<!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 6.00.2716.2200" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV>Richard,<BR><BR>Working through a temperament/stretch can be very complicated; whatever<BR>method you choose, you need to properly represent the varying amounts of<BR>inharmonicity. I used 5 different inharmonicity readings from my piano to<BR>generate inharmonicity constants for the rest of the piano. With the<BR>inharmonicity constants, I constructed all of the overtones based on a<BR>theoretically correct equally temperament (2^(1/12)). Next, I readjusted the<BR>D3-A4 temperament based on B/A^(1/19), and then tuned the remaining 3:1<BR>12ths pure.<BR><BR>Because we know all the frequencies, determining beatrates are very easy,<BR>but there are a lot of numbers!<BR><BR><BR>Bradley M. Snook</DIV> <DIV><BR> </DIV></BODY></HTML>