Moog Monday: On Synthesizers: String Tone Simulation, Part I

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(This column originally appeared in the February 1978 issue of Contemporary Keyboard magazine.)

Some people think that synthesizers were developed primarily to imitate orchestral instruments. Others hold the view that there is something basically dishonest about using electronic instruments to simulate acoustic instrument colors—timbral thievery, as it were. I have always regarded synthesizers as general-purpose tools that should be used for whatever makes musical sense. Very often it makes musical sense to construct tone colors that are related to orchestral timbres. Furthermore, acquaintance with the acoustic properties of familiar musical instruments helps a musician to understand why musical tones sound the way they do, and therefore enables him or her to work more creatively with synthesizers.

My next few columns will discuss acoustic tone sources and the properties of the sounds they produce. I will also talk about how to go about simulating acoustic instrument tone colors on variable synthesizers. However, I will not dispense recipes for specific tone colors. After all, each model of synthesizer requires different control settings, the frequency response and equalizer settings of your amplification will be critical, and, last but not least, your ability to accurately simulate an orchestral timbre will often depend as much on your playing technique as on the panel control settings.

String Instrument Acoustics
The violin bow is coated with rosin, which makes it grip the string. As the bow is drawn across the string, the string follows the bow at the point of contact. When the string pulls on the bow with a greater force than the rosin can hold, the string breaks loose and snaps back, and the cycle starts over. The string motion causes the violin's bridge to rock back and forth with a sawtooth-wave-like motion. Of course, the amount of bridge motion is very small, but it is enough to set the entire violin body into complex vibration.

Although structurally simple, the violin body has a great many mechanical resonances. The strength of the resonances and the evenness of their spacing throughout the spectrum determine a violin's sound quality. Fine violins have a main wood resonance very close to 440Hz, the frequency of the open A string. Other strong resonances are the cavity resonance (caused by the acoustic properties of the air inside the violin box, rather than the box itself) near 294Hz, the frequency of the open D string, and a wood resonance close to the frequency of the open G string. In addition, there are literally dozens of lesser resonances that are set into vibration by the harmonics of the tones.

What are the effects of these resonances? First, they increase the acoustic output of the violin. A violin with a weakly resonant body just sounds weak and soft. But more important for our purposes, the multiple closely-spaced resonances emphasize some harmonics and suppress others in a nearly random manner. Furthermore, when the pitch of the tone is changed even a little bit (in vibrato, for instance), the amplitudes and phases of all the harmonics vary markedly. You can see this if you watch a violin signal on an oscilloscope; the waveform is complex and always changing. As the pitch of the string signal changes, the amplitude of each harmonic rises and falls independently of the others. The total sound appears to be of constant loudness with a warm, rich quality.

Max Matthews's Electric Violin
Dr. Max Matthews is director of the Acoustic and Behavioral Research Center at Bell Labs. Over the years, he has actively participated in electronic music research. His projects in this area have ranged from building a 96-input mixer for composer John Cage to performing pioneering work in computer synthesis. One of Matthews's most interesting projects is a violin that uses conventional strings and fingerboard, but replaces the violin body with a set of special electrical resonances. The rigid plastic bridge on Matthews's instrument is mounted on a block of solid wood. Pickup magnets are located on the bridge, under each string. The string signals thus produced are analogous to the vibrations that go through the bridge and into the body of a conventional violin. They contain all the harmonics of the string tones, but are not modified by any acoustical resonances.

The significant aspect of Matthews's instrument is the manner in which the raw string signal is processed to achieve the characteristic violin timbre. The string signal is fed through an electrical filter array that is an electrical analog of a violin body. Matthews's design calls for 36 separate resonant filters whose center frequencies run from 175 to 8,000Hz! The resonant filters are connected in parallel; the string signal goes through all the filter sections simultaneously. The output of the filter array has the warmth and richness characteristic of the tone of a fine conventional violin. Many trained violinists who tried Matthews's electric fiddle said that it was the best violin they had ever played.

The results of Dr. Matthews's research are important to those who wish to synthesize string tones. Of course, hooking Matthews's filter array to a keyboard-controlled sawtooth wave signal will not make an Isaac Stern out of a keyboard player. However, the multiple resonance filter array does provide optimum filtering for a good string simulation. Its frequency response is a succession of fairly sharp peaks. The dips between adjacent peaks are 10-15dB below the peaks themselves (see the illustration). The peaks are evenly spaced about six to the octave. Care is taken to space the peaks so that, no matter what the string signal frequency, some harmonics will be emphasized and others will be attenuated.

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The phase shift of the filter array merits special mention. Like the frequency response, the phase shift vs. frequency graph contains a series of peaks and dips. The most rapid phase changes occur at the peaks and dips of the frequency response. Now, phase change is equivalent to frequency shift. When the string frequency changes rapidly (as in vibrato), the harmonics are therefore slightly out of tune with each other!

Thus, a well-synthesized violin tone is an incredibly complex collection of subtle, fleeting changes that are almost impossible to pin down with electronic measuring instruments. We listeners have no trouble detecting and enjoying them, however. My next column will suggest ways of faking string instrument frequency response with commonly available sound modifiers. (Matthews's type of multiple resonance filter arrays are not yet to be had from your local music store.) We will then talk about other characteristic parameters of string instrument timbres.

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