musicMCT (version 0.1.2)

quantize_hue: Find a scale mod k that matches a given hue

Description

Given any scale, attempts to find a scale defined as integers mod k which belongs to the same hue as the input (i.e. would return TRUE when same_hue() is applied). This function thus is similar in spirit to quantize_color() but seeks a more precise structural match between input and quantization. Note, though, that while quantize_color() should always be able to find a suitable quantization (if nmax is set high enough), this is not necessarily true for quantize_hue(). There are lines in \(\mathbb{R}^n\) which pass through no rational points but the origin, so some hues (including ones of musical interest like the 5-limit just diatonic scale) may not have any quantization.

Usage

quantize_hue(set, nmax = 12, reconvert = FALSE, edo = 12, rounder = 10)

Value

If reconvert=FALSE, a list of two elements: element 1 is set with a vector of integers representing the quantized scale; element 2 is edo representing the number k of unit steps in the mod k universe. If reconvert=TRUE, returns a single numeric vector measured relative to the unit step size input as edo: these generally will not be integers. May also return a vector of NAs the same length as set if no suitable quantization was found beneath the limit given by nmax.

Arguments

set

Numeric vector of pitch-classes in the set

nmax

Integer, essentially a limit to how far the function should search before giving up. Although every real color should have a rational representation in some mod k universe, for some colors that k must be very high. Increasing nmax makes the function run longer but might be necessary if small chromatic universes don't produce a result. Defaults to 12.

reconvert

Boolean. Should the scale be converted to 12edo? Defaults to FALSE.

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.

Examples

meantone_diatonic <- sort(((0:6)*meantone_fifth())%%12)
quantize_hue(meantone_diatonic) # Succeeds
quantize_hue(j(dia), nmax=15) # Fails no matter how high you set nmax.

quasi_guido <- convert(c(0, 2, 4, 5, 7, 9), 13, 12)
quantize_color(quasi_guido)
quantize_hue(quasi_guido)