TUNING digest 1417

>>They want a tuning be consistent and fairly accurate at a given limit
>>before considering it usable at any higher limit.
>
>Note that in my paper, as clarified by you (Carl Lumma), I do not care
>about the 5-limit accuracy of 22tET, only that its 7-limit accuracy be
>at least as great as the 5-limit accuracy of 12tET.

Yeah, but doesn't the 7-limit accuracy depend somewhat on the 5-limit
accuracy? (Isn't the 5-limit a subset of your 7-limit in that example?)

Are you willing to accept a tuning that has good 7 ratios but horrible or
non-existant 5 and 3 ratios?

>>On the right we have those who insist that any ET is usable and "good".
>>Students of this school include Ivor Darreg and Easley Blackwood.
>
>Actually, Easley Blackwood thinks that 12tET is much more usable and
>"good" than any other tuning.

He told me as much on the phone. Indeed, the majority of his work is in
12. But he does believe that any ET is usable. That's all I said. He may
not believe it to the extent that Ivor did...

>The funny thing is that Blackwood's microtonal music is generally much
>better than Darreg's.

Well, this is a subjective thing, but I agree. But I will note that...

1) The best of Ivor's stuff is roughly as good as the best of Blackwood's.
2) The majority of Ivor's work is un-recorded.
3) That in any case, the differences in quality don't have anything to do
with how usuable they thought various et's were.

>>the best 11/9 will be off by the absolute value of the sums of
>>the errors of the 11/8 and 9/8, consistency or no
>
>If you mean the best 11/8 and the best 9/8, then that might not be true,
>although consistency will guarantee that it's true. If you don't mean
>the best 11/8 and the best 9/8, then what do you mean?

That's what I mean. Can you give an example where it's not true?

>>On the other hand, 25 isn't consistent past the five limit, and it has
>>horrible fifths, but its strong 3's and 7's make it great for the
7-limit, >>as Paul Rapaport proved in his "Study in Fives".
>
>Did you mean horrible thirds or strong 5s?

I was badly in need of sleep when I wrote that. I meant that 25 has good
5/4's and 7/4's, but un-usable 3/2's. [That is, horrible fifths, but strong
thirds and sevenths]

Now you may point out Blackwood's assertion that 3/2 in 15/oct is not
un-acceptable, and that this is the same 3/2 in 25. You may point to how
it's used in the Suite for 15-tone Guitar, a work which I absolutely love
to bits, and have the score for.

I will say that the 720 cent interval may function as the dominant in many
parts of that suite, but it does not function as a 3/2. I cannot imagine
any two intervals more sharply contrasting in sound.

>I am writing a thesis on JI notation and so far my research shows most JI
>composers to be in the US, and those who compose microtonally in Europe to
>be using various EQ divisions.

Partch.

C.