Quarter-comma meantone

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	1/7th comma meantone
		The important words in the name "quarter comma meantone" are "comma" Here comma refers to the comma of Didymus or the syntonic comma.
		So when one encounters the term "1/7 meantone" that means the 5th has been tempered or narrowed by 1/7 of the syntonic comma.
		While "meantone" is supposed to refer to the ratio of the tone between the tonic and the major 3rd, there is little in the theory(s) of meantone to suggest this was actually used to construct the scales.
	www.ptg.org /pipermail/caut/2001-May/004094.html (585 words)

	Midkiff.info
		In a quarter-comma meantone, all but one of the fifths are flattened from the pure 3:2 ratio of 701.96 cents by one-fourth of the syntonic comma, or 5.38 cents.
		In a sixth-comma meantone, the fifths are flattened from the pure 3:2 ratio of 701.96 cents by one-sixth of the syntonic comma, or 3.58 cents.
		In a fifth-comma meantone, the fifths are flattened from the pure 3:2 ratio of 701.96 cents by one-fifth of the syntonic comma, or 4.30 cents.
	www.rreid.net /tuning/Midkiff.info (2080 words)

	Meantone temperament
		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.
		Because of the wolf interval which arises when twelve notes to the octave are tuned to a meantone with fifths significantly flatter than the 1/11-comma of equal temperament, well temperaments and eventually equal temperament became more popular.
		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).
	www.sciencedaily.com /encyclopedia/meantone_temperament (1653 words)

	Musical tuning - Wikipedia, the free encyclopedia
		Next to the twelve-equal temperament, which some would not regard as a form of meantone, the best known form of this temperament is quarter comma meantone, which tunes major thirds justly in the ratio of 5:4 and divides them into two whole tones of equal size.
		To do this, eleven perfect fifths in each octave are flattened by a quarter of a syntonic comma, with the remaining fifth being left very sharp (such an unacceptably out-of-tune fifth is known as a wolf interval).
		Meantone temperament, a system of tuning which averages out pairs of ratios used for the same interval (such as 9:8 and 10:9), thus making it possible to tune keyboard instruments.
	en.wikipedia.org /wiki/Musical_tuning (1293 words)

	Syntonic comma
		Quarter comma meantone, on the other hand, uses exact 5:4s for major thirds, but flattens each of the fifths by a quarter of a syntonic comma.
		In Quarter comma meantone, the major and minor tones are made equal to the square root of 5:4.
		The syntonic comma, also known as the comma of Didymus, is a small interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 centss.
	www.theezine.net /s/syntonic-comma.html (325 words)

	mos.html
		Quarter comma meantone continued to be used for church organs for a long time.
		So the effect is that in quarter comma meantone, one of the twelve scales can't be used in the normal way at all.
		Quarter here means a quarter of the value of the comma in cents, not a quarter of its value as a ratio.
	tunesmithy.netfirms.com /ascii_tree/robertwalker/mos.html (1284 words)

	The Organ Forum
		The Syntonic comma, which describes the discrepancy between pure seconds and thirds, is the one referenced by meantone temperaments.
		Commas are just ways of quantifying the inherent errors that crop up when tuning musical instruments, especially those that have all the notes pre-tuned (as with keyboard instruments).
		The Pythagorean comma is the difference between twelve perfectly tuned fifths and seven perfectly tuned octaves.
	www.bargainsail.com /forums/ShowPost.aspx?PostID=3100 (2054 words)

	The Musical Scale
		This tuning is called the Pythagorean tuning, and the ratio between B sharp (not shown on the diagram) and C on that tuning is called the Pythagorean comma, as distinct from the syntonic comma.
		Essentially, the notes on the organ are tuned on the basis of a perfect fifth that has been flattened by the fourth root of the syntonic comma, so that while the fifths are not accurate, the major thirds are exact.
		The syntonic comma is so named because it is the distance between two notes with the same spelling, thus representing the same tone.
	members.shaw.ca /quadibloc/other/musint.htm (1515 words)

