normal_form: Hook's OPTIC normal forms

In musicMCT: Analyze the Structure of Musical Scales

Hook's OPTIC normal forms

Description

Following Hook (2023, 416-18, ISBN: 9780190246013), calculates a normal form for the input set using any combination of OPTIC symmetries.

Usage

normal_form(set, optic = "opc", edo = 12, rounder = 10)

Arguments

set	Numeric vector of pitch-classes in the set
optic	String: the OPTIC symmetries to apply. Defaults to "opc".
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.

Details

This function is designed for flexibility in the optic parameter, not speed. In situations where you need to calculate a large number of OPTIC- or OPTC-normal forms, you should use primeform() or tnprime() respectively, which are considerably faster.

Value

Numeric vector with the desired normal form of set

See Also

primeform(), tnprime(), and startzero() for faster functions dedicated to specific symmetry combinations

Examples

# See Exercise 10.4.8 in Hook (2023, 420):
eroica <- c(-25, -13, -6, -3, 0, 3)
normal_form(eroica, optic="pti")
normal_form(eroica, optic="op")

# See Table 10.4.1 in Hook (2023, 417):
alpha <- c(-5, -11, 14, 9, 14, 14, 2)
num_symmetries <- sample(0:5, 1)
random_symmetries <- sample(c("o", "p", "t", "i", "c"), num_symmetries)
random_symmetries <- paste(random_symmetries, collapse="")
print(random_symmetries)
normal_form(alpha, optic=random_symmetries)

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