Prime form of a set using Rahn's algorithm

Takes a set (in any order, inversion, and transposition) and returns the canonical ("prime") form that represents the \(T_n /T_n I\)-type to which the set belongs. Uses the algorithm from Rahn 1980 rather than Forte 1973.

Usage

primeform(set, edo = 12, rounder = 10)

Arguments

set

Numeric vector of pitch-classes in the 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 same length as set

Details

In principle this should work for sets in continuous pitch-class space, not just those in a mod k universe. But watch out for rounding errors: if you can manage to work with integer values, that's probably safer. Otherwise, try rounding your set to various decimal places to test for consistency of result.

Examples

primeform(c(0, 3, 4, 8))
#> [1] 0 1 4 8
primeform(c(0, 1, 3, 7, 8))
#> [1] 0 1 5 6 8
primeform(c(0, 3, 6, 9, 12, 14), edo=16)
#> [1]  0  2  4  7 10 13