Genesis of Musical Instruments

Let us finish with an example from real life of a development towards increasing specialisation, again turning to the emergence of the modern musical instruments. They are very easily systematized, because they involve few principles for sound production, combined with few methods of operation.

Almost all musical sound is either produced in vibrating air columns or in vibrating strings. Strings and air columns both share the character of being virtually one dimensional media.

A homogeneous one dimensional medium, put in vibration, is essential for the production of musical sound, because this is almost the only instance where the series of ascending eigenvalues corresponds to the natural harmonic overtones of some basic pitch.

The only exception is provided by solid shells, blocks, and air cavities, but those means of sound production are only responsible for a tiny fraction of all musical sounds, being used mainly for special effects in the percussion section of the orchestra,

In dimension higher than one the eigenvalues are no longer harmonic, and they become more closely packed, which is good in its way too, because a soundboard (two dimensional) or an air cavity (three dimensional) can thus amplify sounds produced by for instance a string, which is hardly audible by itself. But they can as a rule not by themselves produce musical sound.

A string can be put in vibration in two ways: by an initial impact, i.e., through striking or plucking, or by bowing. The basic difference is that in the first case the initial impact energy just dissipates over time, and the note becomes progressively weaker. Bowing supplies the system with a constant inflow of energy, and can hence produce a sustained note.

To the first category belong guitars, mandolines, lutes, harps, and harpsichords, which are plucked, the modern grand, the dulcimer, and the clavichord, which are struck.

To the second belong all the members of the modern violin family, those of the once competing viol family, and all their common ancestors, such as rebecs and fiddles. Like other (modern European) instruments they go back to medieval Arabic-Jewish origins in Spain, which is testified even by etymology, by words such as "el oud" for "lute".

Even the bowed string instrument, operated by keyboard, did exist under the name of "Geigenwerk". The strings were organized on semicircular bridges with a set of resined disks beneath, put in rotation by an assistant operating a crank. The strings sounded once they were pulled down in contact with a disk by the keys, a technique that was also employed in the "hurdy-gurdy". It may not even surprise us that Leonardo da Vinci produced a drawing of the principles for the "Geigenwerk".

It is interesting to note that the plucked and bowed string instruments fuse back in history, the names for a plectrum and bow even becoming identical. Some tutors from the 17th Century, such as Thomas Mace, "Musick's Monument" dating from 1676, used to teach lute and viol at the same time, and the pizzicato way of playing bowed strings has remained to our day.

As for wind, the column of air is put in vibration by the lips and air from the lungs (the organ being an exception as it uses the mechanical device of a magazine of air under pressure). In brass just the lips are used, in woodwind either a labium, as in recorders and flutes, or a reed, as in clarinets, oboes, and bassoons.

In some cases, as for the historical trumpet, just the natural harmonics are used, the basic pitch being selected by the pressure provided by the lips and lungs. Otherwise, in flutes, oboes, and bassoons, there are finger holes to define the length of the air column, sometimes, especially in modern instru ments, operated by levers and valves, or else by adjustable slides to the same end, as in the sackbut.

Like the bowed strings, all the wind instruments are constantly supplied with energy, and hence produce a sustained tone.

An organ is essentially a set of woodwind instruments, both of the reed type and of the labium type, mounted on a wind chest and operated from a keyboard.

It is not difficult to see that, far back in history, the wind instruments fuse to a simple kind of whistle, just like the case of string instruments.

Strings and wind alike used to be built in entire families of different sizes. As a rule linear dimensions are reciprocal to pitch, so the volume and weight of a base instrument, sounding one and a half octave below the treble, would have to be increased by a factor of 27!

The usual sizes are the soprano, alto, tenor, and bass. Occasionally there is one above the soprano, such as a sopranino, piccolo, or pardessus, and one below, such as the violone, double base or contra bassoon.

The normal pitch difference between the family members is a fourth or fifth, so together they used to cover the whole musically interesting range of pitches.

The compass for each instrument is usually very well defined, and outside the basic range, the notes are extremely hard to produce so that they do not sound just awkward. A modern recorder tutor by Hans Martin Linde, when instructing the students to play the top notes of the one and a half to two octave compass, introduces the exercises as follows:

"Until now the student has been able to practice at ease without taking note of neighbours or family members. Now is the time, however, to close all doors and windows."

