source file: m1394.txt Date: Thu, 23 Apr 1998 14:46:48 -0400 Subject: RE: JI Tuning Resolution From: "Paul H. Erlich" >Bowed strings could be a prominent exception, but I doubt if anybody >could convincingly make that case for most any other orchestral instrument. >It's almost trivial to demonstrate that that's not true of winds in >general: All you have to so is play them onto an oscilloscope; in many >cases, you can quite clearly see the higher harmonics "walking" through the >oscillogram. I'm afraid I have to disqualify the oscilloscope here. The oscilloscope will have a certain finite sampling time and the period of the waveform, varying slighlty as it does, will never be precisely matched to this sampling time. The oscilloscope utilizes a certain approximation of Fourier's theorem, not the theorem itself. If you study the mechanics of a 1-component driver, such as a bow, reed, or lips, you will understand that regardless of the extent to which the resonant modes of vibration of the instrument deviate from a harmonic series, the driving mechanism will force the waveform to become periodic, which implies exact integer overtones. Don't confuse the resonant modes of vibration with the spectrum of the sound (the two are closely related but not identical!) Looping involves the same timing problems as oscilloscope sampling. J. Kukula had more to say on this subject, is he around? > . . . JI does what it does more in the lower harmonics >than the upper ones I think Harry Partch would disagree with you there. To the extent that higher harmonics are musically relevant at all, the associated intervals require more precise tuning in order to engage those harmonics than do the intervals associated with lower harmonics. On the other hand, it is true that the difference in sensory consonance is greater when you detune a simple ratio by a small amount than when you detune a complex ratio by a small amount. But if you are using more complex ratios as consonances, their sensory consonance is only just barely enough to justify that usage, so you'd better be careful how you tune them! (A simplification, no doubt, but I thought I had to make the point concisely here).