	A beginner's guide to alternative tunings
		Quarter comma meantone is used primarily as an approximation to just intonation.
		The exception to this is Charles Lucy who is a very strong advocate for one meantone in particular.
		As there are two different sizes of tones, the best compromise for a meantone is to average them out.
	www.microtonal.co.uk /start.htm (2366 words)

	Just Temperament and Others
		In quarter-comma meantone temperament the just major third is divided into two equal whole tones.
		The fifths are made smaller and the fourths larger by a quarter of a syntonic comma.
		Expressed in terms of whole number ratios, the ordinary (syntonic or Ptolemaic) comma is the interval between a just major third (5:4) and a Phythagorean ditonic or major third (81:64).
	hyperphysics.phy-astr.gsu.edu /hbase/music/just.html (418 words)

	Organ Ludingworth, St. Jacobi
		The restoration of the organ (1981-1982) was finished by tuning the organ in quarter-comma meantone temperament.
	www.arpschnitger.nl /sludingw.html (122 words)

	Temperament: A Beginner's Guide
		Modified meantone is probably the most appropriate temperament for most of the 'early' organ music we now hear — even though Buxtehude and Bach were clearly among those exploring new tuning systems, their compositional technique remains informed by the meantone system.
		Almost all the fourths and fifths are dead in tune, and the entire comma is 'dumped' on one interval (according to Arnaut de Zwolle between F and Bb), which is therefore unusable.
		The wolf in meantone tuning is so horrible and such an obstacle that, by the later seventeenth century, it was being modified substantially in practice.
	www.albany.edu /piporg-l/tmprment.html (1630 words)

	Margo on Meantone
		The keyboards differ by Vicentino's "diesis" or fifthtone, often 128:125 or ~41.06 cents in 1/4-comma meantone (the distance between G# on the lower keyboard and Ab on the higher one, for example).
		Please let me begin by saying that like many other tunings, 1/4-comma meantone can be precisely defined in mathematical terms, but will vary in "real world" realizations, whether on a 16th-century harpsichord tuned by ear or on a modern synthesizer with limited pitch resolution.
		Note that while Vicentino considers his tuning to divide the whole-tone into five equal parts, he also appears to consider the major thirds "perfect" or pure -- two characteristics which it was shown by the later 17th century actually define two different tunings, 31-tone equal temperament (31-tET) and 1/4-comma meantone.
	www.ptg.org /pipermail/pianotech/2001-January/077900.html (524 words)

	Why I hate Vallotti (or is it Young?) By Ross W. Duffin – pg.2
		These regular meantone systems–1/5, 1/6 comma, etc.–feature good chords in the same places, but although the thirds are not as good as in quarter comma, the fifths are better, and complex harmonies are better.
		ome continued to use quarter comma meantone in spite of its limitations: it’s arguably still the best choice for much music of the early– to mid–17th century and it continued to be used for organs long after that.
		All of these regular meantone systems share one problem interval, however: a "wolf"–one fifth that isn’t even really a fifth because it is so far out of tune.
	music.cwru.edu /duffin/Vallotti/56K/page2.html (863 words)

	Smecno Virtual Organ Set
		It is tuned to the historical quarter-comma meantone tuning.
		The compass of the instrument: C1 - C5 in Hauptwerk terminology, short low octave.
	www.sonusparadisi.cz /organs/smecno/history.0.asp (480 words)

	Dolmetsch Online - Music Theory Online - Pitch, Temperament & Timbre
		But there were other meantone procedures known in the 16th and 17th centuries, especially by 2/7th comma, in which the minor 3rds are pure and the major 3rds beat, and 1/3rd comma.
		A bizarre fact is that equal temperament is really meantone by 1/12th comma, that is every fifth is narrowed by 1/12 of the syntonic comma and the interval between C - D and between D - E are equal.
		Sometimes called the mesotonic scale, the meantone (also written mean-tone) scale was particularly favoured by organists and explains why organ music from the period 1500 to the 19th century was written in a relatively small number of keys, those that this scale favoured.
	www.dolmetsch.com /musictheory27.htm (6533 words)

