source file: m1419.txt Date: Mon, 18 May 1998 15:38:57 -0400 Subject: Reply to Carl Lumma From: "Paul H. Erlich" 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.