View source for User:VectorGraphics/Vector's introduction to 15edo/Chord names and functions

This is a database of names for tertian chords in 15edo.
{| class="wikitable"
|+Triads
!Chord
!Name
!Abbreviation
!Notes
|-
|█▒▒▒▒▓▒▒▒▒▓▒
|Augmented triad
|aug
|
|-
|█▒▒▓▒▒▒▒▒▓▒
|Arto triad
|sus2
|
|-
|█▒▒▒▓▒▒▒▒▓▒
|Minor triad
|min
|
|-
|█▒▒▒▒▓▒▒▒▓▒
|Major triad
|maj
|
|-
|█▒▒▒▒▒▓▒▒▓▒
|Tendo triad
|sus4
|
|-
|█▒▒▓▒▒▒▒▓▒
|Wolfminor triad
|wmin
|
|-
|█▒▒▒▓▒▒▒▓▒
|Diminished triad
|dim
|
|-
|█▒▒▒▒▓▒▒▓▒
|Wolfmajor triad
|wmaj
|
|-
|█▒▒▓▒▒▒▓▒
|Minor diminished triad
|dmin
|
|-
|█▒▒▒▓▒▒▓▒
|Major diminished triad
|dmaj
|
|-
|█▒▒▓▒▒▓▒
|Slendric triad
|sl
|
|}
{| class="wikitable"
|+Tetrads (less sure)
!Chord
!Name
!Abbreviation
!Notes
|-
|<nowiki>█▒▒▒▒▓▒▒▒▒▓▒▒▒▓|▒</nowiki>
|Augmented major 7 tetrad
|aug/maj7
|
|-
|<nowiki>█▒▒▒▒▓▒▒▒▓▒▒▒▒▓|▒</nowiki>
|Major 7 tetrad
|maj7
|
|-
|<nowiki>█▒▒▒▓▒▒▒▒▓▒▒▒▒▓|▒</nowiki>
|Minor major 7 tetrad
|min/maj7
|
|-
|█▒▒▒▒▓▒▒▒▒▓▒▒▓▒
|Augmented 7 tetrad
|aug7
|
|-
|█▒▒▒▒▓▒▒▒▓▒▒▒▓▒
|Dominant 7 tetrad
|7
|may be spelled dom7 to clarify
|-
|█▒▒▒▓▒▒▒▒▓▒▒▒▓▒
|Minor 7 tetrad
|min7
|
|-
|█▒▒▒▒▓▒▒▓▒▒▒▒▓▒
|Wolfmajor 7 tetrad
|wmaj7
|
|-
|█▒▒▒▓▒▒▒▓▒▒▒▒▓▒
|Half-diminished tetrad
|dim/min7
|
|-
|█▒▒▓▒▒▒▒▓▒▒▒▒▓▒
|Wolfminor 7 tetrad
|wmin7
|
|-
|█▒▒▒▒▓▒▒▒▓▒▒▓▒
|Harmonic 7 tetrad
|h7
|may be spelled majh7 to clarify
|-
|█▒▒▒▓▒▒▒▒▓▒▒▓▒
|Minor harmonic 7 tetrad
|minh7
|
|-
|█▒▒▒▒▓▒▒▓▒▒▒▓▒
|Wolfmajor harmonic 7 tetrad
|wmajh7
|
|-
|█▒▒▒▓▒▒▒▓▒▒▒▓▒
|Diminished harmonic 7 tetrad
|dimh7
|
|-
|█▒▒▓▒▒▒▒▓▒▒▒▓▒
|Wolfminor harmonic 7 tetrad
|wminh7
|
|-
|█▒▒▒▓▒▒▓▒▒▒▒▓▒
|Major half diminished tetrad
|dmajh7
|
|-
|█▒▒▓▒▒▒▓▒▒▒▒▓▒
|Minor half-diminished tetrad
|dminh7
|
|-
|█▒▒▒▒▓▒▒▓▒▒▓▒
|Wolfmajor diminished 7 tetrad
|wmaj/dim7
|
|-
|█▒▒▒▓▒▒▒▓▒▒▓▒
|Diminished 7 tetrad
|dim7
|
|-
|█▒▒▓▒▒▒▒▓▒▒▓▒
|Wolfminor diminished 7 tetrad
|wmin/dim7
|
|-
|█▒▒▒▓▒▒▓▒▒▒▓▒
|Major diminished 7 tetrad
|dmaj7
|
|-
|█▒▒▓▒▒▒▓▒▒▒▓▒
|Minor diminished 7 tetrad
|dmin7
|
|-
|█▒▒▓▒▒▓▒▒▒▒▓▒
|Slendric diminished 7 tetrad
|sl/dim7
|may be spelled as a major 6th, sl/maj6
|-
|█▒▒▒▓▒▒▓▒▒▓▒
|Major diminished-augmented tetrad
|dmaj/aug5
|may be spelled as a minor 6th, dmaj/min6
|-
|█▒▒▓▒▒▒▓▒▒▓▒
|Minor diminished-augmented tetrad
|dmin/aug5
|may be spelled as a minor 6th, dmin/min6
|-
|█▒▒▓▒▒▓▒▒▒▓▒
|Slendric augmented tetrad
|sl/aug5
|may be spelled as a minor 6th, sl/min6
|-
|█▒▒▓▒▒▓▒▒▓▒
|Slendric tetrad
|sl5
|
|}

