Intonation - why are strings different lengths

[sharkboy]

Is it just me that has a little trepidation about taking set-up advice from someone called Buzz?

[Musashimonkey]

[quote name='sharkboy' timestamp='1447194094' post='2905774']
Is it just me that has a little trepidation about taking set-up advice from someone called Buzz?
[/quote]

Me too, but I'm sold now, sounds good on my MTD's. 😀

[Norris]

There is a whole pile of complicated maths behind it. I saw a luthier website a couple of weeks ago when I was looking at fret positions for my guitar build. Unfortunately I can't remember the name of the site, but if you search for a bridge compensation calculator you'll probably find it (acoustic guitars have a fixed bridge, so the compensation has to be built in). I'll link it later when I'm on a proper computer

[EssentialTension]

[quote name='Norris' timestamp='1447228846' post='2905872']
... bridge compensation calculator ...
[/quote]

[url="http://liutaiomottola.com/formulae/compensation.htm"]http://liutaiomottola.com/formulae/compensation.htm[/url]

[Norris]

[quote name='EssentialTension' timestamp='1447230287' post='2905877']
[url="http://liutaiomottola.com/formulae/compensation.htm"]http://liutaiomottola.com/formulae/compensation.htm[/url]
[/quote]

That's the fella - thanks ET

[EssentialTension]

[quote name='Norris' timestamp='1447231346' post='2905881']
That's the fella - thanks ET
[/quote]

The whole of that site is of some interest.

[Norris]

[quote name='EssentialTension' timestamp='1447231440' post='2905883']

The whole of that site is of some interest.
[/quote]

It certainly is a good read if you're interested in the science stuff

[pfretrock]

[quote name='EssentialTension' timestamp='1447230287' post='2905877']
[url="http://liutaiomottola.com/formulae/compensation.htm"]http://liutaiomottol...ompensation.htm[/url]
[/quote]

D'Addario publish unit weights for their strings, I've not seen this from other manufacturers.

PDF download at the top of this page:

[url="http://www.daddario.com/DAstringtensionguide.Page?sid=3c81f5b1-3cba-4723-9486-a7958656af1b"]http://www.daddario....86-a7958656af1b[/url]

EDIT: I see they link to the PDF!


(I restrung my electro-acoustic bass, so now the intonation with the fixed bridge is terrible, but hey, my ears are not that good)

Edited November 11, 2015 by pfretrock

[PaulWarning]

[quote name='pfretrock' timestamp='1447236200' post='2905925']
(I restrung my electro-acoustic bass, so now the intonation with the fixed bridge is terrible, but hey, my ears are not that good)
[/quote]I've got the same trouble with mine as well, I have to have the B string slightly flat open to get the fretted notes right.
Not bass related but intonation related, why do some acoustics have that saddle where the B string is further back than the others?[attachment=204830:bridge.jpg]

Edited November 11, 2015 by PaulWarning

[EssentialTension]

[quote name='PaulWarning' timestamp='1447236486' post='2905930']
... why do some acoustics have that saddle where the B string is further back than the others?[attachment=204830:bridge.jpg]
[/quote]

That's explained in the article linked above.

The thicker the string core the more compensation is necessary. The plain B is thicker than the core of the wound G, so more compensation. Or something like that anyway.

[Silvia Bluejay]

[quote name='HowieBass' timestamp='1447091129' post='2904783']
Regarding compliance - I'm assuming it's due to the thickness/stiffness of the B string that it becomes difficult to achieve perfect intonation up at the dusty end - or maybe it's just my bass where it's a problem. I can generally get perfect intonation on all the other strings on my Curbow 5 past the 19th fret and beyond (and indeed on all my 4 string instruments too). Do taper wound strings improve this situation?
[/quote]

Intonating the low B on normal 34 inch scale basses is very often a pain, especially with flats on, as the low B tends to be much thicker than the other strings, and the bridge design needs to choose between accommodating the E, A, D and G or the low B, so the former win because there are more of them! I have removed the spring from the low B saddle on all of my 5-stringers to obtain the correct length for intonation.

Players of 35 inch scale and over - is the situation any better?

Edited November 11, 2015 by bluejay

[PaulWarning]

[quote name='EssentialTension' timestamp='1447263505' post='2906274']
That's explained in the article linked above.

The thicker the string core the more compensation is necessary. The plain B is thicker than the core of the wound G, so more compensation. Or something like that anyway.
[/quote]right, but what I don't get is that only some acoustics have this type of bridge, and would it be so difficult to have adjustable saddles on an acoustic?

