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Topic: Equal temperament

Related Topics

Meantone temperament

Just intonation

Musical tuning

Regular temperament

Well temperament

Just intonation

Mathematics of the Western music scale

Pythagorean tuning

Interval (music)

Wolf interval

Pythagorean comma

Microtonal music

Musical acoustics

Scale (music)

Minor third

	Equal temperament - Wikipedia, the free encyclopedia
		Equal temperament is a scheme of musical tuning in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios).
		True equal temperament was not theoretically possible until 1863 when Hermann Helmholtz published the first rigorous scientific study of tone and acoustics.
		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.
	en.wikipedia.org /wiki/Equal_temperament (1977 words)

	Equal temperament
		Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios).
		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 intonation intervals.
		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 temperament, as a disgrace.
	www.mp3.fm /Equal_temperament.htm (1748 words)

	22 equal temperament - Wikipedia, the free encyclopedia
		In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps.
		Inspired by the division of the octave into 22 unequal parts in the music theory of India, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy.
		In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after 19 equal temperament, and J. Murray Barbour in his classic survey of tuning history, Tuning and Temperament.
	en.wikipedia.org /wiki/22_equal_temperament (692 words)

	Paul Rapoport: About 31-tone equal temperament
		In 31-tone equal temperament, the smallest interval is called a diesis, as it is close to the diesis of meantone tuning in size and also is the interval between any tone and the tone twelve perfect fifths away, less seven octaves.
		Furthermore, 31-tone equal temperament alone may receive different treatments in composition, some of which are more tonal than others, some of which may use an equality of the third, fifth and seventh harmonics and their close approximations in 31-tone equal temperament to derive many new types of scales.
		As shown earlier, the chromatic scale familiar from 12-tone equal temperament is `unequal' in 31-tone equal temperament, because the combination of chromatic semitones and diatonic semitones produces a combination of intervals of 2 and 3 dieses respectively.
	www.xs4all.nl /~huygensf/doc/rap31.html (5499 words)

	Tuning Systems
		Equal temperament is well suited to music that changes key often, is very chromatic, or is harmonically complex.
		Equal temperament has a clear scientific/mathematical basis, is very straightforward, does not require retuning for key changes, and is unquestioningly accepted by most people.
		And in order for a hundred cents to equal one semitone, the size of a cent must be the number that, when you multiply it 100 times, ends up being the same size as a semitone; in other words, the hundredth root of the twelfth root of two.
	cnx.org /content/m11639/latest (4072 words)

	Understanding Temperaments
		Equal temperament was used quite early on fretted instruments (it's the only arrangement that works, because many strings share a fret).
		Temperaments in which the good fifths (11) are all the same size (except for the wolf), such as Aaron's meantone we have just seen, are called regular.
		The inequality of equal temperament is 0.0; in practice however, the inequality of a competent tuner's work might be around 1.0 (based on data in Grove's, 1965, article on tuning).
	pages.globetrotter.net /roule/temper.htm (4098 words)

	Equal Temperament Tuning
		Equal temperament is the name given to a system of dividing the chromatic scale into 12 equal half steps.
		Harmonic tones at the 7th fret are pure 5ths, while in equal temperament each 5th must be lowered slightly.
		How to help your ear accept equal temperament: It is easier to face a problem if we are prepared in advance and expect it.
	users.adelphia.net /~cygnusx_1/equal_temperament.html (1216 words)

	Early Music Myths - Equal Temperament
		All modern keyboard instruments use equal temperament, and so all modern music is equally out of tune.
		Equal temperament sounds OK on a modern piano, because it has a very thick sound which masks slight tuning errors.
		Bach knew all about equal temperament, and probably experimented with it, but he didn't regard it as a serious proposition for tuning keyboards.
	www.diabolus.org /myths/equal-temperament/equal-temperament.htm (814 words)

