Package index • musicMCT

Core MCT Functions

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

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 (and interscalar) interval matrix
simplify_scale() best_simplification(): Best ways to regularize a scale

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_anaglyph_ineqmat(): Define hyperplanes for cross-type voice leadings
make_black_ineqmat() make_gray_ineqmat(): Define hyperplanes for transposition-sensitive arrangements
make_infrared_ineqmat(): Define hyperplanes for infrared arrangements
make_offset_ineqmat(): Translate a hyperplane arrangement to a new center
make_roth_ineqmat() get_roth_ineqmat() make_rosy_ineqmat(): Define hyperplanes for Rothenberg arrangements
make_white_ineqmat() make_pastel_ineqmat(): Define hyperplanes for 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
roth_ineqmats: Hyperplane arrangements for Rothenberg arrangements

Work directly with the information contained in a sign vector

anazero_fingerprint(): Are regularities within or between sets in a pair?
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?

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?

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)

Concepts from traditional pitch-class set theory

clockface(): Visualize a set in pitch-class space
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
normal_form(): Hook's OPTIC normal forms
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)

Applications of the DFT to set theory, a la Lewin, Quinn, et al.

dft(): The musical Discrete Fourier Transform of a pitch-class set
set_to_distribution() distribution_to_set() s2d() d2s(): Convert between pitch-class sets and distributions

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

Tools that make it convenient to manipulate objects in R

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

Concepts related to representations of scales as algebraic words

asword(): Algebraic word of a set's step sizes
clampitt_q(): Voice leadings between inversions with maximal common tones
isgwf(): Is a scale n-wise well formed?
iswellformed(): Well-formedness, Myhill's property, and/or moment of symmetry
realize_stepword(): Define scale by entering its relative step sizes

Ways to read & save data for use outside of R

ianring(): Look up a scale at Ian Ring's Exciting Universe of Music Theory
readSCL(): Import a Scala (.scl) file as a scale
writeSCL(): Create a Scala tuning file from a given scale