I've been comparing the notation of various equal scales to traditional

12-tet notation, but I realized that I should probably be comparing them to

7-tet, especially with a scale that has good major and minor thirds. In

12-tet, three of the (unmarked) thirds are major and four are minor, but

all of the thirds in 7-tet are the same. So I briefly experimented with

16-tet notations to find one that represents major thirds as uniformly as

possible, since the major third is the best consonance in 16-tet. This is

what I came up with:

C Fb Eb C# D E F Gb Ab F# G A Bb Cb A# B C

Although it's not a very good notation scheme, all but one of the thirds

are major (which is as good as you can get with anything other than 7-tet

thirds). A better notation system for my needs is this:

C C# D D# Eb E E# F F# G G# Ab A A# B B# C

Three of the major thirds are written with sharps; in fact, all of the ones

that are written with sharps in 12-tet except for D-F. And just as in

12-tet, all but one of the fifths (D-Ab) are written without accidentals.

So it's at least as good for 16-tet as traditional notation is for 12-tet,

in comparison to the 7-tet "ideal".

Daniel Wolf's "neo-pelog" scale is just as good, and it has the interesting

property that the major and minor thirds are the exact opposite of the

traditional major scale.

I went back to 20-tet to see what I could come up with. This is a scale

that has similar properties to the first 16-tet scale above; all but one of

the thirds without accidentals are "major" (actually closer to 11/9).

C Cz C# Dh D Eh E Ez F Fz F# Gh G Ah A Az A# Bh B Ch C

(It also makes a good notation for 10-tet.)