# Conflict between intonation and fret spacing?

Discussion in 'Luthier's Corner' started by kegbarnacle, Dec 18, 2003.

1. ### kegbarnacle

Nov 18, 2003
Phoenix
As I'm finishing up my bass, I'm wondering about bridge placements. Fret distances are calculated based upon the scale length of the bass. But most bridges allow you to adjust the intonation - essentially shortening and lengthening the vibrating length of the string. So one string will have more of a vibrating length than another on the same bass. Does this not affect where the fret should be placed or where you would finger a fretless? It seems to me that fret placement is an exact science - most fret calculators give you something like four decimal places. And when you play a fretless, you can be a hair off and it sounds out of tune with the band.... But then you can adjust the bridge any way you want??!?

2. ### pkr2

Apr 28, 2000
coastal N.C.
there really isn't a conflict. The frets are spaced to work with a string of a particular mass/length ratio. if the mass of the string changes, the length must be adjusted to compensate for the change. That's why the E string has a longer speaking length than the G string. The proper name for the adjustable bridge saddles are the compensators.

H. Snyder

3. ### pilotjonesSupporting Member

Nov 8, 2001
US-NY-NYC
Well... something like that. The frets are not spaced to work with particular strings; they are placed in ideal positions for a string of a particular length. The string stretches as you deflect it from a straight line by fretting it; this raises the pitch. This is (mostly, but not perfectly) compensated for by making the open string length longer. And this compensation distance will vary according to the string used, both because of differing weights and because of different core constructions.

Theoretically, if you could find a way to bring the fret up to the string, so that it did not stretch when fretting, no compensation would be necessary.

4. ### kegbarnacle

Nov 18, 2003
Phoenix
All of that makes sense. I would expect string mass (which would include gauge and length) to play a role in this. But that only adds to the problem. Why can you change string gauges and make bridge adjustments as you see fit, but frets must be placed exactly? You can alter your bridge all you want, but a 35" scale has different fret placements down to four decimal places than a 34" scale?

What gives?

5. ### kegbarnacle

Nov 18, 2003
Phoenix
or do you only make bridge adjustments if you change string gauge? That makes sense. But i've never seen a bass or bridge or string marked with any sort of "Ideal Length" or anything like that.

6. ### pilotjonesSupporting Member

Nov 8, 2001
US-NY-NYC
For example: A bass has 35" scale. The frets are laid out for 35" scale, following the formulas - Dividing the string in half raises it by an octave; to raise it by some number of semitones of a twelve-tone equal-tempered scale, you must shorten it by an appropriate multiple of the twelfth root of 2. If the string did not stretch when fretting, this would be all you need. But, the string does stretch when you fret it.

So, the string stretch is compensated for in this manner:

The saddle is moved back by, for example, .375". What you actually have now on the open note is a 35.375" scale string.

Now the frets are laid out for 35.000 scale. These frets are a little closer together than they would be if you fretted it for the actual 35.375. So, when you use the first fret, the string is not shortened enough by a slight bit, which would make the note a bit flat. But, the string is also stretching when you fret it, which raises the pitch. Ideally, the pitch increase due to the string stretching would exactly make up for the pitch flatness due to the frets being placed for 35.000 instead of 35.375.

In the real world, this compensation is not perfect, but it is close enough.

You will get best intonation up and down the neck by:
- Using the lowest action that you are happy with. This decreases the amount of string stretch, and the amount of compensation required.
- Using a zero fret, or using a nut cut as low as possible (which would be equal to the fret height). This also minimizes the string stretch.
- Having the correct amount of slight forward bow on the neck. Too much and the string will be high off the upper frets, and it will go sharp up there; too flat and you will have to raise the bridge so much to get the low notes to stop buzzing, that again the high notes will go sharp.
- Theoretically, either a heavier, high tension or a lighter, low tension string will be less affected by the stretching, and thus will have less intonation compensation error. If you're interested, you can use the 2nd sheet of my spreadsheet to figure which of these it is. (The figures for increase in pitch due to plucking also hold for increase due to fretting.) Also, the effect of a lighter or heavier core can be figured the same way.