Lattice
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.
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
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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)