<I realize this is not re-inventing the wheel, but to the aural tuners out there, do you expand your temperament and why.?.? Phil> I don't see the need. If the faster-beating intervals, including those wider than an octave, progress smoothly with no big jumps in beat rate, and if the slower-beating ones, including twelfths, double and triple octaves, sound good (relatively beatless), why spend longer than necessary on the temperament, unless of course, there are weird scale anomalies? The tuning you leave on the piano is one big "expanded temperament". <<This is the area of the piano which requires the utmost in precision. Even an error of 1 cent is audible and does affect the quality of harmony. The tolerance for an error on the PTG Exam in this area is 1 cent. (B. Bremmer)>> I read somewhere that the smallest pitch difference the average person (including most musicians and some tuners) can hear is about 3 cents, so when I read tuning articles where a few tenths of a cent are being quibbled over, I just have to wince. Now if all my customers were concert artists, that'd be different.... This is not to say I don't agree with Bill Bremmer's other statement that "A really well tuned piano requires a great deal of precision. The old fashioned ways of setting a temperament with 4ths & 5ths, then simply tuning out the octaves will produce mediocre if not very poor results by today's standards." --David Nereson, RPT, Denver --David Nereson, RPT
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