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Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). The best known example of such a system is twelve-tone equal temperament, sometimes abbreviated to 12-TET, which is nowadays used in most Western music. Other equal temperaments do exist (some music has been written in 31-TET for example), but they are so rare that when people use the term equal temperament it is usually understood that they are talking about the twelve tone variety.The distance between each step and the next is aurally the same for any two adjacent steps, though, because steps form a geometric sequence, the difference in frequency increases from one to the next. A linear sequence of one frequency difference would create ever smaller intervals ( ratios), such as the harmonic series. See also logarithmic scale.
1 History
The first person known to introduce a mathematically accurate specification for equal temperament is Chu Tsai-Yu in the Ming Dynasty, who published a theory of the temperament in 1584. Soon after, European mathematicians Simon Stevin (1585) and Marin Mersenne (1636) accurately described equal temperament, independently from China.
Twelve tone equal temperament was introduced in the West to permit the playing of music in all keys with an equal amount of mis- tuning in each, without having to provide more than 12 pitches per octave on instruments, while still roughly approximating just intonationJust intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. Any interval tuned in this way is called a just interval . Another way of considering just intonation is as being based on members of the harmonic intervals. This allows much more facile harmonic motion, while losing some subtlety of intonation. True equal temperament was not available to musicians before about 1870 because scientific tuning and measurement was not available. And in fact, from about 1450 to about 1800 musicians tolerated even less mistuning in the most common keys, like C major. Instead, they used approximations that emphasized the tuning of thirdFor the musical definitions of third see the following intervals: Major third Minor third The mediant, and the chord built on the mediant, is often called simply the third as it is the third degree of the diatonic scale. See also Ladder of thirds. Third's or fifthA fifth may mean any of three things: 1. In music, see the intervals: perfect fifth augmented fifth diminished fifth circle of fifths The dominant, and the chord built on the dominant, is often simply called the fifth as it is the fifth scale degree.s in these keys, such as Meantone temperamentMeantone temperament is a system of musical tuning. In it, the major third is tuned to a particular ratio ( 5:4), and then divided in half to make two whole tones of equal size. Since two fifths up and an octave down make up a whole tone, : four fifths up.
At the time equal temperament was beginning to take hold in the West, many people perceived the much-increased mis-tuning of the music, relative to meantone temperamentMeantone temperament is a system of musical tuning. In it, the major third is tuned to a particular ratio ( 5:4), and then divided in half to make two whole tones of equal size. Since two fifths up and an octave down make up a whole tone, : four fifths up, as a disgrace. Those in opposition to equal temperament worried that the temperament, by degrading the purity of each chord, would degrade the purity of music. The composers against equal temperament included Giuseppe TartiniGiuseppe Tartini ( April 8, 1692 February 26, 1770) was an Italian composer and violinist born in Piran, a town of Istria, now in Slovenia. It appears Tartini's parents intended for him to become a Franciscan priest, and in this way he received the basic.
Equal temperament does have a weak point in tonal music. Group of musicians such as string ensemble or a capella, where tuning by microtones can be possible simultaneously during concerts, often prefer to tune the parts comprising each chord in just tuning relative to one another, in order to maximize the effect of consonanceConsonance is a stylistic device, often used in poetry. It is the repetition of consonant sounds in a short sequence of words, for example, the "t" sound in "Is i t blun t and fla t " Alliteration differs from consonance insofar as alliteration requires t. Other instruments, such as wind, keyboard, and fretted-instruments, use equal temperament or quasi-equal temperament, when the instruments have technical limitations to be tuned exactly equal. The dissonance of such temperaments is known to be noticed by an average audience. Some claim that this especially troubling in the lower register, and that this had somewhat constrained composers in the classical and romantic eras from writing chords narrower than octave for the left hand in keyboard music, while such examples in cello parts of string quartets are more common. Others hear the dissonance as most troubling in the higher register, where beating between harmonics of mistuned consonances is faster, and where combinational tones, often an entire semitone out-of-tune in equal temperament, are louder.
On the other hand, J. S. Bach wrote The Well-Tempered Clavier to demonstrate the musical possibilities of well temperament, where in some keys the consonances are even more degraded than in equal temperamnet. There is some reason to believe that when composers and theoreticians of this era wrote of the "colors" of the keys, they described the subtly different dissonances of particular tuning methods, though it is difficult to determine with any exactness the actual tunings used in different places at different times by any composer. Well-tempermaments were gradually supplanted by equal temperament over the course of the 19th century, and it is in the environment of equal temperament that the new styles of symmetrical tonality and polytonality, atonal music such as that written with the twelve tone technique or serialism, and jazz (at least its piano component) developed and flourished.
