Talk:Chain-of-fifths notation

What about 53edo?

Do you supposed that this circle of fifths notation makes sense for 53edo at all, or is it really completely impractical? I mean, I have an idea as to how I would do it... --Aura (talk) 00:17, 15 November 2020 (UTC)

It's a subset of ups and downs notation. It's possible to notate any "single-ring" EDOs, in which every note can be accessed by a stack of fifths.

Btw it's never dictated that only double sharp to double flat should be used. Without higher-order sharp/flats, larger edos are very limited. 26edo, for example, requires Gx to Abb to access every note in the key of C major. Now modulate to any key with more than three accidentals and boom. FloraC (talk) 06:15, 15 November 2020 (UTC)

For the record, I have made a two-ring circle chart for 24edo before, and I will say that I have a few tricks for positioning the additional rings relative to one another. If your main ring starts with C-Natural, and F-Demisharp and G-Demiflat are both on the same secondary ring, then the secondary ring is positioned so that F-Demisharp and G-Demiflat are the same distance from C-Natural. However, if your main ring starts with C-Natural, and F-Demisharp and G-Demiflat are on two separate rings, then the two separate secondary rings are perhaps best aligned with the primary ring so that F-Demisharp, C-Natural and G-Demiflat form a straight line.

Sufficient condition

The decisive point for the usability of this notation is, that the representations of octave and fifth are relatively prime. I'd like to introduce this without making the article to a mathematical text, maybe there is somebody willing to help. I also wonder if the precision of the fifth representation is relevant at all. This would open the discussion about really interesting cases like 23edo. --Xenwolf (talk) 12:13, 15 November 2020 (UTC)