4 ms·
The Tonnetz
- mci 1y agoA recent blog post on thatsmaths.com was about Tonenetz, a diagram of harmonic relationships of notes. Tonenetz means 'tone network' in German :-)
- gus_massa 1y agoDo you have a link to the post in thatsmaths?
- mitchbob 1y agohttps://thatsmaths.com/2025/10/16/music-and-maths-are-inextricably-intertwined/ https://thatsmaths.com/2025/10/16/music-and-maths-are-inextr...
- pasteldream 1y ago> 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.
- tshaddox 1y agoI 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 https://www.garygarrett.me/?p=342 More introduction to the lattice: https://www.garygarrett.me/?p=995 https://www.garygarrett.me/?p=995 https://www.garygarrett.me/?p=1632 https://www.garygarrett.me/?p=1632 https://www.garygarrett.me/?p=1696 https://www.garygarrett.me/?p=1696 Some comparison audio between equal temperament and just intonation: https://www.garygarrett.me/?p=1812 https://www.garygarrett.me/?p=1812 Some songs with lattice animations: https://www.garygarrett.me/?p=103 https://www.garygarrett.me/?p=103 https://www.garygarrett.me/?p=1253 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-Expression/dp/0892815604 https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...
- manbitesdog 1y agoAs 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 1y agoI 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.
- kazinator 1y ago"Almost Tonnetz" fail: https://en.wikipedia.org/wiki/Stradella_bass_system https://en.wikipedia.org/wiki/Stradella_bass_system Accordion buttons have a row of roots with major thirds off on a diagonal, but in a shifted way that you don't have minor thirds on the opposite diagonal. E.g. there is no CEG triangle. If the layout did that, you could hit minor and major triads chords by pressing triangles on the first two rows.
- pasteldream 1y agoWhy did they make it like that? I assume accordion makers were aware of the convenience of the harmonic table layout, and had good reasons for choosing something else.
- kazinator 1y agoFor the background understanding (minus interactive play) the Wikipedia page is a better starter: https://en.wikipedia.org/wiki/Tonnetz https://en.wikipedia.org/wiki/Tonnetz Also shows the Tonnetz in the configuration where fifths are horizontal.
- npilk 1y ago> Discovered by Euler Figures...
- deleted 1y ago[deleted]
- shannifin 1y agoLearned about the tonnetz (among other models) from the book "Audacious Euphony"... Challenging (and unfortunately too expensive now), but fascinating stuff... https://www.amazon.com/dp/019977269X https://www.amazon.com/dp/019977269X