Equal-temperament - Factbites

Equal-temperament - Factbites
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Topic: Equal-temperament

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	Equal temperament - Wikipedia, the free encyclopedia
		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.
		Equal temperaments allow the use of integer notation; a single integer can be used to represent the pitch.
	en.wikipedia.org /wiki/Equal_temperament (1899 words)

	Mathematics of musical scales - Wikipedia, the free encyclopedia
		The tempering can involve either the irregularities of well temperament or be constructed as a regular temperament, either some form of equal temperament or some other regular meantone, but in all cases will involve the fundamental features of meantone temperament.
		In equal temperament the half step, rather than the fifth or third, is the basis of tuning.
		The interval 81/80, called the syntonic comma or comma of Didymus, is the key comma of meantone temperament, and the fact that it becomes a unison in meantone temperament is a key fact of Western music.
	en.wikipedia.org /wiki/Mathematics_of_musical_scales (1129 words)

	draft.html
		[equal] The beating of the chords in equal temperaments, most evident in the thirds, when compared to unequal temperaments such as the Werkmeister unequal temperament in the good keys where the Pythagorean comma is not distributed is a noticable difference, described sometimes as annoying or distracting.
		Equal temperament intervals sound consonant because the disonances of nonoctave intervals is within the 5% critical bandwidth criteria for consonance.[equal][critical bandwidth] The just, mean-tone, and pythagorean temperaments are open temperaments.
		Equal temperament involves raising the lower note or lowering the higher note for the proper beat rate[the physics of sound].
	people.cs.uchicago.edu /~dtshoda/CS295_files/working_dir/draft.html (2800 words)

	Scales: Just vs Equal Temperament
		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....).
		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.
	www.phy.mtu.edu /~suits/scales.html (626 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)

	Aural Pure 5ths Equal Temperament
		Originally, the standard approach to setting equal temperament was to first establish the octave and then by using a circle of 4ths and 5ths, one could divide up the octave evenly by contracting the 5ths each by 1/12 of the 24 cent comma.
		Equal temperament was found to be more of a struggle than at first expected.
		After all, since the advent of equal temperament we have been condition- ed to listening to 3rds which beat more than 7 beats per second.
	www.ptg.org /pipermail/pianotech/1997-May/017310.html (1636 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)

	Alternate Temperaments -Terry Blackburn on the Web!
		Equal temperament takes the tuning 'error' (comma, or the disparity between a pure octave and an octave generated by tuning perfect fifths), and spreads it equally between each step of a chromatic scale.
		Granted, some of the nuances may be missing for pieces that have their origins in another temperament, but pieces depending on equal temperament may be destroyed by the placement of various mis-tuned intervals.
		In comparison to all the art and effort that has gone into designing temperaments that minimize mis-tuning and preserve the beauty of perfectly tuned intervals, equal temperament is quite arbitrary.
	www.terryblackburn.us /music/temperament (2003 words)

	Equal Temperament is not a myth
		Equal Temperament follows the 'democratic' principle that all keys are equal at least in this respect.
		The principle of Equal Temperament is that it 'divides' the octave into 12 equally sized semitones.
		The only problem is that only 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 (1041 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.
		On equal temperament this is uniformly dull, and music of this type fails dismally to engage the listener.
		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'.
	www.users.dircon.co.uk /~oneskull/3.6.04.htm (1780 words)

	052003.html
		Equal Temperament to Pythagorean Interval Interval Contexts, cont.
		But when considering only Equal Temperament and the harmonic series, the more semitone divisions existing in the octave of equal temperament, the denser the available pitches, and therefore more closely accessible the harmonic series frequency tunings for all key areas, assuming a logarithmic function is used to divide the octave into n equal frequencies.
		Equal temperament as a tuning procedure singularly applys logarithmically to set temperament on all pitch frequencies within an octave.
	people.cs.uchicago.edu /~dtshoda/CS295_files/working_dir/052003.html (4334 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.
		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.
		In equal temperament, the lack of purity is spread equally among all keys.
	users.bestweb.net /~rmp (1205 words)

	Equal Temperament
		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.
		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.
	hyperphysics.phy-astr.gsu.edu /hbase/music/et.html (311 words)

	Equal Temperament
		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.
		The differences shown between semitones in Pythagorean and Equal Temperament are representative of the classic difficulties encountered in the building up of musical scales.
		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)

	Guitar Files - 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.
	www.theguitarfiles.com /guitarfile-print-123.html (1211 words)

