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:
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?
I only listened briefly on laptop speakers, but it did sound like sometimes the same note of a chord would play at a different octave, almost like it was trying to do voice leading from the previously played chord.
> the defects of this tuning method became evident and the more flexible “well-tempered” tuning scheme was devised. This ensures that the ratio of pitch between every two adjacent notes is precisely the same.
The author seems to have confused well-temperament and equal temperament.
It is also odd that he calls just intonation a “simplification” of Pythagorean tuning.
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...
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?
I only listened briefly on laptop speakers, but it did sound like sometimes the same note of a chord would play at a different octave, almost like it was trying to do voice leading from the previously played chord.
A recent blog post on thatsmaths.com was about Tonenetz, a diagram of harmonic relationships of notes. Tonenetz means 'tone network' in German :-)
Do you have a link to the post in thatsmaths?
https://thatsmaths.com/2025/10/16/music-and-maths-are-inextr...
> the defects of this tuning method became evident and the more flexible “well-tempered” tuning scheme was devised. This ensures that the ratio of pitch between every two adjacent notes is precisely the same.
The author seems to have confused well-temperament and equal temperament.
It is also odd that he calls just intonation a “simplification” of Pythagorean tuning.