<HTML>n a message dated 1/2/01 7:05:11 PM Central Standard Time, cneuman@phy.duke.edu (Charles Neuman) writes: What is the temperament of a guitar? As I understand it, the strings are tuned to each other in perfect intervals, so it can't be equal temperament. The frets determine the intervals on each string. Do they make an equal tempered scale on each string? There lots of interesting comments.  Both Richard and Ed I agree with.  What I have seen so many people do is to tune the bottom 4 strings pure and the B3 to the E4 as pure with the E2-E4 double octave pure:  essentially a Pythagorean tuning.  Then when the strum the chords they want to ply, it sounds terrible so they start trying to make them sound sweeter.  It's as simple as that. Some experienced musicians know how to get what they like more methodically than others but in general, they have no concept of a *tempered* interval, only a pure one.  Other string players mostly try for pure 4ths or 5th, as the case may be.  O good bass player, however knows to tune his 4ths wide.   In many cases, these "pure" intervals may in fact be tempered just a bit haphazardly, and may, in fact, be tempered the wrong way.  It is all in how much experience and in depth knowledge the individual musician has. Here is my take on the guitar:  It is *designed* for Equal Temperament.   There, aren't you surprised?  I actually admitted that a musical instrument was *intended* to be tuned in ET!  However, (and you *knew* I was going to say something that would *destroy* the monolithic ideal of ET, didn't you?) a true and perfect ET is rarely attained for the same reasons it is difficult on the piano.  People don't know enough about how to get the temperament truly equal so they make typical errors which are the result of typical but misguided tuning habits. A guitar nicely tuned in ET does not sound bad but it is possible to create somewhat of a Well-Tempered sound but only within a narrow range.  It is analogous to the Pythagorean type sound you get from tuning pure 4ths.  All you have to do is temper your 4ths a little more than for ET and you will have a sweeter sounding guitar.  But again, only up to a certain and limited point.  You cannot go all the way to 1/4 Syntonic Comma Meantone.  But what you can do is get about half way there with what ends up being a Vallotti type temperament. The following is something I saved for some reason from a post I made a year and a half ago on this subject.  Be sure to search the archives if you are interested.  There are some who claim that only ET will work, otherwise the guitar is simply mistuned.  After that, I will post the two schemes which represent the two Well-Tempered possibilities there are for the six string guitar. "I have only the most basic skills with a guitar but sometimes "necessity is the mother of invention".  I was among the cast of a production of The Man of La Mancha when it became apparent to me that I could help the guitarist a little by tuning his instrument for him.  The circumstances were that the Opera company, with its proverbial limited budget, could not find or afford an available well-qualified guitarist. They did find someone who was a student of Spanish style guitar playing who looked good in the costume they had for him.  He not only had trouble tuning his instrument but also following the ensemble.  Everyone pitched in to help him, including me.  He had a fine guitar.  The fact that the guitar has a fret board which serves as a grid for ET is obvious.  I however theorized that you could still make a Well Tempered Tuning out of it by slightly altering the pitch of the various strings. Now, the guitar does not have a C string.  The tonality of C is usually the center and starting point of all usable HT's.  There is one HT however which can easily be tuned from A and still get the proper C tonality, the Vallotti.  It is a very easy HT for ET tuners to understand:  All 5ths (or 4ths) between two black keys or a black and a white key are pure, the rest of the 4ths & 5ths between the white keys are tempered exactly twice as much as in ET. I could see how I could temper the strings of the guitar, E-A-D-G-B-E exactly the way I would on the piano, twice as much as in ET.  I reasoned that the frets then would provide the in between notes exactly the same as they would be found in a completely worked out scale.  It apparently worked. I showed the orchestra conductor the results.  G Major for "Little Bird, Little Bird", as sweet as candy.  Then I showed him the difference between the serenity of A minor and the dark, disturbing sound of Bb and Ab minor.   Both keys are found in the score.  The conductor was impressed and I had the guitarist tune each of his strings to the program I made for him in my SAT each time before he went on.  He ended up having a nice, on-pitch, professional sound. But what I have shown you is about the one and only thing that you can do besides tuning in strict ET.  That is the limitation of the guitar.  You cannot do any and all other kinds of temperament schemes.  On another occaision, I saw a guitarist who, to my surprise, seemed to know how to do the very same thing I had experimented with.  The guitarist at the event was named Kevin Gallagher.  I hear he is from New York. It was obvious to me that he knew many different ways in which he could manipulate the tuning of his guitar.  He also used some nonstandard tunings where he lowered the lowest two strings to make them play entirely different notes.  He was adept at pulling on the string to stretch it out and stabilize it after having changed the pitch radically.  The audience and other musicians waited patiently for him each time he retuned.  I have never seen a guitarist tune so meticulously and in such a variety of ways." Chart for Well-Tempering the Guitar in either the 18th Century (Vallotti style) or the late 19th Century Victorian style. *All values are read on octave 4*  (very important) 18thC  Victorian E2:  -4.0     -2.0 A2:   0.0      0.0 D3:   2.0      1.0 G3:   4.0      2.0 B3:  -2.0     -1.0 E4:   0.0      0.0 Bill Bremmer RPT Madison, Wisconsin </HTML>