Fred wrote: >I've written this opinion before: use a thinner string. The thicker >string requires >more tension to get to the given pitch (same string length obviously being a >given). For those with a bent for math and physics, the mass of the >string is the >significant factor here. While thinner wire has a bit more strength per cross >sectional area (due to the working of the wire in the drawing >process), that factor >is relatively irrelevant. Agreed. As I wrote previously, the improvement is minimal for high carbon steel wire, but there is some increase with decrease in gage size even with steel wire (see the old Newton thread discussion). >Think of it this way: a "perfect scale" would have a single diameter wire, >doubling length every octave. Every note would have exactly the same tension >in this theoretical scale. Depends how you define "perfect scale". A perfectly Pythagorean scale exists independent of any consideration of tensions. All that's required is equal stress on every note and lengths that double every octave. This can be achieved just as well with different gages and tensions, so the requirement of same tension throughout is irrelevant. Wire strength is best related to stress, which is more of less the same for any diameter (modulo the slight increase with decreasing diameter discussed above), rather than tension. >So we make a compromise curve that foreshortens lengths to less than 2:1 per >octave. If we used a single diameter wire on this foreshortened scale, the >tension would drop dramatically from top note to bottom, with resultant tone >being awful. So, to compensate, we increase the diameter of the wire by >increments - so that tension will stay fairly high (a thicker >diameter wire requires >a higher tension to produce the same pitch). Although this is the accepted wisdom I don't agree with this being the reason for a same-gage scale sounding bad. Even a Pythagorean scale with identical diameter wires and hence tensions would sound bad. Thicker wires in the bass are needed to compensate for the nonlinearity of the human ear (psycho-acoustics), so the bass sounds as loud as the treble. You need comparatively more acoustic energy in the bass strings or they will be perceived as weak and thin sounding. >It's a counterintuitive concept, but one which I learned many years ago from >painful experience with a badly scaled harpsichord, and a lesson I haven't >managed to forget since. "Try it, you'll like it" <g> Yes. And with historical iron wire the tensile pickup is not insignificant - you gain about 1/5 semitone per semitone decrease in diameter. This is the factor which allows treble scales to be stretched in fortepianos and harpsichords in the last few notes. Stephen -- Dr Stephen Birkett Associate Professor Department of Systems Design Engineering University of Waterloo Waterloo, Ontario Canada N2L 3G1 E3 Room 3158 tel: 519-888-4567 Ext. 3792 fax: 519-746-4791 PianoTech Lab Room E3-3160 Ext. 7115 mailto: sbirkett[at]real.uwaterloo.ca http://real.uwaterloo.ca/~sbirkett
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