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Topic: Syntonic comma

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	Comma - Open Encyclopedia (Site not responding. Last check: 2007-10-14)
		comma is the name used for one of the punctuation symbols.
		The term comma is also used in music theory for various small intervals that arise as differences between approximately equal intervals.
		A comma is also a type of butterfly, common in the United Kingdom.
	open-encyclopedia.com /Comma (127 words)

	Schisma - Wikipedia, the free encyclopedia
		In music, the schisma, also spelled skhisma, is the ratio between a Pythagorean comma and a syntonic comma and equals 32805/32768, which is 1.9537 cents.
		It is also the difference between the syntonic comma and the diaschisma.
		Because the difference between a grad and a schisma is so small, a rational intonation version of equal temperament may be realized by flattening the fifth by a schisma rather than a grad, a fact first noted by Johann Kirnberger, a pupil of Bach.
	en.wikipedia.org /wiki/Schisma (234 words)

	Syntonic comma -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-14)
		A just perfect fifth has its notes in the (The number of occurrences within a given time period (usually 1 second)) frequency ratio, which is equal to 702.96 cents, and four of them are equal to 2807.82 cents.
		This difference is significant because on a (A stringed instrument that is played by depressing keys that cause hammers to strike tuned strings and produce sounds) piano keyboard, four fifths is equal to two octaves plus a major third.
		In (Click link for more info and facts about just intonation) just intonation using prime factors up to 5, the syntonic comma is the ratio between the major tone of 9:8 and the minor tone of 10:9 (so is 81:80).
	www.absoluteastronomy.com /encyclopedia/s/sy/syntonic_comma.htm (311 words)

	Meantone temperament - Wikipedia, the free encyclopedia
		This is achieved by tuning the perfect fifth a quarter of a syntonic comma flatter than the just ratio of 3:2.
		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.
		It is useful because it gives us an idea of the melodic qualities of the tuning, and because if R is a rational number, so is (3R+1)/(5R+2), which is the size of fifth in terms of logarithms base 2, and which immediately tells us what division of the octave we will have.
	en.wikipedia.org /wiki/Meantone_temperament (1611 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.
		The syntonic comma is the ratio 9/8 divided by 10/9, which is the ratio between a pure C-D interval and a pure D-E interval.
		In a mean-tone temperament, the fifths are distorted by a certain fraction of the syntonic comma, which Paul described.
	www.albany.edu /piporg-l/meantone.html (1334 words)

	Onelist Tuning Digest # 483 message 26, (c)2000 by Joe Monzo (Site not responding. Last check: 2007-10-14)
		The syntonic comma is four fifths minus a third, so we can write it as s=4v-t.
		Paul is using 'comma' here in a very generic sense to mean a small interval, which in many cases will be used as a unison vector to delimit the boundaries of a periodicity-block.
		Since Beethoven, "bridging" through syntonic comma and any (and therefore, all) of the other 'commas' paul mentions above (in connection with Mathieu) has been a feature of western triadic music, hence the use of 12-tone equal (or well) temperament.
	sonic-arts.org /td/monzo/o483-26new5limitnames.htm (2611 words)

	Comma (music) - Encyclopedia, History, Geography and Biography
		In music theory, a comma is a small or very small interval between two notes which, though it is almost not to be heard, is introduced by computing their frequencies.
		Pythagorean comma or ditonic comma (ratio between 7 justly tuned octaves and 12 justly tuned fifths.
		schisma is the interval between Pythagorean comma and syntonic comma
	www.arikah.net /encyclopedia/Comma_%28music%29 (127 words)

	The two commas (Site not responding. Last check: 2007-10-14)
		Ignoring the span of octaves, the Pythagorean comma is that of twelve 5ths over the octave or 23.460 cents sharp.
		The syntonic comma is four pure 5ths over the just 3rd or 21.5 cents sharp.
		The old theorists proposed temperaments from cycles of fifths and since the syntonic comma was used to get the thirds, most of meantones were expressed as some fraction of that comma.
	www.ptg.org /pipermail/pianotech/2000-April/062952.html (429 words)

	How to choose Temperament? ((long)
		What confuses many people is that the Pythagorean comma is found by the difference between 7 octaves and 12 fifths, the Syntonic comma is found by comparing the result of four Just fifths to its first resultant third, which is, as Ric said, is a very wide Pythagroean third.
		The syntonic comma: "One era's feature..." While the Pythagorean comma seems to be a "bug," since it limits us to 11 perfect fifths out of 12 per octave, the syntonic comma might more justly be called an artistic feature of Gothic music and tuning: the active and unstable quality of thirds and sixths.
		The syntonic comma, in contrast, is a congenial feature: stable fifths and fourths in their ideal ratios, and active thirds and sixths, both mesh nicely with the harmonic style.
	www.ptg.org /pipermail/pianotech/2000-April/062778.html (2042 words)