	CBH Technical Library — Temperaments XI — How to tune Third-comma Meantone
		This aside, after your experience with Quarter-comma Meantone, you’ll find the actual tuning procedure is remarkably similar.
		Yes, there will be a wolf—Aghast!—even larger than that of our beloved Quarter-comma Meantone.
		To tune successful minor thirds, the lowest coincident harmonics that you will be listening for—either conciously or not—are a little higher than any of the temperaments discussed previously: You must be listening not to the actual notes you are playing, but in fact in the region two octaves and a fifth above your bottom note.
	www.hpschd.nu /tech/tmp/mean-third.html (674 words)

	Stichting Huygens-Fokker: Siemen Terpstra: Theory of meantone and 31-ET harmony
		This is done by tempering the fifths by one-quarter of a comma, so that the two pitches D and \D of Just Intonation form a compromise pitch of about midway in size - the meantone.
		The theoretical language in use, meanwhile, was largely inherited from the meantone era, with its distinction of sharps and flats.
		The 'pure' meantone tuning can be expressed as a line of fifths in which the ratios are all multiples of two and the fourth root of five.
	www.xs4all.nl /~huygensf/doc/terp31.html (5979 words)

	Wellesley College Music Department: Facilities
		The spicey dissonances which are the unique province of quarter-comma meantone temperament were something that organ composers of the 17th century knew from childhood—and they soon learned how to use these sounds for their special artistic ends.
		The original purpose of the quarter-comma meantone temperament was to create a new kind of consonance, based on the mathematical purity of the major third.
		The characteristic dissonance of quarter-comma meantone temperament is repeatedly exploited by these composers to produce asense of climax of a sort never encountered in any other music.
	www.wellesley.edu /Music/facilities.html (1188 words)

	Features for Musicians and Composers, and Scale Designers
		Or the quarter comma meantone tunign that was in vogue until just before Bach - or the pythagoreans tunings of Medieval music - or the more evenly tuned well temperaments suitable for Chopin etc. Modern tunings include the musical geometries of Erv Wilson, and ones based on the harmonic series, and non octave tunings (e.g.
		The same methods can be used to play in quarter note scales on a normal keyboard by transposing one half of it up by a quarter tone, or using the two keyboards method.
		less than a quarter tone apart, you may need to use a midi keyboard mapping that sends several midi in notes to the same midi out note, varying the pitch bends only - if so you need to change the note numbers too before sending them on.
	www.robertinventor.com /features.htm (3560 words)

	MTO 10.1: Wibberley, Syntonic Tuning: Creating a Model for Accurate Electronic Playback
		Where an unavoidable accumulation of commas causes a composition to undergo an audibly significant and irreversible rise or fall in base pitch, the assumption should be that Syntonic tuning is the wrong soundscape for that piece and that Pythagorean tuning was intended by the composer.
		It is still advisable, however, to provide for a certain number of comma shifts either way, if only to test the effect of Syntonic tuning in such cases and adjudge the impact of the pitch change.
		Indeed this adjustment can sometimes be greater than a single comma over the course of a whole piece, so what needs to be provided for is two or three complementary values for each note sharpwards and flatwards.
	www.societymusictheory.org /mto/issues/mto.04.10.1/mto.04.10.1.wibberley3.html (8647 words)

	The Keyboard Tuning of Domenico Scarlatti
		Much early music relies on the strong consonance patterns of quarter-comma meantone tuning to shape phrases, and becomes dull and lifeless without it.
		In open tunings, such as those based on the meantone system, A flat is not the same pitch as its enharmonic G sharp; in circular tunings they are the same.
		If one wishes to understand the musical language of early keyboard composers, the tuning in which their music was conceived and heard is important.
	www.sankey.ws /consonance.html (1563 words)

