Musical Tone and Perceived Dissonance (2011)
Musical tone and perceived dissonance

      
      
      

      Why does a perfect fifth sound so satisfying when a brash tritone is just a half step away?It seems we have a physiological correlate to these psychological effects. As sounds arrive, the basilar membrane vibrates like an oblong drum head, stimulating tiny hair cells attached to nerves. Each hair cell corresponds to a perceived frequency, working like little band-pass filters.One hair cell will be stimulated over some small range of input frequencies: for instance, hairs for middle C (262 Hz), will also react to sounds between 230 Hz (roughly A♯3) and 290 Hz (roughly D4). We’d say, then, that the critical bandwidth at middle C is around 60 Hz. Researchers have found that the bandwidth of a given hair equates to around a whole step on the western musical scale, basically the whole way up and down the keyboard.As for the tritone: when a sound vibrates two hairs with overlapping critical bandwidths (like C5 at 523 Hz and C♯5 at 554 Hz), we perceive it as rough and rattling. Why are we wired that way? No study has conclusively determined the answer, but I’d wildly speculate that such sounds share acoustic properties with noise from friction. Rustling leaves; shuffling paws? Or screaming? Maybe it’s just a warning sign when our brain can’t readily separate two tones.Whatever it is, this effect alone can’t explain tritones’ impudence. Take C4 (262 Hz) and F♯4 (370 Hz): they’re several bandwidths apart, but they still sound dissonant when played together on my piano.That’s because when you play a C4 on the piano, you are also playing a bunch of other tones: 523 Hz (C5), 786 Hz (G5), 1048 Hz (C6), and so on for the next three integer multiples of C4’s frequency. The tone, or timbre of an instrument—what separates the sound of a flute from that of an oboe—largely derives from the relative strengths of these extra tones (harmonics) to the pitch you meant to play (the fundamental).So, your C4 (262 Hz) includes an inadvertent and somewhat quieter G5 (786 Hz). Note two of the tritone—the F♯3 (370 Hz) will include an extra bit of F♯4 (740 Hz). These two harmonics have colliding tiny-hair-bandwidths, just like the minor second we discussed earlier: hence the rough sound.Even fairly consonant chords, like a major third, feature these collisions. C4 (262 Hz) and E4 (330 Hz) will clash at the third harmonic of the former (C5 at 1048 Hz) and the second of the latter (B4 at 990 Hz). Those harmonics are much quieter than the fundamental and first harmonic, though, so the major third grates less than the tritone.Remember, though: the harmonics for a given note are produced at different relative intensities from instrument to instrument. This means that the same interval, played on different kinds of horn, could sound substantially more or less dissonant! Moreover, musicians can control their instruments’ tone (i.e., in part, their harmonics’  amplitudes) at will while they play. Sing an “ah”, then raise and lower your soft palate. You’ll hear your voice’s tone change substantially. (And you’ll sound ridiculous.)Did composers subconsciously account for instruments’ tonal effect on consonance when arranging their pieces? Is it possible that excellent musicians intuitively adjust the tone of their instruments to modulate the dissonance produced by the harmonies they form? Could this account for the sudden beauty of a chord in one ensemble’s rendition of a piece you’ve heard a thousand times?
    