# Harmonic lattice diagram

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English Wikipedia has an article on:

A **harmonic lattice diagram** (**lattice**) is an instrument to visualize relations of tones. It's a projection of a multi-dimensional structure onto a 2D screen.

English Wikipedia has an article on:

The **Tonnetz** is the lattice that represents 12edo's mapping of 5-limit intervals. **Vogel's Tonnetz** is a 7-limit version of Euler's 5-limit Tonnetz.

## Examples

A square lattice representing marvel temperament.

A hexagonal lattice representing 41edo's mapping of 5-limit intervals, using ups and downs notation.

A hexagonal lattice representing a subset of 7-limit intervals, using color notation.

## External links

- Beginner's guide to lattices: See chapter 1.3 of
*Alternative Tunings: Theory, Notation and Practice*by Kite Giedraitis (2016) - "lattice/lattice diagram" on Tonalsoft Encyclopedia
- "Octave Equivalent Music Lattices" by Graham Breed (2008)
- "Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7-) Harmonic Lattice of Notes" by Adriaan Fokker (1969)
- "Harmonic Lattice Diagrams" by Joseph L. Monzo (1998)