intervals is below.

	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ Intervals of mosh		\|+ Intervals of mosh
	\|-		\|-

Overthink: /* Chords */ added chord names

2025-11-28T01:23:32Z

Chords: added chord names

@@ Line 73: / Line 73: @@
 In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral (P1-P3-M5) chords on C, E, F, G, and A, a P1-d3-m5 chord on D, and a P1-P3-m5 chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant.
-This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D.
+This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in our scale is P1-M2-M4-M5. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) = [[66:72:88:99]], or P1-m2-m4-M5. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a P1-M2-m4-M5 cent chord on C, and a P1-m2-m4-m5 chord on B and D. We need names for these chords, and once again we can borrow from diatonic:
-We need names for these chords, and once again we can borrow from diatonic.
+''Note: This is not the best construction. Chords are better constructed as a chain of three fourths (4/3 or 11/8) or fifths (3/2 or 16/11).''

Overthink: /* Intervals */ no break space

2025-11-28T01:07:04Z

Intervals: no break space

← Older revision		Revision as of 01:07, 28 November 2025
Line 8:		Line 8:

	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
	\|+ 24edo mosh scale		\|+ 24edo mosh scale
	\|-		\|-
	! Note !! Cents !! Ratio		! Note !! Cents !! Ratio
Line 32:		Line 32:

	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
	\|+ Intervals of mosh		\|+ Intervals of mosh
	\|-		\|-
	! Interval !! Cents !! Ratio !! note on C		! Interval !! Cents !! Ratio !! note on C

Overthink: /* 3L 4s (mosh) */ collapsible tables

2025-11-28T01:06:29Z

3L 4s (mosh): collapsible tables

← Older revision		Revision as of 01:06, 28 November 2025
Line 7:		Line 7:
	The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap\|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.		The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap\|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.

	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
	\|+ 24edo mosh scale		\|+ 24edo mosh scale
	\|-		\|-
Line 31:		Line 31:
	Just like diatonic, this scale has major and minor intervals, which are found on different notes of the scale. A table of such intervals is below.		Just like diatonic, this scale has major and minor intervals, which are found on different notes of the scale. A table of such intervals is below.

	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
	\|+ Intervals of mosh		\|+ Intervals of mosh
	\|-		\|-

Overthink: Cleanup and slight expansion

2025-11-28T01:04:48Z

Cleanup and slight expansion

@@ Line 2: / Line 2: @@
 == 3L 4s (mosh) ==
 The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.
 {| class="wikitable"
-|+ 24edo mosh
+|+ 24edo mosh scale
 |-
 ! Note !! Cents !! Ratio
@@ Line 25: / Line 28: @@
 | C || 1200 || 2/1
 |}
-In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral chords on C, E, F, G, and A, a 0¢-300¢-650¢ chord on D, and a 0¢-350¢-650¢ chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant. This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in 24edo is 0-200-550-700 cents. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) [[66:72:88:99]], or 0-150-500-700 cents in 24edo. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a 0¢-200¢-500¢-700¢ cent chord on C, and a 0¢-150¢-500¢-650¢ chord on B and D.

Overthink: /* 3L 4s (mosh) */ expanded theory

2025-11-19T02:17:03Z

3L 4s (mosh): expanded theory

← Older revision		Revision as of 02:17, 19 November 2025
Line 2:		Line 2:

	== 3L 4s (mosh) ==		== 3L 4s (mosh) ==
	The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap\|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below.		The 3L 4s MOS has a step pattern of LssLsLs, where L is a major second and s is a neutral second. We borrow note names from [[5L 2s]] (diatonic) as C, D, E, F, G, A, B. We use sharp (typed as #) and flat (typed as b) to denote an increment and decrement by {{nowrap\|L-s}}, or a quarter tone. A table of intervals of this scale in 24edo is below. Note that other tunings can be used, but overall structures are the same.

	{\| class="wikitable"		{\| class="wikitable"
Line 25:		Line 25:
	\| C \|\| 1200 \|\| 2/1		\| C \|\| 1200 \|\| 2/1
	\|}		\|}
			In diatonic, chords are built by Root-3rd-5th. We can try to use the same logic here. This gives us neutral chords on C, E, F, G, and A, a 0¢-300¢-650¢ chord on D, and a 0¢-350¢-650¢ chord on B. This construction, however, is flawed, as none of these chords can be written with particularly simple ratios, and therefore these chords aren't very consonant. This scale is in the [[2.3.11 subgroup]], with the fundamental otonal consonance being [[8:9:11:12]] (or one of its different voicings), which in 24edo is 0-200-550-700 cents. A different construction, Root-2nd-4th-5th, is now needed. The utonal inverse of 8:9:11:12 is 1/(8:9:11:12) [[66:72:88:99]], or 0-150-500-700 cents in 24edo. The otonal 8:9:11:12 chord occurs on F and A, and the utonal 1/(8:9:11:12) chord occurs on E and G. Neither chord occurs on C, B, or D, with a 0¢-200¢-500¢-700¢ cent chord on C, and a 0¢-150¢-500¢-650¢ chord on B and D.