	The Changing Scale
		Aron developed a quarter comma meantone temperament without realizing it - named this because the offset of one fourth was applied to the scale with a wolf tone offset of seven fourths.
		Here is Aron's quarter comma meantone temperament scale, reproduced chromatically, and below is a table that shows the offset it creates (table 1).
		This offset from an exact octave is known as the Pythagorean comma.
	www.johnminor.net /writings/overview.htm (2191 words)

	MicroTonal Scales Manual
		Quarter-Comma Meantone - pure G# Quarter-Comma Meantone - pure Ab
		The Meantone scale was in common use by the end of the 15th century.
		Since the entire circle of fifths cannot be 1/4 comma narrow, the total error (+1¾ comma) is left between G
	www.webcom.com /jawknee/Mirage/UPWARD/microtonaldocs.html (2655 words)

	Biography
		In September 2003, he is to produce a recording of works by Samuel Scheidt (ATMA Classique) on the quarter-comma meantone instrument by Hellmuth Wolff at Knox College, University of Toronto.
		Komisaruk's summer 2001 concert tour included solo performances at St. Paul's Cathedral in London (England) and the Washington National Cathedral in Washington, D.C. Among his performances in the 2002/3 season are solo engagements in the United States (Chicago, Pittsburgh) and North Germany (Stralsund).
	www.komisaruk.ca /biography.htm (392 words)

	Tuning-Math Archive Section 9: 8950 - 8974
		What I mean is, when extending meantone to a 7-limit mapping, it will naturally implicate different commas and change the optimal generator a bit, same as before.
		Yes, and there are different choices as to which commas to use to extend meantone to a 7-limit linear temperament.
		Depending on whether n or d is even, R may be the same as D. If it isn't exactly the same, it's going to be close because commas tend to be small (and have to be for the simplification to work) which means the numerator and denominator are of roughly equal size.
	www.robertinventor.com /tuning-math/s___9/msg_8950-8974.html (4987 words)

	Zeke Hoskin: Non-Equal-Tempered Tunings
		This fifth is even worse than in the quarter-comma meantone scale, and the major third is 7.36 cents short of its sweetest value, much better than in twelve-equal but still not good.
		Both Lucytuning and Kornerrup Phi are close to quarter-comma meantone, but come from different theoretical bases.
		As long as you take more than an eighth of a comma from the fifths, the error in the third is less than half a comma.
	www.openaccess.org /~zeke/tuning.htm (2245 words)

	Wolf fifth
		pure fifth, pythagorean wolf, pure, quarter comma meantone tempered fifth, pure, quarter comma meantone wolf, pure, equal temperament tempered fifth, pure.
		the E should be a pure major third (plus two octaves) above the C. So the fifths have to be tempered by a quarter of the difference between a pure major third and the Pythagorean major third, i.e.
	www.tunesmithy.connectfree.co.uk /wolf_fifth.htm (258 words)

	Unusual Musics::Guide::Help
		specifies a pitch with a frequency 1.495 times the base frequency (a quarter-comma meantone fifth).
		An equal tempered pitch is specified by an integer specifiying the number of degrees, the the letter "E", and an integer indicating which degree.
		A float is specified by a floating point number; it must contain a decimal point.
	www.suddensound.com /um/monochord/help.html (989 words)

	Classical Artists Worldwide - Classical Free Pages
		His 2004 release of works from the Tabulatura Nova by Samuel Scheidt (ATMA), is being produced on the quarter-comma meantone instrument at Knox College Chapel in Toronto.
		Kevin Komisaruk has performed as soloist in England, France, Germany, Canada, the United States, and Mexico, and has been heard on network broadcasts of Radio France, SRC and the CBC (Canada).
	www.classical-artists.com /users/profile.php?a=00000396 (89 words)

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In the News (Fri 18 Dec 09)