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

	Equal_Temperament
		Although clearly formulated by Mersenne in 1635, equal temperament did not become generally established in practice until 1800 in Germany and later in England and France.
		Tuning in equal temperament alters the traditional intervals of
		for a comparison of intervals expressed in equal temperament and other tunings; see also
	www.sfu.ca /sonic-studio/handbook/Equal_Temperament.html (188 words)

	Multi-TEMPERAMENT Scales Manual
		Equal temperament was probably known in the 1700s or earlier, but was not considered a satisfactory scale due to the impurity of all intervals.
		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.
		Each of the 14 temperaments on this disk is a subtle change in the way the notes within each octave are tuned.
	www.webcom.com /jawknee/Mirage/UPWARD/multitempdocs.html (1300 words)

	No. 380: Equal Temperament
		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.
		Equal temperament is as Western as apple pie.
		His great polemic for equal temperament was, of course, his book of keyboard pieces with varied key signatures.
	www.uh.edu /engines/epi380.htm (532 words)

	History of Tuning and Temperament
		Just intonation, meantone and equal temperament are classified as regular systems because all, or all but one of the 5ths, are tempered equally.
		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.
	www.terryblackburn.us /music/temperament/stoess.htm (2797 words)

	Equal Temperament Company
		Equal Temperament Solutions was founded in 2002 by Matthew Fries and Michael Sanita.
		Equal Temperament Solutions uses the ClickTime Web Timesheet for our time tracking.
		Out of a commitment to the music community, Equal Temperament Solutions supports a few non-profit music organizations with free design, hosting and maintenance services.
	www.equaltemp.com /company.shtml (219 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.
		In the one known as Werckmeister Temperament III the black 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.
		One approach to mean tone temperament on keyboards with only one set of black 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#.
	www.midicode.com /tunings/temperament.shtml (3005 words)

	MSN Encarta - Equal Temperament
		Equal Temperament, in music, a type of temperament (tuning of a scale) in which every semitone within an octave is exactly equal.
		Become a subscriber today and gain access to:
	encarta.msn.com /encyclopedia_762505559/Equal_Temperament.html (76 words)

	Equal Temperament
		EQUAL TEMPERAMENT (Eric and Stacey Jones) is a husband/wife percussion duo dedicated to the performance and generation of new works for percussion duo.
		EQUAL TEMPERAMENT'S CD "Parhelion" is available at Eroica Classical Recordings
		The duo has commissioned works by several composers including Erik Santos, Jeffrey Peyton, David Jarvis, and Thomas Brett.
	www.msu.edu /user/joneser8 (51 words)

	LucyTuning, meantone, equal temperament
		In 12-note equal temperament, where every fifth is narrow by 1/12 of a ditonic comma, the large interval ("whole step") is exactly the size of two small intervals ("half step").
		The only temperament in which these two types of semitones are equivalent is equal temperament.
		This is a brief comparison among three varieties of meantone temperament: "LucyTuning," 1/4 syntonic comma meantone, and 12-note equal temperament.
	www-personal.umich.edu /~bpl/templucy.html (600 words)

	The Equal Tempered Scale and Peculiarities of Piano Tuning
		The initial task of a piano tuner is known as setting the temperament, that is, to tune a section in the middle of the keyboard to an equal tuned temperament.
		In the equal tempered scale, the twelve intervals are spread evenly between the octaves.
		Understanding the equal tempered scale and the rational for the stretching of the upper octaves in piano tuning involves an understanding of something about both the physics of sound, and the history of music.
	www.precisionstrobe.com /apps/pianotemp/temper.html (4260 words)

	Equal Temperament
		Equal tempered 4ths are wide by 1 beat per second.
		Equal tempered 5ths are narrow by ½ beat per second.
		Tuning and Temperaments Early Music Institute School of Music IU Bloomington
	www.music.indiana.edu /som/piano_repair/temperaments/Equal.html (304 words)

	An Introduction to Historical Tunings
		Equal temperament - the bland, equal spacing of the 12 pitches of the octave- is pretty much a 20th-century phenomenon.
		This is even closer to equal temperament; even so, when I switched to it, my piano tuner had to return twice within two months before it began to stabilize.
		Those who attack equal temperament, the tuning of our modern pianos - as I do on my Just Intonation Explained page - seem to be attacking the great European musical tradition itself.
	www.kylegann.com /histune.html (3158 words)

	Temperament
		To those who know better, equal temperament's compromised tuning is as ungrateful to the ear as "soiled and faint colors are to the eye.".
		But major thirds in equal temperament are tempered seven times as much as the fifths.
		Creating twelve equal steps in an octave changed the proportions that had been used for the various musical intervals, some more drastically than others.
	www.72note.com /temperaments/temperament.html (949 words)

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