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Topic: Meantone temperament

	Kids.Net.Au - Encyclopedia > Meantone temperament
		Meantone temperament is a system of musical tuning.
		The most common form of meantone temperament tunes all the major thirds to the just ratio of 5:4 (so, for instance, if G is tuned to 400Hz, B is tuned to 500Hz).
		Quarter comma meantone is particularly suitable for music which treats the third as a consonant interval.
	www.kids.net.au /encyclopedia-wiki/me/Meantone_temperament (336 words)

	Meantone temperament Information
		In general, a meantone is constructed the same way as Pythagorean tuning, as a chain of perfect fifths, but in a meantone, each fifth is narrowed by the same amount (or equivalently, each fourth widened) in order to make the other intervals like the major third closer to their ideal just ratios.
		Most meantone temperaments share this problem, except for the case where the fifth is exactly 700 cents (tempered by approximately 1/11 of a syntonic comma) and the meantone becomes the familiar 12-tone equal temperament.
		Meantone temperament has had considerable revival for early music performance in the late 20th century and in newly-composed works specifically demanding meantone by composers including György Ligeti and Douglas Leedy.
	www.bookrags.com /Mean_tone (659 words)

	Meantone and Temperament in Bach's Time
		In meantone, all but one of the fifths are flattened from the pure 3:2 ratio by 1/4 of the syntonic comma.
		In a mean-tone temperament, the fifths are distorted by a certain fraction of the syntonic comma, which Paul described.
		Gottfried Silbermann used a milder sort of meantone, in which the 5ths are tempered by 1/6 comma, which is circular.
	www.albany.edu /piporg-l/meantone.html (1334 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		Meantone temperament represents a frequency ratio of approximately 5 by means of four fifths, so that the major third, for instance C-E, is obtained from two tones in succession.
		The meantone tuning with pure 5/4 intervals is quarter-comma meantone, with a fifth of size 696.58 cents.
		On the other hand, 18 meantone fourths up and two octaves down will also work, and the 11 is pure using this method for a fifth of size 696.05 cents, close to the 696 cents of 50 equal temperament.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=septimal_meantone_temperament (502 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		Meantone temperament is a musical temperament, which is a system of musical tuning.
		Quarter-comma meantone is the most well known type of meantone temperament, and the term meantone temperament is often used to refer to it specifically.
		Though quarter-comma meantone is the most common, other systems which flatten the fifth by differing amounts but which still equate the major whole tone, which in just intonation is 9/8, with the minor whole tone, tuned justly to 10/9, are also called meantone systems.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=meantone_temperament (866 words)

	Regular Temperaments
		An alternative way to think of a regular temperament, which may be more useful for constructing musical scales, is to represent each note of the temperament as a combination of one or more multiples of a generator (a repeated interval of the temperament, from which all the notes of the temperament can be derived).
		In the case of meantone, where the generator can be defined as the meantone approximation of a perfect fourth (4:3), this results in the mapping <1, 2, 4] for the octave and <0, -1, -4] for the fourth.
		Temperaments with 7-limit approximations typically have four elements in their val and monzo vectors, representing the prime factors 2, 3, 5, and 7.
	www.io.com /~hmiller/music/regular-temperaments.html (2082 words)

	meantone
		On the meantone helical lattice it can be seen that all of the axes in the rectangular lattice become spirals: the green 5-limit axes form the four twisted strands of the helix, and the pink 3-limit axes form one long tight spiral connecting the four strands together.
		As with pythagorean tuning, meantone is a chain-of-5ths type of tuning, in which the generator of the chain is the "perfect-5th" (or equivalently but with opposite sign, the "perfect-4th").
		Meantone cycles which are based on tempering by a fraction of a syntonic comma, which is a 5-limit interval, can have some of their pitches graphed on a lattice diagram.
	tonalsoft.com /enc/m/meantone.aspx (3111 words)

	Meantone temperament
		Meantone temperament is a system of musical tuning.
		The most common form of meantone temperament tunes all the major thirds to the just ratio of 5:4 (so, for instance, if G is tuned to 400Hz, B is tuned to 500Hz).
		Quarter comma meantone is particularly suitable for music which treats the third as a consonant interval.
	www.ebroadcast.com.au /lookup/encyclopedia/qu/Quarter_comma_meantone.html (311 words)

	Meantone temperament: Definition and Links by Encyclopedian.com
		Meantone temperament is a system of musical tuning.
		The most common form of meantone temperament tunes all the major thirds to the just ratio of 5:4 (so, for instance, if G is tuned to 400Hz, B is tuned to 500Hz).
		Quarter comma meantone is particularly suitable for music which treats the third as a consonant interval.
	www.encyclopedian.com /me/Meantone-temperament.html (349 words)

	Understanding Temperaments
		The need for temperament arises because it is impossible to have octaves, fifths, thirds, etc., all pure at once, or, in other words, because the ratios of the different pure intervals are incompatible.
		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.
		But it is atypical of irregular temperaments because it is completely regular and all keys are musically equivalent with their uniform and active thirds (and no stable thirds as in meantone).
	pages.globetrotter.net /roule/temper.htm (4098 words)

	Meantone
		Equal temperament has no interval in it that can be expressed as a rational number (because it's all based on an irrational number, the twelfth root of 2).
		In the 18th century a certain theoretical prestige was enjoyed by 1/6-comma mean-tone temperament and by the corresponding theoretical division of the octave into 55 equal parts, five of which constituted a diatonic semitone and four a chromatic one.
		One starts from a regular meantone (whether it's 1/4, 1/5, or 1/6...to taste) and then raises the sharps somewhat and/or lowers the flats somewhat (to taste) so more of the tonalities can be used in music.
	www.bach-cantatas.com /Topics/Meantone.htm (2919 words)

