I just discovered what a Tonnetz is, and I'm amazed by the treasure of information that is hidden in this diagram:

Tonnetz on wikipedia

Among others, it's easy to find major/minor/augmented/diminished chords, or the diatonic chords for any given key (more examples in the "25 Practical Applications of the Tonnetz Chart" video.)

I'm curious about the numbers below the notes, though. They seem to represent the number of semitones above A♭, written in duodecimal (with χ=10, Ɛ=11).

Is there any particular reason why A♭ could have been chosen, or was it completely arbitrary? C might have been a more natural choice, for example.


After @Richard's answer, I tried to update the chart, using C as reference. Work in progress:

Tonnetz with C as reference

  • Possibly the central black key on piano, in which case, it could have been D instead? Duodecimal 'cos there's 12 notes.
    – Tim
    Sep 4, 2022 at 14:40
  • 1
    Maybe there's just something about A getting assigned the number 1 that looks appealing?
    – Dekkadeci
    Sep 5, 2022 at 12:01
  • @Dekkadeci: Interesting, I didn't think about that. But then, B is 3. :-/ Sep 5, 2022 at 12:03

2 Answers 2


There's nothing inherent in the Tonnetz that suggests A♭ should be particularly emphasized as a point of reference, no.

Now, I would argue that C being in the middle of this Tonnetz likely is intentional, because it limits the number of doublesharps and doubleflats on the outside boundaries. Imagine, for example, that C in the middle was actually a D♭; this would result in a B♭♭♭ in the upper-left corner! But this C in the middle could have just as easily been the 0 reference point instead of A♭.

It may be that this particular Tonnetz was being used as an analytical tool for a piece in A♭, in which case the semitonal measurements above this pitch add an extra layer of context.

  • 1
    Thanks a lot, this makes sense. I translated the numbers with Inkscape, so that they use C as reference. Do they look correct? i.sstatic.net/8OsCT.png Sep 4, 2022 at 20:08
  • @EricDuminil It all looks great! And I'll throw in a vote for you replacing the Wikipedia version with this one!
    – Richard
    Sep 4, 2022 at 20:13
  • Nice. It's been a while I didn't upload anything to Wikipedia, I'll check the process. Sep 5, 2022 at 20:56
  • I'm apparently not yet allowed to modify wikipedia pages, and would need to be certified first. Are you allowed to? Would you be interested in uploading the updated Tonnetz in C? Jan 21, 2023 at 14:00

Richard --

If you are interested in the tonnetz, the I encourage you to read Wikipedia's article on Dynamic Tonality (https://en.wikipedia.org/wiki/Dynamic Tonality), and to watch its Video #4.

The Tonnetz is usually presented as an abstraction. That's how it was presented in the YouTube video that you cited. Many of the comments on that video were along the lines of "who needs a tonnetz? Just look at the fretboard!" For guitarist, that is not an unreasonable perspective.

However, the tonnetz is a tangible artifact of the octave-reduced Stack of Fifths that generates the Wicki-Hayden note-layout (see the Dynamic Tonality videos).

These videos show that, no, there is nothing special about A-flat.

Please let me know if you have any follow-up questions.


Jim Plamondon

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