The Frequencies of Music
June 3, 2005
Sound is air in motion — pushed, pulled, beaten, blown, plucked, talked, or sung into motion. Music is sound's highest achievement, a wonderfully varied mixture of patterned vibrations sent into the air by all kinds of instruments, from a cricket's hind legs to a massive pipe organ.
The frequencies of music, the various repetitions that make up the sound of instruments, are represented somewhat by the charts printed in equipment reviews in various audio/video magazines. But those charts look (and often are) so abstract that it's easy to forget that music is the point of it all. We are trying to remedy that here with the chart below, in which the frequency markings strung out along the bottom baseline are related to the frequency ranges shown above them of the various instruments in an orchestra.
If you've never had a chance to look at the way frequency response corresponds to the sound of instruments, you might want to note first that the divisions along the bottom line of our chart are anything but even. When most people first visualize the frequency range from 20 Hz to 20,000 Hz, they imagine a nice, linear, tape-measure span of measurement, on which the marked increments are as equal as the inch or centimeter markings on a ruler. But when you look at an actual response chart, the measures along the lateral line are definitely not an equal distance apart. In fact, the seemingly "small" span between 20Hz and 40 Hz is actually wider than the 6,000 Hz of difference between 10,000 and 16,000Hz. That's because the vibrations of the heavy-hitting bass instruments of music are ponderous and far apart, while the successively higher pitched instruments going up the scale vibrate faster and faster, and closer together. The frequency scale of music (and all sound) isn't linear but logarithmic — which is probably why mathematics and music often seem to go so well together.
Our chart, courtesy of Stereo Review, is fun. It will give you an idea (if you didn't have one already) of where musical instruments lie across the audible frequency range. And there are surprises. Who would have thought, if they hadn't already known, that the bottom of the harp's range went below a double bass's, or that the contrabassoon aced them both? Or that the top of the oboe's range edged out the soprano voice? Or that the piccolo's top note topped the violin's? Or that the same harp that went so low also went right up near the top of the violin's and piccolo's range? Or that the guitar's top note was under 1,000 Hz? Look around the chart for a bit, and we'll go further after that.
Copyright © 1980 by Hachette Filipacchi Magazines, Inc. Reprinted from Stereo Review, April 1980, with permission.
While the chart begins to provide a grasp of where instruments lie across the frequency range, it has some critical omissions. The pipe organ, for instance,which goes down into subterranean regions, isn't represented. Neither is the bass drum, which has lots of energy below 50 Hz. Most critically, however, the chart portrays only the fundamental tones that instruments generate. What it doesn't show is the overtones, the harmonic frequencies, that give instruments their characteristic sound — their timbre.
Harmonics are what let you tell instruments apart. Without them, similar instruments that played the same frequencies would sound the same. The harmonics are produced not by the notes, but by the method by which the musician sets those notes into motion and the materials used to produce the notes. The plucking of a string on a guitar, or the bowing of the string on a violin, is a lot different from the metallic resonance of a flute as air is blown through it by pursed lips, or the sound of a drum's membrane when it's struck by a hand or a drumstick. Everything counts — the "attack" frequencies at the onset of notes (which are tremendously different from instrument to instrument), the "decay" frequencies at the end of those notes, the various resonances set in motion by the materials used for instruments, the differences between media excited from outside (like the string or the drum) and those excited from inside, like the flute and the trumpet. And besides upper harmonics, there are also subharmonics. The world of music is incredibly rich and varied.
We could go further, but what our chart does is give you a beginning taste of what "Hz" (cycles per second) really mean musically. There are charts that show the harmonics of instruments as well as the fundamentals, but we've never seen one that shows the varying harmonic intensities of all instruments in comparison with each other. (If you have, please let us know!) As we said earlier, the point is music. While we at PSB are intent on doing justice to the sound of crashing buses and dinosaur footfalls as well as flutes and violins and snare drums, it's the sound of music that keeps our juices flowing.