	A beginner's guide to temperament
		In equal temperament all the notes in the scale are shifted by the same amount in order to resolve the problem.
		In this temperament the major thirds are perfectly in tune and the fourths and fifths slightly compromised - except for one hideously catastrophic fifth, usually between G sharp and E flat, the famous 'wolf'.
		Other circulating temperaments have been devised in modern times, almost all of them suffering from the grave defect that they are difficult to commit to memory and therefore difficult to use in practice (you can't tune an organ with a book in one hand).
	www.users.dircon.co.uk /~oneskull/3.6.04.htm (1780 words)

	Historical Tuning
		In equal temperament, it is possible to play in all keys without re-tuning, and an interval in one key has the same frequency ratio as the same interval in any other key.
		In equal temperament, the lack of purity is spread equally among all keys.
		Equal temperament is the present-day tuning, Bach used well temperament, meantone was used just prior to Bach, and the Pythagorean tuning was and is still only an academic standard.
	users.bestweb.net /~rmp (1205 words)

	Well v.s. equal temperament
		Equal temperament is appropriate for some music of the 20th century, especially atonal music, and music based on the whole tone scale, but not for the works of the 18th and 19th centuries.
		Equal temperament, the modern and usually inappropriate system of tuning used in western music, is based on the twelfth root of 2.
		One main drawback to equal temperament is that all major thirds are quite a bit off from where they ought to be, roughly fourteen percent of a semitone.
	www.math.uwaterloo.ca /~mrubinst/tuning/tuning.html (1354 words)

	Equal Temperament (Site not responding. Last check: 2007-10-22)
		The equal tempered scale is the common musical scale used at present, used for the tuning of pianos and other instruments of relatively fixed scale.
		One of the advantages of the equal tempered scale is that it is the same in any musical "key", so that compositions may be freely transposed up or down without changing the musical intervals.
		The equal tempered intervals may be compared with Just and Pythagorean temperaments which maintain the exact-integer-ratio rule for the main intervals, while equal temperament departs from that standard.
	hyperphysics.phy-astr.gsu.edu /hbase/music/et.html (311 words)

	equal temperament on Encyclopedia.com (Site not responding. Last check: 2007-10-22)
		Temperament at 9 months of very preterm infants born at less than 29 weeks' gestation: the epipage study.
		Temperament characteristics of premature infants in the first year of life.
		Temperament and peer acceptance in early childhood: Sex and social status differences.
	www.encyclopedia.com /html/x/x-equaltem.asp (344 words)

	History of Tuning and Temperament
		In equal temperament, every 5th is narrow by 2 cents, (702 - 2 = 700), and every 4th is wide by 2 cents, (498 + 2 - 500).
		In 1940, L. Lloyd wrote an article entitled The Myth of equal Temperament in which he described the improbability of singers, or players of any instrument with variable intonation of being able to sing or play in true equal temperament; or, a keyboard instrument actually being tuned to theoretically correct equal temperament.
		Just intonation, meantone and equal temperament are classified as regular systems because all, or all but one of the 5ths, are tempered equally.
	www.terryblackburn.us /music/temperament/stoess.htm (2797 words)

	Equal Temperament Name
		Equal Temperament is the modern musical tuning system on which all western music is based - a system of spacing the chromatic scale into 12 equal steps.
		The problem is that pure intervals don't add up to equally spaced steps, so a chord played in one key sounds beautiful and pure while the same chord played in another key sounds out of tune.
		Equal Temperament Solutions' founders, Matthew Fries and Michael Sanita, are both musicians and wanted a company name that reflected that interest.
	www.equaltemp.com /name.shtml (229 words)

	No. 380: Equal Temperament
		His great polemic for equal temperament was, of course, his book of keyboard pieces with varied key signatures.
		Equal temperament is as Western as apple pie.
		Bach wrote for the well-tempered clavier, not for an instrument of equal-temperament -- that the wide use of equal temperament came in with the large orchestras of the nineteenth century.
	www.uh.edu /engines/epi380.htm (532 words)

