<HTML> <HEAD> <TITLE>Re: trichords unisons</TITLE> </HEAD> <BODY> <BLOCKQUOTE>BEATS are based on physical cycles per second. A440 means 440 c= ycles per second; if that is played along with anothert string at A439, the = 440 cycles per second and the 439 cycles per second will make a "beat&q= uot; of one per second as the two strings go in and out of phase with each o= ther. CENTS are an arbitrary mathematical division of a semitone's "distance= " into 100 parts. Cents at A440 are based on the distance to A#, which = vibrates at 466.2 cycles per second, so each cent there is about 26.2/100 or= .262. So the cents distance from 439 to 440 is just under four cents. </BLOCKQUOTE> || ||| || ||| || ||| || ||| || ||| || ||| || ||| || ||| jason kanter * piano tuning * piano teaching bellevue, wa * 425 562 4127 * cell 425 831 1561 orcas island * 360 376 2799 || ||| || ||| || ||| || ||| || ||| || ||| || ||| || ||| <BLOCKQUOTE>From: "Paul Chick \(EarthLink\)" <tune4@ear= thlink.net> Reply-To: pianotech@ptg.org Date: Wed, 5 Jun 2002 08:10:33 -0500 To: <pianotech@ptg.org> Subject: Re: trichords unisons </BLOCKQUOTE> <BLOCKQUOTE><TT>Richard Brain fog this morning is giving me trouble understanding the difference/similarity of cents and bps (beats per second). You stated the difference between 440 and 439 (1Hz) is almost 4 cents. This= interval beats at about one bps.  Where did I get the idea that the 1 = Hz difference between 440 & 439 was nearly 4 bps.  Being an aural tun= er I can relate to beat rates easier than cents deviations.  The math/science o= f tuning is not my strong suit.  Do you know of a book that would explai= n this?  My curiousity is getting to me.  Thanks for your continued= input to the list.  Many are grateful for your skills and insights. Paul Chick ----- Original Message ----- From: "Richard Moody" <remoody@midstatesd.net> To: "Pianotech" <pianotech@ptg.org> Sent: Tuesday, June 04, 2002 11:51 PM Subject: Re: trichords unisons > > > The difference between 440 and 439 is almost 4 cents. > From 880 to 879 nearly 2 cents.   From 1760 to 1759 almost 1= > cent.    All of these intervals beat at one bps. > The reason the cents get smaller is > that the intervals of one cycle per second difference are > smaller at higher frequencies.   Any two frequencies make an= > interval. > An interval can be expressed as the ratio of their > frequencies and that > can then be expressed as cents.  The interval 440/439 is > larger than > 880/879.  Twice as large actually as they are an octave > apart.   ---ric > > > </TT></BLOCKQUOTE><TT> </TT> </BODY> </HTML>