<!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 Jean-Jacques,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>It all depends on what you're listening = for.  Piano tuners of course are used to listening for beats, and they are = quite sensitive to the presence of beats, how fast they are, where they are, etc.  Normal everyday people, and even musicians, listen for how = sharp or flat a note is, overall.  Ten cents of sharpness sounds the same = (in deviation of pitch), whether it is towards the bass or towards the = treble.  Those who doubt this should consider that *100* cents sharpness (i.e. = the next half step) also sounds the same, irrespective of octave.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Why does a larger deviation in = Hertz in the treble sound similar to a smaller deviation in the bass?  That's = just the way our sensory systems work.  All of our senses see proportional = changes as equidistant.  The difference between 1 and 2 is the same = difference as between 4 and 8.  Both are doublings.  This works with taste, = hearing, sound, touch, and olfaction.  In the case of hearing, the same is = true with loudness.  Each doubling of amplitude, 6 dB SPL, sounds similar, = whether the sound is soft or loud.  (Or for you people who prefer dealing = in power, each doubling of power, 3 dB SPL, sounds similar.)</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>In the end, we just can't resolve = differences of, say, 5 Hz in high pitched sounds, while they are incredibly conspicuous = in low pitched sounds.  Another way of looking at this is that a beat rate = of 1 beat per second (1 Hz) in the high treble is pretty much = meaningless.  The same beat rate in the low bass is much more meaningful.</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 dir=ltr 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=jjgranas@zigzag.pl = href="mailto:jjgranas@zigzag.pl">Jean-Jacques Granas</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, March 16, 2004 = 2:51 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Beats vs cycles vs = cents</DIV> <DIV><BR></DIV> <DIV><FONT face=Arial size=2>Hello one and all,</FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>Dare I suggest (and perhaps live to = regret it) that beats, with all their imperfections for tuning purposes, are = nevertheless a natural acoustic phenomenon that exists whether we are there to hear = it (or tune the stubborn thing) or not.</FONT></DIV> <DIV><FONT face=Arial size=2>Cents on the other hand aren't = something you actually hear, are they? When I tune in the deep base (the last 4-6 = unisons, depending on the piano), I don't listen to beats of course, because = otherwise In would be there all day. I just find the place where the octave or = fifth sound most pleasant, with occasional help from friends in the = 3rd  octave, but is what I am hearing 'cents'?</FONT></DIV> <DIV><FONT face=Arial size=2>After all, 100 beats to half a tone = (or thereabouts) it is only a scale, like 1000 meters to a kilometer, 12 = inches to a foot, or 5, .... feet (what was it?)  to a mile.</FONT></DIV> <DIV><FONT face=Arial size=2>Or am I missing something = ?</FONT></DIV> <DIV> </DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>Peace-Paz-Paix-Pokój</FONT></DIV> <DIV><FONT face=Arial size=2>Jean-Jacques Granas</FONT></DIV> <DIV><FONT face=Arial size=2>Warsaw, Poland</FONT></DIV></BLOCKQUOTE></BODY></HTML>