MUSICAL STRINGS

Part I -- Ivor Darreg

Nearly all musicians have some experience with stringed instruments; most of us own one or more. Before people made strings, there were the sinews of animals and the stringlike fibres of plants, so the history of strings goes back beyond human reckoning. To produce musical tones, a string generally has to be stretched, so most music historians begin with the hunter's bow -- once archery became well-developed, the varied sounds of the bowstring under tension would have been heard and then our natural impulse to experiment would have led to the invention of all manner of stringed instruments.

There are so many books on the history of musical instruments now, and most of them are illustrated, so we need not duplicate their information. Suffice it to say that the cataloguing of stringed instruments is very difficult, simply because the names in different languages are so misleadingly confused: one name will mean several instruments or several instruments will have the same name. Or both at once! This makes the history of what instruments had what kinds of strings on them obscure. We will never really know certain parts of the string-story; some of it has to be filled in by Educated Guesses.

For instance, the term chord, derived from ancient Greek khorde, which primarily meant gut. We won't be too much out of line if we assume that the Ancient Greeks used gut strings on their instruments. Knowing from our own experience how gut strings behave, we won't expect too much micrometric precision in those days from those early experimenters with stringed instruments. On the other hand, their long centuries of continued use proves that gut strings have certain desirable properties, so we will respect them for that.

Enough of history; we are more concerned with gut strings of today. Let's reassure all the cat-fanciers -- musical strings are made of sheep-gut, and the "cat" name is either a wornout joke or something to do with the pochette or kit, a tiny 3-stringed fiddle used by dancing-masters. For a cello D string, it takes 40 or more individual fibres, twisted together. Naturally, on a doublebass the strings have even more fibres to make up the larger diameters. Gut strings are still used to some extent, and besides the violin family they may be found on viols and some harps. A few really fussy classical guitarists often use them despite the breakage and expense; and of course the players of 16th-century instruments like the lute or theorbo may insist on them.

The main objection to gut strings is really safety: when they break they can mjure the hand, or face in the case of a violinist. Being made up of multiple twisted fibres, they may go "false" before they completely break. So for most people gut strings are now almost entirely replaced with nylon or similar synthetic material. Some of the aforementioned classical guitarists may use silk strings in certain places. We may be fairly confident that researchers in their laboratories around the world are already working on other synthetic materials that may overcome any alleged disadvantages of nylon for musical strings. The possibilities are so vast in chemistry that we have to be optimistic about this. To get technical for a moment, gut and silk are protein-based, while nylon, the principal substitute for them, is a nitrogen-containing long-chained polymer, so in some respects it resembles the protein fibres.

Some fairly recent experiments in France were alleged to show that gut strings on violins had a different kind of elastic behavior than nylon has; therefore the subsidiary tones were different. All these materials are elastic and they stretch after pulling up to pitch, so have to be retuned. They tend to have a higher damping or dissipation factor than metal strings, so their sustain-time is shorter. On the violin family instruments, this high damping factor is an advantage, since it means the strings will not ring too long after the bowing stroke stops. Of course the price paid for that is extremely short pizzicato notes.

Nylon strings are usually monofilament, that is one single solid piece, rather than many fibres twisted together. They can be made of many filaments if desired. They are much more uniform than gut strings, so are more predictable in behavior.

Strings are produced in different gauges. In this country the string diameter is expressed in thousandths of an inch, while abroad it is expressed in millimeters, and we are gradually converting to the metric system, so both systems will be found in use. In addition to the above gauges, the spring-steel music wire used for strings is often sold by arbitrary gauge numbers -- these numbers, however, are gradually going out of use. Ordinary iron, copper, brass, and bronze wire is often sold by B & S gauge numbers which do not coincide with the music-wire gauge -- indeed, these numbers run in the opposite direction! Thus for our musical strings there will be four incompatible series of numbers involved. Instrumen designers should take care. Don't say we didn't warn you. Some fine Utopian day in the future, every string will be gauged in millimeters.

