Package index • musicMCT

Core MCT Functions

Essential tools for analyzing scale structures and the hyperplane arrangments of Modal Color Theory.

Scalar Properties

Gather information about individual scales

brightnessgraph(): Visualize brightness relationships among modes of a scale

colornum(): Reference numbers for scale structures

eps() delta() ratio(): The brightness ratio

howfree(): Count a scale's degrees of freedom

ineqsym(): Symmetries of hyperplane arrangements define equivalent scales

primary_hue() primary_colornum() primary_signvector() primary_color(): Primary colors

quantize_color(): Find a scale mod k that matches a given color

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

same_hue(): Do two scales lie on the same ray?

saturate(): Modify evenness without changing hue

scale_palette(): Orbit of a scale under symmetries of hyperplane arrangement

sim(): Scalar interval matrix

simplify_scale() best_simplification(): Best ways to regularize a scale

Hyperplane Arrangements

Define and manipulate the arrangements which characterize the spaces

get_relevant_rows(): Which hyperplanes affect a given generic interval?

ineqmats: Hyperplane arrangements for MCT spaces

make_roth_ineqmat() make_rosy_ineqmat(): Define hyperplanes for Rothenberg arrangements

make_white_ineqmat() make_pastel_ineqmat(): Define hyperplanes for quasi-white arrangements

makeineqmat() getineqmat(): Define hyperplanes for the Modal Color Theory arrangements

populate_flat(): Randomly generate scales on a flat

project_onto() match_flat(): Closest point on a given flat

Sign vectors

Work directly with the information contained in a sign vector

brightness_comparisons(): Voice-leading brightness relationships for a scale's modes

comparesignvecs(): Do two sign vectors represent adjacent colors?

set_from_signvector(): Create a scale from a sign vector

signvector(): Detect a scale's location relative to a hyperplane arrangement

step_signvector(): Specify a scale's step pattern with a sign vector

svzero_fingerprint(): Distinguish different types of interval equalities

whichsvzeroes() countsvzeroes(): Which interval-comparison equalities does a scale satisfy?

Other Properties

Tests for miscellaneous scalar properties that aren’t directly tied to MCT.

evenness(): How even is a scale?

isproper() has_contradiction() strictly_proper(): Rothenberg propriety

optc_test(): Does a scale lie in the canonical fundamental domain for OPTC symmetries?

Scales and Intervals

Basic tools for defining musical objects

carlos_step(): Define a step size for one of Wendy Carlos's scales

convert(): Convert between octave measurements

coord_to_edo() coord_from_edo(): Coordinate systems for scale representation

edoo(): Perfectly even scales (the color white)

j(): Convenient just-intonation intervals and scales

maxeven(): Maximally even scales

meantone_fifth(): Define a tempered fifth for various meantone scales

surround_set(): Random scales uniformly distributed on a hypersphere around an input

z(): Frequency ratios to logarithmic pitch intervals (e.g. semitones)

Set Theory

Concepts from traditional pitch-class set theory

emb() cover(): How many instances of a subset-type exist within a scale? How many scales embed a subset?

fortenum(): Forte number from set class

fortenums: Allen Forte's list of set classes

ifunc(): All intervals from one set to another

isym() isym_index() isym_degree(): Test for inversional symmetry

ivec(): Interval-class vector

primeform(): Prime form of a set using Rahn's algorithm

sc(): Set class from Forte's list

sc_comp(): Set class complement

signed_interval_class(): Ordered pitch-class interval represented as interval class with sign

tc(): Transpositional combination & pitch multiplication

tn() tni() startzero() charm(): Transposition and Inversion

tnprime(): Transposition class of a given pc-set

tsym() tsym_index() tsym_degree(): Test for transpositional symmetry

zmate(): Twin set in the Z-relation (Z mate)

Subsets

Tools for exploring subset-superset relationships in scales

intervalspectrum() spectrumcount(): Specific sizes corresponding to each generic interval

subset_multiplicities(): Count the multiplicities of a subset-type's varieties

subset_varieties(): Specific varieties of scalar subsets given a generic shape

subsetspectrum(): Subset varieties for all subsets of a fixed size

Utilities

Tools that make it convenient to manipulate objects in R

fpunique(): Unique real values up to some tolerance

rotate(): Circular rotation of an ordered tuple

Voice Leading

Tools for studying how sets are connected by voice leadings

flex_points(): Voice-leading inflection points

minimize_vl(): Smallest voice leading between two sets

tndists(): Distances between continuous transpositions of a set

vl_dist(): How far apart are two scales?

vl_generators(): Which transpositions give elementary voice leadings?

vl_rolodex(): Minimal voice leadings to all transpositions of some Tn-type mod k

vlsig(): Elementary voice leadings

whichmodebest(): Smallest crossing-free voice leading between two pitch-class sets

Word Theory

Concepts related to representations of scales as algebraic words

asword(): Algebraic word of a set's step sizes

isgwf(): Is a scale n-wise well formed?

iswellformed(): Well-formedness, Myhill's property, and/or moment of symmetry

realize_setword(): Define scale by entering its relative step sizes

Input/Output

Ways to read & save data for use outside of R

readSCL(): Import a Scala (.scl) file as a scale

writeSCL(): Create a Scala tuning file from a given scale