Particle displacement - Revision history

en>Maggyero: /* Mathematical definition */

2014-11-14T12:55:39Z

Mathematical definition

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	In Western [[musical notation]], a '''dotted note''' is a [[note]] with a small dot written after it. In modern practice the dot increases the [[duration (music)\|duration]] of the basic note by half of its original value. If the basic note lasts 2 [[beat (music)\|beats]], the corresponding dotted note lasts 3 beats. A dotted note is equivalent to writing the basic note [[tie (music)\|tie]]d to a note of half the value, or with more than one dots, tied to notes of progressively halved value.<ref>Gardner Read, ''Music Notation: A Manual of Modern Practice'' 2nd Edition. Boston: Allyn & Bacon, Inc. (1969): 114, Example 8-11; 116, Example 8-18; 117, Example 8-20.</ref> Any number of dots may be added to a note; ''n'' dots serve to lengthen the note by <math>1 - \tfrac{1}{2^n}</math> of its original duration.{{citation needed\|date=September 2012}}

	Although notes with more than three dots do not occur often, one can determine the length of any given note ''a'' with ''n'' dots: <math>a_n=a\left(1+\tfrac 12+\tfrac 14+ \cdots + \tfrac 1{2^n}\right)=2a-\frac a{2^n}</math>.
	~~{\| align=right~~
	~~\|[[File:dotted notes.svg]]~~
	\|}

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	~~[[File:dotted notes3.svg\|right\|frame\|Example 1. Dotted notes and their equivalent durations~~. The ~~curved lines~~, ~~called [[Tie (music)\|ties]]~~, ~~add the note values together.]]~~
	~~If the note~~ to ~~be dotted is on a space, the dot also goes on the space, while~~ if ~~the note is on a line~~, the ~~dot goes on the space above (this also goes for notes on ledger lines)~~.<~~ref~~>~~Glen Rosencrans, ''Music Notation Primer''. New York: Passantino (1979): 29~~<~~/ref~~> ~~However~~, ~~if a dotted note~~ on ~~a line is part of a [[chord (music)\|chord]] where a higher note is also on a line~~, the ~~dot for~~ the ~~lower note is placed in the space below: [[File:Dotted chord.png\|14px]] <ref>Ted Ross.~~ ''~~Teach Yourself The Art of Music Engraving & Processing'' Hansen Books, Florida.</ref>~~

	~~The dots on dotted notes, which are located~~ to the ~~right~~ of ~~the note, are~~ not ~~to be confused with~~ the ~~dots which indicate~~ [~~[staccato]] [[articulation (music)\|articulation]~~], ~~which are located above or below~~ the ~~note as shown in the 3rd and 4th notes~~ of ~~Example 2.~~

	~~Theoretically, any note value can~~ be ~~dotted, as can [[rest (music)\|rest]]s of any value. If~~ the ~~rest is in its normal position, dots are always placed in third staff space from~~ the ~~bottom~~.<~~ref~~>~~Read (1969): 119; 120, Example 8-28. The author points out the obvious fact "that it is impossible to tie rests."~~<~~/ref~~>

	~~The use of a dot for [[Augmentation (music)\|augmentation]] of a note dates back at least to the 10th century~~, ~~although the exact amount~~ of ~~augmentation~~ is ~~disputed; see [[Neume]]~~.

	~~Dots can be used across [[bar (music)\|barlines]]~~, ~~such as~~ in ~~[[H~~. C. ~~Robbins Landon]]'s edition of Joseph Haydn's [[Symphony No. 70 (Haydn)\|Symphony No. 70 in D major]]~~, ~~but most writers today regard this usage as obsolete~~ and ~~recommend using a tie across the barline instead~~.<~~ref~~>~~Read (1969): 117–118~~. ~~"Ranging from Renaissance madrigals~~ to ~~the keyboard works of Johannes Brahms, one often finds such a notation as the one at the left below~~.~~" (~~The ~~next page shows an example labeled "older notation" of two measures of music in 4/4~~ of ~~which the second measure contains, in order: an augmentation dot, a quarter note and~~ a ~~half note.</ref>~~

	~~More than one dot~~ may ~~be added; each dot adds half of the duration added by the previous dot~~, ~~as shown in example 1.~~

	~~==Double dotting==~~
	~~A double-dotted note is~~ a ~~note with two small dots written after it. Its duration~~ is ~~1¾ times (1x + ½x + ¼x = 2x − ¼x) its basic [[note value]]~~.

	~~The double-dotted note is used less frequently than the dotted note. Typically, as in the example below~~, it is ~~followed by a note whose duration is one-quarter the length~~ of ~~the basic note value, completing the next higher note value~~.

	~~Before the mid 18~~<~~sup~~>th<~~/sup~~> ~~century, double dots were not used. Until then,~~ in ~~some circumstances~~, ~~single dots could mean double dots. <ref>{{cite book\|last=Taylor\|first=Eric\|title=The AB Guide to Music Theory Part I\|year=2011\|publisher=ABRSM\|isbn=978-1-85472-446-5\|page=18}}</ref>~~

	~~[[File:Double-dotted note.svg\|frame\|right\|Example 2. The first two notes show a double-dotted [[eighth note]] followed by a [[thirty-second note]], that are connected with a [[Beam (music)\|beam]].]]~~
	~~Example 2 is a fragment of~~ the ~~second movement of [[Joseph Haydn]]'s [[string quartet]], [[Opus number\|Op~~.~~]] 74~~, ~~No. 2, a [[variation (music)\|theme and variations]]~~. The ~~first note~~ is ~~double-dotted~~. ~~Haydn's theme was adapted for piano~~ by ~~an unknown composer; the adapted version~~ can be ~~heard {{Audio\|Meditation -- Josef Haydn~~.~~mid\|here}} (3~~.~~7 [[Kilobyte\|KB]] [[MIDI]] file).~~

