New Chords and New Tunes

(Something to Fret About)

by

Ivor Darreg [1978]

Before the advent of our present-day tuning system of 12-equal temperament, which employs 12 equal semitones (one-fret intervals) per octave, many other systems -- some using more than 12 tones, others less -- existed. Like the modes that originated centuries ago to evoke different emotions, the type of tuning used on an instrument can suggest various images and feelings to the listener. In the sixteenth and seventeenth centuries, the equal temperament system became the most common in Western music, even though it narrowed down the possibilities for mood-evoking textures available to the musician.

All fretted instruments have inherently imperfect intonation, due to variations in the dimensions of frets. The fact that simply fretting a string causes it to bend (changing its pitch), and the inaccuracies in the vibrating patterns of the strings themselves. The equal temperament system is intended to evenly distribute these discrepancies over the range of the instrument so as to make them unnoticeable, or at least accentable, at any given location. Thus, the notes between octaves are only barely, and equally, out of tune. Among other advantages, the system permits the free use of inversions. and it facilitates transposition. In some other schemes, certain intervals are more accurate, because the imperfections are unequally distributed.

Twentieth century musicians and composers have sometimes felt stifled by the 12-tone system. Those concerned with the use of different sounds have looked to new models: Some have used microtones (pitches spaced closer together than the usual semi-tone); others have looked to synthesizers or to exotic instruments; and some have experimented with music concrete (splicing tape-recorded sounds in different ways to produce unusual effects). Despite the varying methods, these experimenters have been concerned with one common approach to music: xenharmonics. (The word combines the Greek term, xenos, or strange, with harmony -- thus, strange or unusual harmoities.) Xenharmonics can be applied to nearly all instruments, although this article concerns itself with modifying the guitar's fretboard so as to enable the instrument to recreate moods from the past and to be used for composing new types of music as well.

Today's guitarist has a wide range of variations on the basic instrument to choose from: acoustic, electric, small or large, 6-string or 12-string, unusually shaped, and multicolored. The list seems endless, and innovators come up with more ways to change the guitar all the time -- except for the fretting. One must look long and far, indeed, before seeing a guitar or other fretted instrument with any pitch scheme other than the normal 12 frets per octave. Even the fretless guitars and basses (and the steels) will have this 12-tone pattern inlaid or stenciled on their finger-boards.

A guitarist who also plays a keyboard instrument will recognize at once that this pattern conforms exactly to the 12 keys per octave found on conventional keyboards; this correspondence has held both instruments in place, musically speaking, for several hundred years. During that time many composers have come and gone, investigating all the possibilities of an octave divided into 12 equal parts.

During the times of Bach or Beethoven, there were still many unexplored harmonic and melodic forms based on the 12-tone system. But now, the more attractive of these possibilities secm to have been depleted. Therefore, today's composers are left with few original options for creating new types of music within the 12-tone system. In trying to avoid the traditional use of harmony. The result is usually something that is nearly impossible to sing, and probably hard to remember.

Another disadvantage is that, paradoxically, the harder the ultramodern composers try to be original, the greater the risk becomes of sounding like their contemporaries, simply because they are trying to sound so different as to make, their individual styles almost totally unrecognizable. While mathematicians claim that there are millions of ways to rearrange the ordinary 12 tones -- especially if the tonality (key) principle is given up -- many of these ways still sound too similar, even though they may look novel and different enough when written. Actually, we don't hear very much atonal (no tonal center) or other forms of nontraditional music played on fretted instruments, which could mean that guitarists have an intuitive sense that this would not be the best way to go. Rather, some are trying tone-bending, while others are getting between those frets by using a bottleneck or other slide. However, these expedients do not change the basic system: They are ornaments or embellishments tacked onto the main structure, not fundamental alterations of it.

Pitch-bends and slides are seldom written down in sheet music -- it's sort of an underground thing that has never been totally systematized. Yet, if the need weren't there, we wouldn't hear so many people doing something about it: bassists playing glissandi (slides) on fretless basses, guitarists -- particularly in the blues realm -- bending notes, etc. The question then follows: Can this use of non-I 2-tone notes be systematized? Is the existing 12-frets-per-octave configuration the only way to fret? And if not, how many possibilities are there? How many are worthwhile?

These questions bring us to the problem of reconciling the conflicting demands of melody and harmony. Those bent tones and sliding pitches are very expressive, melodically, but they don't belong to the usual nomal (chordal) scheme. The chords derived from our ordinary 12-tone equal temperament tuning sound rougher and more restless than such chords in just tuning (an earlier system, characterized by acoustically perfect thirds and fifths that make triads sound purer than in equal temperament, although some other chords sound far less harmonious). Certain 12-tone chords also sound harsher than those from other available temperaments, such as the 31-tone system, which uses 31 notes per octave. Now that we have electric guitars with longer sustaining time and more powerful amplifiers, the crudeness inherent in 12-tone harmonies is magnified.

