<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> Kent .. you might find Harold Conklins article "Design and tone in the mechanoacoustic piano"... parts 1,2, and 3 available from  JASA.. interesting. Also the articles in "5 Lectures on the Acoustics of Pianos" edited by Askenfelt has a whole bunch on this. This second is tough to get ahold of tho. The first can be ordered from <a href="mailto:sosmail@carl.org">sosmail@carl.org</a> Richard Brekne I.C.P.T.G.  N.P.T.F. Bergen, Norway   Kent Swafford wrote: <blockquote TYPE=CITE>Ron Nossaman wrote: > Not that I'd do any better gathering data myself, but at least I >could determine first hand why I was still confused. I played around with >an old Strobo-Con in a killer octave a while back to see what I could see. >With one string, the pitch went up on the attack and stayed high for about >1.5 seconds, then drifted down a bit. Adding the second string, the attack >pitch height was the same, and the decal pitch was the same (as nearly as I >could tell), but the dwell time at the higher pitch went to about a second. >Adding the third string left the pitches the same again, but the high dwell >fell to a little over a half second. No real measurement on the time >durations, just tuner's relative time sense. This was with one of my >boards, and I haven't gotten to try it on anything else, so there's nothing >remotely informative here, though I was surprised at what I saw. I have no information to offer as to _why_ "unison coupling" exists, but I thought I would chime in here that my observations match yours, Ron, fairly closely. The phenomenon exists on many pianos. I describe it like this: The frequency of vibrating piano strings is not stable, but tends to lower as the string continues to sound. In electronic music, the graphic representation of the changing amplitude, frequency, or other measurable character of a tone is known as the "envelope." My observation then is that strings sounding together have little or no frequency that is not present when the strings are sounding singly. It appears rather that the envelope, that is, the change in frequency of the vibrating strings over time, is accelerated for some reason when the strings sound together. In other words, the flatness observed when strings sound together may just be because the strings get to the flat part of the envelope faster, fast enough that the sharper part of the envelope goes by fast enough that it can be missed. For what it is worth, an explanation for why this phenomenon was not observed and described until just a few years ago might be that, if the phenomenon occurs throughout the scale, as I believe it does, then, if the temperament throughout the scale of the piano is tuned with single strings, then the temperament of the piano with all strings of the unisons sounding will simply be "shifted" slightly flat with few ill effects to the temperament. It also is possible that the apparent frequency shift caused by unison coupling is as small or smaller than the normal frequency shift caused by loud and soft playing, perhaps making the effect negligible in practice. Kent Swafford</blockquote> </html>