(probably daft) Intonation question...

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HAL9000HAL9000 Frets: 7392
Why is it the fiddle that it is? I guess the physics is that if the length of the string from the nut to the 12th fret is the same as the length from the 12th fret to the bridge saddle then the intonation should be spot on. However the reality is that simply doesn't appear to be true. I have an old Strat that if you set up, say, the A string that way it is noticeably sharp at the 12th fret and even worse at the higher frets. The saddle actually needs quite a bit of adjustment to get the intonation correct. And yes I did measure with the string held down at the 12th. I'm guessing the width of the fret wire and the radius of the saddle all contribute?
I play guitar because I enjoy it rather than because I’m any good at it
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  • And the inaccuracies of where the frets actually sit on the board - it's basically best guess.

    Part and parcel of a fretted instrument. Look at microtonal guitars and imagine intonating those!
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  • dafuzzdafuzz Frets: 1521
    Possibly something to do with neck relief? No idea but I hate adjusting intonation too.
    All practice and no theory
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  • ICBMICBM Frets: 58105
    edited November 2013
    It's much simpler than that - as you fret the string, you're actually bending it. This makes it go sharp - more so the further up the neck you go because the action height is greater, so the further you have to bend the string to fret it. In order to bring it back to pitch, you make it longer than the "correct" length. Luckily, the same amount of compensation is roughly correct at each fret position, exactly because the action goes up, so you need a proportionally greater length increase, ie the *same* increase but on a shorter string length… if that makes sense!

    The reason for the 'stair step' layout of the saddles is because the thicker the string, the more the pitch rises when you bend it… but that mostly apples to the *core* of a wound string (not the whole thing) so the D intonates about the same as the B and the A the same as the G. because their cores are roughly the same diameters.

    Adjusting intonation is very easy, it shouldn't be a chore. You just check the tuning on a fretted note high up the neck, and if it's sharp you move the saddle backwards and if it's flat you move the saddle forwards. You can use any reference for the note - the 12th fret harmonic, another string that you've tuned 'perfectly' to the one you're adjusting, or a tuner. Once it's done it should stay done for the same gauge and brand, and probably for the same gauge but different brands. If the intonation is then later out, change the strings before fiddling with the intonation!

    "Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski

    "Just because I don't care, doesn't mean I don't understand." - Homer Simpson

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  • Paul_CPaul_C Frets: 5701
    you can see that with a "normal" six string electric set, the thicker the plain string, the further back it (usually) goes, then the same for the wound strings, in two groups of three - if it's an acoustic with a std. set, it's the two plain and the four wound strings in two angled lines.

    each string, even when it's exactly the same claimed (if you took 20 "9s" you'd probably find some that were 8.5, some that were 9.5) thickness, intonates slightly differently.
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  • ICBMICBM Frets: 58105
    edited November 2013
    Paul_C said:
    each string, even when it's exactly the same claimed (if you took 20 "9s" you'd probably find some that were 8.5, some that were 9.5) thickness, intonates slightly differently.
    No it doesn't. If a plain string made from the same type of steel (and they all are, to a very close degree) and is the same thickness then it will intonate exactly the same. The tolerance on string gauges is a lot tighter than that too - probably better than +/- .0001" for the plain strings, and a little more for wound ones because they're made from two wires and the compression and tension as they're wound on may vary slightly. For wound strings the core-to-wrap ratio matters because the intonation is mainly determined by the core, which is where some variability from one brand to another does come in.

    The difference in intonation even between two gauges such as a .009" and a .010" is negligible anyway. It's fairly rare to have to adjust the intonation much even when changing gauges - so much so that PRS can make a stoptail bridge with fixed intonation (with overall adjustment at the two ends, but not much) and it will intonate fine with any gauge from at least 9-42 up to 11-50.

    "Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski

    "Just because I don't care, doesn't mean I don't understand." - Homer Simpson

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  • mike_lmike_l Frets: 5692
    I check mine when I change strings, and have stretched the new strings. open and 12th fret and 12th fret harmonic. all fall within 1cent on a boss tuner.

    Ringleader of the Cambridge cartel, pedal champ and king of the dirt boxes (down to 21) 

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  • mike_l said:
    I check mine when I change strings, and have stretched the new strings. open and 12th fret and 12th fret harmonic. all fall within 1cent on a boss tuner.
    Great!   :)
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  • HAL9000HAL9000 Frets: 7392
    mike_l said:
    I check mine when I change strings, and have stretched the new strings. open and 12th fret and 12th fret harmonic. all fall within 1cent on a boss tuner.
    Surely the 12th fret and 12th fret harmonic are the same? Would you better to check, say, the low E string at the 17th and check that it's in tune with the A?
    I play guitar because I enjoy it rather than because I’m any good at it
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  • HAL9000 said:
    Surely the 12th fret and 12th fret harmonic are the same? Would you better to check, say, the low E string at the 17th and check that it's in tune with the A?
    Is that the idea though. They should be the same, but if the intonation is out then they're not.
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  • mike_lmike_l Frets: 5692
    edited November 2013
    HAL9000 said:
    mike_l said:
    I check mine when I change strings, and have stretched the new strings. open and 12th fret and 12th fret harmonic. all fall within 1cent on a boss tuner.
    Surely the 12th fret and 12th fret harmonic are the same? Would you better to check, say, the low E string at the 17th and check that it's in tune with the A?

