emb: How many instances of a subset-type exist within a scale? How...

In musicMCT: Analyze the Structure of Musical Scales

How many instances of a subset-type exist within a scale? How many scales embed a subset?

Description

David Lewin's EMB and COV functions: see Lewin, Generalized Musical Intervals and Transformations (New Haven, CT: Yale University Press, 1987), 105-120. For EMB, given a group ("CANON") of transformations which are considered to preserve a set's type, find the number of instances of that type in a larger set (scale). Lewin characterizes this generally, but emb() only offers T_n and T_n / T_nI transformation groups as available canonical groups. Conversely, Lewin's COV function asks how many instances of a scale type include subset: this is implemented as cover() (not cov()!).

Usage

emb(subset, scale, canon = c("tni", "tn"), edo = 12, rounder = 10)

cover(subset, scale, canon = c("tni", "tn"), edo = 12, rounder = 10)

Arguments

subset	Numeric vector of pitch-classes in any representative of the subset type (Lewin's X)
scale	Numeric vector of pitch-classes in the larger set to embed into (Lewin's Y)
canon	What transformations should be considered equivalent? Defaults to "tni" (using standard set classes) but can be "tn" (using transposition classes)
edo	Number of unit steps in an octave. Defaults to 12.
rounder	Numeric (expected integer), defaults to 10: number of decimal places to round to when testing for equality.

Value

Integer: count of subset or scale types satisfying the desired relation.

Examples

emb(c(0, 4, 7), sc(7, 35))
emb(c(0, 4, 7), sc(7, 35), canon="tn")

# Works for continuous pc-space too:
emb(j(1, 3, 5), j(dia))
emb(j(1, 2, 3, 5, 6), j(dia))
emb(j(1, 2, 4, 5, 6), j(dia), canon="tn")

emb(c(0, 4, 7), c(0, 1, 3, 7))
emb(c(0, 4, 7), c(0, 1, 3, 7), canon="tn")

emb(c(0, 4), c(0, 4, 8))
cover(c(0, 4), c(0, 4, 8))

harmonic_minor <- c(0, 2, 3, 5, 7, 8, 11)
cover(c(0, 4, 8), harmonic_minor)
cover(c(0, 4, 8), harmonic_minor, canon="tn")

musicMCT documentation built on June 21, 2026, 9:06 a.m.