Detwelvulate!

by

Ivor Darreg

Fretted instruments -- and especially the guitar -- have reached an all-time peak of popularity. While the keyboards, such as the piano, cannot easily be redesigned for more tones per octave, it is quite practicable and not too expensive to remove the 12-tone frets from a fingerboard and re-fret to some non-twelve scheme. Indeed, it has now become the logical starting-point for those who wish to explore new scales and new moods.

True, the traditional strings -- violin, viola, cello, and bass -- have no frets, and the voice is free to roam where it will. But-the twelve-tone equal temperament tuning is everywhere around us, and thus has PROGRAMMED us with psychological frets such that we cannot imagine the other pitches between those imposed artificial half-steps, and a method of de-conditioning our ears is necessary. The psychological programming is much more real than you would think -- just try going against it if you don't believe me!

If it takes a student piano tuner about six months to learn where to put the twelve customary tones in their assigned places, obviously it may take longer for the would-be xenharmonist to tune by ear to some non4welve system. So a good many people give up without trying -- they read the fascinating descriptions of new instruments and their possibilities, but don't know how they would tune a new instrument even if it were given them. (I speak from experience.)

Even if you are an experienced keyboard player, I still suggest: start experiencing the new tunings and new moods and greater possibilities by taking up the guitar. Either have a guitar re-fretted to the 19-tone scale, or do it yourself if you can. This is the best entering wedge, no matter what other non-12 scale or scales you will eventually prefer. The reasons are: 1) 19-tone being approximately "third-tones", the new intervals will jar your habit-patterns out of their preprogrammed ruts; and 2) the 19-per-octave frets are not so close together as to bother the average person's fingers getting in between them.

I suppose I must insert a "disclaimer" here: I am not against just intonation; indeed I compose in just systems and have used them on the cello and other instruments for 40 years. I build just instruments. Some of you may place just, calm, perfect intervals as the main priority. Nevertheless, all of us are up against a tremendous ear-conditioning problem -- with 12-tone-tempered music assailing us day in and day out for all our lives, we have to do something DRASTIC to escape its influence.

If you ever learned to speak a foreign language such as French or Russian, you will know what I mean! The tyranny of habit fights you every step of the way.

In order to hear the subtleties of just intonation such as the comma 81:80 and the septimal intervals 64:63 and 36:35, it is better to start by de-conditioning our hearing with wider intervals which differ sufficiently from 12-tone intervals to force new listening habits. And a 19-tone guitar will do this for us.

Another advantage of starting with 19-tone is that you can read conventional guitar sheet music right off and play 95% of it in l94one without any alteration in the notation, even though it may sound strange in places well that's how it should sound anyway. With 19, it's not necessary to bother inventing new accidental signs.

That is to say, we have to start SOMEWHERE, and from experience of a number of real live people this is the best way to begin detwelvulating. If you insist on doing things the HARD way, go ahead, but why? This method works better. It also costs less to start this way.

After you have used l94one enough to appreciate its mood, you can go on to other scales: 22-tone, which has another mood, and which does involve notation problems but is no more difficult on the guitar.than 19; 3l4one, which supplies an exceptionally calm and serene mood much needed by all of us in these troubled times. Then, after exploring those important temperaments, one can go on to 17-tone with great brilliance and impact, to 24-tone (quartertone) which conserves and contains 12-tone, to 34-tone which includes 17 but supplies more restful harmonies than 17, and after these, the sky is the limit -- plenty of virgin territory for everyone to explore for a long time to come. If I don't propagandize here for 13 or 27 or some other number of frets per octave, it's merely because I have not had time to explore them yet, so don't want to prejudice you one way or the other until I have HEARD those systems.

Just-intonation fretting is possible, but it raises tuning and fingering problems. Even to play in one key, such as C major, it is necessary to introduce a pair of tones a comma 81:80 apart, which is approximately 1/55 octave, and for many people such a pair of frets is too close together for their fingers. If we are to carry just intonation far enough to do any justice to it, we must provide quite a number of commatically-spaced pairs of triplets of frets, and besides that, as shown by Partch and other practitioners of just intonation -- including me -- the septimal or 7-based intervals and maybe the 11-based intervals should be represented by one or two extra frets. This is simply too much complication for anybody who is just beginning to go outside the Twelve-Tone Environment. You have to be fairly advanced to cope with such difficulties.

