Introduction to Computer Music: Volume One

9. What is resonance?

There is much more to what makes an instrument sound like a particular instrument, or your voice sound like your voice and not your neighbors, besides the spectral envelope of the excitation source. One such element is resonance. If you have ever stretched a string across a cardboard box and plucked it, you likely noticed the resultant timbre did not sound like a fine acoustic guitar. That is because cardboard boxes do not have the same resonating characteristics as both the material and shape of a guitar body. When a guitar string is plucked, it vibrates and creates a rich spectrum of harmonic partials. The string itself is called the excitation source. The disturbed air molecules cause the guitar body to vibrate through sympathetic vibrations. The larger vibrating surface area creates higher amplitudes by causing substantially more air to move.

The guitar body does not proportionately amplify all of the frequencies of the string. Instead, some frequencies are amplified more than others. This quality is called resonance. Unless instruments are able to change their shape with each note, most exhibit a complex of many resonant frequencies that do not change, or are fixed. The specific complex of resonances are called formants, and those that do not change are called fixed formants. When different frequencies are applied to these fixed resonances, some partials may be excited more than others. This is part of what gives instruments both their overall tone quality and their registral characteristics — that is, they have noticeably different tone qualities playing low pitches than playing high ones, since differing partials of their spectra are being enhanced. Cellists are familiar with a "wolf tone," which is a particular pitch in which there are virtually no lower partials resonated, creating an unpleasant "dead" result. (When purchasing an instrument, cellists look for ones where the wolf tone falls in between equal-tempered pitches.) Digital samplers can change pitch by simply speeding up or slowing down the replay rate of a recorded sound to change its pitch. However, if we took the lowest ‘C’ Steinway grand piano sample and transposed it up 4 octaves, the result would be much more akin to a cheap honky-tonk instrument, since the true acoustic effect would have been to transpose all of the fixed resonances of the Steinway. "Alvin and the Chipmunks" made a living by such transposition.

We use formants everyday—they are the vowel sounds we produce when speaking. Our vocal cords are the excitation source, but they don’t change shape for each vowel. Instead, we change the shape of our oral cavity, which (along with our sinuses) creates a specific complex of resonances resulting in an ‘A’, ‘O’, ‘U’ etc. Unlike instrumental fixed formants, when we produce diphthongs (vowels that morph from one into another, such as "ai-yo" or "oo-ee"), we smoothly change the shape of our oral cavity and hence the resonating characteristics. Later on, when we study synthesis, we will discuss resonant filters that allow us to enhance or reduce certain specific frequency areas of a signal.

Tubes of various diameters and lengths also have easy-to-calculate resonating frequencies, as demonstrated by blowing across the opening of a bottle. Whether the tube is open on both ends, or closed on one end, or cylindrical or conical in shape will also affect the resonant frequency. The vibrating air column set up in such resonators also produces standing waves, discussed in the next chapter. See the Hyperphysics air column reference below for further study. The entire woodwind and brass families of acoustic instruments produce sound in this way. Recently, physical modeling synthesis software has made use of the resonator principles to recreate similar phenomena with software, without the physical restrictions of the real world. For example, a program might model a 200'-long flute.

For further study, see Hyperphysics->Resonance, Hyperphysics->Resonance of Air Columns

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