---------------------- multipart/alternative attachment Ron, Thanks for the detailed response. I appreciate the time it took for you to write it. Dave S. In a message dated 1/21/2006 1:11:04 P.M. Pacific Standard Time, rnossaman@cox.net writes: > Anyone willing/able to state the ABCs of logarithmic and/or > semi-logarithmic piano string scaling? What kind of scaling is Ron N, > and Del using? Look at the scale breaks where the struts are. You'll often find the break% changing substantially across that scale break. That's because the log progression was disrupted because the bridge wasn't dog-legged enough to maintain the progression. So the break% goes high on one side, and/or low in the other. Lower break% means greater pitch change with overall string length changes. In other words, a uniform break% across a scale break will stay in tune much better. So to figure a smooth log progression from C-8, down to a spot in the scale were you still like the break% figure, do this. You start with the top end. Say you want C-8 to be 54mm long. That's your basis. Then choose a unison down scale having a length and break% you think you like. Break% is determined from frequency and length. A string at a given length and frequency will have (about) the same break% whatever gage wire is on it. Once you have both ends of your log progression chosen - C-8 (#88) at 53mm, and say, C-3 (#28), at 1220mm, use something like this to calculate each speaking length between the two targets. =EXP(((88-Un)*((LN(1220)-LN(53))/(88-28)))+LN(53)) If you had chosen C-8 (#88) at 54mm, and E-3 (#32) at 1024mm, you'd have =EXP(((88-Un)*((LN(1024)-LN(54))/(88-32)))+LN(54)) So: exp(LN(length of 88)+ increment) = #87 exp(LN(length of 87)+ increment) = #86 exp(LN(length of 86)+ increment) = #85, etc. Then build the bridge to maintain the progression across the scale breaks. This will give you a nice smooth break% progression. Tension is adjusted by changing wire size as necessary. >I know sometimes in Del's scale designs, he will have > the long bridge (some factor of it) follow the semi-logarithmic > progression (or is it logarithmic?), but then he will abandon that on > the bass bridge - I think because of physical limitations of the > soundboard/plate, etc. - what's that all about? What are some of the > ramifications of all that? On the bass bridge, you have more options. You can juggle tension, break%, Impedance (Z), and inharmonicity without being tied to the length and pitch determining break%, as is the case with plain wire. Want to raise break%? Use a smaller diameter core. Want more tension and a higher Z? increase wrap diameter. > If many manufacturers don't follow a log or semi-log progression on > their long bridges, what do they follow? (Watch out, there may be some > worms in that can!) They follow the leader, I guess. There is a notion that the footprint of the bridge should be as straight as possible to not (presumably) impede the rocking motion of the bridge and kill the sound. So to obtain this supposed benefit across the break, the log progression, tension, Z, break% (and tuning stability), and inharmonicity curves are compromised. It's also considerably easier to bend a bridge that doesn't have the extreme doglegs necessary to maintain the log progression. Sometimes, they split the difference, bringing bridge pin row spacing down to under 10mm at the break to try to fit the log progression on a too straight bridge. They haven't adopted your trick of just ending laminations at the doglegs, apparently fearing the sound will leak out the end grain. Personally, I build in the dogleg, and end laminations at same. If the jog in the footprint kills the sound, and what's left over leaks out the open ended laminations, I like the effect and plan to keep doing it. Ron N Dave Stahl Dave Stahl Piano Service 650-224-3560 _http://dstahlpiano.net/_ (http://www.dstahlpiano.net/) ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/47/b8/dd/46/attachment.htm ---------------------- multipart/alternative attachment--
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