You nailed my next probable question - how to they combine when nonconsecutive?

First of all, though 12- and 15-edo aren't consecutive edos, they're consecutive equal divisions of 1\3 octave (their gcd), since 12-edo divides 1\3 octave into 4 equal parts, and 15-edo divides 1\3 octave into 5 equal parts. So if we shift our focus a little, we can see them as consecutive.

I think it generally makes sense to view two edos as the equal division of their gcd when comparing them.

Some general thoughts:

The largest difference an edo's tone could have to the nearest adjacent tone from another edo is halft the step size from that other edo. If the first edo is even, and the second one is odd, this will always (and only) happen in the middle (between 1\2 octave and the adjacent notes from the odd edo).

However, the largest difference between a tone from the odd edo and the nearest adjacent tone from the even edo can still be larger (example: 2-edo and any large odd edo, like 53).

In addition, the difference doesn't have to increase continuously towards the middle, even if it is largest there.

I assume the reason for the described behaviour of consecutive edos is related to the fact that I compared them by stacking single step intervals, and that these used generators are farey pairs.

A single step in 11-edo can be written as 1\11 (= 1/11 octave), and a 12-edo step as 1\12. A farey pair is a pair of two reduced fractions a/b and c/d with a*d - c*b = +-1. So 1\11 and 1\12 are a farey pair, because 1*12 - 1*11 = 1, and the same holds true for any single step intervals from consecutive edos.

If we look at 13- and 19-edo, we realize that 1\13 and 1\19 is not a farey pair. However, 2\13 and 3\19 are, since 2*19 - 3*13 = -1. So, let's compare them by stacking these generators (2\13 = 38\247, and 3\19 = 39\247):

13-edo: 0 38 76 114 152 190 228 266=19 57 95 133 171 209 247=0

19-edo: 0 39 78 117 156 195 234 [273=26 65 104 143 182 221] 260=13 52 91 130 169 208 247=0

Here again, the difference is largest in "the middle":

- The greatest difference between a 13-edo note and the closest 19-edo note is between 12\13 = 228\247 and 18\19 = 234\247 (or between 1\13 and 1\19), i.e. 6 steps in 247-edo = 29.1 cents.
- The greatest difference between a 19-edo note and the closest 13-edo note is between 8\19 = 104\247 and 5\13 = 95\247 (or between 11\19 and 8\13), i.e. 9 steps in 247-edo = 43.7 cents.

Note that both 26- and 19-edo support meantone/flattone, and 3\19 and 4\26 = 2\13 are the wholetones generated by stacking two meantone/flattone fifths. That's why stacking 3\19 and 2\13 leads to similar scales. Also note that the "bad representation" of 11\19 in 13-edo isn't a bad thing, because 11\19 is close to 15\26 (also a farey pair!), the meantone/flattone fifth that is "missing" in 13-edo, and makes a nice addition. ;)

If we generate a 13-tone MOS by stacking 3\19 wholetones (6 upwards, 6 downwards), it should contain the notes that are closest to 13-edo:

0 1 3 4 6 7 9 10 12 13 15 16 18 19

The remaining notes from 19-edo are probably* closer to notes that are in 26-edo, but "missing" in 13-edo:

2 5 8 11 14 17

* too lazy to check :P

Are you familiar with moments of symmetries, and the Stern-Brocot tree (aka Wilson's

Scale Tree)? The latter is pretty useful for finding MOS's, farey pairs, or other generator pairs that are similar in size and lead to same or similar temperaments.