John's Temperament v2

I squeezed a few more good intervals out of my scale by sustituting 7/5 for sqrt(2). The scale is perfectly symmetric/mirrored except for the 7/5 tritone (although 7/5 does go with 2/1).

1/1
16/15
10/9
6/5
5/4
4/3
7/5
3/2
8/5
5/3
9/5
15/8
2/1

I tempered this scale and this is what I got...

0.0c
115.119c
188.333c
314.794c
388.008c
498.045c
575.736c
701.955c
811.992c
885.206c
1011.67c
1084.88c
1200.0c

Of all possible intervals an octave or less wide (unison and octave and 11 in between), over 12 keys you have 156 (13x12) possible intervals and with my scale 105 of these are good. That's a hit rate of just over 67%. All these intervals are within 6.775877 cents accuracy. More on this later.

John.

John>"Of all possible intervals an octave or less wide (unison and octave and
11 in between), over 12 keys you have 156 (13x12) possible intervals and with my scale 105 of these are good. That's a hit rate of just over
67%. All these intervals are within 6.775877 cents accuracy. More on
this later."

Nice work! :-) At least mathematically...that really does sound like you are "beating 12TET" far as accuracy for major second or larger ratios.
However, I still think you can hit 80% even with the full 12 tones...particularly if you use alternative fifths like 22/15 and 50/33 and 13/9 (they "look" fairly large but try them...they sound much less dissonant than their high-numbered fractions would seem to imply).

It seems, minus the gap between 9/5 and the 4/3 on the next octave (which turns out to be 1.46666 AKA 22/15, one of the good alternative 5ths IMVHO)...your scale is basically a mean-tone scale. IE a perfect spiral of fifths...but I'm confident by deviating from that spiral in a few more places and using more alternative 5ths you can iron out quite a few impure intervals in other places. I still say you can hit 80% if you use alternative 5ths wisely. :-)

-Michael