[EssentialTension]

[quote name='PaulWarning' timestamp='1447270931' post='2906346']
right, but what I don't get is that only some acoustics have this type of bridge, and would it be so difficult to have adjustable saddles on an acoustic?
[/quote]

I guess it's more difficult and costly and so most cheap acoustics have a generally compensated bridge not individual saddles.

Some do have individual saddles ...

[url="http://www.portlandguitar.com/Split%20Saddle%20Bridge.html"]http://www.portlandguitar.com/Split%20Saddle%20Bridge.html[/url]

[BigRedX]

[quote name='PaulWarning' timestamp='1447270931' post='2906346']
right, but what I don't get is that only some acoustics have this type of bridge, and would it be so difficult to have adjustable saddles on an acoustic?
[/quote]

On an acoustic stringed instrument the bridge is the mechanism by which the vibrations of the string are transferred to the soundboard and thereby amplified. Unfortunately the more adjustment you build into the bridge the less efficient it becomes as more of this transfer is lost.

[PaulWarning]

[quote name='BigRedX' timestamp='1447272745' post='2906368']
On an acoustic stringed instrument the bridge is the mechanism by which the vibrations of the string are transferred to the soundboard and thereby amplified. Unfortunately the more adjustment you build into the bridge the less efficient it becomes as more of this transfer is lost.
[/quote]right, that makes sense

[EssentialTension]

[quote name='BigRedX' timestamp='1447272745' post='2906368']
On an acoustic stringed instrument the bridge is the mechanism by which the vibrations of the string are transferred to the soundboard and thereby amplified. Unfortunately the more adjustment you build into the bridge the less efficient it becomes as more of this transfer is lost.
[/quote]

Ah, yes, well spotted. I guess the loss of transfer would apply to an under the bridge piezo pickup too.

[EssentialTension]

[quote name='Dropzone' timestamp='1447083849' post='2904677']
Can anyone answer, why are strings different lenths ie, the risers at the bridge are not all in a straight line. Surely an octave is half the wavelength so why are they not all the same? Ta in advance Mike
[/quote]

From the Fender setup guide. Implies an answer to your question by telling what to do ....

[quote]
[b] INTONATION (ROUGHING IT OUT)[/b]

You can preset the basic intonation of your bass by taking a tape measure and measuring from the inside of the nut to the center of the 12th fret (the fret wire itself; not the fingerboard). Double that measurement to find the scale length of your bass.

Adjust the first-string bridge saddle to this scale length, measuring from the inside of the nut to the center of the bridge saddle.

Now adjust the distance of the second saddle back from the first saddle, using the gauge of the second string as a measurement. For example, if the second string is .060" (1.5 mm), you would move the second-string saddle back .060" (1.5 mm) from the first saddle.

Move the third saddle back from the second saddle, using the gauge of the third string as a measurement.

Adjust the fourth saddle in the same manner (and fifth if you have a five-string bass).

[i]Note: If you're using a taper-wound fourth string (and fifth if it's a five-string bass), use the actual gauge of the string for your measurement rather than the dimension of the tapered portion of the string.[/i]

[url="http://www2.fender.com/support/articles/bass-guitar-setup-guide/"]http://www2.fender.c...ar-setup-guide/[/url]
[/quote]

[Count Bassy]

I've experimented with compensated nuts/zero frets, and I've got to say that the effect was remarkable, tuning in the first 3 or 4 frets was noticibly better, without having to try too hard, and the variations at the bridge became much smaller. However the lower the action at the nut/zerofret the less noticable it becomes, and these days I have it a lot lower than I used to.

[Mornats]

This page from Eltham Jones' site (a renowned luthier around this way) may be of interest to people following this topic, in particular with regards to every fret other than the 12th being a compromise: http://www.edgeguitarservices.co.uk/scheitenballs/

[EssentialTension]

[quote name='Mornats' timestamp='1447702273' post='2909669']
This page from Eltham Jones' site (a renowned luthier around this way) may be of interest to people following this topic, in particular with regards to every fret other than the 12th being a compromise: [url="http://www.edgeguitarservices.co.uk/scheitenballs/"]http://www.edgeguita.../scheitenballs/[/url]
[/quote]

Thanks for that.

I can see Buzz has definitely got some history problems.

I've never had tuning problems myself.

EADG and off we go.

