EDOs 12, 18, 19, 22 and 23 compared

18EDO has the following good intervals within 6.776 cents accuracy: 9/8, 7/6, 12/7, 13/7 and 2/1.
I found only two triads (an octave or less wide) where all the dyads in the triad are within 6.776 cents of the five good intervals listed above...
1, 5, 19
1, 15, 19.
If the keys in 18EDO are named 1 to 18 then 19 is the octave. Of course these triads will work in all keys.

23EDO has the following good intervals within 6.776 cents accuracy: 9/8, 7/6, 6/5, 11/7, 5/3, 12/7, 11/6 and 2/1 (more than any other EDO less than 27).
I found six triads (an octave or less wide) where all the dyads in the triad are within 6.776 cents of the eight good intervals listed above...
1, 6, 21
1, 6, 24
1, 7, 24
1, 16, 21
1, 18, 24
1, 19, 24
If the keys in 23EDO are named 1 to 23 then 24 is the octave. Again these triads will work in all keys.

22EDO has the following good intervals within 6.776 cents accuracy: 7/6, 5/4,
9/7, 11/8, 8/5, 12/7 and 2/1. Not only does it have eleven good triads but also has four good tetrads. Very impressive. Again, all the dyads in each chord are within 6.776 cents of the seven good intervals listed above.

1, 6, 11, 16
1, 6, 16, 23
1, 8, 16, 23
1, 8, 18, 23
1, 9, 16
1, 11, 18
1, 6, 11
1, 6, 16
1, 11, 16
1, 6, 23
1, 16, 23
1, 8, 16
1, 8, 23
1, 8, 18
1, 18, 23

If the keys in 22EDO are named 1 to 22 then 23 is the octave. Again these chords will work in all keys.

19EDO has only four good intervals within 6.776 cents accuracy: 6/5, 5/3, 13/7 and 2/1 so it's unlikely to compete with 22EDO.

12EDO also has only four good intervals within 6.776 cents accuracy: 9/8, 4/3, 3/2 and 2/1.

So it seems that not only is 22EDO the most versatile EDO less than 25 but it has more than twice the number of good triads or tetrads (15, 4 tetrads and 11 triads) than any other EDO less than 25.

So if I had to choose an EDO it would be 22, by a mile.

John.