Since the electric guitar became popular, its amplification can overcome some of the difficulty associated with the duller tones stopped on the strings of a fretLESS fingerboard. Such fretless guitars and basses are now on the market. You may wish to add painted or inlaid position markers for certain just intervals, as Partch did in his Adapted Guitars. If such a guitar has painted markings for 12-tone, don't remove them; this is good practice to see how much the just intervals differ from the l2-tone temperament -- simply add the markers for just. Your fingerboard then becomes a useful Comparison Chart. It is of course entirely possible to point on or inlay additional markers for l94one or other temperaments also. Preferably in different colors.

Personally, I prefer to meet the just-intonation problem in another way: the Hawaiian or steel guitar has no frets, mere fret-LINES which conventionally are placed where 12-tone frets would have been. By inventing new instruments on this principle, and expanding them to greater length and more strings, it is possible to obtain just intervals and chords at any pitch whatsoever by simply placing the "steel" where we hear the desired tone or chord. With these instruments the refretting process reduces to drawing a fret-line-chart on cardboard or plastic and laying it under the strings. Maybe there is a friendly pawnshop near you with a steel guitar. If so, Instant Justice!

Don't try to take the marking of just intervals too far, because they will merely bewilder you. Carry out the just markings to at least 20 notes per octave, and maybe 30, but if they cover each other up and make things look untidily complicated, you have defeated your own purpose. In actual practice, you can ESTIMATE commas and septimal commas even where they have not been marked.

It will be obvious enough that, desirable as many-toned temperaments such as 41, 43, 53, 65, 72, 77, etc. are going to be on certain instruments, such temperaments carried down a fretboard will soon end up as a solid sheet of metal! Even the colored markers for them would fuse into a modernistic design which would completely hide the ground-color of the fingerboard. This article is about how to START, not about the more advanced stages. We are trying to provide you with an affordable entrance to this fascinating field. We don't want to give any more alibis to Professional Procrastinators.

Now we come to considerations of How-To. Frets are made of brass or bronze or nickel-silver alloy, in a sort of T-section pattern, usually with little barbs on the web so that when pressed or hammered into the sawed groove or kerf, they hold firmly. Since strings are slightly stretched by pressing them down against a fret, precision of intonation on fretted instruments is limited. Usually a correction of the nut must be made -- it should be 1 to 1 1/2 mm closer to the first fret than theory would demand. This again depends on what kind of strings are used, and can be circumvented by the device of having a zeroth fret about 3 mm from the nut. Differences in the characteristics of strings still require, in many cases, adjustable bridges to compensate for errors in intonation.

Fingerboards cost enough that generally we must re-use them. The old frets can usually be re-used also, if they are not worn too much by strings cutting into them. With prying tools, carefully coax them out of the old 12-tone grooves, and fill in the slots with plastic wood or similar material, which may be stained down with woodstain or shoe-dye. Ordinarily, leave the octave fret (formerly 12th fret) in. Once in a while you can't do this because you wish to change the scale length, or because the new fret material is too different from the old. Beyond the first few frets, say beyond a fifth or minor sixth, if the new calculated fret position is a millimeter or less from the old 12-tone l)osition, leave that old fret alone! No one will EVER know.

With fewer tones, such as 17 or 19, it generally will be possible to put frets all the way down the fingerboard, but by the time we reach 22 or 24 or 31, it is wise to stop inserting frets when they get too close for practical use. Beyond that point, simply engrave lines into the fingerboard and color the grooves with white or yellow paint; and in some cases it helps to cement a thin sheet of clear plastic over it so that the strings won't be pressed down too far. Similar common sense suggests that it is not necessary to carry the frets beyond the octave across all six strings, because nobody stops the bass strings up there anyway.

