Stable Schiedmayer (Kawai built)

[Ron Nossaman]

> 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