The 12-tone system does afford a certain melodic brilliance, while sacrificing harmoniousness in the major and minor thirds and sixths. This creates the restlessness mentioned previously, and it does not permit much subtlety. All the tempered scales will have their own biases, moods, and personalities, so that the composer's tastes and the intended moods of the music will influence the choice of scale. The just scale, with its major thirds that sound more harmonious than those found in the equal temperament system, theoretically includes more possibilities for harmonic variety when extended over a large enough range, but then we must deal with the physical limitations of the guitar, such as its slightly less than four-octave range.

There is obviously a limit to the number of frets that can be placed on a fingerboard, since they will eventually grow together into a solid sheet of metal, making the instrument fretless again. (I've had more than one nightmare about that.) It would be possible to fret a guitar to a just scale-up to a point-but some of the frets would be too close for comfort. So the untempered intervals are better realized on a fretless fingerboard or with a steel guitar; both are very adapatable to just tunings. This physical restriction also means that certain tempered scales, such as the 53-. 65-, or 72-note scales, will have to be investigated by means of electronic synthesizers. organs, computers, and the like.

Some scales lack what is described in classical terminology as consonant, or agreeable, chords. And while they may have melodic value, the harmony-oriented guitarist will probably pass them over. A guitar with a movable bridge faciIitates experimentation with one of these systems. Try this: Move the bridge down until the 13th (instead of the 12th) fret sounds the octave of the open string. This will give an approximation of the 13-tone equal temperament. Though all the intervals are strange and wacky, the melodic possibilities may intrigue you.

By experiments such as these, it is possible to narrow down the number of systems to be considered for fretted instruments to a reasonable figure. Through my own experiences, and those of other people, I have a good idea of which systems the newcomer to the field of xenharmonics and microtones should try first -- specifically, the 19-, 22-, and 31-tone scales, in that order -- before going on further.

Obviously, a change from the 12-tone system requires a refretting of the instrument. Determining the correct positions of the frets was a difficult mathematical exercise before the advent of computers. With the aid of numerical tables supplied by theorists Dr. John H. Chalmers, Jr. and Ervin M. Wilson, I have compiled tables to locate frets on guitars and other instruments in order to produce a wide range of tuning systems.

For steel guitars, the procedure is considerably easier: Draw a chart according to the table and lay it on or fasten it to the fretboard below the strings. Whether you should refret guitars yourself or have it done by an expert depcnds upon your skill, experience, and attention to detail. Patience and care are required, since the process cannot be hurried.

Let's briefly run through the principal non-12-tone systems: The 19-tone temperament has a rather aggressive and outspoken mood about it. Minor chords sound very good in it: the minor 3rds and major 6ths have practically perfect intonation. No special signs aside from the sharp, flat, or natural signs are needed to write 19-tone music, since the ordinary notation fits it very well. But unlike the 12-tone, in thie 19-tone system there are no enharmonic equivalents (pitches with more than one possible name) except E# and Fb and B# and Cb. Of course, this means that 19-tone will sound different, but depending upon your musical goals, this can be an improvement. Instead of there being one diminished 7th chord with four spellings (inversions) for each pitch, there are actually four different chords:

In this 19-tone system. there are exaggerated blues effects, pungent dissonances, and greater contrast between concords (consonances) and discords (dissonances). There is an added note between B and C, another between E and F, so brilliant ornaments are possible. The nineteenth (an interval of one fret in the 19-tone system) of an octave is equal to about a third of a tone in standard 12-tone equal temperament. This is much like a cousin to the third-tone (18 pitches per octave) system devised by Ferruccio Busoni (who also theorized about the sixth-tone scale) 70 years ago.

The 22-tone temperament has an entirely different mood from the 19-tone, and it seems to appeal to different kinds of personalities. It is of a somewhat more restful character, though not as calm as 31-tone. It favors major and 7th chords rather than minor, and its blues effect is gentler than that of 19-tone. While a great deal of brdinary existing music can be performed in 22-tone, the problem of naming the notes and writing them is extremely difficult to overcome. This is the main reason why this temperament is seldom discussed. What I do in my own compositions is to write the nearest quarter-tone, trusting to the performer's common sense the ability to choose the appropriate notes.

It might also be advantageous to make use of microtonal composer Julian Carrillo's system of notation, which assigns to every pitch a number. That way, each pitch has its own identity, rather than being treated as an alteration of other pitches. The sharp fifths and major seconds of 22-tone give it a certain brilliance (the corresponding intervals in 12-, 19-, and 31-tone are tuned flat); The 22 unequally-spaced srutis, or non-12-tone intervals, of the scale used in India are not really the equivalent of the 22-tone-equal fretting, though there is a second-cousin resemblance. The 22-tone scale is well-suited to rendering the enharmonic tetrachord of the ancient Greeks:

Of all the scales possible to fret on the guitar, the 31-tone is the calmest and most serene, and the chords are smooth and harmonious, even those with sevenths. The 31-tone scale has recently come into prominence because of experiments by theorists and composers in the Netherlands and elsewhere. It was devised by the great physicist Christiaan Huygens, who researched another plucked-string instrument -- the harpsichord.

