Official Luthiers Forum!

This is an attempt to keep a former thread in play, by one not particularly qualified to do so, and quite tired to boot. Ed Kottick wrote a wonderfully complete yet concise article on the subject, for the predecessor to
'American Lutherie', about twenty-five years, iirc. I'll bet Alan Carruth remembers it, and I wish he was
writing now. Still, I think the issue is imp't enough in principle that a layman might shed a bit of light,
to be happily corrected in case of error (and there will be errors).

The real issue in tuning any musical instrument is the *Pythagorean Comma*: the musical intervals do
not add up acoustically as they appear to mathematically. Put most simply, twelve *fifths* do not fit
into seven *octaves*. This leads to all kinds of problems, and there have been many attempts at solution
of same. I used to have a book of 3-400 pages listing the various temperaments that have been used in
attempting to deal with the Pythagorean Comma. Equal Temperament is our 18th c. solution to an
insoluble problem, and it works ok; *it's also what our ears are used to*. In this system, octaves and
unisons are perfect and pure (not the same thing), fifths and fourths are beat slightly, major thirds
are beat strongly (far from pure) anf minor thirds are...well, don't ask.

The slightly larger point I'm trying to make is that equal temperament itself, while a worthy goal for
the guitar in making the inst more-or-less playable in all keys, is just one way of dealing with
the bigger problem, and achieving equal temperament in itself *will not* circumvent or surmount
the issue of getting all intervals to play in tune *in more than one key*. I hope this post stimulates
more discussion and debate, and that any mistakes I've made will be corrected. Again, I wish I had
Ed Kottick's article; this was all well explained by a Master. CW

I'll have to lok up that Kottick article; it's been a long time.

I have a book entitled 'Lute, Viols and Temperaments', in which the author points out that, for fretted instruments, there is not much of a choice except equal temperament. All the other systems use more than one size of semitone, and thus would call for crooked frets. I've seen those for sale, BTW, but, of course, if you want to use something other than standard tuning.....

Even if you get the frets in the right places, and compensate the saddle and/or nut perfectly (HA!) there are still things that can throw off the tuning and intonation. The most important one is probably the fact that top of the guitar moves, and the bridge with it. Notes close to a strong top resonance can be pulled sharp or flat, depending on the frequency relationships. The thing is that only notes close to a resonance will be effected; the rest of the notes on that string will be more or less right.

As an example; if your 'main top' resonance is a bit higher in pitch than the open G string, the pitch of the open string will be pulled sharp (iirc). Naturally, to get the tuner to say the right thing you'll slack off on the tension just a litte. The problem is that the G# will be pulled _flat_ by the top motion, and since you already slacked off the string a bit, it will be even flatter. The pitches will get a bit better as you go up, but they won't be right.

Careful placement of the top and air resonances can help with this, and a heavier bridge will probably help more, at the cost of a little volume. But there's no way to eliminate this issue entirely on a guitar that you can hear.

The wonder is that this is not more of a problem than it is.