Software

Chord Geometries

ChordGeometries represents chords and voice leadings in a variety of 3D geometrical spaces. You can enter chords on a MIDI keyboard or using the Keyboard window. Voice leadings between successive chords are represented by continuous paths in the spaces. Go to the Chord Geometries 1.1 page.

Chord graph explorer

This is a small Python program that allows you to explore a network of relationships linking chords in a wide range of musical contexts. Basically, whenever you have a chord whose size is relatively prime to that of its enclosing scale you can form a "generalized circle of fifths" (see Geometry and the Quest for Theoretical Generality). You can then scramble these voice leadings as discussed in section 3.11 of A Geometry of Music to get a collection of isomorphic voice-leading lattices. This means you can transfer musical patterns from one lattice to another. My program will graph them for you, embody various patterns in musical notation, allow you to embed multiple patterns, etc. It requires music21, numpy, scipy, and matplotlib. Read the comments for more explanation. Download now.

Voice-leading utilities

Simple python programs using music21 to perform routine voice-leading calculations: determining the most efficient voice leadings between chords, etc. Download now.

Voice Leading

This is a little Max object, written in Java, that finds the most efficient voice leading between chords. Very useful for algorithmic composition. Download now.

Pitch Mapper

Pitch Mapper is no longer supported, but is still available as a download (Mac OS X only). I've rewritten this in python. Download now.

About Me

Dmitri Tymoczko (b. 1969, Cambridge, Massachusetts) is a composer and music theorist who teaches at Princeton University. His book A Geometry of Music (Oxford) has been described as "a tour de force" (The Times Literary Supplement), a "monumental achievement" (Music Theory Online), and, potentially, a modern analogue to Schoenberg's Harmonielehre (The Musical Times). His first three CDs, Beat Therapy ("far reaching yet utterly entertaining," Newmusicbox), Crackpot Hymnal ("ebullient ... polystylistic ... kinetic ... vividly orchestrated and vibrantly paced," Sequenza21), and and Rube Goldberg Variations ("foot tapping," "sassy," Limelight), are available from Bridge Records. A fourth, Fools and Angels is available from New Focus.