Consonance and Dissonance

Transcript

In Western music, consonance denotes a combination of concurrent notes that sounds pleasant to most people, while dissonance denotes a combination that sounds unpleasant. Consonance and dissonance are central to Western music—they are routinely used to manipulate tension in musical pieces and have been argued to constrain the structure of musical scales. The origins of the aesthetic contrast between consonance and dissonance has fascinated scholars since the time of the Greeks, because it is not obvious why some note combinations should be pleasant and others unpleasant. Throughout most of the 20th century, consonance and dissonance were believed to be differentiated by roughness—rapid modulations in amplitude, due to beating between overtones. Dissonance was believed to be produced by excessive roughness produced by particular note combination. However, recent evidence suggests that the pleasantness of musical chords is more closely related to whether the aggregate frequency spectrum is harmonic. The spectrum tends to be approximately harmonic for consonant chords but inharmonic for dissonant chords. Although the established notions of consonance and dissonance are at least somewhat specific to Western music, there remains considerable interest in the possibility of a biological basis for the distinction. Preferences for consonant over dissonant chords appear to emerge early in development, but it remains unclear whether there is an innate basis for the preference or whether it is instead learned from exposure to Western music.

Figure 1 shows the average pleasantness ratings given to different musical chords played with various natural and synthetic instruments. It is apparent that some chords are heard as pleasant while others are heard as unpleasant, largely independent of the instrument playing the notes. The high- and low-rated chords are conventionally termed “consonant” and “dissonant,” respectively. Scholars have long been fascinated by the large variation in the aesthetic effect of different chords.

Figure 1Pleasantness of different musical chords, as rated by American undergraduate listeners. Listeners were presented with isolated two-note and three-note chords (intervals and triads, respectively) and rated their pleasantness on a seven-point scale. The notes of each chord were either recordings of a saxophone or professional singer, or synthesized tones or vowel sounds.

Ancient scholars famously noted that consonant note combinations are associated with simple integer ratios, whereas dissonant note combinations are not. Notes in an octave relationship, for instance, have fundamental frequencies (F0s) that differ by a factor of two, and notes composing a perfect fifth have F0s in the ratio of 2:3, whereas dissonant intervals involve ratios that are more complex. These relations were apparent long before the advent of modern science because the note F0 is determined by string length for stringed instruments. The Greeks were convinced of the aesthetic value of such ratios, and for them the story ended there. [Page 251]In modern times, however, scientists have looked for an acoustic basis for the difference between consonance and dissonance.

H. L. F. Helmholtz is generally credited with noting that consonant and dissonant intervals differ in the extent to which they produce a phenomenon known as beating. Beating results whenever two or more frequencies are present at once—the frequencies shift in and out of phase over time, alternating between constructive and destructive interference, such that the resulting waveform waxes and wanes in amplitude (Figure 2a). Amplitude modulations of moderate rate (20–200 hertz or Hz) are generally regarded as unpleasant and produce a sensation known as roughness. Helmholtz noted that the frequency components in consonant intervals tend to either exactly overlap or fall relatively far apart, such that they do not produce audible beating (Figure 2c).

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