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The Tonnetz

The Tonnetz

5 comments

·October 18, 2025

juancroldan

As an indie music composer, this kind of unusual tone arrangement is great for creativity, thanks! I noticed that the same triangle will play different chords from time to time, is that on purpose?

tshaddox

I first became aware of this concept many years on Gary Garrett's blog, where he primarily refers to it as "the lattice." His introduction to the concept gives a brief history:

https://www.garygarrett.me/?p=342

More introduction to the lattice:

https://www.garygarrett.me/?p=995

https://www.garygarrett.me/?p=1632

https://www.garygarrett.me/?p=1696

Some comparison audio between equal temperament and just intonation:

https://www.garygarrett.me/?p=1812

Some songs with lattice animations:

https://www.garygarrett.me/?p=103

https://www.garygarrett.me/?p=1253

I also like this book which Gary recommends, although it's very challenging and I never made it all the way through:

https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...

mci

A recent blog post on thatsmaths.com was about Tonenetz, a diagram of harmonic relationships of notes. Tonenetz means 'tone network' in German :-)