[DSRP Evidence](https://dsrpevidence.org/)

# The Geometry of Musical Chords

## Details

**Authors** Tymoczko, Dmitri

**Year** 2006

**Publisher** Science 313(5783), 72–74

**Kind of work** article

**Discipline** Music Theory

**Secondary disciplines** Mathematics

**Applied** false

[Read it at the publisher](https://doi.org/10.1126/science.1126287) 
10.1126/science.1126287

## In authors' words

### What they set out to do (purpose)

To model musical chords geometrically so that relations between chords can be described and compared across musical styles.

### How they did it (methods)

Geometric model in which chords are points in an orbifold and line segments represent mappings between the notes of two chords.

### What they found (results)

Composers across many styles use short segments between structurally similar chords, which are possible only when chords are nearly symmetrical under translation, reflection or permutation. Consonant and dissonant chords show different kinds of near-symmetry, suggesting they serve different compositional purposes.

## Commentary

### In short

A mathematical space of chords shows that composers in many styles move between chords that are close together, and that consonant and dissonant chords differ in their symmetries.

### Response

Treating chords that differ by transposition, reflection or reordering as the same object is a distinction-drawing choice, and the chord is modeled as a whole built of notes. The mappings between chords supply the relational structure. Perspective is not carried in the account. The evidence is a formal model whose support from musical practice was not assessed here beyond the abstract.

**Patterns it shows** D, S, R

Formal proof or model

**Added** 2026-10-20

**How to cite this** Tymoczko, Dmitri (2006). The Geometry of Musical Chords. Science 313(5783), 72–74.