How to fix intonation ?

[MC5C]

Now to add relief into the equation - if you have a lot of relief, the middle frets will have to stretch proportionately farther than the frets above and below the relief curve in the neck. The only way to accommodate that is to design in the relief, lock it in with a theoretically stiff neck, and move the fret positions to idealized locations. I hope no one takes this seriously, but it's true....

[Monsoon1]

Originally Posted by Rodger Knox

Nothing changes the scale length once the fret slots are cut. The scale length is a number used to determine the distances between frets, and has nothing to do with compensation. The vibrating length of the string is what changes with compensation, and along with string mass and tension determines the pitch produced.

Exchanging the term scale length for compensation, it still winds up that 1/16" change in string length still equals 1/16" of change, vs pressing a string down 1/16" where it's as you pointed out, much less of a change.

[charles Tauber]

Originally Posted by Monsoon1

Exchanging the term scale length for compensation, it still winds up that 1/16" change in string length still equals 1/16" of change, vs pressing a string down 1/16" where it's as you pointed out, much less of a change.

I don't understand what point you are making. Scale length is one thing, compensation is another. Hence one can't "exchange" them. They are different things, though related.

As pointed out, you can move the nut and/or saddle anywhere you want, but it doesn't change the scale length - where the frets are located relative to each other.

Depressing a string 1/16" produces only a small change in vibrating string length, not a 1/16" change in length.

[bausin]

Never mind. I could only edit my post, not delete it.

[Monsoon1]

Originally Posted by charles Tauber

I don't understand what point you are making. Scale length is one thing, compensation is another. Hence one can't "exchange" them. They are different things, though related.

As pointed out, you can move the nut and/or saddle anywhere you want, but it doesn't change the scale length - where the frets are located relative to each other.

Depressing a string 1/16" produces only a small change in vibrating string length, not a 1/16" change in length.

I'm saying that regardless of using the wrong term, changing the string length by 1/16" is a greater change than pressing the string in by 1/16".

[Monsoon1]

Originally Posted by charles Tauber

Not Alan, but yes. The nature of the beast.

I thought the problem on a guitar was because of the string being stretched as it's being fretted. But that doesn't happen on an electronic keyboard. Is there an imperfection to the scale?

[John Arnold]

I thought the problem on a guitar was because of the string being stretched as it's being fretted. But that doesn't happen on an electronic keyboard. Is there an imperfection to the scale?

You are confusing intonation wth the tempered scale. Intonation is concerned with how accurate the note is to being in tune. But 'in tune' usually means the tempered scale. The equal-tempered scale is structured so that only the octaves are perfect. All other intervals are approximate to what sounds 'pure' or true. For example, the tempered major third sounds sharp. If you tune the major thirds by ear, the upper string will be flat when it is used for anything other than the third in a chord. Example, if you tune to an open G chord, the second string will be flat when you play a C or D chord, where the B string becomes the root instead of the third.

Open E good up in 1st positions, weird down on 13/14.

By 'weird', do you mean sharp or flat?
If a note is sharp, you need to lengthen the string. If it is flat, you need to shorten it.
Instead of playing chords, you need to play individual notes. The problem with chords is explained above.

[charles Tauber]

Originally Posted by Monsoon1

I thought the problem on a guitar was because of the string being stretched as it's being fretted. But that doesn't happen on an electronic keyboard. Is there an imperfection to the scale?

As John pointed out, there are two separate things that are involved. The first is what are the desired pitches you want your instrument or voice to achieve. This is related to temperament. The second is how closely is your instrument able to achieve the desired pitches. This is "intonation".

Some of the earliest scientific work done on sound and music is attributed to Pythagoras. To make a long story short, he identified sounds that are "consonant" and sounds that are "dissonant" and created a 12-tone scale that is now the basis of Western music. The scale is based on intervals between two pitches (string lengths) that are all ratios of whole numbers. That is 1:1, 1:2, 2:3, etc. The system has an inherent flaw known as the Pythagorean Comma. The flaw is that the system produces two different sizes of semi-tone, the result of which is that the same note will sound perfectly in tune with one note and sound quite out of tune relative to another.

People have known about the Pythagorean Comma for centuries and have tried many different methods to eliminate it or avoid it. For example, for a very long time, musicians avoided large changes in key signature within a single piece of music. Lute makers (and players), with the moveable, tied frets of lutes, tried many, many different schemes, including moving the nut relative to the frets (now called "nut compensation"), moving the frets around (now seen in schemes with "special" fret placement) and so on.

Numerous systems have been devised to "temper" the problem of the Pythagorean Comma. Most music of the Western culture has now nearly universally adopted the system of equal temperament as the standard of what pitches an instrument should achieve. Equal temperament is a system that produces a compromise that allows all notes to be equally in - and out - of tune in every key. Nearly all guitars use a fret placement designed to achieve equal temperament.

The catch is that equal temperament is a compromise. Even if an instrument perfectly achieves the desired pitches of equal temperament, the instrument will still sound out of tune: equal temperament isn't what the ear wants to hear as "in tune".


