Analyze the Structure of Musical Scales


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Documentation for package ‘musicMCT’ version 0.2.0

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A B C D E F G H I J M O P Q R S T V W Z

-- A --

asword Algebraic word of a set's step sizes

-- B --

best_simplification Best ways to regularize a scale
brightnessgraph Visualize brightness relationships among modes of a scale
brightness_comparisons Voice-leading brightness relationships for a scale's modes

-- C --

carlos_step Define a step size for one of Wendy Carlos's scales
charm Transposition and Inversion
clockface Visualize a set in pitch-class space
colornum Reference numbers for scale structures
comparesignvecs Do two sign vectors represent adjacent colors?
convert Convert between octave measurements
coord_from_edo Coordinate systems for scale representation
coord_to_edo Coordinate systems for scale representation
countsvzeroes Which interval-comparison equalities does a scale satisfy?
cover How many instances of a subset-type exist within a scale? How many scales embed a subset?

-- D --

d2s Convert between pitch-class sets and distributions
delta The brightness ratio
dft The musical Discrete Fourier Transform of a pitch-class set
distribution_to_set Convert between pitch-class sets and distributions

-- E --

edoo Perfectly even scales (the color white)
emb How many instances of a subset-type exist within a scale? How many scales embed a subset?
eps The brightness ratio
evenness How even is a scale?

-- F --

flex_points Voice-leading inflection points
fortenum Forte number from set class
fortenums Allen Forte's list of set classes
fpunique Unique real values up to some tolerance

-- G --

getineqmat Define hyperplanes for the Modal Color Theory arrangements
get_relevant_rows Which hyperplanes affect a given generic interval?
get_roth_ineqmat Define hyperplanes for Rothenberg arrangements

-- H --

has_contradiction Rothenberg propriety
howfree Count a scale's degrees of freedom

-- I --

ianring Look up a scale at Ian Ring's _Exciting Universe of Music Theory_
ifunc All intervals from one set to another
ineqmats Hyperplane arrangements for MCT spaces
ineqsym Symmetries of hyperplane arrangements define equivalent scales
intervalspectrum Specific sizes corresponding to each generic interval
isgwf Is a scale n-wise well formed?
isproper Rothenberg propriety
iswellformed Well-formedness, Myhill's property, and/or moment of symmetry
isym Test for inversional symmetry
isym_degree Test for inversional symmetry
isym_index Test for inversional symmetry
ivec Interval-class vector

-- J --

j Convenient just-intonation intervals and scales

-- M --

makeineqmat Define hyperplanes for the Modal Color Theory arrangements
make_black_ineqmat Define hyperplanes for transposition-sensitive arrangements
make_gray_ineqmat Define hyperplanes for transposition-sensitive arrangements
make_offset_ineqmat Translate a hyperplane arrangement to a new center
make_pastel_ineqmat Define hyperplanes for white arrangements
make_rosy_ineqmat Define hyperplanes for Rothenberg arrangements
make_roth_ineqmat Define hyperplanes for Rothenberg arrangements
make_white_ineqmat Define hyperplanes for white arrangements
match_flat Closest point on a given flat
maxeven Maximally even scales
meantone_fifth Define a tempered fifth for various meantone scales
minimize_vl Smallest voice leading between two sets

-- O --

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

-- P --

populate_flat Randomly generate scales on a flat
primary_color Primary colors
primary_colornum Primary colors
primary_hue Primary colors
primary_signvector Primary colors
primeform Prime form of a set using Rahn's algorithm
project_onto Closest point on a given flat

-- Q --

quantize_color Find a scale mod k that matches a given color
quantize_hue Find a scale mod k that matches a given hue

-- R --

ratio The brightness ratio
readSCL Import a Scala (.scl) file as a scale
realize_setword Define scale by entering its relative step sizes
rotate Circular rotation of an ordered tuple
roth_ineqmats Hyperplane arrangements for Rothenberg arrangements

-- S --

s2d Convert between pitch-class sets and distributions
same_hue Do two scales lie on the same ray?
saturate Modify evenness without changing hue
sc Set class from Forte's list
scale_palette Orbit of a scale under symmetries of hyperplane arrangement
sc_comp Set class complement
set_from_signvector Create a scale from a sign vector
set_to_distribution Convert between pitch-class sets and distributions
signed_interval_class Ordered pitch-class interval represented as interval class with sign
signvector Detect a scale's location relative to a hyperplane arrangement
sim Scalar (and interscalar) interval matrix
simplify_scale Best ways to regularize a scale
spectrumcount Specific sizes corresponding to each generic interval
startzero Transposition and Inversion
step_signvector Specify a scale's step pattern with a sign vector
strictly_proper Rothenberg propriety
subsetspectrum Subset varieties for all subsets of a fixed size
subset_multiplicities Count the multiplicities of a subset-type's varieties
subset_varieties Specific varieties of scalar subsets given a generic shape
surround_set Random scales uniformly distributed on a hypersphere around an input
svzero_fingerprint Distinguish different types of interval equalities

-- T --

tc Transpositional combination & pitch multiplication
tn Transposition and Inversion
tndists Distances between continuous transpositions of a set
tni Transposition and Inversion
tnprime Transposition class of a given pc-set
tsym Test for transpositional symmetry
tsym_degree Test for transpositional symmetry
tsym_index Test for transpositional symmetry

-- V --

vlsig Elementary voice leadings
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

-- W --

whichmodebest Smallest crossing-free voice leading between two pitch-class sets
whichsvzeroes Which interval-comparison equalities does a scale satisfy?
writeSCL Create a Scala tuning file from a given scale

-- Z --

z Frequency ratios to logarithmic pitch intervals (e.g. semitones)
zmate Twin set in the Z-relation (Z mate)