Tonnetz algorithms

I'm looking for applied algorithms for Riemannian tonnetz.

I was thinking first of the "big bang" approach with some of the 3D projections of tonnetz, but those are overshoot.

• Well, I have no idea about this side of music theory, but I'm interested to see the answers :-) Jun 1 '14 at 15:37
• Not sure what the question is. Do you want to know how to construct an alogorithm that projects a Riemann tonnetz unto a hypercube? Or do you want to know what the applications are of such a projection? This article does some stuff with projecting tonnetz perhaps the references are useful to you: dmitri.mycpanel.princeton.edu/tonnetzes.pdf Jun 1 '14 at 17:14
• +0 right now because I have no idea what's being asked. I usually abstain from voting on questions outside my understanding, so I'm not necessarily unhappy with your question, just underqualified to evaluate it. However, unless you're confident that enough other people have knowledge about the type of music theory you're asking about, you might get better responses if you edited your question to provide some background. Jun 1 '14 at 18:24
• What do you want to achieve with it? I recently caught on tonnetz, and I just took a sheet of paper, drawed it. I'm using cut out paper templates in the shape of a key (cut out that captures all notes that belong in one key) Jun 3 '14 at 18:29
• I've used the tonnetz concept to visualize chords and chord progressions, so I could see creating an algorithm to draw and animate a tonnetz. But as Roland asks, what is your goal? Music analysis? Visualization? Algorithmic composition? One problem I've always had with the tonnetz is that it does a poor job of visualizing melodic motion so voices appear to jump around chaotically (which is OK -- that's not it's purpose). I read one description, though, that compared voices moving on a tonnetz to chess pieces on a chess board. I'll have to see if I can find it again. Jun 3 '14 at 19:22

2 Answers

I'm writing them in a spreadsheet. So far so good but it's far from complete.

https://docs.google.com/spreadsheets/d/1AL18KVDIsJvRTpW567dVlJRfrORWA9k_sh6rBYqu5lc/edit?usp=sharing

• Where are the sharps? Dec 25 '15 at 22:06

I know it's been a couple of years, but I finally got around to writing the complete tonnetz algorithm. This generates a non-standard tonnetz based on Pythogorean right scalene trianges (of ratio 3:4:5).

Salient features: 1). The Circle of Fifths is helical (planar projection) 2). The pitch classes align in the piano orientation 3). Each Key & Pitch Class is given its own domain. 4). Keys are incident to the COF 5). PC's are the same as a chromatic scale

Not shown: 1). A Fifth is the hypotenuse of its associated Major & minor thirds 2). Major & minor thirds form a right angle 3). The sweep of scales are the hypotenuse of a Tritone & a Major 3rd.

[Spreadsheet tonnetz algorithm] (link:) https://docs.google.com/spreadsheets/d/1ilMDmSrsBcM_7rjvHK_7_nKFIGhlZQGCWJutMDho3Qo/edit?usp=sharing

Illustrated version: