Everything about Equal Temperament totally explained
Equal temperament is a
musical temperament, or a system of
tuning in which every pair of adjacent notes has an identical
frequency ratio. In equal temperament tunings an
interval — usually the
octave — is divided into a series of equal
steps (equal frequency ratios). For modern
Western music, the most common tuning system is
twelve-tone equal temperament, sometimes abbreviated as
12-TET, which divides the octave into 12 (
logarithmically) equal parts. It is usually tuned relative to a standard pitch of
440 Hz.
Other equal temperaments exist (some music has been written in
19-TET and
31-TET for example, and Arabian music is based on
24-TET), but in western countries when people use the term
equal temperament without qualification, it's usually understood that they're talking about 12-TET.
Equal temperaments may also divide some interval other than the octave, a
pseudo-octave, into a whole number of equal steps. An example is an equally-tempered
Bohlen-Pierce scale. To avoid ambiguity, the term
equal division of the octave, or
EDO is sometimes preferred. According to this naming system,
12-TET is called
12-EDO,
31-TET is called
31-EDO, and so on; however, when composers and music-theorists use "EDO" their intention is generally that a temperament (for example, a reference to just intonation intervals) isn't implied.
History
Historically, there was Seven-equal temperament or Hepta-equal temperament practice in ancient
Chinese tradition.
Vincenzo Galilei (father of
Galileo Galilei) may have been the first person to advocate twelve-tone equal temperament (in a 1581 treatise), although his countryman and fellow
lutenist Giacomo Gorzanis had written music based on this temperament by 1567. The first person known to have attempted a numerical specification for 12-TET is probably
Zhu Zaiyu (朱載堉) a prince of the
Ming court, who published a theory of the temperament in 1584. It is possible that this idea was spread to Europe by way of trade, which intensified just at the moment when Zhu Zaiyu published his calculations. Within fifty-two years of Zhu's publication, the same ideas had been published by
Marin Mersenne and
Simon Stevin.
From 1450 to about 1800 there's evidence that musicians expected much less mistuning (than that of Equal Temperament) in the most common keys, such as C major. Instead, they used approximations that emphasized the tuning of
thirds or
fifths in these keys, such as
meantone temperament. Some theorists, such as
Giuseppe Tartini, were opposed to the adoption of Equal Temperament; they felt that degrading the purity of each chord degraded the aesthetic appeal of music.
String ensembles and vocal groups, who have no mechanical tuning limitations, often use a tuning much closer to
just intonation, as it's naturally more
consonant. Other instruments, such as some
wind,
keyboard, and
fretted-instruments, often only approximate equal temperament, where technical limitations prevent exact tunings, other wind instruments, who can easily and spontaneously bend their tone, most notably
double-reeds, use tuning similar to string ensembles and vocal groups.
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 temperament. It is reasonable to believe that when composers and theoreticians of earlier times wrote of the moods and "colors" of the keys, they each described the subtly different dissonances made available within a particular tuning method. However, it's difficult to determine with any exactness the actual tunings used in different places at different times by any composer. (Correspondingly, there's a great deal of variety in the particular opinions of composers about the moods and colors of particular keys.)
Twelve tone equal temperament took hold for a variety of reasons. It conveniently fit the existing keyboard design, and was a better approximation to
just intonation than the nearby alternative equal temperaments. It permitted total harmonic freedom at the expense of just a little purity in every interval. This allowed greater expression through
modulation, which became extremely important in the 19th century music of composers such as
Chopin,
Schumann,
Liszt, and others.
A precise equal temperament wasn't attainable until
Johann Heinrich Scheibler developed a
tuning fork tonometer in 1834 to accurately measure pitches. The use of this device wasn't widespread, and it wasn't until 1917 that
William Braid White developed a practical aural method of
tuning the piano to equal temperament.
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.
General properties of equal temperament
In an equal temperament, the distance between each step of the scale is the same
interval. Because the perceived identity of an interval depends on its
ratio, this scale in even steps is a
geometric sequence of multiplications. (An
arithmetic sequence of intervals wouldn't sound evenly-spaced, and wouldn't permit transposition to different keys.) Specifically, the smallest
interval in an equal tempered scale is the ratio:
» (35.1 cents)
Alpha and Beta may be heard on the title track of her 1986 album
Beauty in the Beast.
Further Information
Get more info on 'Equal Temperament'.
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