just one interval... I mean...

>>No, but it may be close enough to help the triad by the effect I mention...
>>
>>I find RMS to be good enough conceptually and empirically for most
>>purposes.
>
>Carl, you seem to be contradicting yourself.

The 720 cent fifth has an RMS error of 18, the 15tET triad of ~14. Where's
the contradiction?

>Compare the 15-tET major triad with one whose pitches are 0 395 720. Which
>one has lower RMS error? Which one has a close-enough-just-interval?

The one-just-interval observation is supposed to make small differences
when the RMS is nearly the same. It is not supposed to significantly
change the RMS ranking. In this case, a brief listening test found the
15tET triad slightly better despite the slightly lower RMS of your chord.
Do you disagree?

>>In particular, it may be better, when the RMS error is in a certain range,
>>to keep one or more interval just and heap all the error onto the other(s)
>>than to spread the error out. I haven't had time to test this, but it
>>could make sense -- the just interval(s) help lock down the periodicity of
>>the chord.
>
>OK, but then you have no reason to stick to RMS error.

I like RMS for the same reasons you do.

>Why is it that 6:5 can lock down the periodicity but 7:5 can't?

The 7:5 should be able to, but the power to lock should go down as the
limit goes up. I'm also suggesting that the :4 intervals are more
important. I did say all 5-limit intervals could be weighted equally, but
perhaps the 5:4 is slightly stronger than the 6:5, and perhaps 3:2 is
stronger than either. But I doubt these distinctions will make much
difference until the 7-limit.

-C.