source file: m1400.txt Date: Wed, 29 Apr 1998 14:57:40 -0500 (CDT) Subject: RE: Difficulties in Piano Construction From: Paul Hahn On Wed, 29 Apr 1998, Paul H. Erlich wrote: > Gary wrote, > > If I remember correctly, [Ivor] said that it would tend to go out > >of tune more quickly in anything other than equal-temperament. > > If the total tension of the strings were held constant, then there is no > reason that tuning to an unequal tuning would lead to less tuning > stability than one had in equal temperament. That makes sense to me--but I'd hate to go against the hands-on experience of a tuner. Ed Foote, what say you? (IIRC, Ed was the tuner on the list who was using unequal temperaments on modern pianos, yes?) > Daniel wrote, > >There are arguments about ET and the piano based upon > >the stretched intonation of the partials of the > >rigid piano wire. I have great trouble in supporting > >these arguments historically, however, because the > >early pianos were wired at a much lower tension > >than modern instruments and were considerably less > >stretched. [snip] > > That seems contrary to the evidence as well as scientific theory. [snip] > > "Physically, . . . the inharmonicity of single piano strings . . . > becomes decreased as the pitch is raised. ([This] is implied in fact by > the formula of inharmonicity by Fletcher.)" As I recall, the greater harmonicity that results from greater string tension is the reason that historical keyboard instruments are scaled so that the strings are very near their breaking stress, regardless of the metal used. Occasionally we have discussions on the Harpsichord list about this. Intuitively, the phenomenon can be explained this way: as string tension increases, the component of the restoring force in the vibration caused by string tension (ideal-stringlike behavior) increases, becoming greater in relation to the component caused by string stiffness (bar-like behavior), which remains constant--and ideal strings vibrate harmonically while bars do not. --pH http://library.wustl.edu/~manynote O /\ "Churchill? Can he run a hundred balls?" -\-\-- o NOTE: dehyphenate node to remove spamblock. <*>