<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META charset=US-ASCII http-equiv=Content-Type content="text/html; charset=US-ASCII"> <META content="MSHTML 6.00.2900.2912" name=GENERATOR></HEAD> <BODY style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: #ffffff"> <DIV><FONT size=3></FONT> </DIV> <BLOCKQUOTE dir=ltr style="MARGIN-RIGHT: 0px"> <DIV class=OutlookMessageHeader dir=ltr align=left><FONT face=Tahoma size=2>-----Original Message-----<BR><B>From:</B> pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org]<B>On Behalf Of </B>KeyKat88@aol.com<BR><B>Sent:</B> Saturday, September 30, 2006 2:43 AM<BR><B>To:</B> pianotech@ptg.org<BR><B>Subject:</B> Two to the one twelth power <BR><BR></FONT></DIV> <DIV>Greetings, </DIV> <DIV> </DIV> <DIV>       Punching 2 to the 1/12 power into my calculator, it gives me 1.05946285.  How far does this number go on? Is it a number like Pi that goes on and on? What sort of software will let me see how far it can go?  If I am doing harmony calculations, how far is it practical to go? What is the norm? </DIV> <DIV> </DIV> <DIV>Julia</DIV> <DIV>Reading, PA<SPAN class=734273109-30092006><FONT size=3> </FONT></SPAN></DIV> <DIV><SPAN class=734273109-30092006></SPAN> </DIV> <DIV><SPAN class=734273109-30092006><FONT size=3>My calculator gives 1.059463094.  I've always used 1.0594631, but when reversing the operation with the first number, the result is 1.999999992, and with the second, 2.000000128, so the mantissa is longer, but how much, I don't know.  I doubt it goes on forever -- my intuitive feeling, not being a mathematician, is that the 12th root of 2 is of a different nature from pi, i.e. I think it's finite whereas pi may be infinite.  (?)  </FONT></SPAN></DIV> <DIV><SPAN class=734273109-30092006>    <FONT size=3>--David Nereson, RPT</FONT></SPAN></DIV></BLOCKQUOTE></BODY></HTML>