Musical Intervals & Voice Texture¶

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Abstractions about pitch relationships and multi-voice texture in music, including interval structures such as the musical interval, all-interval tetrachord and major limma, textural organization of simultaneous voices like counterpoint and musical texture, and tonal reference points such as the tonic and atonality.

8 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

All-Interval Tetrachord — A four-note pitch-class set whose six unordered dyads realize each of the six interval classes exactly once, yielding interval vector ⟨1,1,1,1,1,1⟩.
Atonality — Deliberately withhold a tonal centre by constructing pitch relations that resist tonicisation, denying the ear the gravitational hierarchy it uses to parse tonal grammar, so a constructed no-privileged-pitch surface is organised by motif, interval, rhythm, and texture instead.
Consecutive Fifths — Consecutive fifths occur when the same two musical voices form a perfect-fifth class at two successive structural events, a detectable relation whose avoidance or use depends on the governing contrapuntal style.
Counterpoint — Write several voices that are each a complete, independent melody while every vertical slice they form is also defensible harmony — a dual demand a catalogue of local voice-leading rules turns into beat-by-beat checks.
Major Limma — A just-intonation interval of frequency ratio 135:128, approximately 92.18 cents, derivable as the difference between a 9:8 ditone and a 6:5 minor third.
Musical Interval — A structured relation between two musical pitches, described through acoustic size, direction, register, diatonic number and quality, or an interval-class reduction under a tuning system.
Musical Texture — Classify a musical passage by how many simultaneous melodic lines it contains, whether they are independent or doubled, and whether one dominates while the others provide coordinated support.
Tonic (music) — In music, "tonic" refers to the originating note or chord of a particular key .