No guitar will ever perfectly achieve the desired pitches: no guitar will ever have perfect intonation. (Electronic keyboards, for example, can, but will still sound out of tune due to the pitches being equal temperament, rather than Pythagorean tuning.) However, many guitars do not have even "good" intonation - they do not accurately achieve the pitches of equal temperament over the range of the instrument. That they do not achieve "good" intonation is a design and setup issue, rather than a fundamental aspect of the instrument.

The question is how close to perfect is good enough? The answer varies with the listener. A "good" ear can distinguish between two pitches 2 cents (2/100ths of a semitone) apart. My experience is that many guitars achieve around 10 cents over the range of the instrument. For many players and listeners that is good enough. For others it is not and sounds out of tune. Regardless, even if the guitar perfectly achieved the desired pitches, the pitches it produces are not what the ear wants to hear as "in tune": even if the guitar plays perfectly in accordance with equal temperament, it will still sound out of tune.

The starting point for "playing in tune" is to have accurate intonation. If the notes an instrument produces are "all over the place" - some sharper than the target and some flatter than the target - attempting to tune the instrument as best as possible will be an exercise in futility, in chasing one's own tail. As you get one note in tune, on one string, relative to another note on another string, then compare it to a third note on a different string, it's like trying to build a foundation on Jello where everything moves.

Once one has accurate intonation, one must chose a consistent method of tuning the pitches (tensioning the strings) of the instrument. If using comparative methods, but for octaves, one can't mix harmonics with fretted notes: harmonics belong to Pythagorean tuning, fretted notes belong to equal temperament and differ except at the octave.

In the end, one choses how "arbitrarily close" is close enough for ones own ears and playing.


A more detailed description of the subject, including an introduction to nut compensation, can be found in the unabridged version of my Basic Guitar Setup: http://charlestauber.com/luthier/Res...1-Sept2018.pdf

[Monsoon1]

Originally Posted by John Arnold

You are confusing intonation wth the tempered scale. Intonation is concerned with how accurate the note is to being in tune. But 'in tune' usually means the tempered scale. The equal-tempered scale is structured so that only the octaves are perfect. All other intervals are approximate to what sounds 'pure' or true. For example, the tempered major third sounds sharp. If you tune the major thirds by ear, the upper string will be flat when it is used for anything other than the third in a chord. Example, if you tune to an open G chord, the second string will be flat when you play a C or D chord, where the B string becomes the root instead of the third.



By 'weird', do you mean sharp or flat?
If a note is sharp, you need to lengthen the string. If it is flat, you need to shorten it.
Instead of playing chords, you need to play individual notes. The problem with chords is explained above.

Again, does this effect an electronic keyboard?
Yes/no

[Monsoon1]

Originally Posted by charles Tauber

As John pointed out, there are two separate things that are involved. The first is what are the desired pitches you want your instrument or voice to achieve. This is related to temperament. The second is how closely is your instrument able to achieve the desired pitches. This is "intonation".

Some of the earliest scientific work done on sound and music is attributed to Pythagoras. To make a long story short, he identified sounds that are "consonant" and sounds that are "dissonant" and created a 12-tone scale that is now the basis of Western music. The scale is based on intervals between two pitches (string lengths) that are all ratios of whole numbers. That is 1:1, 1:2, 2:3, etc. The system has an inherent flaw known as the Pythagorean Comma. The flaw is that the system produces two different sizes of semi-tone, the result of which is that the same note will sound perfectly in tune with one note and sound quite out of tune relative to another.

People have known about the Pythagorean Comma for centuries and have tried many different methods to eliminate it or avoid it. For example, for a very long time, musicians avoided large changes in key signature within a single piece of music. Lute makers (and players), with the moveable, tied frets of lutes, tried many, many different schemes, including moving the nut relative to the frets (now called "nut compensation"), moving the frets around (now seen in schemes with "special" fret placement) and so on.

Numerous systems have been devised to "temper" the problem of the Pythagorean Comma. Most music of the Western culture has now nearly universally adopted the system of equal temperament as the standard of what pitches an instrument should achieve. Equal temperament is a system that produces a compromise that allows all notes to be equally in - and out - of tune in every key. Nearly all guitars use a fret placement designed to achieve equal temperament.

The catch is that equal temperament is a compromise. Even if an instrument perfectly achieves the desired pitches of equal temperament, the instrument will still sound out of tune: equal temperament isn't what the ear wants to hear as "in tune".


No guitar will ever perfectly achieve the desired pitches: no guitar will ever have perfect intonation. (Electronic keyboards, for example, can, but will still sound out of tune due to the pitches being equal temperament, rather than Pythagorean tuning.) However, many guitars do not have even "good" intonation - they do not accurately achieve the pitches of equal temperament over the range of the instrument. That they do not achieve "good" intonation is a design and setup issue, rather than a fundamental aspect of the instrument.

The question is how close to perfect is good enough? The answer varies with the listener. A "good" ear can distinguish between two pitches 2 cents (2/100ths of a semitone) apart. My experience is that many guitars achieve around 10 cents over the range of the instrument. For many players and listeners that is good enough. For others it is not and sounds out of tune. Regardless, even if the guitar perfectly achieved the desired pitches, the pitches it produces are not what the ear wants to hear as "in tune": even if the guitar plays perfectly in accordance with equal temperament, it will still sound out of tune.