Edited November 16, 2015 by EssentialTension

[tauzero]

[quote name='Damonjames' timestamp='1447185146' post='2905683']
I read online that a handy and accurate way to adjust the intonation is to use the open string and the 13th fret, that way your tuner doesn't get confused with which E/A/D/G it is trying to follow. Obviously the 13th should read a half step up from the open string! Seems to work for me, but anyone else tried this?
[/quote]

[quote name='BigRedX' timestamp='1447187948' post='2905709']
That doesn't work because the position of every fret except the 12th is a compromise.
[/quote]

The position of every fret on the fretboard is calculable. It may be a compromise, but if you don't tune in equal temperament then you have problems playing in more than one key, plus it would be easy enough to do on a keyboard instrument but on a fretted instrument you'd need those stupid wiggly frets all over the place (and yes, they'e stupid, unless you're only ever going to play certain chords and never play accompanying any instrument in equal temperament).

That said, I generally do it by ear using the 12th fret harmonic and fretted, using a precision (not Precision) fingernail if I'm doing a fretless bass.

[leftybassman392]

[quote name='Mornats' timestamp='1447702273' post='2909669']
This page from Eltham Jones' site (a renowned luthier around this way) may be of interest to people following this topic, in particular with regards to every fret other than the 12th being a compromise: [url="http://www.edgeguitarservices.co.uk/scheitenballs/"]http://www.edgeguita.../scheitenballs/[/url]
[/quote]

Not wishing to be overly picky, but every fret on the instrument is a compromise, including the 12[sup]th[/sup] (and the 24[sup]th[/sup] if there is one). It's all a matter of perspective...

In Equal Temperament the only harmonically accurate interval is the octave. However, any octave will do. The 12[sup]th[/sup] fret is only harmonically accurate relative to the open string. If you play notes on, say, the 1[sup]st[/sup] and 13[sup]th[/sup] frets (which would be an exact 2:1 ratio) then the note at the 12[sup]th[/sup] fret is a compromise note since it is 2[sup]11/12[/sup] times the frequency of the 1[sup]st[/sup] fret note. In Equal Temperament all the notes are part of the system, and no note is special.

It's an interesting article (and from what I've read on the subject thus far I have my doubts about the Feiten system too: in particular I'm not convinced it's doing what he claims - still working on that one though so nothing definitive yet). Some of the maths is a wee bit, um, loose; but the main thrust of the article seems to be pretty sound.

The whole point of ET is that you sacrifice a little of the purity of the natural harmonic series in the name of flexibility. Having said that, the discrepancies are for the most part very small indeed.

Example:

The natural harmonic ratio (3:2) for the fifth above concert A (normally 440Hz) is E at 660Hz. Using ET you get 659.256 Hz for this note. If you now drop a couple of octaves to put the A at 110Hz on the open 5th string of a guitar or fretted 1st string of a bass you get 165Hz in Pythagorean and 164.814Hz in ET. To be fair, it does progressively expand for the more harmonically 'distant' intervals, but the general idea still holds. Which is as it should be of course - what would be the point of going to this much trouble only for the result to be worse than the original?

And I haven't even mentioned open vs. fretted notes! With the kind of weedy strings most electric guitar players use the discrepancies are a lot bigger than any of the above...

Edited November 17, 2015 by leftybassman392

[tauzero]

I can recommend this book on the subject: [url="http://www.amazon.co.uk/Temperament-Stuart-Isacoff/dp/0571234461/?ie=UTF8&qid=1447786004&sr=8-1&keywords=temperament"]http://www.amazon.co.uk/Temperament-Stuart-Isacoff/dp/0571234461/[/url]

Yes, I have read it

[leftybassman392]

On the subject of luthiery and Equal Temperament, here's a couple of interesting (and related) little factoids.

Firstly, if you know what you're doing it's not that hard to derive all the fret positions from first principles. (I've no doubt that experienced luthiers use templates and/or some kind of automation, but you have to get the numbers from somewhere...)
[spoiler] P[sub]n[/sub] = (1- 2[sup]-(n/12)[/sup]).L where n is the fret number, P[sub]n[/sub] is the distance of that fret from the nut and L is the scale length (traditionally measured in inches but works with cm as well). And yes, I did work it out for myself thanks for asking. [/spoiler]


Secondly, and picking up on the octave point mentioned few posts ago, if you measure the width of any fret space, and then do the same measurement exactly 12 frets up, you'll find it's exactly half the width.

Edited November 18, 2015 by leftybassman392