What is "equal temperament"

Temperament \Tem"per*a*ment\, n. [L. temperamentum a mixing in due proportion, proper measure, temperament: cf. F. temp['e]rament. See Temper, v. t.]

1. Internal constitution; state with respect to the relative proportion of different qualities, or constituent parts.

   The common law . . . has reduced the kingdom to its just state and temperament.
   --Sir M. Hale.

2. Due mixture of qualities; a condition brought about by mutual compromises or concessions. [Obs.]

   However, I forejudge not any probable expedient, any temperament that can be found in things of this nature, so disputable on their side.
   --Milton.

3. The act of tempering or modifying; adjustment, as of clashing rules, interests, passions, or the like; also, the means by which such adjustment is effected.

   Wholesome temperaments of the rashness of popular assemblies.
   --Sir J. Mackintosh.

4. Condition with regard to heat or cold; temperature. [Obs.]

   Bodies are denominated ``hot'' and ``cold'' in proportion to the present temperament of that part of our body to which they are applied.
   --Locke.

5. (Mus.) A system of compromises in the tuning of organs, pianofortes, and the like, whereby the tones generated with the vibrations of a ground tone are mutually modified and in part canceled, until their number reduced to the actual practicable scale of twelve tones to the octave. This scale, although in so far artificial, is yet closely suggestive of its origin in nature, and this system of tuning, although not mathematically true, yet satisfies the ear, while it has the convenience that the same twelve fixed tones answer for every key or scale, C[sharp] becoming identical with D[flat], and so on.

6. (Physiol.) The peculiar physical and mental character of an individual, in olden times erroneously supposed to be due to individual variation in the relations and proportions of the constituent parts of the body, especially of the fluids, as the bile, blood, lymph, etc. Hence the phrases, bilious or choleric temperament, sanguine temperament, etc., implying a predominance of one of these fluids and a corresponding influence on the temperament.

   Equal temperament (Mus.), that in which the variations from mathematically true pitch are distributed among all the keys alike.

   Unequal temperament (Mus.), that in which the variations are thrown into the keys least used.

Equal \E"qual\, a. [L. aequalis, fr. aequus even, equal; akin to Skr. ?ka, and perh. to L. unus for older oinos one, E. one.]

1. Agreeing in quantity, size, quality, degree, value, etc.; having the same magnitude, the same value, the same degree, etc.; -- applied to number, degree, quantity, and intensity, and to any subject which admits of them; neither inferior nor superior, greater nor less, better nor worse; corresponding; alike; as, equal quantities of land, water, etc.; houses of equal size; persons of equal stature or talents; commodities of equal value.

2. Bearing a suitable relation; of just proportion; having competent power, abilities, or means; adequate; as, he is not equal to the task.

   The Scots trusted not their own numbers as equal to fight with the English.
   --Clarendon.

   It is not permitted to me to make my commendations equal to your merit.
   --Dryden.

   Whose voice an equal messenger Conveyed thy meaning mild.
   --Emerson.

3. Not variable; equable; uniform; even; as, an equal movement. ``An equal temper.''
   --Dryden.

4. Evenly balanced; not unduly inclining to either side; characterized by fairness; unbiased; impartial; equitable; just.

   Are not my ways equal?
   --Ezek. xviii. 29.

   Thee, O Jove, no equal judge I deem.
   --Spenser.

   Nor think it equal to answer deliberate reason with sudden heat and noise.
   --Milton.

5. Of the same interest or concern; indifferent.

   They who are not disposed to receive them may let them alone or reject them; it is equal to me.
   --Cheyne.

6. (Mus.) Intended for voices of one kind only, either all male or all female; -- opposed to mixed. [R.]

7. (Math.) Exactly agreeing with respect to quantity.

   Equal temperament. (Mus.) See Temperament.

   Syn: Even; equable; uniform; adequate; proportionate; commensurate; fair; just; equitable.

n. the division of the scale based on an octave that is divided into twelve exactly equal semitones; "equal temperament is the system commonly used in keyboard instruments"

An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Equal intervals also means equal ratios between the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor.

In equal temperament tunings, the generating interval is often found by dividing some larger desired interval, often the octave (ratio 2:1), into a number of smaller equal steps (equal frequency ratios between successive notes). For classical music and Western music in general, the most common tuning system for the past few hundred years has been and remains twelve-tone equal temperament (also known as 12 equal temperament, 12-TET, or 12-ET), which divides the octave into 12 parts, all of which are equal on a logarithmic scale. That resulting smallest interval, the width of an octave, is called a semitone or half step. In modern times, 12TET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one pitch is tuned to A440, and all other pitches are some multiple of semitones away from that in either direction, although the standard pitch has not always been 440 and has fluctuated and generally risen over the past few hundred years.

Other equal temperaments exist. They divide the octave differently. For example, some music has been written in 19-TET and 31-TET. Arabic music uses 24-TET. In Western countries, when people use the term equal temperament without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments that divide the octave and ones that divide some other interval (or that use an arbitrary generator without first dividing a larger interval), the term equal division of the octave, or EDO is preferred for the former. According to this naming system, 12-TET is called 12-EDO, 31-TET is called 31-EDO, and so on.

An example of an equal temperament that finds its smallest interval by dividing an interval other than the octave into equal parts is the equal-tempered version of the Bohlen–Pierce scale, which divides the just interval of an octave and a fifth (ratio 3:1), called a "tritave" or a " pseudo-octave" in that system, into 13 equal parts.

String ensembles and vocal groups, who have no mechanical tuning limitations, often use a tuning much closer to just intonation, as it is naturally more consonant. Other instruments, such as some wind, keyboard, and fretted instruments, often only approximate equal temperament, where technical limitations prevent exact tunings. Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles and vocal groups.