Intonation and string length

[walcen]

Hi Guys, as I'm still relitively new to this luthiery stuff I have a burning technical question that's been buging me for yonks.
We know that the brake off point between the nut and the bridge saddle determines our scale length, and aparently the scale length determines the pitch of the instrument at a given key, I think.

And I know that the over all lenght of the strings between the mechine head and the tail stop piece dictates the tention required to achive a give key. So by moving a tail piece ferther down the body toward the strap pin would not alter the intonation but the string would be under greater tention.

Soooo, is there a formula for tail stop posission? I guess that maintaining a minimal string length would relieve neck tention but how would it affect over all tone.

If it's all too Zen for ya just tell me to bugger off.

kindest regards to all

Wal

ps

please forgive my spelling but my spell check is broken.

[Ball Peen]

Hi Walcen,
My understanding is scale length determines the tension. Shifting the tailpiece fore or aft makes no difference to the tension.
On violins the string length behind the bridge is called the after length and is set at 1/6 the scale length. Archtop guitars have a fiddle style tailpiece,
but I haven't heard any talk of correct after length. Mandolins have a very long after length and I've been meaning to ask about that one myself.

[walcen]

[QUOTE=Ball Peen;1582489] Shifting the tailpiece fore or aft makes no difference to the tension.

The above statement is what I'm having some of the trouble understanding. You see if you tune a string to the key of lets say E and then you move the tail piece back 50 mm effectively making the whole string longer and then tune the same string to E again, that string must me under more tension, yes?

[petersemple]

I don't think so. If you have a certain length of string between bridge and nut, then mathematically it will need to be at a particular tension to be in tune to a particular note. It shouldn't matter how long the string actually is. You could have a string that is 1km long, with a bridge and nut set 25.5 inches apart, and the tension in the string would be the same as any strat. The tension of the string at tune will depend on the distance between the bridge and nut (assuming the same string, because string diameter and composition will have a big effect too, but if we ignore them).

What could potentially be affected by the distance between the bridge and the tailpiece may be the angle that the string makes crossing the bridge. That can affect the amount of pressure that the strings exert down through the bridge, which I believe can alter tone. For the same reason a guitar that strings through a tailpiece can sound different to a guitar that strings through the body. There is different tension down through the saddle, but the string will still be at the same tension.

[Ball Peen]

[QUOTE=walcen;1582501]

Shifting the tailpiece fore or aft makes no difference to the tension.

The above statement is what I'm having some of the trouble understanding. You see if you tune a string to the key of lets say E and then you move the tail piece back 50 mm effectively making the whole string longer and then tune the same string to E again, that string must me under more tension, yes?

I read that in Bob Benedettos book. He says everyone has trouble with it. If you shift the bridge ( longer scale ) , use a heavier string or change the pitch ( say G to A ) tension is greater. Sorry I can't explain it better. Maybe someone else can.
I'll have a go. If it takes x tension to bring a string to pitch, the tension behind the bridge is the same in front of the bridge
no matter how long the after length.

[Cliff Rogers]

.... if you tune a string to the key of lets say E and then you move the tail piece back 50 mm effectively making the whole string longer and then tune the same string to E again, that string must me under more tension, yes?

Yes but.... assuming it is a fretted instrument, your frets are now all in the wrong places.
If you change the scale length of your instrument, you also have to change the fret spacing.

Intonation is correct if the fretted note at the 12th fret is one octave higher than the open note.
If it is wrong, you have to adjust the bridge saddle position to correct it.

If you want to change the scale length of you instrument & stay in the same key, longer needs to be tighter & you can compensate by using lighter strings.
If you use a shorter length scale in the same key, the strings need to be looser & you can compensate by using thicker strings.

Please remember: If you change the scale length of your instrument, you also have to change the fret spacing.

[Ball Peen]

Yes but.... assuming it is a fretted instrument, your frets are now all in the wrong places.
If you change the scale length of your instrument, you also have to change the fret spacing.

Intonation is correct if the fretted note at the 12th fret is one octave higher than the open note.
If it is wrong, you have to adjust the bridge saddle position to correct it.

