source file: m1400.txt Date: Wed, 29 Apr 1998 15:39:19 -0400 Subject: RE: Difficulties in Piano Construction From: "Paul H. Erlich" Gary wrote, >I have heard that too, from Ivor Darreg, who did a lot of piano tuning >in his day. If I remember correctly, he 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. 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. (La Monte Young's _Well Tuned Piano_ = >deliberately uses a lower tension to reduce, but not >eliminate the stretching. That seems contrary to the evidence as well as scientific theory. Check out _Change in the Characteristics of Piano Tones under Different Concert Pitches_ by Tomoyasu Taguti and Osamu Tokuyama Konan University, Higashinada, Kobe, Japan presented at University of Edinburgh INTERNATIONAL SYMPOSIUM ON MUSICAL ACOUSTICS 19-22 August 1997: "This paper reports an acoustical measurement and a listening experiment on the tones of a piano where A4 is tuned to 436Hz(L:low), 442Hz(N:normal), and 445Hz(H:high)" "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.)" "the inharmonicities in cents were {20(L), 17(N), 10(H)} at the 10th partial, and {45(L), 42(N), 35(H)} at the 20th partial."