<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=US-ASCII"> <META content="MSHTML 6.00.2900.2802" name=GENERATOR></HEAD> <BODY id=role_body style="FONT-SIZE: 10pt; COLOR: #000000; FONT-FAMILY: = Arial" bottomMargin=7 leftMargin=7 topMargin=7 rightMargin=7><FONT id=rol= e_document face=Arial color=#000000 size=2> <DIV> <DIV> <DIV>Ron,</DIV> <DIV> </DIV> <DIV>Thanks for the detailed response.  I appreciate the time it took f= or you to write it.</DIV> <DIV> </DIV> <DIV>Dave S.</DIV> <DIV> </DIV> <DIV> </DIV> <DIV>In a message dated 1/21/2006 1:11:04 P.M. Pacific Standard Time, rnossaman@cox.net writes:</DIV> <BLOCKQUOTE style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"><= FONT style="BACKGROUND-COLOR: transparent" face=Arial color=#000000 size= =2>> Anyone willing/able to state the ABCs of logarithmic and/or <BR>> semi-logarithmic piano string scaling? What kind of scaling is Ron N, <BR>= > and Del using? <BR>Look at the scale breaks where the struts are. You'll o= ften find the <BR>break% changing substantially across that scale break. That's= <BR>because the log progression was disrupted because the bridge wasn't <BR>dog-legged enough to maintain the progression. So the break% goes <BR>= high on one side, and/or low in the other. Lower break% means <BR>greater pitch= change with overall string length changes. In other <BR>words, a uniform break% across a scale break will stay in tune much <BR>better. So to figur= e a smooth log progression from C-8, down to a <BR>spot in the scale were you still like the break% figure, do this. <BR>You start with the top end. Say= you want C-8 to be 54mm long. That's <BR>your basis. Then choose a unison down= scale having a length and <BR>break% you think you like. Break% is determi= ned from frequency and <BR>length. A  string at a given length and freque= ncy will have (about) <BR>the same break% whatever gage wire is on it. Once yo= u have both ends <BR>of your log progression chosen - C-8 (#88) at 53mm, and= say, C-3 <BR>(#28), at 1220mm, use something like this to calculate each speaking <BR>length between the two targets.<BR><BR>=EXP(((88-Un)*((LN(1220)-LN(53))/(88-28)))+LN(53))<BR><B= R>If you had chosen C-8 (#88) at 54mm, and E-3 (#32) at 1024mm, you'd <BR>have<BR><BR>=EXP(((88-Un)*((LN(1024)-LN(54))/(88-32)))+LN(54))<BR><B= R>So:<BR>exp(LN(length of 88)+ increment) = #87<BR>exp(LN(length of 87)+ increment) = #86<BR>exp(LN(length of 86)+ increment) = #85, etc.<BR><BR>Then build th= e bridge to maintain the progression across the scale <BR>breaks. This will = give you a nice smooth break% progression. Tension <BR>is adjusted by changing = wire size as necessary.<BR><BR><BR>>I know sometimes in Del's scale designs,= he will have <BR>> the long bridge (some factor of it) follow the semi-logarithmic <BR>> progression (or is it logarithmic?), but then he= will abandon that on <BR>> the bass bridge - I think because of physica= l limitations of the <BR>> soundboard/plate, etc. - what's that all about= ? What are some of the <BR>> ramifications of all that?<BR><BR>On the bas= s bridge, you have more options. You can juggle tension, <BR>break%, Impedan= ce (Z), and inharmonicity without being tied to the <BR>length and pitch determining break%, as is the case with plain wire. <BR>Want to raise brea= k%? Use a smaller diameter core. Want more tension <BR>and a higher Z? increas= e wrap diameter.<BR><BR><BR>> If many manufacturers don't follow a log or= semi-log progression on <BR>> their long bridges, what do they follow? (Watch out, there may be some <BR>> worms in that can!)<BR><BR>They fol= low the leader, I guess. There is a notion that the <BR>footprint of the bridg= e should be as straight as possible to not <BR>(presumably) impede the rocki= ng motion of the bridge and kill the <BR>sound. So to obtain this supposed benefit across the break, the log <BR>progression, tension, Z, break% (and= tuning stability), and <BR>inharmonicity curves are compromised. It's also= considerably easier <BR>to bend a bridge that doesn't have the extreme dog= legs necessary to <BR>maintain the log progression. Sometimes, they split the difference, <BR>bringing bridge pin row spacing down to under 10mm at the break to <BR>try to fit the log progression on a too straight bridge. They= <BR>haven't adopted your trick of just ending laminations at the <BR>dogle= gs, apparently fearing the sound will leak out the end grain. <BR>Personally, = I build in the dogleg, and end laminations at same. If <BR>the jog in the footprint kills the sound, and what's left over leaks <BR>out the open end= ed laminations, I like the effect and plan to keep <BR>doing it.<BR><BR>Ron N<BR></FONT></BLOCKQUOTE></DIV> <DIV></DIV></DIV> <DIV> </DIV> <DIV><FONT lang=0 face=Arial size=2 FAMILY="SANSSERIF" PTSIZE="10"= >Dave Stahl<BR><BR>Dave Stahl Piano Service<BR>650-224-3560<U><BR><A href="http://www.dstahlpiano.net/">http://dstahlpiano.net/</A></U></FONT><= /DIV></FONT></BODY></HTML>