The epsilon chord (ε) is a four-note chord characterised by a property of diatonic completeness: within it appear, each exactly once, all six possible diatonic distances within the heptatonic system — second, third, fourth, fifth, sixth and seventh.
The name of the chord derives from Epsilon Lyrae, a stellar system formed by four main stars, adopted as a symbolic image of the relationship among the four notes of the chord.
For the relationship among the alpha chord, epsilon chord, sigma chord, Golomb rulers and all-interval chords, see the entry Zygote Chords.
Structure
The epsilon chord constitutes a single structural type, defined by the diatonic interval vector [1 1 1 1 1 1]. Its exemplary form is:
C–D–G–B
that is, in terms of degrees relative to the root:
1 – 2 – 5 – 7
Considering the internal pairs of the set C–D–G–B, one indeed obtains all six possible diatonic distances:
C–D= secondC–G= fifthC–B= seventhD–G= fourthD–B= sixthG–B= third
Principal Diatonic Variants
The principal diatonic variants of the epsilon chord are four. They do not constitute independent structural types, but qualitative realisations of the same vector form, organised in two pairs: major and minor, each accompanied by its mirror chord.
| Type | Chord | Structure | Mirror chord | Mirror structure |
|---|---|---|---|---|
| major | C–D–G–B | 0 2 7 11 | C–E–A–B | 0 4 9 11 |
| major | C–E–A–B | 0 4 9 11 | C–D–G–B | 0 2 7 11 |
| minor | C–D–G–B♭ | 0 2 7 10 | C–E♭–A♭–B♭ | 0 3 8 10 |
| minor | C–E♭–A♭–B♭ | 0 3 8 10 | C–D–G–B♭ | 0 2 7 10 |
In all these cases, the fundamental property remains unchanged: each epsilon chord contains all six possible diatonic distances exactly once.
Intervallic Property
The specificity of the epsilon chord lies in the fact that, although formed by only four notes, it manages to generate all the internal diatonic relationships of the heptatonic system. This completeness manifests not in chromatic terms, but in terms of generic diatonic degrees.
In the case of the chord C–D–G–B, the diatonic interval vector is:
[1 1 1 1 1 1]
The same principle holds for the other principal diatonic variants, which differ in concrete intervallic quality and arrangement, but preserve identical diatonic completeness.
Mirror Chord
Like other structures in the vector catalogue, the epsilon chord also possesses a mirror chord, obtained by specularly inverting the arrangement of distances relative to the root.
For example, the chord C–D–G–B has as its mirror C–E–A–B, while the chord C–D–G–B♭ has as its mirror C–E♭–A♭–B♭.
Mirror chords share the same diatonic vector property, while presenting a different internal arrangement of distances.
Butterfly Chords
Epsilon chords also play a constructive role in the formation of Butterfly Chords, in which two epsilon structures are joined in mirror form around a central axis.
Related Entries
Diatonic Interval Vector
Diatonic Class Vector
Butterfly Chords