<!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>A beat happens every time two = frequencies drift past each other by one cycle (one complete vibration).  In other = words, if you have two notes at 440 and 441 Hz (i.e. 440 and 441 cycles per = second), respectively, there will be a resultant beat frequency of one beat per second.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>For those of you with heads stuck in = physics or acoustics books, take heed that there is no acoustic energy at the beat frequency, provided there is linearity in the system, but that's = been argued back and forth before!</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>And yes, there are 100 cents between = one half step and the next, where each note is roughly 2^(1/12) or 1.0595 times = the frequency of the previous half step and 2^(-1/12) or 0.944 times = the frequency of the next half step.  A cent, at any frequency, would = be roughly 1-2^((1/12)/100) or 0.0005778 times that frequency.  = At 440 Hz, a cent would be roughly 0.25 Hz.</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> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV>----- Original Message ----- </DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <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> Monday, March 15, 2004 = 5:44 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>Hi Joseph,</FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>So if I understand this right, cents are units along a scale leading from one half tone to the next, = while beats are pegged to the specific unison's frquency. Did I understand = this right?</FONT></DIV> <DIV> </DIV> <DIV><FONT face=Arial size=2>Peace</FONT></DIV> <DIV><FONT face=Arial = size=2>jj</FONT></DIV></BLOCKQUOTE></BODY></HTML>