The frequency (fundamental pitch in hertz or vibrations per second) of a string is governed by its mass and stiffness. Obviously, tightening a string increases the stiffness or restoring force, and winding something over the string increases its mass. Memorize the following: To tune a string an octave higher (twice the frequency), QUADRUPLE the tension. Not double as you might think.

That means that those valuable old violins, which were designed for a much lower pitch than that in use today -- perhaps a whole-tone lower in many cases, and then still lower if certain people tuned "by guess and by gosh" in those days -- must now bear a much greater tension than they were designed for. The tension on 12-string acoustic guitars is so great that it has been the custom for some time to tune them low. Some of the lutes and viols and other instruments of the past were very delicate and if we are to read the notation with the present assumption that Middle A is 440 Hz, perhaps all the music for these instruments should be transposed down enough to ensure their continued survival. The alternative would be for the constructors of new copies or versions of these old instruments to beef up the design to withstand the higher tension, and/or to shorten the active string lengths.

If you are making new stringed instruments, allow for some increased tension in your basic design, so they won't collapse if accidentally tuned too high. Actually, some of the historical pitches were very high, so the traditionalists who are sure of their data may have to allow for that in some cases. To give you an idea of how string tension can add up, early pianos had relatively thin strings and used much the same kind of wire as comparable harpsichords. In the later 19th century, pianos went from wooden to metal frames, used tighter and thicker strings, then special high-carbon spring steels were developed, and the tension for a concert grand went over 20 tons! It's probably more than that now. Even the raising of a piano's pitch from 435 to 440 Hz will add half a ton of tension to the frame. Now this rise from an older standard (French pitch) to a newer one is about a tenth of a whole-tone.

Harpsichords and clavichords were strung with various kinds of wire. Brass is a rather indefinite term, meaning an alloy of copper and zinc, but it comes in different proportions, and can be made soft and rather limp, or hard and springy. Today, the alloy known as phosphor bronze is often used instead. It, too, comes in different proportions of alloying metals. Quite a number of other alloys could be used for musical strings -- some metallurgist might like to experiment. Various kinds of harps and psalteries have been strung with brass and in the Near East some still are. Contemporary harpsichords and clavichords often are strung with brass or bronze for the lower notes and then steel for the higher registers. The timbre of brass or bronze as compared with that of steel is noticeably different.

Obviously, when the harpsichord was at its height, they did not have the kind of spring steel that is available today, so when iron or earlier steel was used for strings, the tone was different. Don't be too finicky about all this: when building such instruments today, design for today's materials, since they are available and less expensive, and the modifications of timbre to get something suitable for early music can be made in other ways. What I really mean here is that an exact cookbook copy of an ancient harpsichord is probably not worth the trouble-new music is being written for harpsichords and they are no longer mere revivals and strictly-museum stuff. Not long ago I heard a broadcast of an allegedly "authentic copy" clavichord which sounded like a twangy bluegrass banjo with a terrific jazzy snap, and I am sure the early composer alleged authentic clavichords often sound like something with all the expressive delicacy and tender sentiment of an electric typewriter. Of course that might have been the performer.

Musical Strings - Part II

Now that the guitar is so popular, let's turn guitar strings. While it should be obvious that nylon-string guitar is not designed to bear the tension of street strings, many people ruin their instruments by just that blunder. Guitar strings are now a big business and they come in a bewildering variety. So it should be possible to find the proper gauges of string to give the proper tension and playing feel for any guitar. If magnetic pickups are used, then the string must be of magnetic material. Nonmagnetic strings can be amplified by pickups on the bridge or body. Remember that rule about an octave rise in pitch requiring 4 times the tension! This means that a gauge of string producing a certain tension on a short-scale guitar will have a much greater tension for the same pitch on a longer-scale guitar. Similar considerations obtain for other fretted instruments such as mandolins and banjos.

