Recording - February 2012 - 60

A side note (pun intended) is that in the modern era of electronic instruments, we must quantify a frequency-to-pitch reference in order to ensure all instruments are compatible. This reference is typically A (above middle C) equalling 440 Hz, but this has varied throughout the history of music, and in some cases this reference will still vary. analogy, the drumhead oscillated back and forth, creating compressions and rarefactions in air pressure. The speed of a source’s vibrations translates to the frequency of its sound. Measured in Hertz (Hz), frequency refers specifically to the number of times per second air pressure cycles from its zero-valued resting place, through a compression, then a rarefaction, and finally back across its zero value to begin the cycle anew. Hertz is the number of cycles per second (CPS) of a sound, and young, healthy human ears can hear roughly between 20 and 20,000 Hertz. As you may already know, human ears perceive higher frequency sounds as higher in pitch. What exactly is pitch? Pitch is the human perception of frequency, and our brains do funny things while perceiving and organizing pitch. In the case of sounds Timbre In the aforementioned bass drum example, I discussed a drumhead vibrating at a specific frequency and amplitude. In reality, the actual sound produced would not be this simple in construction. In addition to the main frequency, both the drumhead and the drum shell would simultaneously resonate at other frequencies as well. We call the main frequency, which is usually the lowest in Hertz and the loudest in amplitude of all those frequencies generated simultaneously, the fundamental, and it is the pitch of the fundamental that is often assigned a musical note value. The other frequencies contained in the sound, which are typically higher than the fundamental, are called overtones. In every sound, the overtones vary, both in frequency and in amplitude, and it is this

a real-world timbre its subtle characteristics. Then again, a sound that doesn’t have a defined fundamental pitch and musically definable harmonic overtones, like a bass drum (we all agree that it has a “low” pitch but we can’t match its pitch exactly on a bass or a keyboard for example), has more non-harmonic than harmonic overtones, even if it has a pleasantly resonant quality that lends itself to musical uses. Take this a step further, and a sound with mostly or only nonharmonic overtones becomes what we call noise. The numbering of overtones can be confusing. Since the fundamental is “in harmony” with the harmonic overtones it sets up, it is “harmonic #1”. Over and above the fundamental’s frequency comes the first (harmonic) overtone, and it is therefore the 2nd harmonic. 1st overtone = 2nd harmonic. Theory & practice Last month we began this Fundamentals column by considering aesthetics, and in the process I discussed how in the recording studio we must reconcile musician-speak terms such as louder, warmer, and brighter, with technical

Asking an engineer to turn the bass down by 2 dB is much easier than asking for a reduction of 0.015931267 Volts!
that vibrate at a steady frequency, our ears often assign a musical note value to the pitch. When sitting at a piano, the note D, to the right of middle C, is both higher in pitch and in frequency than middle C. It is important to realize, however, that although frequency is a physical phenomenon that can be scientifically quantified in Hertz, pitch is relative depending on the person and culture doing the listening. Yes, higher frequencies are always higher in pitch, but what musical note gets assigned what frequency can vary considerably. To illustrate this point, let’s compare a group of people singing “Happy Birthday” with the same song being played on an electric keyboard. Without any reference (such as a pitch pipe), the singers will perform the song in a key ungrounded to a specific frequency. The keyboard, however, is most likely tuned to a precise set of frequencies. In both cases, we as listeners perceive the same song because the intervals between notes are roughly the same in frequency, regardless of the reference-pitch starting place.
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unique combination that is referred to as a sound’s timbre. Pronounced “tam-ber”, timbre is, in musician-speak, the “tone” of a sound. It is timbre that differentiates instruments and people’s voices. A clarinet and a soprano saxophone produce the same pitches in a similar manner, but their timbre is distinctive. Note that overtones are also commonly referred to as harmonics. To a point, both words can be used interchangeably. As you look more deeply into what makes different waveforms and their timbres—learning to program analog synthesizers will take you there, for example—you’ll find “harmonic series” like the overtones of the sawtooth wave (all harmonics present) or the square wave (only the odd-numbered harmonics present), and how a manipulation of the amplitude of those harmonics (filtering) alters the timbre. Few sounds are so pure in their overtone components that they contain only harmonic overtones—it is the others, the non-harmonic overtones, that give many

vocabulary such as Hertz and amplitude. Because of the dual nature of the recorded arts, that it is both an art and a science, all of the technical terms discussed this month have parallel musician-speak terminology. Decibel accuracy is often replaced with subjective requests for louder or softer. The timbre of a sound, i.e. its harmonic makeup, is frequently referred to as its brightness, dullness, or warmth. Learning how to translate this language into engineering jargon is just part of the job. Of course, crucial to the translation process is a grounded knowledge of the physics of audio. Stay tuned for next month’s Fundamentals, in which the physics discussed this month are applied to real-life recording techniques. Eric Ferguson (ferguson@recordingmag .com) recently escaped Los Angeles after a dozen years of freelance audio engineering. He is currently on the faculty of the New England School of Communications (NESCOM) in Bangor, ME.

Recording - February 2012

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