	Theory
		This difference, that is, the one between the B# obtained from the «fifth» and the C obtained from the «octave», defines the Pythagorean comma.
		Algongside these three parameters we have a fourth one, the schism, that is, the difference between the Pythagorean and the syntonic comma.
		It follows that the Pythagorean third is larger of the pure third of 2/3 (8/12) of Pythagorean comma minus a schism.
	spazioinwind.libero.it /seicentoitaliano/uk/teoria/teoria_uk.htm (1070 words)

	The term comma has various uses comma comma is... (Site not responding. Last check: 2007-10-14)
		"comma comma" is the name used for one of the punctuation symbols.
		The term "comma" is also used in music theory music theory for various small interval intervals that arise as differences between approximately equal intervals.
		A "comma" is also a type of butterfly butterfly, common in the United Kingdom United Kingdom.
	www.biodatabase.de /comma (137 words)

	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.
		The difference between 81/64 and 5/4 (or 80/64) is the syntonic comma.
		Thus if we see that the syntonic comma is 21.5 cents, then 1/4 of that is 5.375 cents.
	www.ptg.org /pipermail/caut/2001-May/004094.html (585 words)

	Regular meantone strains - www.larips.com (Site not responding. Last check: 2007-10-14)
		A and C have been established at one syntonic comma apart, since there was one pure major third employed to get there.
		E and C have been established at one syntonic comma apart, since there was one pure major third employed to get there.
		F# and C have been established at one syntonic comma apart, since there was one pure major third employed to get there.
	www-personal.umich.edu /~bpl/larips/meantone.html (1467 words)

	Stichting Huygens-Fokker: Logarithmic Interval Measures
		The chromatic and diatonic semitones are 4 and 5 commas.
		In regular meantone temperaments where the tempering of the fifth is expressed in a fraction of a comma, the comma is the syntonic comma.
		The syntonic comma is 11.008 schismas, the Pythagorean comma 12.008, and the minor diesis 21.016 schismas, so practically 11, 12 and 21.
	www.xs4all.nl /~huygensf/doc/measures.html (2184 words)

	A method for optimally distributing any comma (Site not responding. Last check: 2007-10-14)
		In this example we can have (a) 3's and 7's narrowed by 1/3 comma (4.6 c), or (b) 5's widened by 1/3 comma, or (c) 3's and 7's narrowed by 1/6 comma while 5's are widened by 1/6 comma, and all the cases in between.
		The errors introduced are less than 2 cents, which is less than the typical tuning accuracy of most non-electronic instruments, and are a positive benefit in preventing cancellation of partials or apparent merging of individual voices (with harmonic timbres), and of course one also gains in the number of available harmonies.
		In the case of distributing the syntonic comma, when the only intervals of interest are 1:2, 2:3, 4:5, and we are willing to temper the octave, the optimum consists in widening the octaves by 1/7-comma and narrowing the fifths by 1/7-comma, which results in major thirds which are 1/7 comma wide.
	uqconnect.net /~zzdkeena/Music/DistributingCommas.htm (3302 words)

	[No title]
		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.
		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.
		The logical extension of this trend is a one-twelfth (Pythagorean, not syntonic) comma meantone, which is precisely equal temperament.
	www.rreid.net /tuning/Midkiff.info (2080 words)

	Expert About co:Comma
		A comma splice is a type of run-on whereby two independent clauses—or complete sentences—are incorrectly joined by a comma.
		One of the legal dialing 'digits' is a comma which has a special meaning to your modem: wait 2 seconds*.
		I wonder whether it may refer to the practice of putting a comma after the penultimate item in a list, before the and—for example ‘eggs, bacon, and sausage’ rather than ‘eggs, bacon and sausage’, which is how I would write it.
	www.expertsite.biz /dir/co/comma.htm (1645 words)

	How to convert a ratio to cents
		A pure fifth is 701.955 cents, and the syntonic comma is 21.5063 cents.
		Of couse, the quarter comma meantone isn't the only meantone scale of interest, and one will want to be able to find the cents values for any meantone scale.
		We see that quarter comma meantone scale has fifths that are flattened more than they are for equal temperament.
	tunesmithy.netfirms.com /on_site_tree/robertwalker/mean_tone_in_cents.html (738 words)