The starting point for "playing in tune" is to have accurate intonation. If the notes an instrument produces are "all over the place" - some sharper than the target and some flatter than the target - attempting to tune the instrument as best as possible will be an exercise in futility, in chasing one's own tail. As you get one note in tune, on one string, relative to another note on another string, then compare it to a third note on a different string, it's like trying to build a foundation on Jello where everything moves.

Once one has accurate intonation, one must chose a consistent method of tuning the pitches (tensioning the strings) of the instrument. If using comparative methods, but for octaves, one can't mix harmonics with fretted notes: harmonics belong to Pythagorean tuning, fretted notes belong to equal temperament and differ except at the octave.

In the end, one choses how "arbitrarily close" is close enough for ones own ears and playing.


A more detailed description of the subject, including an introduction to nut compensation, can be found in the unabridged version of my Basic Guitar Setup: http://charlestauber.com/luthier/Res...1-Sept2018.pdf

Ok, now I get it. Interesting stuff.

[Alan Carruth]

Another way to think about temperament is to look at the 'circle of fifths'. Tune your A string to 110 Hz. Pluck it and touch it at the 7th fret. This divides the string into three more or less equal parts, so you hear a pitch that it three times the number of cycles per second; 330 Hz, an interval of a 12th above the open A. That's the open high E string, more or less, so you tune to that. Now do the same to get another pitch. You'll need to drop down an octave now and again to stay within the compass of the guitar: when you do that you're dividing the frequency by two. In theory, when you have done this 12 times you'll be back to A= 110 Hz, but in practice it doesn't work. That's because you've always been multiplying the frequency by three, and dividing it by two, and there's no way you can multiply a number by three and divide it by two any number of times and get back to the original number.

The difference between the pitch you started with and the one you end up with is the Pythagorean Comma. The problem of temperament is all about trying to get around that comma. Usually the trick is to cut it up into smaller pieces and distribute them around in different places. If you put it all into one interval you can play in one key pretty well, but others might not work. If it's all in the interval from C-F# (the 'wolf') you can play in the key of C with few problems, just so long as you don't play the wolf. If you want to go to G you've got problems. Various 'mean tone' schemes divide the comma into different numbers of pieces. Quarter comma mean tone allows you to play in two keys and the related minors and sounds pretty good so long as you stick to those. 12 tone equal temperament divides the comma into 11 pieces, and puts one into each interval. It allows you to play in all keys and be equally out of tune in the same way in each of them, so you can modulate freely. It also means that each of the semitones is the same size, which allows for straight frets. Mean tone temperaments have two different sizes of semitones.

Somebody always claims that Bach's 'Well Tempered' tuning was the same as 12-Tone Equal Temperament. So far as I've been able to find out, it's not. For various arcane reasons ET doesn't work well on pipe organs, and Bach was primarily an organist. They tend to use unequal temperaments, where there are semitones of a number of different sizes. By getting clever about those sizes and how they're laid out you can play in all keys, but each one sounds a bit different. Organists will talk about the different 'affects' of different keys, saying that C major works differently from G major, for example. In ET it doesn't but for them it does.

So, 'temperament' concerns the way you treat the comma. 'Intonation' is how close you come to actually playing in tune according to the chosen temperament.

[John Arnold]

Again, does this effect an electronic keyboard?
Yes/no

Yes. It 'affects' it. Most instruments have fixed notes and are designed to play in different keys. As a result, they use equal temperament.

[D. Shelton]

Originally Posted by murrmac123

Do you possess an electronic tuner ?

No longer. It was a BFTS unit that I must've included when I sold the Lowden.

[D. Shelton]

Originally Posted by charles Tauber

The ability to do so is the starting point: if you can't identify the problem, you won't be able to fix it.

Start by obtaining an electronic tuner that is calibrated in "cents" - 100ths of a semitone. One inexpensive option is an application for a phone, such as IStorboSoft by Peterson (less than $15).

Install a new set of strings of your choice.

Tune the open bass E string using the tuner. Check the pitch of 12th fret fretted note using the tuner. Write down how many cents sharp or flat it is. Check the pitch of the first fretted note (F), writing down how many cents sharp or flat it is. Repeat for the second and third frets.

Repeat the above for the remaining strings, giving you a "chart" of what is sharp and what is flat.

Once you've done that, come back and we can discuss the results, what they mean and what action is required, if any.

Than you for the clear starting point. It will take me a while to get around to it, but that's what I'll do. Just the 1,2,3 and 12 frets on all strings ?

[charles Tauber]

Originally Posted by D. Shelton

Than you for the clear starting point. It will take me a while to get around to it, but that's what I'll do. Just the 1,2,3 and 12 frets on all strings ?

You can measure all of the frets for a full map of the instrument, but the most important one's are the first fret and the 12th fret. They are the minimum necessary to assess nut placement and saddle placement.