    They should all be the same, and 24th fret too.

    So, a high e, would all read e at 0/12/24 fret, and 12th fret harmonic, if not the intonation is out.

    edit, I should have said the tuner reads e and is dead on, if it reads e (or other than e), but the gauge is off centre on any position then the intonation is out.

    It would be much easier to show this than write it.

    Ringleader of the Cambridge cartel, pedal champ and king of the dirt boxes (down to 21) 

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  • But to set the intonation you just need to do 12th fret harmonic vs 12th fret fretted note.
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  • Or you can use a capo on the third fret (say) and check the fretted note and harmonic at the 15th, removing any effects the nut may have.
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  • vizviz Frets: 8304
    Unless the frets are out, in which case you'd want to play bottom E and 12th fretted E to make a compromise.
    Anything that isn’t pentatonic is pretentious wank -  LastMantra
    more on the strength of my ability to own a PA than to play a guitar” - ICBM
    Be yourself. Everyone else is taken. Better to sound like an individual than a clone” - Merlin
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  • viz said:
    Unless the frets are out, in which case you'd want to play bottom E and 12th fretted E to make a compromise.

    If the frets are out then surely setting the intonation is (a) impossible (whereabouts on the mis-fretted board to you want it to intonate correctly?) and (b) the least of your problems!

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  • vizviz Frets: 8304
    True!
    Anything that isn’t pentatonic is pretentious wank -  LastMantra
    more on the strength of my ability to own a PA than to play a guitar” - ICBM
    Be yourself. Everyone else is taken. Better to sound like an individual than a clone” - Merlin
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  • imaloneimalone Frets: 747
    ICBM said:
    The reason for the 'stair step' layout of the saddles is because the thicker the string, the more the pitch rises when you bend it… but that mostly apples to the *core* of a wound string (not the whole thing) so the D intonates about the same as the B and the A the same as the G. because their cores are roughly the same diameters.
    Is it not actually more the speaking length effect of string thickness? Stretch dependence (rather than tension dependence) of pitch should be relatively independent of gauge (except for changing proportion of wind to core, which is not trivial, but not an effect for plain strings).
    Or: T/A = E s / l
    (2fl)^2 = T / rho = T / (A d) = E s / (l d)
    l length (ignoring different scale and string length for simplicity), T tension, s string extension, A cross section area, d bulk density, rho length density, f frequency.

    HAL9000 said:
    Surely the 12th fret and 12th fret harmonic are the same? Would you better to check, say, the low E string at the 17th and check that it's in tune with the A?
    Do you mean 12th fret harmonic and open? 12th fret harmonic and 12th fret can be different, since 12th fret harmonic is in the middle of the string speaking length and 12th fret itself is not necessarily (which is why you're adjusting intonation). 12th fret harmonic and open should be the same, though I've seen them different with old strings (not sure why, maybe stiffness or accumulated dirt, one reason to use fresh strings for intonating).
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  • ICBMICBM Frets: 58105
    edited November 2013
    imalone said:
    Is it not actually more the speaking length effect of string thickness? Stretch dependence (rather than tension dependence) of pitch should be relatively independent of gauge
    No, not at all - it's the stretch dependence which causes the pitch dependence. Try bending the top E and the G (plain) by the same amount sideways at the same fret (so the speaking length is the same) and see which changes pitch fastest.

    "Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski

    "Just because I don't care, doesn't mean I don't understand." - Homer Simpson

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  • WezVWezV Frets: 12623
    edited November 2013

    I do the standard 12th fret harmonic compared to 12th fretted note, but I also check 5th fret against 17th fret quite often too.  tune to make the 5th fret note in tune (ignore if open string is in tune or not), adjust intonation till 17th fret also plays in tune

     

    the first check is usually best and all you need to do if you know your guitar is set-up right already.  if all is good setting one way will mean the other is fine anyway

     

    the 5th and 17th fret check helps to see for nut or fret placement issues.  nut issues are way more common and much easier to fix than fret placement issues. 

    occasionally you come across an old guitar with issues and you have to balance between the harmonic/12th fret method and the  5th/17th method to get something that plays mostly in tune over most of the fretboard -  without modding the guitar

     

    compensated nuts change the rules a bit too, genreally the string needs less compensation with these. 

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  • Isn't the point of intonating the guitar is so that harmonic and 12th fret are the same pitch?
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  • WezVWezV Frets: 12623
    edited November 2013

    no, the point of intonating a guitar is to get as many of the notes on the fretboard playing in tune as possible.

     

    getting harmonic and 12th fret to the same pitch is one way of measuring this.  one way that works well most of the time, assuming everything else is set-up correctly

     

    if you have the time you should go through every note on your guitar with a tuner,  you will start to see how inaccurate it really is

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