On Apr 19, 2010, at 5:53 AM, Laurence Libin wrote: > It's well known that as far back as the Renaissance equal > temperament was one of many options among which musicians could > select depending on taste and the demands of the music. It still is, > but precise 100-cent semitones remain, it seems to me, a theoretical > ideal seldom achieved (or maybe even desirable) in practice except, > perhaps, on electronic instruments. At any rate I think it's fair to > say that true ET is less prevalent on pianos today than many people > suppose, and that euphonic results, however achieved, matter more > than strict adherence to any theoretical model. Do we agree? > Laurence Well, I 'm not sure we know a whole lot about what results are actually euphonic, other than as a matter highly individual personal opinion. And the more precisely one tries to define ET, the less clear it all becomes. Most of the talk about using aural means to adjust ETD generated tunings is actually adjustment of what is closer to scientific ET to make the predicted beat rate progressions happen on an instrument with uneven inharmonicity. Real, scientific ET would be setting an ETD at 0.0 for all notes and tuning fundamentals. What tuners aim at is a "virtual reality" creation, what we might call "aural ET.". I do think it is a very interesting question whether a precise "aural ET" is preferable aesthetically to a somewhat randomly imprecise one, or to a subtly adjusted one in which adjustments are made according to a planned pattern. Experience suggests that the difference is pretty subtle, unnoticeable to most people until the parameters become quite wide (for a piano tuner). BTW, we should bear in mind that acousticians say the least perceptible difference of pitch is in the realm of 6 cents or so, varying somewhat up and down the pitch range. This has been established by a number of independent tests, in which the subjects are to say which of two pitches is higher than the other. This is, of course, two pitches played separately in sequence. And I haven't been able to find out anything about the type of subject selected for the tests (I know I can hear smaller differences in most circumstances). But it is very suggestive, and puts our agonizing over tenths of a cent into perspective. Regards, Fred Sturm University of New Mexico fssturm at unm.edu
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