Zero frets and saddle placement: an inquiry

Martin Koch wrote:
> 
> William, certainly I will check your pages frequently.
> 
> By the way I have two questions too:
> 
> 1) I like to use a zero-fret. What do you think about that?

That's a very "European" thing to do. Almost nobody does that over here.
With a zero-fret you need two things: a zero fret and a spacer nut
behind it. The zero-nut is just a zero-nut. Simplicity would militate
against a zero-fret. Then there's the argument that since the zero-nut
is made of bone and the first fret is made of metal, logically there
should be a difference in the sound of the open string versus the sound
of the fretted string. But in practice, it never has been considered a
flaw in the guitar's design except for those few people who think that,
logically, there should be a difference. There may be an argument for it
in that a zero nut must be cut more carefully, and thus requires
somewhat more skill and time to execute. That would be a good argument
for its use in mass production, but not a very good one in luthierie.


 
> 2) I'm not very certain on how to place the saddle on an acoustic guitar.
> I believe that the best way is to mount an temporary extra tailpiece and
> to find the individual saddle-locations for a given set of strings like
> described in Don Teeters book.

I don't think that's a very good method. 

 
> But when I don't want to do it this way:
> You write in THE book that the exact scalelength should be in the middle
> and in front of the slanted saddle-slot. (And that's the way I always
> did it. But I can't explain it)
> It means that the string-length for the treblestrings is shorter then
> the scale-length. 

No, its not.

>I understand that the bass-strings have to be longer
> to make up for the increase in pitch when the string is pressed down.

That's true.

> But isn't the same true for the treble strings? 

Absolutely.

>The treble strings must
> be way too high this way. 

No, the compensation ends up just right.

>I believe that all strings have a higher pitch
> when pressed down. Am I right?

Yes. The pitch increases when you press down because you increase the
tension slightly when you do so. The compensation balances it out.


> Why? I don't understand that completely.


The saddle slopes 3.17 mm over its 7.62 cm length. If you pivot the
saddle at it's centerpoint, the treble saddle-end travels 1.58 mm
towards the nut. The bass saddle-end travels 1.58 mm away from the nut.

Now when you locate the bridge when you glue it down you must
a) locate the front edge of the bridge parallel to the frets
b) locate the centerline of the bridge to lie along the centerline of
the fingerboard
c) locate the center point of the saddle (that is, the central
pivot-point of the sloped line of the saddle) so that, when measured
down the extended centerline of the fingerboard, the saddle's central 
pivot point lies at the end of the scale length PLUS 3.81 mm (the compensation 
of the saddle measured at the center pivot point). 

Now, if the center of the saddle is 3.81 mm beyond the scale length, how
can the treble saddle end, which has pivoted only 1.58 mm towards the
nut, result in the string length of the treble string being shorter than
the scale length?

Besides, the treble string isn't located at the end of the saddle!
Indeed, it's located about two-thirds down the length of the saddle
portion between the pivot point and the saddle-end. Thus the actual
compensation of the treble string is two thirds of the distance that the
saddle end has rotated towards the nut. Two thirds of 1.58 mm is 1.05
mm. The same occurs viceversa with the bass string. So we can say that
the treble string is compensated  3.81 minus  1.05 mm which equals 2.76
mm; and the bass string is compensated 3.81 mm PLUS 1.05 mm which equals
4.86 mm.


Schwerverstaendlich?


Cordially yours,

 
William R. Cumpiano