<!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 bgColor=#ffffff> <DIV><FONT face=Arial size=2>Hi Don et al.,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>What you write is of course true.  = A cent is a cent is a cent -- same difference in pitch, no matter whether treble, = tenor, or bass.  I wonder if this isn't one point in favor of electronic tuning.  After all, aural tuning relies on counting beats, and beat = rate would vary with overall pitch.  However, beats are irrelevant to = electronic tuning.  I can't really speak from experience, as I only tune electronically.  Any thoughts from you aural tuners?</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Peace,</FONT></DIV> <DIV><FONT face=Arial size=2>Sarah</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=dgilmore@kcmpi.net href="mailto:dgilmore@kcmpi.net">Don = Gilmore</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, March 16, 2004 = 10:21 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Beats vs cycles vs = cents</DIV> <DIV><BR></DIV> <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>> </BLOCKQUOTE></BODY></HTML>