The epsilon (ε) chord is a four-note chord characterized by a property of diatonic completeness: within it, all six possible diatonic intervals within the heptatonic system—second, third, fourth, fifth, sixth, and seventh—appear exactly once.
The name of the chord derives from Epsilon Lyrae, a star system consisting of four main stars, taken as a symbolic image of the relationship between the four notes of the chord.
For the relationship between 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 scale degrees relative to the root:
1 – 2 – 5 – 7
Considering the internal pairs of the set C–D–G–B, all six possible diatonic intervals are indeed obtained:
C–D= secondC–G= fifthC–B= seventhD–G= fourthD–B= sixthG–B= third
Main diatonic variants
The main diatonic variants of the epsilon chord are four. They do not constitute independent structural types, but qualitative realizations of the same vector form, organized into two pairs: major and minor, each accompanied by its own 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 intervals exactly once.
Intervallic property
The specificity of the epsilon chord lies in the fact that, despite being made up of 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 applies to the other main diatonic variants, which differ in concrete interval quality and arrangement, but retain identical diatonic completeness.
Mirror chord
Like other structures in the vector catalog, the epsilon chord also has a mirror chord, obtained by inverting the arrangement of the intervals with respect 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 intervals.
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