When a piano is tuned, the ideal situation is to place a sequence of 12 chromatic pitches in the frequency range of each octave such that the fifth and octave of each note are pure. This can be easily done by using the circle of fifths to generate a sequence of 12 perfect fifths, scaling the generated frequencies to drop them into the correct octave.
However, there is a discrepancy between a perfectly tuned octave and the octave resulting from a tuned circle of fifths. This ‘error’ means that we can have either perfectly tuned fifths, but out of tune octaves; or perfectly tuned octaves, with the last fifth glaringly out of tune.
Clearly, the first option is not acceptable because the ear cannot tolerate out-of-tune octaves. So, the second option is chosen. The out-of-tune fifth is handled by using a scheme to distribute the error among the other fifths, by nudging (i.e., tempering) each fifth either up or down enough to make space for some of the error. Tempering the fifths also affects the quality of the major thirds, since all notes are part of the circle of fifths. Many temperaments have been devised to maximise different aspects of harmonic quality, all with compromises to others. For example, some maximise pure thirds while others emphasise pure fifths at the expense of the thirds.
In Equal Temperament (ET), the frequencies of the twelve chromatic pitches in each octave are placed equidistant apart so that the frequency ratio of any pair of adjacent notes is the same. In other words, every semitone has an equal perceived step-size. This gives ET two distinct characteristics:
- All the major thirds have the same too-wide size. This causes all the keys to sound the same, i.e., there are no differences in key colour or character. All minor thirds are all the same too-narrow size, causing the minor keys to be equally devoid of differences in key colour.
- ET does not contain any pure intervals; every interval is dissonant to some degree. As a result, the piano always sounds ‘noisy’, because consonant intervals and chords simply do not exist in ET.
Equal temperament scales have been around since 1584, but did not become widely used until the 19th century. By then, Western music had become increasingly complex. Musical compositions were being created in all twenty-four major and minor keys. And as well as changing keys mid-piece, harmonic progressions often mixed chords from other key signatures with the diatonic chords. ET was the only practical method for tuning fixed pitch instruments. Without it, fixed pitch instruments would have needed retuning constantly (even in the middle of a performance) to facilitate these new compositional techniques.
ET became the global standard temperament for tuning keyboards, fretted string instruments (primarily guitars) and other fixed pitch instruments, for the following reasons:
- All 24 major and minor keys are playable.
- Keys can be transposed freely without ever reaching an unusably dissonant key.
- There are no issues when playing in ensemble with other ET tuned instruments.