	Keyboard temperament analyzer/calculator - Bradley Lehman (Site not responding. Last check: 2007-10-14)
		A TU is defined as 1/720th of the interval of a ditonic (Pythagorean) comma.
		The syntonic comma is the interval difference between the "Pythagorean" major third generated by four fifths ((3/2)^4) vs. the pure major third in that same octave (4*(5/4)).
		The syntonic comma is therefore ((3/2)^4) / (4*(5/4)), or 81/80.
	www-personal.umich.edu /~bpl/temper.html (2467 words)

	comma -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-14)
		There are two commonly cited commas, the Pythagorean comma and the comma of Didymus, or syntonic comma.
		By the end of the 16th century writers of English were using most of the marks described by the younger Aldo in 1566; but their purpose was elocutionary, not syntactical.
		In biblical texts points and commas are used to mark the middle and end of verses; and in the commentaries points mark the end of sentences.
	www.britannica.com /eb/article-9024943?tocId=9024943 (554 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		The syntonic comma was seen as beneficial in medieval music where 3rds were not meant to be consonant.
		The regular temperaments are usually specified by the fraction of the syntonic comma that is used to reduce each fifth.
		As a last example, if the syntonic comma is spread evenly across all of the 5ths, we have Equal Temperament.
	www.j2b.co.uk /tuning/commas.htm (524 words)

	Bill Alves - The Just Intonation System of Nicola Vicentino (Site not responding. Last check: 2007-10-14)
		As can be seen in the table, this difference of 21.5 cents is in fact the syntonic comma and is no more insignificant than Vicentino's comma or many of the steps between the other adjacent intervals.
		The comma is not included in the gamut because it is smaller than the smallest step necessary to realize the enharmonic genus; however, it does play a role in the tuning of the archicembalo.
		This is the statement Barbour interpreted as indicating 1/4-syntonic comma temperament, and he showed how his division of the octave into thirty-one tones very cleverly extends this temperament into practically a closed system closely approximating 31-tone equal temperament [14].
	www2.hmc.edu /~alves/vicentino.html (2833 words)

	comma
		The comma is a valuable, useful punctuation device because it separates the structural elements of sentences into...
		Comma usage is in some respects a question of personal writing style: some writers use commas liberally, while...
		Comma splices, fused sentences, and run-ons are three types of mechanical errors created by incorrectly joining independent clauses.
	www.nieddu.biz /legge/comma+.cgi (782 words)

	How to calculate the cents values for a mean tone scale from the size of the comma
		Since we want the interval c to e to be a pure 5/4, all the fifths in C' G' D A e need to be flattened slightly in order to achieve 5/1 for the interval from C' to e.
		In fact, each one needs to be flattened by a quarter of a syntonic comma - which of course is why these scales are called quarter comma.
		In fact, they are flattened by so much that at the two ends of the cycle of fifths one has to have one wolf fifth that is far sharper than normal, rather than flat as it is in pythagorean tunings.
	tunesmithy.netfirms.com /japplets/mean_tone_in_cents.htm (949 words)

	Syntonic comma: Definition and Links by Encyclopedian.com - All about Syntonic comma
		Syntonic comma: Definition and Links by Encyclopedian.com - All about Syntonic comma
		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 cents.
		In Pythagorean tuning, the minor tone, is relaced by the major tone of 9:8.
	www.encyclopedian.com /sy/Syntonic-comma.html (337 words)

	Articles - Comma (music) (Site not responding. Last check: 2007-10-14)
		In music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways.
		syntonic comma, the difference between four perfect fifths and two major thirds plus two octaves
		Equal temperament was introduced as a way of avoiding commas, since enharmonic notes are tuned identically in that system.
	www.mafox.com /articles/Comma_%28music%29 (190 words)

	Vallotti: 55 division (Site not responding. Last check: 2007-10-14)
		Dividing the octave into 55 equal parts creates units of 21.818c, each of which is reasonably close to the syntonic comma at 21.506c.
		Since the diatonic (major) and chromatic (minor) semitones of 1/6 comma meantone differ by about a syntonic comma, it is possible to see the diatonic semitone as consisting of 5 units (or commas) and the chromatic semitone as consisting of 4 units (or commas).
		1/5 comma meantone equates with the 43 division (this is discussed by some 18th-century theorists).
	music.cwru.edu /duffin/Vallotti/T1/55division.html (231 words)

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