Uath-72 generalized keyboard

>
>>>Great! What is this generalized keyboard you're getting? I had a hell of
>>>a time stretching my hands to play that piece.
>
>>Everybody buy one!
>
>>http://www.catalog.com/starrlab/uzone.htm
>
>This site contains no price or ordering info. Can someone help?


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First of all, I can't believe how much interesting material there was in
the last two tuning digests, and it might take me a while to reply to
all of it (if I ever do). But I think the first message in TD 1418 was
sort of mostly directed at be, so I'll take that one on first.

>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?)

Yes.

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

If the 7:4, 7:5, AND 7:6 are good, and we're talking about an equal
temperament with pure octaves, then the ratios of 5 and 3 can't be that
bad.

>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.

In that case, I should shut up. I've only heard "Detwelvulate." The
whole of Blackwood's etudes were made more powerful to me by the ending
of the last one (in 19), which rocks.

>>>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?

Easy -- 12-tone equal temperament. The best 11/8 is off by -48.68 cents,
the best 9/8 is off by 3.91 cents, and the best 11/9 is off by 47.41
cents.

>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.

To me, the triads in 15-equal on the classical guitar sound almost as
good as those in 12-equal. This is partially due to the very pure minor
thirds. With consonant triads, the 720 cents interval is certainly
functioning as a 3/2. It has very little chance of being interpreted as
any other just ratio.