<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1400" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY> <DIV>Sure you do, Ric.  Cents are what it's all about.  Cents = ARE what you perceive in pitch.  Being off 100 cents takes you to the next note.  50 cents takes you half way there, no matter what note = you're on.  Ten cents out of tune sounds like ten cents out of tune, no = matter what your beat frequency is.  As you said, there are minor = discrepancies when tuning, but you are pedantically missing the point.  </DIV> <DIV> </DIV> <DIV>Using beats to tune a string is just a convenient crutch.  It = wouldn't do you much good when tuning a solo clarinet, would it?  To tune an = A0 (27.5 Hz) to a beat frequency of one cycle per second in comparison to = another A0 string would require it to be at 27.5 + 1 = 28.5 Hz.  This is = 62 cents sharp!  That's wayyyyy off.  It's closer to Bb!  And 62 = cents sharp sounds just as bad for A0 as it would for C7, or A-440, or any = other note.  </DIV> <DIV> </DIV> <DIV>For comparison, a beat frequency of 1 Hz for C7 only means = it's less than half a cent off!</DIV> <DIV> </DIV> <DIV>Beats are a phenomenon related to the *difference* in frequency (subtraction); cents are a phenomenon related to the *ratio* of = frequencies (division), which is what music itself is based on.  Sure, you = can hear beats, but as you can see it really has no relationship to what you = hear pitch-wise at all.</DIV> <DIV> </DIV> <DIV>Don A. Gilmore<BR>Mechanical Engineer<BR>Kansas City </DIV> <DIV> </DIV> <DIV> </DIV>> I really have to take issue with this. No one <<percieves>> cents at <BR>> all.  Our perceptions = of out of tuneness have far more to do with how <BR>> "clean" any given = interval relationship sounds, or how close any <BR>> interval is to what we = expect of it. This is exactly beat related. <BR>> Cents is an idealization, a mathmatical representation or modeling of <BR>> musical pitch. There = is no musical way of defining <<in tuneness>> based <BR>> on = cents to begin with. Only close approximations.  Beats are used both = <BR>> individually and whollistically to create a musical effect... the very = <BR>> best tuners know exactly what kind of vibrational effects they want a = <BR>> piano to send out through the air for each interval and are very good at = <BR>> achieving these. Many tuners I know speak of a the overall <<tone>> of a <BR>> tuning.... in kind of voicing sense. <<Voicing>> through tuning is a <BR>> mulitpartial = prospect to begin with, which removes it from a simple <BR>> cents perspective = from the get go.<BR>> <BR>> 100 cents is not always a half step in real = piano frequencies.... it is <BR>> at best only a half step for one partial = at a time.  Pitch perception is <BR>> a conglomerate of all partials, = their relative loudness, and a good deal <BR>> more.<BR>> <BR>> Cheers<BR>> RicB<BR>> _______________________________________________<BR>> pianotech list = info: <A href="https://www.moypiano.com/resources/#archives">http://www.ptg.org= /mailman/listinfo/pianotech</A><BR>> </BODY></HTML>