User:Overthink/22edo decatonic theory: Difference between revisions

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== The white keys ==

In diatonic, the white keys are in a mode such that, on C, there is a [[major triad]] on the tonic, dominant, and subdominant. Here, the main chords are ''tetrads'', with the '''major tetrad''' being P1−M4−P7−M9, approximating [[4:5:6:7]], and the '''minor tetrad''' being ~~P1-m4-P7-m9~~, approximating [[70:84:105:120|1/(7:8:10:12)]]. Unfortunately, there is no mode of the pentachordal scale which places the major tetrad on the tonic, dominant, and subdominant of the same key, but the ssLsssLsss mode gets as close as possible. Hence, we will place the white keys on this mode above C.

In diatonic, the white keys are in a mode such that, on C, there is a [[major triad]] on the tonic, dominant, and subdominant. Here, the main chords are ''tetrads'', with the '''major tetrad''' being P1−M4−P7−M9, approximating [[4:5:6:7]], and the '''minor tetrad''' being P1−m4−P7−m9, approximating [[70:84:105:120|1/(7:8:10:12)]]. Unfortunately, there is no mode of the pentachordal scale which places the major tetrad on the tonic, dominant, and subdominant of the same key, but the ssLsssLsss mode gets as close as possible. Hence, we will place the white keys on this mode above C.

{| class="wikitable right-~~all~~"

{| class="wikitable right-3 right-4"

|+ style="font-size: 105%" | The white keys

|-

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|-

| C || P11 || 1200.0 || 22

|}

The notes are named so that C, D, E, F, G, A, and B represent the [[Zarlino]] diatonic scale, with R, S, and T filling the gaps. Using the Root−4th−7th−9th construction, we find the tetrads on each note.

{| class="wikitable"

|+ style="font-size: 105%" | Tetrads on white keys

|-

! Note !! Notes of chord !! Intervals of chord !! Name

|-

| C || C−E−G−S || P1−M4−P7−M9 || Major

|-

| R || R−F−A−B || P1−M4−A7−M9 || Aug.

|-

| D || D−T−S−C || P1−M4−A7−M9 || Aug.

|-

| E || E−G−B−R || P1−m4−P7−m9 || Minor

|-

| F || F−A−C−D || P1−M4−P7−m9 || Major−minor

|-

| T || T−S−R−E || P1−M4−P7−M9 || Major

|-

| G || G−B−D−F || P1−M4−P7−M9 || Major

|-

| A || A−C−E−T || P1−m4−P7−m9 || Minor

|-

| S || S−R−F−G || P1−m4−P7−m9 || Minor

|-

| B || B−D−T−A || P1−m4−P7−M9 || Minor−major

|}

@@ Line 58: / Line 58: @@
 == The white keys ==
-In diatonic, the white keys are in a mode such that, on C, there is a [[major triad]] on the tonic, dominant, and subdominant. Here, the main chords are ''tetrads'', with the '''major tetrad''' being P1−M4−P7−M9, approximating [[4:5:6:7]], and the '''minor tetrad''' being P1-m4-P7-m9, approximating [[70:84:105:120|1/(7:8:10:12)]]. Unfortunately, there is no mode of the pentachordal scale which places the major tetrad on the tonic, dominant, and subdominant of the same key, but the ssLsssLsss mode gets as close as possible. Hence, we will place the white keys on this mode above C.
+In diatonic, the white keys are in a mode such that, on C, there is a [[major triad]] on the tonic, dominant, and subdominant. Here, the main chords are ''tetrads'', with the '''major tetrad''' being P1−M4−P7−M9, approximating [[4:5:6:7]], and the '''minor tetrad''' being P1−m4−P7−m9, approximating [[70:84:105:120|1/(7:8:10:12)]]. Unfortunately, there is no mode of the pentachordal scale which places the major tetrad on the tonic, dominant, and subdominant of the same key, but the ssLsssLsss mode gets as close as possible. Hence, we will place the white keys on this mode above C.
-{| class="wikitable right-all"
+{| class="wikitable right-3 right-4"
 |+ style="font-size: 105%" | The white keys
 |-
@@ Line 86: / Line 86: @@
 |-
 | C || P11 || 1200.0 || 22
+|}
+The notes are named so that C, D, E, F, G, A, and B represent the [[Zarlino]] diatonic scale, with R, S, and T filling the gaps. Using the Root−4th−7th−9th construction, we find the tetrads on each note.
+{| class="wikitable"
+|+ style="font-size: 105%" | Tetrads on white keys
+|-
+! Note !! Notes of chord !! Intervals of chord !! Name
+|-
+| C || C−E−G−S || P1−M4−P7−M9 || Major
+|-
+| R || R−F−A−B || P1−M4−A7−M9 || Aug.
+|-
+| D || D−T−S−C || P1−M4−A7−M9 || Aug.
+|-
+| E || E−G−B−R || P1−m4−P7−m9 || Minor
+|-
+| F || F−A−C−D || P1−M4−P7−m9 || Major−minor
+|-
+| T || T−S−R−E || P1−M4−P7−M9 || Major
+|-
+| G || G−B−D−F || P1−M4−P7−M9 || Major
+|-
+| A || A−C−E−T || P1−m4−P7−m9 || Minor
+|-
+| S || S−R−F−G || P1−m4−P7−m9 || Minor
+|-
+| B || B−D−T−A || P1−m4−P7−M9 || Minor−major
 |}