Plucking wears strings faster than bowing or hammering, and when done with a plectrum, still faster, so that wound strings will often go "false" or out of tune with themselves long before breaking. Many professionals change their strings quite often. If possible, change strings one at a time so that some tension will be kept on the instrument.

Some instruments have sympathetic strings. These are not played directly except when tuning them. They respond to certain notes played on the regular strings and sustain them, somewhat as the damper pedal permits sympathetic vibration on a piano, or electric guitarists use "reverb" apparatus. These strings are often very thin, partly because they are not subject to wear, and their tension can be lower the thinner they are. Tight strings would collapse the instrument.

Non-piano keyboard instruments and the fretted instruments just mentioned have relatively thin strings compared to pianos. Wound guitar strings generally have windings which cover most of the string, so that the entire vibrating length has a uniform amount of winding. This means that most harpsichord and fretted-instrument strings have a series of harmonics fairly well in tune with the theoretical integer multiples of the fundamental. Harmonics of course are the partial tones which make up the complex tone-quality of the instrument. The string, all at once, vibrates as a whole, in halves, in thirds, in quarters, in fifths, etc. to quite a high number of equal parts. Now in the modern piano, especially smaller pianos with more wound strings, the situation is different: the strings are so thick that they behave somewhat as stiff rods. High tension is used to control this behavior. Wound piano strings have windings which do not extend all the way from bridge to bridge. A short length near the bridges is bare. The lowest pitched strings are double-wound, and the second winding does not extend quite as far as the first one does. This means that such strings are necessarily out of tune with themselves. The tone has a built-in vibrato or beat. The partial tones are not exact integer multiples of the fundamental frequency, but go sharp of it.

This irregularity is added to the winding problem just discussed. After some years of use, piano strings get fatigued and go dull. The windings may loosen, causing a fuzzy tone. Now that the expense of restringing a piano is so outrageous, few people have it done when needed. Therefore it is almost certain that a used piano will not have that new brilliant tone. And if you are interested in recycling a defunct piano and reincarnating it as some new kind of instrument, probably non-12-tone, you won't be able to salvage the strings. Almost everything else will have some use or other. Bass strings for pianos have to be made to order "special" -- there is little standardization. Now we come to another property of musical strings, especially steel ones.

The principal mode of vibration for a stretched string is the transverse mode-from side to side-and this is the mode producing most of the sound and for which it is tuned and designed. But a string can also vibrate longitudinally, from end to end, rather like the column of air in an organ pipe. The pitch of this longitudinal mode is very high, and dependent mostly on the velocity of sound in the material -- the velocity of sound in steel is incredihly high. A piano bass string may have a longitudinal fundamental 4 octaves higher than the bass note for which it is made. It will have its own harmonic series which goes up too high to bother about. It generally is out of tune with the bass note, this being one of the things that makes a piano sound like a piano -- very hard to imitate electronically. It's something like the pinch of secret spices in the chef's recipe. It also means that better pianos have audible components at pitches not in the 12-tone equal temperament. Since its pitch depends on the length of the string, compact pianos with shorter strings for these bass notes can never have the same longitudinal component sounds as a concert grand.

The velocity of sound is slower in other materials, so brass and gut and nylon strings will have lower-pitched longitudinal components for a given bass pitch and length.

For a given pitch, the longer the string, the better the tone, up to a point. First, the breaking-point of course. Then, the point at which the instrument would collapse under the strain of many tight strings. Then a point at which the tone becomes thin and tinny and disagreeable-too many higher harmonics and not enough fundamental -- probably just beyond three meters (ten feet). I put this in, in case you are getting Big Ideas -- there is a point of diminishing returns.

If a string is too loose, it will start behaving like a rod and/or a spring, with all kinds of inharmonic vibrations. Or you may attach various things at some point along a string to make its vibrations more or less irregular. The "prepared piano," for instance, but Helmholtz tried that idea out first. Or the prepared guitar: get various sizes of alligator clips from an electronic store and try clipping them onto a guitar string and you will get all kinds of funny sounds.

