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

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→Modes: half-complete table
 
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| Perfect 5th || 490.9 || 9 || [[4/3]], [[21/16]]
| Perfect 5th || 490.9 || 9 || [[4/3]], [[21/16]]
|-
|-
| Augmented 5th || 545.5 || rowspan=2 | 10 || placeholder
| Augmented 5th || 545.5 || rowspan=2 | 10 || [[11/8]]
|-
|-
| Diminished 5th || 545.5 || style="text-align: left" | placeholder
| Diminished 6th || 545.5 || style="text-align: left" | [[27/20]], [[15/11]]
|-
|-
| Perfect 6th || 600.0 || 11 || [[7/5]], [[10/7]]
| Perfect 6th || 600.0 || 11 || [[7/5]], [[10/7]]
|-
|-
| Augmented 6th || 654.5 || rowspan=2 | 12 || placeholder
| Augmented 6th || 654.5 || rowspan=2 | 12 || [[40/27]], [[22/15]]
|-
|-
| Diminished 7th || 654.5 || style="text-align: left" | placeholder
| Diminished 7th || 654.5 || style="text-align: left" | [[16/11]]
|-
|-
| Perfect 7th || 709.1 || 13 || [[3/2]], [[32/21]]
| Perfect 7th || 709.1 || 13 || [[3/2]], [[32/21]]
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== The white keys ==
== 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)]]. More about this will be discussed later. 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-3 right-4"
{| class="wikitable right-3 right-4"
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|}
|}


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.
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.
 
== Modes ==
''Complete the table''
{| class="wikitable"
!Name
!Brightness
! Step pattern
!Intervals
!Note names on C
!Appears in white keys on
|-
| Scandium
| +5
| LsssLsssss
| P1, A2, M3, M4, P5, A6, A7, M8, M9, P10, P11
| C, R#, D#, E, F, T#, G#, A, S, B, C
| D
|-
| Titanium
| +3
| LsssssLsss
| P1, A2, M3, M4, P5, P6, P7, M8, M9, P10, P11
| C, R#, D#, E, F, T, G, A, S, B, C
| G
|-
| Vanadium
| +3
| sLsssLssss
| P1, P2, M3, M4, P5, P6, A7, M8, M9, P10, P11
| C, R, D#, E, F, T, G#, A, S, B, C
| R
|-
| Chromium
| +1
| sLsssssLss
| P1, P2, M3, M4, P5, P6, A7, M8, M9, P10, P11
| C, R, D#, E, F, T, G, Ab, S, B, C
| T
|-
| Manganese (Major)
| +1
| ssLsssLsss
| P1, P2, M3, M4, P5, P6, A7, M8, M9, P10, P11
| C, R, D, E, F, T, G, A, S, B, C
| C
|}
 
== Chords ==
''First explain what chords are there''
 
Using the Root−4th−7th−9th construction, we find the tetrads on each note.


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