Why are the saddles always in a step pattern?

[NickInMesa]

I always wondered why, when adjusting the saddles to tune perfectly at 0 and 12, I always end up with shorter strings as I go towards the high string, ending up with a step pattern?

On all my basses. On everybody's basses.

What's the physics behind that?

[Ric5]

it is a matter of physics ...

[seanm]

I believe the higher the frequency the shorter the scale length you want all other things being equal.

I believe there is a article on fanned frets that explains it better.

[The modifier]

Originally Posted by NickInMesa

I always wondered why, when adjusting the saddles to tune perfectly at 0 and 12, I always end up with shorter strings as I go towards the high string, ending up with a step pattern?

On all my basses. On everybody's basses.

What's the physics behind that?

Not all basses, ive seen some were they intonate in a complete unpatterned fashion, but normally they intonate as you described

[CodaPDX]

I believe it has to do with the actual speaking length of the string versus it's theoretical length. The physics used to describe a string instrument like the bass typically make two important assumptions - first, that width of the string is insignificant with respect to it's length, and second, that the string is free to rotate freely around the endpoints of its speaking length (ie, the nut/frets and bridge), somewhat as if it was connected by a hinge.

While this is a very good approximation, it's not completely accurate. Strings are physical objects with a definite width to them, and cannot make instantaneous turns, such as when crossing over a nut or bridge. Instead of a hinge, picture the string being held rigidly so the part closest to the bridge or nut is forced to be horizontal at all times. Bridges and nuts are typically designed to minimize this as much as possible by having a sharply delineated breakover point, but there still remains a short portion of the string just inside of the nut or bridge that does not vibrate much.

By adjusting the intonation, you can correct for this by adding a small amount to the speaking length of the string. Ideally, you'd be able to do this at both ends to get the most accurate intonation as possible, but the fact that you fret the string at one end makes adjustments at that end moot. Now, the wider the string is, the stiffer it will be and the more it will resist bending, and the longer this dead length inboard of the bridge and nut will be. Therefore, the thicker the string, the more you typically have to lengthen the speaking length of the string in order to arrive at a correct intonation.

[xgator4u]

I remember as a lad back in the 70's when I was first learning,,, to set up the instrument the 1st or highest pitch string should be 34'' or what ever scale from nut to bridge. Then add the width of the next string to the length of the first and so on. This ultimately always resulted in the step pattern you described. man times they are a changin.

[NickInMesa]

Thanks, I actually learned something.

[EADG mx]

Look into fanned frets. Similar concept. I'm not a physicist, mathematician, or luthier by any means but this is my understanding:

Compare the scale length of a ukulele to a guitar to a bass. Let's suppose in theory, higher pitched strings require lighter strings and shorter scale length, for the purposes of optimal string tension and timbre. By this logic all string instruments should have fanned frets, in theory. When working with an instrument that has a uniform scale length, the closest we can get is to work with the string saddles.

Really not much basis in scientific fact, but it makes sense to me.

[JustDavid]

Originally Posted by CodaPDX

I believe it has to do with the actual speaking length of the string versus it's theoretical length.

Coda, I think you nailed it.

Great explanation!! Thanks.

[msiner]

There is an interesting explanation in the Fender Setup Guide under "Intonation (Roughing it out)" that basically talks about the string gauge determining how far back a saddle should be.

[4FretlessMetal]

just an interesting note, every other bass I've played has had either a stepwise pattern or random pattern just like you guys have described. However my current bass actually intonates with a straight pattern, go figure