The instance of the French base viol, which had a compass of near four octaves, was quite an exception but it could not compete in loudness with either the cello or the viola in their proper more restricted ranges.

This already is a partial answer to the natural query: Why not just make one size of instrument of each kind? There are basic physical principles for the diversity. Length, surface area, and volume all are relevant for note production. The two latter increase with the square and cube of the length dimension respectively; so if all three factors matter we can expect well defined sizes to be associated with various pitches. Length is reciprocal to pitch, and hence it is impossible to produce a low note on a small instrument. Increasing surface area and volume of the cavity, however decrease structural strength, and therefore big instruments have to be more robust than small. There is then a necessary loss in suppleness, so, even if a high

7.15 A "Genesis" of Musical Instruments 181

violin note may be played on a double bass, the quality of sound is much better on the violin. Note that the reverse is not even possible.

All this provides instances of increasing specialization, combined with joint use to enhanced overall performance. Only together do the instruments of a family cover the entire audible range for the human ear restricted to the subset of musically interesting pitches. As mentioned, an individual instrument compass seldom covers more than a few octaves, whereas the range for a modern grand, which is supposed to represent all the musically interesting sounds, is 7 octaves with frequencies from about 20 to about 2500 Hz.

In particular the appearance of families holds for recorders and viols, which were played in consorts in the period when homogeneous sound was appreciated.

Besides jointly covering the entire range, the use in consorts made polyphony available. For wind instruments this is the only possibility for polyphonic music.

The case is different for strings. As almost all stringed instruments are provided with several strings, there is also a possibility of making them sound simultaneously. The purpose shows up in the way the instruments are tuned, those intended for melody, for instance violins and celli, tuned in fifths, those intended for harmony, for instance viols and lutes, usually tuned in fourths and thirds. The latter type usually also have more strings and frets to make the chords sound.

In some instances the use remained ambiguous. The viols were used for melody in consorts, but the bases were also used for solo purposes or for accompanying voice. The names for the various types, consort basses versus division basses, indicate the differences in use. There still remains one type of consort music: The string quartet.

The Baroque introduced a new focus on the "broken consort", using different types instruments together for their different timbres.

A harmony instrument, such as a harpsichord, theorbo or chitarrone (large base lute), together with a base melody instrument, such as a cello, base viol, or bassoon, provided the foundation for the entire construction. Over it various treble instruments, violins, recorders, flutes, oboes, or the human voices, provided the soli. In this way sonatas and trio sonatas, but also cantatas and concertos were born.

This is a track on which we still are, except that the base fundament, the "basso continuo" lost its role by the end of the 18th Century.

This simple taxonomy for musical instruments is inspired by D'Arcy Wentworth Thompson's "On Growth and Form", where the forms of living organisms are discussed against the background of surprisingly few physical principles concerning structural strength, diffusion, surface tension, and overcoming friction to locomotion,

René Thom in his "Stabilité structurelle et morphogenèse" (1972), mentioned above, took Thompson's outlook as a start for studying structural change in living organisms, and in recent studies of the locomotion of animals, such issues as the "gear" shifts from walk to trot to gallop for horses extend this "physicalistic" outlook to pure dynamics. See Ian Stewart, "Fearful Symmetry" (1992).

In fact, if we take not only the instruments themselves, but also their use, in consideration, then the "gear shift" idea is highly relevant for music making. Anybody playing a bowed string instrument knows how to use the whole arm in slow movements and only the hand in fast ones, thus setting up an undulating movement of the three joints.

This, of course, is nothing but using a pendulum of varying length as appropriate for the desired period of oscillation. The system of three coupled pendula is mathematically quite complex, and may result in chaotic as well as periodic motion.

A closer mathematical study of the natural frequencies of such a coupled system might in fact yield interesting information concerning tempi in fast and slow movements, because most composers worked with, rather than against, nature. In the case of woodwind, double-tongue, and triple-tongue techniques serve the same purpose as the different movement gears of the arm. All this, in combination with the Darwinian development idea, would provide an excellent paragon to shape a development theory after.

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