melodic-contour

Melodic contour theory in TypeScript. Implements the core formalisms from Morris (1987), Friedmann (1985), and Marvin and Laprade (1987).

What is contour theory?

Melodic contour describes the shape of a melody - its pattern of ups and downs - independent of specific intervals. A contour segment (CSeg) represents this shape as a sequence of ranked positions: the lowest note becomes 0, the next higher note 1, and so on.

Install

npm install melodic-contour

API

cseg(pitches: number[]): number[]

Maps a pitch list to contour integers by rank. Throws if pitches repeat.

validateCseg(c: number[]): void

Validates a CSeg (distinct integers 0..n-1). Throws if invalid.

comMatrix(c: number[]): number[][]

Comparison Matrix. COM[i][j] = sign(c[j] - c[i]) in {-1, 0, +1}.

cas(c: number[]): number[]

Contour Adjacency Series. Signs of successive differences.

casVector(c: number[]): [number, number]

[ascents, descents] from the CAS.

csim(a: number[], b: number[]): number

Contour Similarity. Fraction of matching entries above the COM matrix diagonal. Range [0, 1].

cint(c: number[]): number[][]

Contour Interval Matrix. Upper triangle: CINT[i][j] = c[j] - c[i] for j > i.

retrograde(c: number[]): number[]

Reverses a CSeg.

inversion(c: number[]): number[]

Inverts a CSeg: maps each x to (n-1) - x.

retrogradeInversion(c: number[]): number[]

Reversal of the inversion.

equivalenceClass(c: number[]): number[][]

Returns unique forms among {Prime, Retrograde, Inversion, RetrogradeInversion}.

contourReduction(cseg: readonly number[]): ContourReductionResult

Applies Morris's contour-reduction algorithm to reduce a CSeg to its prime form.

Returns { prime: readonly number[]; depth: number } where:

• prime is the reduced CSeg (distinct integers 0..k-1 by relative height, always a valid CSeg).
• depth is the number of reduction passes that removed at least one interior point. An already-irreducible contour has depth 0.

Algorithm (Morris 1993): The first and last elements are always retained. On each pass, interior points that are neither a local maximum nor a local minimum among the currently-retained neighbors are removed. Each pass that removes at least one point increments the depth. Passes continue until the contour is stable.

Examples:

import { contourReduction } from "melodic-contour";

// A monotonic contour reduces to just its endpoints:
contourReduction([0, 1, 2, 3, 4]); // { prime: [0, 1], depth: 1 }

// An arch contour is already irreducible:
contourReduction([0, 2, 1]);        // { prime: [0, 2, 1], depth: 0 }

// A 7-element contour with one non-extreme interior point:
contourReduction([0, 5, 3, 4, 1, 2, 6]); // { prime: [0, 4, 2, 3, 1, 5], depth: 1 }

Reference: Morris, R. D. (1993). New directions in the theory and analysis of musical contour. Music Theory Spectrum, 15(2), 205-228.

Usage

import { cseg, comMatrix, cas, casVector, csim, equivalenceClass } from "melodic-contour";

const c = cseg([60, 67, 62, 64]); // [0, 3, 1, 2]
const com = comMatrix(c);
const series = cas(c);            // [1, -1, 1]
const [asc, desc] = casVector(c); // [2, 1]
const sim = csim(c, c);           // 1
const forms = equivalenceClass(c); // [[0,3,1,2],[2,1,3,0],[3,0,2,1],[1,2,0,3]]

References

• Morris, R. D. (1987). Composition with Pitch-Classes. Yale University Press.
• Friedmann, M. L. (1985). A methodology for the discussion of contour: Its application to Schoenberg's music. Journal of Music Theory, 29(2), 223-248.
• Marvin, E. W., and Laprade, P. A. (1987). Relating musical contours: Extensions of a theory for contour. Journal of Music Theory, 31(2), 225-267.