My Quest For Intonation

[Crusader]

When I was about 15 I was told that Fender and Gibson have different methods in their fret spacing but neither is perfect. I thought this had to be rubbish, I thought there has to be a perfect mathematical formula to find the right pitch for each note. There actually is, but about 15 years ago I started looking into it and found I had opened such a "can-of-worms" it's best left alone! Now I have learnt about "Just Intonation" and the Tempered tuning system and have conceded defeat

Now my aim is just to find a fret spacing that will intonate to the tuner a little better than production-line guitars. A couple of weeks ago I got my latest build to the stage where I can start doing things. Making it was just an annoying process I had to go through to get to what I really want to do. Experiment with fret spacing. This may all seem pointless to some people because I know men like Novak and Anders Thidell have gone down this path but its what makes me tick, its my hobby

Here is the guitar in its current stage with a few frets with the tang removed and just glued on

To do my experimenting I ground the tang off some fretwire and bent it over at the end so it hangs at the correct angle. So far I have only experimented with the 6th string. I shall show results of this later

Other experimenting I have done is to find out how much each string increases in pitch when bending at the 12th fret. A string under low tension will increase in pitch more than a string under greater tension and these tests might help make some decisions

Long before the guitar was built I realised string gauge is important and I went for a 46-to-10 gauge set. I have compared the increase in pitch of the 46 set with a 52 set which I have on the LP

Focusing on the 46 gauge string I did these tests where I bent the string as far as I could

Thats about all I've done so far and I hope it has been interesting. I will post up more results later

[Ken Bennett]

How does your experiment measuring the increase in pitch of bent strings help you figure out an ideal intonation scheme?

[Tim37]

your gonna run in to problems even doing it that way because if you have the frets set up for one string the other five ar gonna still have intonation problems.

www.truetemperament.com solved the problem but its not the easiest way of doing things.

[borge]

true temperament is a whole different kettle of fish.

Equal temperament has been the standard across all instruments for hundreds of years, true temperament has massive limitations hence its all but unused today.

[Johnny Foreigner]

also, how much the pitch changes on fretting depends on how hard you fret. You can't legislate for different playing styles - you and I playing exactly the same guitar might have different results because you fret lightly and I push the string all the way to the fretboard.

[Crusader]

also, how much the pitch changes on fretting depends on how hard you fret. You can't legislate for different playing styles...

True but any problems I face doing this I'm sure you will encounter with any guitar

How does your experiment measuring the increase in pitch of bent strings help you figure out an ideal intonation scheme?

It will help me have some idea of how much the pitch increases when playing fretted notes (Measure the distance between the fret and string with feeler gauge) And I might find a particular string gauge or brand more desirable. Notice that the 52-11 set has more variation in how much it increases in pitch than the 46-10

Another thing I have been doing is figuring out how much increase and decrease in pitch there is if you move the fret up or down 0.5mm I have a Graphics calculator that can give me a formula for this and one of the formulas it spat out for me is

Y = 51805.0909X^-0.999999

Where Y is the pitch in Hertz and X is the distance from the theoretical bridge

Now here's a chart I made showing the Intonation of the few frets I've put on so far

The 6th string frets have been placed by the tuner and the 1st string frets by the standard fret spacing formula, although some of the frets didn't end up exactly where I wanted them to be. Anyway they will soon come off because straight away I see that I can't get the 3rd string to intonate. I need a shorter scale length for the 1st string. I know there will be a lot of bugs to iron-out but like I say I'm not aiming for True Temperement

[SwedishLuthier]

The problem with intonation is that we sometimes head out to fight wind mills...

Just intonation vs equal temperament:

http://en.wikipedia.org/wiki/Just_intonation

Short version (IIRC):

Just intonation; you can only play one specific scale but you will have perfect intonation.

Equal temperament; You can play every scale but all of them will have some imperfections

A bit of history:

When the equal tempered piano was introduced JS Bach was so amazed that he wrote a complete set of preludes and fuges to utilize the possibilities to play more than one scale on the same keyboard:

http://en.wikipedia.org/wiki/The_Well-Tempered_Clavier

[Crusader]

The problem with intonation is that we sometimes head out to fight wind mills...

Lots of Laughs, you're absolutely right there!

Equal temperament; You can play every scale but all of them will have some imperfections

Yes and they say it lacks "character" especially with modes ie: Phrygian, Lochrian, Dorian etc

A bit of history:

When the equal tempered piano was introduced JS Bach was so amazed that he wrote a complete set of preludes and fuges to utilize the possibilities to play more than one scale on the same keyboard:

http://en.wikipedia.org/wiki/The_Well-Tempered_Clavier

Before I had the internet one of my favourite sources of information was a book called "The Oxford Companion To Music" by Percy A. Scholes and I read the section about Bach with great interest

[Mattia]

Given the fact thicker strings require greater compensation due to their inherent inileasticity, it's no surprise variance will be greater for thicker guage strings thatn for thinner guage strings, which behave more like an 'ideal' theoretical string.

If you want to re-invent history in a madcap manner, you can design a swappable fingerboard arrangement and build use all sorts of 'wacky' fret layouts - there are some articles on the subject in one of the early Big Red Books.

[Crusader]

Given the fact thicker strings require greater compensation due to their inherent inileasticity, it's no surprise variance will be greater for thicker guage strings thatn for thinner guage strings, which behave more like an 'ideal' theoretical string..........

So a string that is less elastic will have more increase in pitch

and a string which is more elastic will have less increase in pitch, is that correct?

[Crusader]

When doing this sort of research you sometimes come up with results which are the opposite of what you might expect. For example I thought the thicker strings would increase in pitch less than the thinner strings because I thought they would be under greater tension. On the other hand they might all be under the same tension and the different results are due to other factors. I know there are mathematical formulas involving thickness, mass and length to determine string tension but I hope I don’t have to learn all that to achieve my goals

In any case what I have learnt recently may change the whole angle of what I initially intended. I have read more about fanned frets and the reason for it is the same as why grand pianos are better than uprights. A longer string will achieve a deeper note with a thinner string and therefore have less inharmonicity. Cut a long story short it leads me to thinking that different fret factors may not be necessary and this will be the focus of my next tests and experiments

[rhoads56]

Good to see someone out there experimenting! And from Perth too!

[ccfreedom]

Beautiful and good.

[Crusader]

Thankyou, I hope it is helpful to someone or at least interesting. What I have shown here is just a sample of what I've been doing over the past couple of years with guitars I've made. It all started when I had one of them on the saw ready to chop the neck off (various reasons)then it occured to me I had not checked it's intonation. So it was saved and it turned out to be fairly good

Good to see someone out there experimenting! And from Perth too!

Nice day for the beach today wasn't it? Hey, recognise that maple cap and those frets?

Well I will keep going with this when I have time, see how things turn out

[mstjean]

This company makes necks and guitars that go way beyond fanned frets and into OMFG territory:

http://www.truetemperament.com/site/index.php

The FAQ explains that it's not an attempt at any kind of "just" intonation. But it looks as if they might have done the same kind of careful plotting that you've undertaken.

Matt