<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD><TITLE>Re: Piano Design (was Interestingly Stable)</TITLE> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <STYLE type=text/css>BLOCKQUOTE { PADDING-BOTTOM: 0px; PADDING-TOP: 0px } DL { PADDING-BOTTOM: 0px; PADDING-TOP: 0px } UL { PADDING-BOTTOM: 0px; PADDING-TOP: 0px } OL { PADDING-BOTTOM: 0px; PADDING-TOP: 0px } LI { PADDING-BOTTOM: 0px; PADDING-TOP: 0px } </STYLE> <META content="MSHTML 5.50.4134.100" name=GENERATOR></HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>I'd like to add that the idea of "log" = scaling (also know as geometric progression) is not new at all. I was used in = some harpsichords and fortepianos at least since the = 18th century. Some of these had scales where the string length would double every = octave = using an octave ratio of  1:2 (also called Pythagorean scaling). = So, to calculate the length of each string, one needs just to start from a = given legth for the highest note and multiply it with the 12th root of 2 to get next = lower note string length. </FONT></DIV> <DIV><FONT face=Arial size=2>Others would use tapered scales, based = on a smaller progression factor, for instance the ratio 1:1.945 for octaves, as = proposed by Jakob Bleyer in 1811. So, the smaller the factor, the shorter the = lower string lengths get, if you start from the same length of the = highest note.</FONT></DIV> <DIV><FONT face=Arial size=2>But these facts were known even before that.</FONT></DIV> <DIV><FONT face=Arial size=2>For instance, some of the fortepianos = built by Stein used tapered scaling with the octave ratio of = 1:1.95.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2> Calin Tantareanu<BR>----------------------------------------------------<BR>&nb= sp;<A href="http://calintantareanu.tripod.com">http://calintantareanu.tripod.= com</A><BR>----------------------------------------------------</FONT></D= IV> <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=sec@overspianos.com.au = href="mailto:sec@overspianos.com.au">Overs Pianos</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, July 05, 2004 = 4:58 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Piano Design (was Interestingly Stable)</DIV> <DIV><FONT face=Arial size=2></FONT><BR></DIV> <DIV>I do not assume or state that my ideas are the only valid ones. = And I certainly didn't put forward the idea with any delusion that it might = gain your respect. Furthermore, I dispute that log scaling is my idea = alone. While I came up with it independently many years ago<FONT color=#0000ff> = (during 1985 in fact, while servicing a Bösendorfer for the Sydney = International Piano Competition - in those days it used to take me four hours to design a = new log scale using a HP11C pocket calculator, 9 seconds per inharmonicity calc)</FONT>, there are a number of technicians who contribute to this = list who share my view, and who almost certainly came up with idea = independently as well. If you were paying attention you would have noticed that others, = such as Del Fandrich and Ron Nossaman, are similarly convinced about the = inadequacy of hockey stick scaling. The primary reason, I believe, why factories = persist with this archaic scaling is that they lack the courage to move the = break up to where it aught to be for pianos of a given size. Unfortunately, = company supporters such as yourself appear to be so busy defending the = corporate position that alternative ideas are likely to be put-down before they = are given serious scrutiny.</DIV> <DIV>couple of years.</DIV></BLOCKQUOTE> <DIV dir=ltr><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>Ron O.</DIV> <DIV><BR></DIV><X-SIGSEP><PRE>-- </PRE></X-SIGSEP> <DIV><FONT face="Times New Roman" color=#0000ff size=+1><B>OVERS = PIANOS - SYDNEY</B></FONT></DIV> <DIV><FONT color=#000000><I>   </I></FONT><FONT color=#0000ff><I>Grand Piano Manufacturers</I></FONT><FONT color=#000000><BR>_______________________</FONT></DIV> <DIV><FONT color=#000000 size=-2><BR></FONT><FONT = color=#000000>Web http://overspianos.com.au</FONT></DIV> <DIV><FONT = color=#000000>mailto:info@overspianos.com.au<BR>_______________________= </FONT></DIV></BLOCKQUOTE></BODY></HTML>