source file: m1399.txt Date: Tue, 28 Apr 1998 14:33:08 -0400 Subject: RE: JI Tuning Resolution From: "Paul H. Erlich" >Brass instruments really are aperiodic. I read about this since >the last time it came up. The worst tuned partials are the low >ones for a conical tube. Even valve horns rarely play the >fundamental for this reason. > Graham Breed This is another case of confusing the modes of resonance with the spectrum of an actual tone. The former is not a harmonic series but depends on the shape of the instrument. Good brass makers sacrifice the first resonance so that the others can come close to a harmonic series. Still, the lowest resonances are typically dozens of cents off a harmonic series. But the tone itself contains exactly harmonic partials. If you don't believe me, read Dave HIll's recent post, where he found that brass partials are a fraction of a cent off of harmonic, which is far less than the dozen cent type errors in the lowest modes of resonance. Even if you don't believe that Dave Hill's methodology led to the errors of a fraction of a cent, clearly the modes of resonance and the spectrum of a played tone are clearly two different things. The reason the "fundamental," or more precisely the lowest resonant mode, isn't used by horn players is that none of its harmonic overtones coincide with resonances of the instrument. Hence mode-locking can't occur, and a steady tone can't be produced, let alone one with a nice timbre. A different, quiet "fundamental" can, however, be played by a skilled lipper, which is of the "subharmonic" variety: The harmonic overtones are engaging the resonances of the instrument, keeping the lips vibrating in a steady pattern, while the fundamental is far from the lowest resonance and is only weakly amplified at best.