tc: Transpositional combination & pitch multiplication

In musicMCT: Analyze the Structure of Musical Scales

Transpositional combination & pitch multiplication

Description

Cohn (1988, \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.2307/745790")}) defines transpositional combination as a procedure that generates a pc-set as the union of two (or more) transpositions of some smaller set. tc() takes the small set and a vector of transposition levels, returning the larger pc-set that results. (Pierre Boulez referred to this procedure as pitch "multiplication", which Amiot (2016, \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1007/978-3-319-45581-5")}) shows to be not at all fanciful, as a convolution of two pitch-class sets.)

Usage

tc(set, multiplier = NULL, edo = 12, rounder = 10)

Arguments

set	Numeric vector of pitch-classes in the set
multiplier	Numeric vector of transposition levels to apply to set. If not specified, defaults to set.
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

Numeric vector of length \leq length(set) \cdot length(multiplier)

Examples

tc(c(0, 4), c(0, 7))
tc(c(0, 7), c(0, 4))

pyth_tetrachord <- j(1, t, dt, 4)
pyth_dia <- tc(pyth_tetrachord, j(1, 5))
same_hue(pyth_dia, c(0, 2, 4, 5, 7, 9, 11))

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