musicMCT (version 0.1.2)

primary_hue: Primary colors

Description

In traditional pitch-class set theory, concepts like normal order and primeform() establish a canonical representative for each equivalence class of pitch-class sets. It's useful to do something similar in MCT as well: given a family of scales, such as the collection of modes or a scale_palette(), we can define the "primary color" of the family as the one that comes first when the scales' sign vectors are ordered lexicographically. primary_hue() uses ineqsym() to return a specific representative of the primary color which belongs to the same palette of hues as the input. Because primary_hue() focuses on hues rather than colors, it may not highlight the fact that two scales have the same primary color. Thus, for information about broader families, primary_colornum() returns the color number of the primary color, primary_signvector() returns the sign vector, and primary_color() itself uses quantize_color() to return a consistent representative of each color.

Usage

primary_hue(
  set,
  type = c("all", "half_palette", "modes"),
  ineqmat = NULL,
  edo = 12,
  rounder = 10
)
primary_colornum(set, type = "all", ...)
primary_signvector(set, type = "all", ...)
primary_color(set, type = "all", nmax = 12, reconvert = FALSE, ...)

Value

A numeric vector representing a scale for primary_hue(); a single integer for primary_colornum(); a signvector() for primary_signvector(); and a list like quantize_color() for primary_color().

Arguments

set

Numeric vector of pitch-classes in the set

type

How broad of an equivalence class should be considered? May be one of three options:

• "all", the default, uses the full range of scale_palette() relationships

• "half_palette" uses scale_palette() with include_involution=FALSE

• "modes" uses only the n modes of set

ineqmat

Specifies which hyperplane arrangement to consider. By default (or by explicitly entering "mct") it supplies the standard "Modal Color Theory" arrangements of getineqmat(), but can be set to "white," "roth", "pastel," or "rosy", giving the ineqmats of make_white_ineqmat(), make_roth_ineqmat(), make_pastel_ineqmat(), and make_rosy_ineqmat(). For other arrangements, the desired inequality matrix can be entered directly.

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.

...

Arguments to be passed to primary_hue()

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.

Examples

major_64 <- c(0, 5, 9)
primary_hue(major_64)
primary_hue(major_64, type="modes")

viennese_trichord <- c(0, 6, 11)
# Same primary color as major_64:
apply(cbind(major_64, viennese_trichord), 2, primary_signvector)

# But a different primary hue:
primary_hue(viennese_trichord)

# Only works with representative_signvectors loaded:
primary_colornum(major_64) == primary_colornum(viennese_trichord)

primary_color(major_64)
primary_color(viennese_trichord)