	History of Pitch - Tuning Forks A440 C523.3
		Equal temperament was proposed by Aristoxenus, a pupil of Aristotle, and had been in use in China for some centuries before.
		In 1842 the organ of St. Nicholas, in Newcastle-upon-Tyne, was tuned to equal temperament, and this is believed to be the first organ to be tuned in this way in England for a concert.
		Meantone was the most common scale used at that time.
	www.uk-piano.org /history/pitch.html (1016 words)

	Tuning History 2
		Meantone temperament, in which you have pure thirds, is especially good for lute and vihuela music from the first half of the 16th century.
		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.
		With temperament, a modification of tuning is needed and radical numbers are used to express some or all of the intervals, [7] e.g.
	www.musemath.com /miscellany/tuninghistory_2.html (3871 words)

	A beginner's guide to temperament
		Temperament is one of those subjects that attracts a) buffs and b) incomprehensible jargon.
		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)

	Meantone temperament Details, Meaning Meantone temperament Article and Explanation Guide
		The most common form of meantone temperament tunes all the major thirds to the just ratio of 5:4 (so, for instance, if A is tuned to 440 Hz, C#' is tuned to 550 Hz).
		Since (9/8) / (10/9) = (81/80), the syntonic comma, the fundamental character of a meantone tuning is that all intervals are generated from fifths, and the syntonic comma is tempered to a unison.
		As discussed above, in the 1/4-comma meantone temperament, the ratio of a tone is, the ratio of a semitone is, and the ratio of a fifth is.
	www.e-paranoids.com /m/me/meantone_temperament.html (1644 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)

	The Russell Collection of Early Keyboard Instruments - 'Equal Harmony'
		Chromaticism is even more poignant in Smith's temperament than in any of the normal seventeenth- and eighteenth-century cyclical or regular temperaments which use major thirds which are either pure or slightly wide.
		Nonetheless it is true that the difference between Smith's temperament and the easy-to-tune ¼-comma meantone temperament is only marginal in its musical effectiveness or in its use on an instrument equipped with the enharmonic lever arrangements suggested by Smith.
		It is of course possible to use ¼-comma meantone temperament equally well on either an organ or a harpsichord equipped for Smith's 'Equal Harmony' without modification to the physical operating mechanism.
	www.music.ed.ac.uk /russell/conference/robertsmithkirckman.html (2885 words)

	Just Temperament and Others
		Just temperament refers to a musical scale or musical intervals which maintain exact integer ratios between pitches.
		Pythagorean temperament maintains just intervals for the fifth and fourth but departs for some other intervals.
		In quarter-comma meantone temperament the just major third is divided into two equal whole tones.
	hyperphysics.phy-astr.gsu.edu /hbase/music/just.html (418 words)

	Equal temperament
		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.
		It doesn't fit the Meantone mold that shaped the development of Western harmony and tonality since the Rennaissance, though it does fit schismatic temperament and the Pythagorean tuning of medieval music, and is sometimes used in Turkish music theory.
	www.mp3.fm /Equal_temperament.htm (1748 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.
		The table showing the frequencies of the meantone temperament fails to distinguish between what, in equal temperament, would be enharmonic pairs but which, in meantone, all differ by 41¢ (about 2/5 of a semitone!).
		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)

	looking at Meantone, (long)
		In fact, the writers of these sources were so unconscious of alternatives to what we call 'meantone temperament' for the uncompromised tuning of non-keyboard instruments that they had no name for this system at all; they thought of what we call 'meantone temperament' simply as correct intonation.
		Tosi, in 1723, considered the correct tuning system to be what we would today call a form of regular meantone temperament with more than twelve notes to the octave, or what we might call for short 'extended regular meantone temperament'.
		The 1/6-comma temperament is the one implied by Türk's statement of 1791, previously cited from Boyden, that sharps are a 'comma' lower than the equivalent flats; it also seems to be the most common basis fro the irregular temperaments described by Barbour in _Tuning and Temperament_.
	www.ptg.org /pipermail/pianotech/2001-June/086789.html (1183 words)

	Ravel, Kawai & 1/7 Comma Meantone
		The 1/7 Comma Meantone Temperament (1/7MTT) was invented by a Frenchman, Jean Baptiste Romieu in 1758.
		The EB properties of both 1/7 and 1/8 Comma meantone (and Modified Meantone) Temperaments cause close harmony played in the simple keys (with 0-3 sharps or flats) to sound much purer than they really are.
		If the very name of the temperament scares you, just remember that ET may also be defined as a 1/11 Syntonic Comma Meantone Temperament.
	www.ptg.org /pipermail/pianotech/2000-April/062592.html (674 words)

	The Jon Rose Web - Temperament
		or the last 400 years, an ironically similar period for which slavery of another kind was in existence in Europe, the use of unequal temperament was slowly banished as the dictates of the composer demanded an irreducible unit of pitch capable of unproblematic modulation..
		Tuning systems such as Meantone, Kirnberger, Silbermann, and Vallotti emphasized the different sounds of home keys, and an improvisationary modulation to a distant key was a truely exotic sonic journey.
		In the near keys, irregular temperaments resemble meantone, and in the remote keys, they resemble (the near keys of) Pythagoras' tuning (with the tense thirds).
	www.jonroseweb.com /f_projects_temperament (1399 words)

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