If a string has an appreciable diameter, such as the bottom strings on the doublebass or even the cello, it is possible to set them into torsional vibration. Bowing, especially, may do this, to cause the string to twist and untwist on its axis. These vibrations will be inharmonic and will depend on the elasticity and damping of the string's core and windings if any. Probably this is one reason why there are various kinds of metal cello and doublebass and other bowed-instrument strings, having a nonmetallic damping winding between the steel core and the winding proper. This would increase the damping factor and tend to damp out unpleasant squeaky high harmonics as well as the longitudinal and torsional modes. A plain metal string on a cello can make the most annoying screeches imaginable, but the specially-wound damped strings are quite satisfactory.

A string can be viewed as an energy-storage device, something like a pendulum, or a coil-spring with a weight hung on the end of it. During each vibration, the energy imparted by striking or plucking is alternately stored in the momentum of the string's mass and in springiness when at the extremes of its amplitude on either side of the rest point. The string itself cannot move very much air, so there is little sound radiated from it directly. A solid-body electric guitar does not take too much energy from the strings, so they sustain longer. Bridges on soundingboards withdraw energy, which then is radiated as sound-this may be gradual, as in some small-bodied instruments, or very rapid and efficient, as in the banjo. In many cases, the bridge introduces what the electronic engineer would call second-harmonic distortion: there is an extra pull on the bridge when the string is deflected either way from the center rest-position, so we get two complete vibrations from the bridge for every single cycle of the string, and thus a tone one octave higher is superposed on the already complex tone of the string. By mounting a pickup on the bridge, this effect can be exaggerated; and by picking up directly from the string itself it can be almost eliminated. A great deal depends on how rigid the bridge is, of course. Many strings are operated near the breaking-point, so there is little margin for tuning too high. On the electric bass, the strings are usually Ioose, giving a rather dull quality as compared with string bass.

The proportions of the various harmonics to fundamental depend upon the point at which the string is struck, plucked, or bowed. Note also that if a magnetic pickup is used, the point along the string where it is placed is more important than what kind of pickup it is. There has been too much experimentation with pickups themselves and too little about where they are placed! Practice and theory do not completely coincide, since the string is not the perfect ideal fiction of the mathematicians. A harpsichord will get variety of timbre by having the different registers pluck the string near or far from the end. On the piano by trial-and-error the striking-point is from 1/7 to 1/8 the string-length in the middle of the compass. This gives a duller tone than most other stringed instruments, and one reason for this, albeit unconsciously rather than deliberately arrived at, is to make the intervals of the ordinary 1 24one temperament sound better, at the expense of the intervals involving 7th or 11th harmonics, which would have clearer definition on a guitar harpsichord or clavichord. Or the violin family for that matter. There you have the reason why every attempt at making quartertone pianos has been such a flop. Quartertones are blamed for what is not fault at all. The evolution of the piano toward a mellower tone and a "fullness" obtained by de-emphasizing the higher harmonics and making the 6th and lower harmonics louder, was a natural accompaniment of the Romantic symphonic style, whereas quartertones and the 22- and 31-tone scales call for a thinner and leaner timbre. Almost by accident, that is what we are getting, as the harpsichord returns and the guitar overtakes the piano, and all manner of electronic fuzzboxes and other effects come on the market: The 17- and 19-tone scales are not that dependent upon timbre.

If you have a stringed instrument, try some experiments: pluck a string (guitar, piano, whatever) in the middle. This will remove the even-numbered harmonics (octave and octave of the others) and the resulting tone will contain mainly harmonics 1, 3, 5, 7, 9, 11 . . . producing a hollow clarinet-like tone.