If all guitars had the same scale length (active string length), I could give a set of tables for that length and take care of everything. Unfortunately, there is no standardization, so I will give the 19-tone frets for 650 mm, approximately 25-5/8 inches, which is a common length, and for 1 meter, so that other lengths can be calculated from that, as for other-sized guitars, banjos, mandolins, etc. You can use the full 1 meter for markings on a monochord. Bass instruments have a bewildering variety of different lengths. Steel guitars generally have a rather short scale length. Tables for many systems -- including just and special unequal temperaments -- will be available from me on special order.

So far I have been assuming the ubiquitous guitar. But there are other freeted and fret-lined instruments. There is a mandolin family corresponding to the violin family. While a 31-tone mandolin would be too difficult beyond the first dozen frets, there is no problem with putting one in 17- or 19-tone. So with banjos, we should mention that the crisp bright tone of a banjo would give a dazzling brilliance in the 17-tone system. There are Near Eastern and Oriental instruments such as the baglama with adjustable frets-these are easy enough to make, being made of a few turns of wire around the neck of the instrument, tightly twisted together in the back, with enough leeway allowed for moving them if one desires to change the tuning.

The VIOLS of the Renaissance had gut frets of this adjustable sort, tied in back with some kind of knot. What with the growing use of the guitar in so many fornis, we might as well revive the viols while we are at it, since their tuning is so similar. Viol frets were carried up only a short distance on the finger-board, so need be installed only for a fifth or sixth from the open string. Still other kinds of moveable or adjustable frets are found on the instruments of China, India, and other countries.

Most people exploring beyond twelve-tone will be interested in making or using a monochord. It is customary nowadays to put a meter ruler down on the soundboard underneath the string(s); one may as well add markers for the just and/or non-12 systems, to permit placing the usual moveable bridges properly. Note that corrections for the two ends of the string may be necessary-perhaps the bridges at either end should also be adjustable.

In summary, the placing of frets or fret lines determines a tuning system without need either for an expensive electronic tuning device or for special training in how to tune by ear which is necessarily a time-consuming process. Once the fret positions have been calculated, that tuning is determined for all time, and all future instruments. It then becomes a mere matter of copying the measurements onto the new fretboard. These figures are also useful in laying out string lengths for other kinds of stringed instruments: harpsichords, clavichords, whatever.

A word about tolerance in the engineering sense: The instruments discussed here are not precision affairs. Nor is an animated musical performance either. It is impossible to eliminate all fretting errors. Fortunately it doesn't matter. So there is no point striving for extra decimal places. Just do it accurately enough to convey the mood of the new tuning system. If you have your instrument repairman do the fretting, as is usually the case, don't ask him for better than 1 mm precision -- the attempt would cost too much, and wouldn't be audible anyway. One millimeter in 650 is better than one fifth of 1%, so let's be reasonable about what we ask for. If someone insists on fret measurements in 32nds and 64ths of an inch, they will have to look elsewhere -- I'm not going to fuss with those awkward fractions, hence I have gone metric in this affair. Hundredths of an inch can be calculated from the millimeter tables on an ordinary pocket calculator.

There is a time- and money-saving hint to pass on: Suppose you want to explore more systems than you can afford guitars for. The tolerances are such that you can fret a guitar to 18-tone (third-tones) and move the bridge so that the 17th, or the 19th, fret sounds the octave instead of the 18th. The resulting other scales will be usable up to at least the octave fret and a little beyond. Thus, three systems for the price of one! And, to make an 18-tone fingerboard out of a 12-tone one, yank out only every alternate fret and leave the 6-tone frets in. Then put three frets where there had been two -- i.e. intercalate two frets between the 6-tone frets left in. Please don't let the mathematicians spoil your fun. Similarly: take a 12-tone instrument and leave ALL the l24one frets in. Place quartertone frets between them. Now you can move the bridge and get passable 23-tone and 22-tone scales -- again up to the octagve fret and a little beyond.

The object of this article is to get you started PLAYING and HEARING non-12-tone tunings and their new effects. No need to be over precise at first: life is too short!