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Alpha Chord

The alpha chord (α) is one of the three main musical zygotes of the SEA system. It is a three-note chord characterised by a property of elementary diatonic completeness: within it appear, each exactly once, all three fundamental diatonic classes — second/seventh, third/sixth and fourth/fifth.

The name of the chord derives from Alpha Centauri, a stellar system formed by three main stars, adopted as a symbolic image of the ternary structure 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 exemplary form of the alpha chord is:

C–G–B

that is, in terms of degrees relative to the root:

1 – 5 – 7

Considering the internal pairs of the set C–G–B, one obtains:

  • C–G = fifth
  • C–B = seventh
  • G–B = third

The corresponding diatonic class vector is therefore:

[1 1 1]

since all three fundamental diatonic classes appear exactly once in the chord.

Intervallic Property

The specificity of the alpha chord lies in the fact that, although formed by only three notes, it manages to generate each of the three fundamental diatonic classes exactly once. This completeness is not chromatic, nor does it coincide with the diatonic interval vector of six positions, but with its most synthetic form of three classes:

  • second / seventh
  • third / sixth
  • fourth / fifth

In the case of the chord C–G–B, the fifth belongs to the third class, the seventh to the first, and the third to the second. The resulting vector is therefore [1 1 1].

Invariance under Inversions

Every inversion of an alpha chord still generates an alpha chord. This occurs because inversions preserve the same three generic interval pairs, even when the bass note changes.

For example, the chord:

C–E–B

and its inversions:

E–B–C
B–C–E

always maintain the three fundamental diatonic classes and therefore produce the same diatonic class vector:

[1 1 1]

In this sense, the distinctive property of the alpha chord does not depend on the concrete arrangement of the notes, but on the relational form they generate.

Mirror Chord

The alpha chord presents a base form and a corresponding mirror chord:

  • base form: C–G–B
  • mirror chord: C–E–B

Both generate the diatonic class vector [1 1 1], since they contain each of the three fundamental classes exactly once.

In the case of the base form C–G–B, the intervallic pairs are:

  • C–G = fifth
  • C–B = seventh
  • G–B = third

In the case of the mirror chord C–E–B, the intervallic pairs are:

  • C–E = third
  • C–B = seventh
  • E–B = fifth

The mirror chord therefore preserves the same relational completeness as the base form, but arranges the three interval classes according to an inverse orientation. The base form and its mirror chord do not constitute two independent structural types, but two orientations of the same vector solution. From them, the respective diatonic variants are then obtained.

Zygote Chords
Epsilon Chord
Sigma Chord
Diatonic Class Vector

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