Pluck it at 1/7 the length and it will seem "normal"; pluck it very near the bridge with preferably a sharp-pointed pick, and it will be "thin" and "tinny." Similar results will be obtained on a violin or cello, but you will have some trouble getting the bow to the middle of the vibrating length-stop the lowest string down some distance and then you probably can bow at the new mid-point to get the clarinet effect. Your first hearing of a clarinet tone out of a viola or cello will be amazing.

Bowing a string produces forced vibrations, of quite a different waveform and harmonic constitution than plucking or striking the same string. The bow catches the string and sticks to it till the added tension exceeds the friction, whereupon the string suddenly escapes the bow and then gets caught again. This produces what the synthesizer enthusiast calls a sawtooth wave-that is how it looks on an oscilloscope. Such a vibration is rich in harmonics and if directly picked up from the string will sound more like an oboe or saxophone than a violin. The wooden body and the enclosed air space of a violin filter out some of these harmonics, while accentuating others, so the principle of the synthesizer is not all that new! Or the electronic organ using formants either. Visually, the effect of the violin soundbox is partly that of rounding off the sharp corners on the sawtooth string waveform. Thus to make an amplified bowed instrument sound like the ordinary kind requires the use of filter circuits something like the recording studio's "equalizers." The gain in picking up directly from the strings is that one's violin or cello technique can be used to produce all kinds of wind-instrument tones, hence a tremendous variety of new sounds. Of course the orthodox antiquarians will have none of this, but what have they done for us lately? Why should they cramp our style? What do we owe them? The rock people have opened Pandora's box and nobody can slam down the lid again-as futile as trying to gather all the windblown feathers to put them back into a leaking pillow.

Most of their sounds come from strings, so that should give you some idea of all the possibilities. Our future depends upon your freedom of thinking! Are you tied down to the piano? Is that the only stringed instrument you know about, and do you take it for granted, or worse, as some kind of idol or pagan deity? If you pluck strings, what is your attitude toward bowed strings? If you bow strings, what is your attitude toward the plucked instruments? Overspecialization and a narrow mind are now expensive luxuries. We can't afford them anymore. Some two centuries ago, progress in music was almost halted, and we have a lot of lost time to make up for. It is time that the different kinds of musicians resumed diplomatic relations. We can't afford the divorce between science and art. This article was written to heal that breach.

The musical string, from ancient times, has figured in musical theory, as the monochord, which still is used to a limited extent. The main merit of the monochord is the ability to measure along the string, and thus to correlate visually-measured proportions with the various consonant and dissonant musical intervals. Back when Pythagoras and his successors were using it, it was the only game in town. Today, we have all manner of sophisticated frequency-measuring and -comparing devices, so it is not quite that important anymore-bear in mind that a real string is not mathematically perfect and certain unavoidable deviations from the mental ideal have to be allowed for. However, if the monochord, or better a measuring instrument with three or four strings so that chords can be measured out with the movable bridges and sounded, is teamed up with these modern electronic devices, we get a comprehensive balanced approach to musical theory and practice which will be very valuable for everyone working for progress in music. That is, don't expect great precision from a monochord, but take advantage of its simultaneous audible and visual presentation of proportions.

Here are a few facts and figures about strings: Shortest vibrating length of a string on the piano top C 4138 Hz at usual pitch: 50 mm or 2 in. Longest usual grand piano vibrating length: about 215 cm or 7 ft. Not necessarily the lowest note. Piano string diameters, exclusive of winding, range from music wire gauge #11 to #26, or .66 mm to 1.6 mm, or .026 inch to .063 inch. Guitar and other fretted instrument string diameters will range from music wire gauge 00 which is .2 mm or .008 inch, to approximately 1.52 mm or .060 inch for an extra heavy wound string inclusive of winding. Nylon and gut strings generally have larger diameters than the aforementioned wire strings. Harpsichord and clavichord strings are mainly the smaller guitar sizes. Piano-string tension may be as much as 77 kg or 170 lb.