The revival of the harpsichord and other instruments of antiquity has created interest in the meantone temperament, a system in which major thirds sound more harmonious than in equal temperament, but enharmonic equivalents (e.g., C# and, Db) sound out of tune. It so happens that there is no practical difference between the 3l-tone equal temperament and the mean-tone temperament carried out to 31 tones, so that 31-tone guitars can give an authentic rendering of the vast musical literature of the seventeenth and eighteenth centuries, which was written for keyboard instruments in the meantone tuning (or something like it).

Like the 19-tone system, 31-tone can be written without new signs, but it is common to use the additional signs devised by A.D. Fokker (who did extensive research in the 1940s into the use of the just intonation system), rather than a mixture including double-sharps and double-flats. Practically everything written for guitar can be played in the 31-tone scale. Here is an example of what ascending and descending whole-tones would look like, notated in Fokker's system:

The effect of the four diminished 7th chords in Fig. 1 is much more subtle in 31-tone than in 19-tone.

The 31-tone system yields approximate fifth-tones and inserts an extra pitch between adjacent semitones -- for example, G and G# -- while there are two tones added between E and F and two more between B and C. It shares with the 24-tone (quarter-tone) system the idea of neutral intervals: configurations of notes in chords or scales which are neither major nor minor, as shown:

The quarter-tone system has been much written about, and there is a considerable amount of quarter-tone music in existence. There are many ways of writing quarter-tones; I recommend composer/theorist Ivan Vyshnegradski's notation;

It is an easy matter to refret a guitar to quarter-tones: Leave all of the 12-tone frets in, and put the 24-tone frets between them. If an unsuspecting guitarist were to play on a 24-tone guitar without looking at the fret, he or she might play a 12-tone piece without even noticing the extra frets.

That's the catch to non-l2-tone playing: When playing a regular piece of music in 19-, 22-, or 31-tone, all the notes of the new systems are reached by familiar intervals, whereas the extra notes introduced by 24-tone (quarter-tone) are accessible only by unfamiliar intervals. And while quarter-tones add many exotic, freaky effects -- especially in melody -- the retention of the familiar 12-tones preserves its restless mood and not-so-calm harmonies. This is whv I urge experimentation with the 19-, 22- and 31-tone systems first.

Suppose you like extremely brilliant effects in melody and are willing to put up with rather harsh chords to get them: You might try the 17-tone system. It turns the rules of traditional harmony upside down. Seconds and sevenths (normally considered the least harmonious and most unstable intervals by traditionalists) are more harmonious than the normally stable thirds and sixths. For instance, G# is actually sharper than Ab, instead of being flatter, as it usually is in most other systems making the distinction between the two. Such characteristics cause some rough-sounding chords, and if some of these clashing tones are sustained, the result may be unpleasant to some people. It might be worthwhile, then, to try this system on a banjo; its sharp attack and decay characteristics lend themselves quite well to this: To get more harmonious chords, while retaining the clean, brilliant mood of 17-tone, one would have to refret to the 34-tone scale, which has been only slightly explored. I have composed a few themes in 34-tone and have devised a notation expressly for it. But no new signs are required for the 17-tone system-just new meanings for old ones.

At the high-pitched end of the finger-board, where the frets for some of these scales get too close together, they are better omitted. Their positions can be indicated by paint-filled grooves, or perhaps with a thin sheet of transparent plastic cement over them for protection. A similar scheme would work for showing the just intervals on a fretless fingerboard.

Now let us consider what can be done with a steel guitar. The tempered scales can be laid out on a chart or plastic sheet and placed underneath the strings. This makes it easy to change charts quickly and switch from one tuning system to another. In fact, for the quarter-tone scale, you can estimate the places halfway between normal 12-tone marker lines already on the instrument and place the steel bar above those positions in order to get quarter-tones. For the just or untempered scale, similar charts can be made. It is possible to learn how much the just intervals, such as the major third, differ from the !2-tone markings. Place the steel bar accordingly, so as to get along without a chart for the preliminary experiments. Generally, a major chord on steel guitars is not tuned relative to the tempered system anyway, since the sharp major thirds of 12-tone producea harsh, grating, or "curdled" sound in the amplifier -- particularly if the volume is on full.

During the last few years I have been building larger instruments to take the sted-guitar principle as far as it is practical to go. I have put from 40 to 64 strings on instrumnets over four feet long, tuning them to both conventional major and minor chords and to exotic chords containing higher members of the overtone series. This permits exploring the advantages of just intoantion -- its cleanness, clarity, and serenity.

The steel guitar is preeminently flexible, and it can play along with other instruments regardless of what system they are tuned to. So my other experiment has been to build contrabass instruments over six feet long, to give the steel guitar tone in this low register depth and solidity. Using special hand-wound pickups, the effect is that of a whole orchestral bass section.

We have had several centuries of profound thoeretical writings, but precious little to hear. Experimental instruments of the past have applied it merely to make old music sound better, not daring to venture into the application of the seventh and eleventh harmonics, for instance, nor to compose melodies having intervals smaller than the semitone. New musical territories away discovery.

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