	Scales: Just vs Equal Temperament
		The "equal tempered scale" was developed for keyboard instruments, such as the piano, so that they could be played equally well (or badly) in any key.
		There are other temperaments which have been put forth over the years, such as the Pythagorean scale, the Mean-tone scale, and the Werckmeister scale.
		For the equal temperament scale, the frequency of each note in the chromatic scale is related to the frequency of the notes next to it by a factor of the twelfth root of 2 (1.0594630944....).
	www.phy.mtu.edu /~suits/scales.html (626 words)

	Multi-TEMPERAMENT Scales Manual
		Each of the 14 temperaments on this disk is a subtle change in the way the notes within each octave are tuned.
		A non-equal temperament must be based on a key that is harmonious with the key in which a piece of music is played or else dissonance will result.
		Equal temperament was probably known in the 1700s or earlier, but was not considered a satisfactory scale due to the impurity of all intervals.
	www.webcom.com /jawknee/Mirage/UPWARD/multitempdocs.html (1300 words)

	Temperament Page
		In Western music, compromise usually results in 12-tone equal temperament: adding together pentatonic (fl key) and heptatonic (white key) scales, so that semi-tones and chromatic intervals are made to coincide.
		(Pi is the ratio between the circumference and diameter of a circle.) Closure to equal temperament is closely approached by Lucy scales of 19, 69, and 88 tones.
		Equal temperaments are truncated when a finite number is reached.
	www.rev.net /~aloe/music/temperament.html (1183 words)

	Equal Temperament is not a myth
		The principle of Equal Temperament is that it 'divides' the octave into 12 equally sized semitones.
		What should matter in defining Equal Temperament in the actual acoustical situation, on the actual piano, is not frequency ratios, but the musical reasons for having Equal Temperament in the first place.
		Those who can tune precision Equal Temperament really understand what it is and what it means, whilst theoreticians have their own criteria that in reality, have very little to do with it.
	www.amarilli.co.uk /piano/nomyth.asp (593 words)

	Equal Temperament
		The differences shown between semitones in Pythagorean and Equal Temperament are representative of the classic difficulties encountered in the building up of musical scales.
		Using just temperament as the reference, it will be noted that major and minor thirds in equal temperament are the most out of tune with the just intervals.
		Another useful type of comparison of temperaments is that encountered in the tuning of a major triad.
	hyperphysics.phy-astr.gsu.edu /hbase/music/et2.html (261 words)

	Equal temperament tuning (Site not responding. Last check: 2007-10-22)
		The octave is divided into 12 units of equal size.
		Many technicians feel equal temperament is the “only” tuning for the modern piano.
		New research indicates true equal temperament was not practiced regularly until the early 20th century.
	campus.murraystate.edu /staff/scott.thile/research/unequal/tsld004.htm (62 words)

	Peterson Tuners Forum 2006 - Equal temperament
		There are 1200 cents in an octave, in the western 12 Tone Equal temperament (12TET) each note is 100 cents away from its immediate neighbours.
		Equal temperament enables all combinations of notes (two notes played together is an interval, three is a triad) to be played.
		Unequal temperaments (of which there are many) favour particular combinations of notes, which are more "in tune" or consonant than in Equal temperament, but their uses are limited to certain specified keys, heres what an Unequal temperament would look like as a ruler:
	www.petersontuners.com /forum/topic.asp?TOPIC_ID=391 (766 words)

	Temperament
		A mean tone temperament is a system of tuning which seeks to close the overlap in the circle of fifths by reducing the size of most of the fifths.
		One approach to mean tone temperament on keyboards with only one set of fl note keys is to pick and mix members of both the ascending and descending series so as to obtain the most even semitone steps, Db, Eb, F#, G# A#.
		In the one known as Werckmeister Temperament III the fl notes, the furthest members of the series of fifths and the most troublesome notes of mean tone temperament, are left in Pythagorean just intonation whilst the white notes are tempered.
	www.midicode.com /tunings/temperament.shtml (3005 words)

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