(probably daft) Intonation question...

ICBM

I wouldn't try to set the intonation at the bridge without making sure the nut is the right height first - and the relief is correct, and the bridge height is correct, in that order. The intonation is the last thing you should adjust because it's affected by all the other adjustments, but does not affect them.

I normally check intonation by tuning the pairs of strings (E/B, G/D and A/E) perfectly using the 5th and 7th fret harmonics, then comparing the 14th-fret note on the high string to the 19th-fret harmonic on the low string, and the 17th-fret note on the low string to the 12th-fret harmonic on the high string. It doesn't matter that tuning like that doesn't produce equal temperament because you're not actually tuning to the interval, you're just using one string as a reference for the other.

GuitarMonkey

WezV said:

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

In which key though?

ICBM

GuitarMonkey said:

WezV said:

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

In which key though?

"As in tune as possible in all keys at the same time, even though not perfectly in tune in any", for me. Some people do prefer to make certain keys more in tune at the expense of others though, which is why you get those weird crooked-fret guitars.

WezV

ICBM said:

I wouldn't try to set the intonation at the bridge without making sure the nut is the right height first - and the relief is correct, and the bridge height is correct, in that order. The intonation is the last thing you should adjust because it's affected by all the other adjustments, but does not affect them.

 

I agree, nut height should always be done first... i was not suggesting that was ignored.    but nut placement can be out and will affect intonation.  rare but not so rare it can be ignored

 

Also some guitars just never quite sound right even with a perfectly cut nut, often a clear sign the nut osition is slightly out, or a  case for a compensated nut.   but adjusting the intoantion to a different set of parameters can often get it much better

ICBM

WezV said: 

Also some guitars just never quite sound right even with a perfectly cut nut, often a clear sign the nut osition is slightly out, or a  case for a compensated nut.   but adjusting the intoantion to a different set of parameters can often get it much better

My 1971 Martin 12-string is like that - apparently quite a lot of early-70s Martins were. Even though I've compensated the bridge saddle, the only way to tune it for playing with open strings is with 'ear compensated tuning'... ie just bugger about with it until it sounds least out . Luckily being a 12, it's better to use heavy strings, tune it down to D (as old 12s always were) and capo it at the 2nd, so the nut placement becomes irrelevant.

imalone

ICBM said:

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.

There is a difference, and something I forgot to take account of, but it's not string gauge. With finger bends across two string spaces:
E+3 -> F+40, 1+37/100
B+8 -> C#+20, 2+12/100
G+8 -> A+40, 2+32/100
That's fairly big. But it's not really gauge, I think it's mainly tuning. That f^2 proportional to stretch thing. A semitone is a certain multiplier, but it's a multiplier of the stretch needed to get to pitch in the first place, so the actual change in difference is still different. The obvious thing to do is try all the strings tuned the same. So all tuned to A:
(E) A+10 -> C-40, 2+50/100
(B) A+13 -> C+38 2+25/100
(G) A+1 -> B-5 2-6/100
So that's a bit weird (the E is very unstable as you might expect, but that's the best reading I could get). The extra issue here is a strat trem. Some of the bend stretch is coming from the trem, not the strings, which is why it goes the other way (the variability on that E goes up to about 2+70/100), the thinner strings take less tension, so the strings get stretched more for the same sideways bend (at the same tuning).
Which made me realise (in the absence of a fixed bridge guitar that I can plug into the computer, and since judging an exact bend distance is tricky), the test to do here is actually to pull the trem back to the body and bend the notes up as far as they go, that guarantees same stretch on all strings (and roughly same ratio stretch, ignoring the difference in length after the nut).
(B) A+8 -> A#+50/B-50 : +42 (couldn't quite lock on between the two)
(G) A-3 -> A+45 : +48
(E) E-2 -> F-17 : 85
(E) E-1 -> A+42 : 43
So, I'm now convinced you're right that the difference in note bending is the main reason for needing different intonation lengths, but I think that's actually due to the different string pitches rather than gauge. (Numbers are elixir super-lights, 648mm scale - Pacifica 112)
Edit:
Having 2&3 tuned to A sounds quite nice.

ICBM

Interesting!

Having thought about that, yes - if you have two strings of the same gauge tuned to different notes, the lower one will go more sharp for the same amount of bend. It's not strictly speaking the pitch itself that's responsible - it's that the equation for pitch vs. tension and mass is not linear, it's a square law - so a heavy string tuned lower will rise in pitch faster than a light one tuned higher, even if their static tension is the same… which they are, at least roughly - that's the point of using heavier strings for lower notes.

mike_l

fretfinder said:

But to set the intonation you just need to do 12th fret harmonic vs 12th fret fretted note.

Yep, I use the others to check the open is in tune and it's now habit to check all the points for my reference