tuning and temperament, in music, the adjustment of one sound source, such as a voice or string, to produce a desired pitch in relation to a given pitch, and the modification of that tuning to lessen dissonance. The determination of pitch, the quality of sound that is described as ‘high” or “low,” is based upon the frequency of sound waves.
Two concepts fundamental to the theory of tuning are those of frequency ratio and of consonance and dissonance. A given musical pitch is determined by the frequency of vibration of the sound wave that produces it, as a′ = 440 cycles per second. An interval, or distance between two pitches, can thus be mathematically described as the ratio of the frequency of the first pitch to the frequency of the second. Various frequency ratios can be reduced to the same basic relationship; for example, 440:220 and 30:15 and 750:375 can all be reduced to the ratio 2:1.
When two tones are sounded together the subjective reaction may be anything from one of perfect consonance to one of extreme dissonance. Dissonance is produced by beats (interference between pulsations of sound waves), and it is found that maximum dissonance occurs when the rate of beats between the two tones is about 33 per second. Consonance results from the absence of beats, which occurs only when the ratio between the frequencies of the two tones is numerically simple. When the two tones are tuned to the same pitch, they are said to be in unison (ratio 1:1) and their consonance is absolute. Next in order of consonance comes the octave (2:1), the interval between c and c′ (encompassing eight notes of the piano keyboard); another highly consonant interval is the fifth (3:2, as from c to g). When a unison, octave, or fifth is slightly mistuned, the resulting combination is markedly dissonant and is judged “out of tune.” The slight mistunings that occur in systems of tempered tuning are necessary for reasons that will be discussed later in this article.
