User:Overthink/Neutral scale theory: Difference between revisions

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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"

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| P1-M2-M4-M5

| M4-P1-M5-M2

| '''Major / M'''

| '''Major / M''' (or no symbol)

|-

| P1-m2-m4-M5

Line 101:

| P1-m2-m4-m5

| m4-P1-m5-m2

| '''Ambi / a''' ~~(Placeholder)~~

| '''Ambi / am'''

|}

On the white keys (C, D, E, ...), we have Csus, Dam, Em, F, Gm, A, and Bam. While this mode has a 3/2 interval above the I, IV, and V, there is a lack of tonality with a sus chord on the root.

=== Modes ===

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"

|+ Modes of mosh (brightest to darkest)

|-

! Name<ref>[https://en.xen.wiki/w/3L_4s#Proposed_names 3L 4s] on Xenharmonic Wiki</ref>

! Intervals

! Chords (from I to VII)

|-

| Dalmatian

| P1, M2, P3, M4, M5, A6, M7

| I, ii, III, IVam, Vsus, VIam, vii

|-

| Galatian

| P1, M2, P3, M4, M5, P6, M7

| I, IIam, IIIsus, IVam, v, VI, vii

|-

| Cilician

| P1, M2, P3, m4, M5, P6, M7

| Isus, IIam, iii, IV, v, VI, VIIam

|-

| Bithynian

| P1, m2, P3, m4, M5, P6, M7

| i, II, iii, IV, Vam, VIsus, VIIam

|-

| Pisidian

| P1, m2, P3, m4, M5, P6, m7

| i, II, IIIam, IVsus, Vam, vi, VII

|-

| Illyrian

| P1, m2, P3, m4, m5, P6, m7

| Iam, iisus, IIIam, iv, V, vi, VII

|-

| 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 ==

@@ 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'''
 |}
+On the white keys (C, D, E, ...), we have Csus, Dam, Em, F, Gm, A, and Bam. While this mode has a 3/2 interval above the I, IV, and V, there is a lack of tonality with a sus chord on the root.
+=== Modes ===
+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"
+|+ Modes&nbsp;of&nbsp;mosh (brightest to darkest)
+|-
+! Name<ref>[https://en.xen.wiki/w/3L_4s#Proposed_names 3L 4s] on Xenharmonic Wiki</ref>
+! Intervals
+! Chords (from I to VII)
+|-
+| Dalmatian
+| P1, M2, P3, M4, M5, A6, M7
+| I, ii, III, IVam, Vsus, VIam, vii
+|-
+| Galatian
+| P1, M2, P3, M4, M5, P6, M7
+| I, IIam, IIIsus, IVam, v, VI, vii
+|-
+| Cilician
+| P1, M2, P3, m4, M5, P6, M7
+| Isus, IIam, iii, IV, v, VI, VIIam
+|-
+| Bithynian
+| P1, m2, P3, m4, M5, P6, M7
+| i, II, iii, IV, Vam, VIsus, VIIam
+|-
+| Pisidian
+| P1, m2, P3, m4, M5, P6, m7
+| i, II, IIIam, IVsus, Vam, vi, VII
+|-
+| Illyrian
+| P1, m2, P3, m4, m5, P6, m7
+| Iam, iisus, IIIam, iv, V, vi, VII
+|-
+| 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/>