If you want to change the scale length of you instrument & stay in the same key, longer needs to be tighter & you can compensate by using lighter strings.
If you use a shorter length scale in the same key, the strings need to be looser & you can compensate by using thicker strings.

Please remember: If you change the scale length of your instrument, you also have to change the fret spacing.

Walcen only wants to increase the after length.

[rhoads56]

Ok, here are the "facts"

1. Scale length is a theoretical rule, used to position the frets.
2. Nut to saddle length (operating string length) = the scale length + compensation
3. Compensation depends on string size (inc. inner core, windings, etc), and string action (the further the string must be pressed to fret it, the more compensation is required)
4. String tension is a factor of operating string length (nut to saddle), and string diameter (inc. inner core, windings, etc), and pitch required.
5. "Dead" string length (behind nut, behind saddle) does not effect the string tension whilst tuned to an open string, but does have an effect on compensation (the increased string tension whilst fretting is spread over both the compensated string length, AND the dead string length). Example, a lengthier dead string length, requires less saddle compensation, than an instrument with less dead string length.

[Cliff Rogers]

Walcen only wants to increase the after length.

Behind the bridge?
If that is the case, doesn't matter a rat's...
It could be 50 miles long, as long as it is the right tension for the note between the nut & the saddle on the bridge....
Mind you, a 50 mile long guitar would be hard to get into a case.

[Ball Peen]

Behind the bridge?
If that is the case, doesn't matter a rat's...
It could be 50 miles long, as long as it is the right tension for the note between the nut & the saddle on the bridge....
Mind you, a 50 mile long guitar would be hard to get into a case.

That's why they are called road cases

[matt_o]

5. "Dead" string length (behind nut, behind saddle) does not effect the string tension whilst tuned to an open string, but does have an effect on compensation (the increased string tension whilst fretting is spread over both the compensated string length, AND the dead string length). Example, a lengthier dead string length, requires less saddle compensation, than an instrument with less dead string length.

Hmm, interesting. I had never thought of that. Would that also then have an effect on the feel of the instrument (because for example when bending the increased tension is distributed over the dead string lenth)?

[rhoads56]

Hmm, interesting. I had never thought of that. Would that also then have an effect on the feel of the instrument (because for example when bending the increased tension is distributed over the dead string lenth)?

Yes.

If you have a longer dead string length, and the saddle and nut are properly cut/lubricated, it will feel different whilst bending. You will still need to bend up to the correct tension to hit that desired note/pitch, which will mean the string is bent further than normal (eg: a shorter dead string length). Despite bending further, it feels a little smoother/easier. It's subtle (both feel and movement). But its there.

[matt_o]

Yes.

If you have a longer dead string length, and the saddle and nut are properly cut/lubricated, it will feel different whilst bending. You will still need to bend up to the correct tension to hit that desired note/pitch, which will mean the string is bent further than normal (eg: a shorter dead string length). Despite bending further, it feels a little smoother/easier. It's subtle (both feel and movement). But its there.

So the string will bend further with a shorter dead string length?

Does the break angle on the 'dead' side of the bridge have an effect then? For example does it make any difference if the strings go straight down through the body after the bridge vs going further back on a lower angle (assuming the length is the same)?

[rhoads56]

So the string will bend further with a shorter dead string length?

other way around.

Does the break angle on the 'dead' side of the bridge have an effect then? For example does it make any difference if the strings go straight down through the body after the bridge vs going further back on a lower angle (assuming the length is the same)?

Yes. Acoustics with a steeper angle usually have more volume than one with a lower angle. The steeper the angle, the more downward force, and therefore more chance of not 'slipping' (friction), and then suffering from detuning after a string bend.

[Humphrey9999]

Thanks, guys, for a very informative thread. Now even I can understand the effects of dead string/after length, compensation etc. Something I'd never considered.

I guess it follows that besides reducing the need for compensation, more dead string should make the action slightly lighter, since the stretch when fretting a string is spread over a greater distance.