> >>>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?
SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: Reply to Carl Lumma PostedDate: 27-10-97 21:51:25 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 27-10-97 21:50:34-27-10-97 21:50:35,27-10-97 20:51:10-27-10-97 20:51:11 DeliveredDate: 27-10-97 20:51:11 Categories: $Revisions:
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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.