# Analyze the Structure of Musical Scales

## Documentation for package ‘musicMCT’ version 0.4.0

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

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

## -- A --

anazero_fingerprint | Are regularities within or between sets in a pair?
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
clampitt_q | Voice leadings between inversions with maximal common tones
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
fpmod | Modulo division with rounding
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
inter_vlsig | Elementary voice leadings
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_anaglyph_ineqmat | Define hyperplanes for cross-type voice leadings
make_black_ineqmat | Define hyperplanes for transposition-sensitive arrangements
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_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
move_to_hyperplane | Intersection of a line with a hyperplane

## -- N --

normal_form | Hook's OPTIC normal forms

## -- O --

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

## -- P --

point_on_flat | Generate one point on arbitrary combination of hyperplanes
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_stepword | 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)