== Functional harmony ==
Functional harmony in zarlino should work similarly to 12edo; here are some key points to keep in mind.


1) The seventh chords on each degree of the LH Ionian scale
{| class="wikitable"
|+
!Degree
!Chord
!Equivalent voicings
!Third
!Fifth
!Seventh
|-
|1
|Imaj7
|
|5
|9
|14
|-
|2
|IImin7
|
|4
|9
|13
|-
|3
|IIIminh7
|Vwmaj/dim7, VIIsl/aug5
|4
|9
|12
|-
|4
|IVmaj7
|
|5
|9
|14
|-
|5
|Vwmajh7
|VIIdmin/aug5, IIdmajh7
|5
|8
|12
|-
|6
|VImin7
|
|4
|9
|13
|-
|7
|VIIdminh7
|IIminh7, IVwmaj/dim7
|3
|7
|12
|}
2) The seventh chords on each degree of the RH Ionian scale
{| class="wikitable"
!Degree
!Chord
!Equivalent voicings
!Third
!Fifth
!Seventh
|-
|1
|Imaj7
|
|5
|9
|14
|-
|2
|IIwminh7
|IVh7, VIdmaj/aug5
|4
|9
|13
|-
|3
|IIImin7
|
|4
|9
|12
|-
|4
|IVmaj7
|
|5
|9
|14
|-
|5
|Vh7
|VIIdmaj/aug5, IIsl/dim7
|5
|8
|12
|-
|6
|VImin7
|
|4
|9
|13
|-
|7
|VIIdmajh7
|IIwmin/dim7, IVwmajh7
|3
|7
|12
|}
I interpret these scales as roughly interchangeable in functional harmony, the same way the sixth and seventh notes of the traditional minor scale aren't well-defined in functional harmony.

=== Defining the dominant ===
The key feature of the dominant function is a tritone that resolves inward to the third on the tonic.This tritone is found on the V and VII chords in both scales. Note that this is not actually a dominant 7 tetrad, but a harmonic 7, as it contains three thirds of different sizes. 

=== Defining the tonic ===
Chords of the tonic function, as triads, contain at least two of the three notes of the tonic triad proper. As in the normal diatonic scale, these chords are the I, III, and VI chords.

=== The subdominant ===
The remaining chords belong to the subdominant function - that is, the II and IV. However, note that in the RH scale, the II chord is a wolfminor chord.