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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 characterized by a property of elementary diatonic completeness: within it, all three fundamental diatonic classes—second/seventh, third/sixth, and fourth/fifth—appear exactly once.

The name of the chord derives from Alpha Centauri, a star system composed of three main stars, chosen as a symbolic image of the chord’s ternary structure.

For the relationship between the alpha chord, epsilon chord, sigma chord, Golomb rulers, and all-interval chords, see the entry Accordi zigote.

Structure

The exemplary form of the alpha chord is:

C–G–B

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

1 – 5 – 7

Considering the internal pairs within the set C–G–B, we obtain:

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

The corresponding diatonic class vector is therefore:

[1 1 1]

since the chord contains each of the three fundamental diatonic classes exactly once.

Intervallic property

The specificity of the alpha chord lies in the fact that, despite being made up of only three notes, it manages to generate all three fundamental diatonic classes exactly once. This completeness is not chromatic, nor does it coincide with the six-position diatonic interval vector, but rather with its more synthetic three-class form:

  • 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. For this reason, the resulting vector is [1 1 1].

Invariance under inversions

Every inversion of an alpha chord still produces an alpha chord. This happens because inversions preserve the same three generic interval pairs, even though the bass note changes.

For example, the chord:

C–E–B

and its inversions:

E–B–C
B–C–E

always retain the three fundamental diatonic classes and thus 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 has 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 each contain all three fundamental classes exactly once.

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

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

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

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

The mirror chord thus preserves the same relational completeness as the base form, but arranges the three interval classes in a reversed orientation. The base form and its mirror chord do not constitute two independent structural types, but two orientations of the same vectorial solution. From these, their respective diatonic variants can then be derived.

Zigoti musicali
Accordo epsilon
Accordo sigma
Vettore delle classi diatoniche

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