Analyze the Structure of Musical Scales
Are regularities within or between sets in a pair?
Algebraic word of a set's step sizes
Voice-leading brightness relationships for a scale's modes
Visualize brightness relationships among modes of a scale
Define a step size for one of Wendy Carlos's scales
Voice leadings between inversions with maximal common tones
Visualize a set in pitch-class space
Reference numbers for scale structures
Do two sign vectors represent adjacent colors?
Convert between octave measurements
Coordinate systems for scale representation
The musical Discrete Fourier Transform of a pitch-class set
Perfectly even scales (the color white)
How many instances of a subset-type exist within a scale? How many sca...
The brightness ratio
How even is a scale?
Voice-leading inflection points
Forte number from set class
Modulo division with rounding
Unique real values up to some tolerance
Which hyperplanes affect a given generic interval?
Count a scale's degrees of freedom
Look up a scale at Ian Ring's Exciting Universe of Music Theory
All intervals from one set to another
Symmetries of hyperplane arrangements define equivalent scales
Specific sizes corresponding to each generic interval
Is a scale n-wise well formed?
Rothenberg propriety
Well-formedness, Myhill's property, and/or moment of symmetry
Test for inversional symmetry
Interval-class vector
Convenient just-intonation intervals and scales
Define hyperplanes for cross-type voice leadings
Define hyperplanes for transposition-sensitive arrangements
Define hyperplanes for infrared arrangements
Translate a hyperplane arrangement to a new center
Define hyperplanes for Rothenberg arrangements
Define hyperplanes for white arrangements
Define hyperplanes for the Modal Color Theory arrangements
Maximally even scales
Define a tempered fifth for various meantone scales
Smallest voice leading between two sets
musicMCT: Analyze the Structure of Musical Scales
Hook's OPTIC normal forms
Does a scale lie in the canonical fundamental domain for OPTC symmetri...
Randomly generate scales on a flat
Primary colors
Prime form of a set using Rahn's algorithm
Closest point on a given flat
Find a scale mod k that matches a given color
Find a scale mod k that matches a given hue
Import a Scala (.scl) file as a scale
Define scale by entering its relative step sizes
Circular rotation of an ordered tuple
Do two scales lie on the same ray?
Modify evenness without changing hue
Set class complement
Set class from Forte's list
Orbit of a scale under symmetries of hyperplane arrangement
Create a scale from a sign vector
Convert between pitch-class sets and distributions
Ordered pitch-class interval represented as interval class with sign
Detect a scale's location relative to a hyperplane arrangement
Scalar (and interscalar) interval matrix
Best ways to regularize a scale
Specify a scale's step pattern with a sign vector
Count the multiplicities of a subset-type's varieties
Specific varieties of scalar subsets given a generic shape
Subset varieties for all subsets of a fixed size
Random scales uniformly distributed on a hypersphere around an input
Distinguish different types of interval equalities
Transpositional combination & pitch multiplication
Transposition and Inversion
Distances between continuous transpositions of a set
Transposition class of a given pc-set
Test for transpositional symmetry
How far apart are two scales?
Which transpositions give elementary voice leadings?
Minimal voice leadings to all transpositions of some Tn-type mod k
Elementary voice leadings
Smallest crossing-free voice leading between two pitch-class sets
Which interval-comparison equalities does a scale satisfy?
Create a Scala tuning file from a given scale
Frequency ratios to logarithmic pitch intervals (e.g. semitones)
Twin set in the Z-relation (Z mate)
Analysis of musical scales (& modes, grooves, etc.) in the vein of Sherrill 2025 <doi:10.1215/00222909-11595194>. The initials MCT in the package title refer to the article's title: "Modal Color Theory." Offers support for conventional musical pitch class set theory as developed by Forte (1973, ISBN: 9780300016109) and David Lewin (1987, ISBN: 9780300034936), as well as for the continuous geometries of Callender, Quinn, & Tymoczko (2008) <doi:10.1126/science.1153021>. Identifies structural properties of scales and calculates derived values (sign vector, color number, brightness ratio, etc.). Creates plots such as "brightness graphs" which visualize these properties.
Useful links