	In a ~~[[French overture]] (~~and ~~sometimes other [[Baroque music]])~~, ~~notes written as dotted notes are often interpreted~~ to ~~mean double-dotted notes,<ref>Adam Carse, ''18th Century Symphonies: A Short History~~ of the ~~Symphony in~~ the ~~18th Century''. London: Augener Ltd. (1951): 28~~. ~~"Contemporary theorists made~~ it ~~clear~~ that ~~the dotted note should be sustained beyond its actual value (the double dot was~~ not ~~then in use), and that the short note or notes should be played as quickly as possible~~."<~~/ref~~> ~~and the following note is commensurately shortened; see [[Historically informed performance]]~~.

	~~==Triple dotting==~~
	~~{{Redirect\|Triple dot\|the punctuation mark~~ that ~~usually indicates an intentional omission of~~ a ~~word~~ or ~~phrase from~~ the ~~original text\|Ellipsis}}~~
	~~[[File:triple-dotted note.gif\|frame\|right\|Example 3]]~~
	~~A triple-dotted note~~ is a ~~note with three dots written after it; its duration is 1⅞ times (1 + ½ + ¼ + ⅛ = 2 − ⅛) its basic note value~~. ~~Use of a triple-dotted note value is not common~~ in ~~the Baroque and Classical periods~~, ~~but quite common in~~ the ~~music~~ of ~~[[Richard Wagner]] and [[Anton Bruckner]], especially in their brass parts. See example 3.~~

	~~An example~~ of the ~~use of double- and triple-dotted notes~~ is ~~the Prelude~~ in G major for piano, [[Preludes (Chopin)\|Op. 28]], No. 3, by [[Frédéric Chopin]]. The piece, in [[time signature\|common time]] (4/4), contains running [[Sixteenth note\|semiquavers]] in the left hand. Several times during the piece Chopin asks for the right hand to ~~play a triple-dotted~~ [~~[half note\|minim]] (lasting 15 semiquavers) simultaneously with the first left-hand semiquaver, then one semiquaver simultaneously with the 16th left-hand semiquaver.~~

	More than three dots are highly uncommon but theoretically possible;<ref>Bussler, Ludwig (1890). ''Elements of Notation and Harmony'', p. 14. 2010 edition: ISBN 1-152-45236-3.</ref> only quadruple dots have been attested.<ref name=CWMN>http://~~www~~.~~informatics.indiana.edu/donbyrd/CMNExtremesBody.htm</ref>~~

	~~==See also==~~
	~~[[File:Dotted eighth~~-~~sixteenth~~.~~png\|thumb\|120px\|"[[Swung note\|Hard swing]]" (3:1): dotted eighth-sixteenth~~.]]
	*[[Swung note]]
	*[[Notes inégales]]
	*[[Tuplet]]
	*[[1/2 + 1/4 + 1/8 + 1/16 + · · ·]]

	~~==References==~~
	~~<references />~~

	~~{{Musical note values}}~~
	~~{{Musical notation}}~~

	~~{{DEFAULTSORT:Dotted Note}}~~
	~~[[Category:Musical notation]]~~
	~~[[Category:Rhythm~~ and ~~meter]]~~

en>Addbot: Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q779457

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Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q779457

← Older revision		Revision as of 04:03, 12 March 2013
Line 1:		Line 1:
	~~Dalton~~ is ~~what~~'s ~~written across his birth certificate but nevertheless~~ , ~~he never really enjoyed~~ that ~~name~~. The ~~most-loved hobby~~ for ~~him and simply his kids~~ is ~~landscaping but he~~'s ~~been~~ [~~http~~://~~Mondediplo~~.~~com~~/~~spip~~.~~php?~~page=~~recherche~~&~~recherche=removing removing~~] ~~on new things~~ as of ~~late~~. ~~Auditing~~ is ~~even his primary income~~ is ~~derived from~~. ~~Massachusetts~~ is ~~where your lover~~ and ~~his wife~~ in ~~real~~ time. He'~~s not godd at design but consider want to check their website~~: http://~~prometeu~~.~~net~~<br><br>~~Also visit my web site~~ [~~http~~:~~//prometeu.net hack clash of clans~~]		In Western [[musical notation]], a '''dotted note''' is a [[note]] with a small dot written after it. In modern practice the dot increases the [[duration (music)\|duration]] of the basic note by half of its original value. If the basic note lasts 2 [[beat (music)\|beats]], the corresponding dotted note lasts 3 beats. A dotted note is equivalent to writing the basic note [[tie (music)\|tie]]d to a note of half the value, or with more than one dots, tied to notes of progressively halved value.<ref>Gardner Read, ''Music Notation: A Manual of Modern Practice'' 2nd Edition. Boston: Allyn & Bacon, Inc. (1969): 114, Example 8-11; 116, Example 8-18; 117, Example 8-20.</ref> Any number of dots may be added to a note; ''n'' dots serve to lengthen the note by <math>1 - \tfrac{1}{2^n}</math> of its original duration.{{citation needed\|date=September 2012}}

			Although notes with more than three dots do not occur often, one can determine the length of any given note ''a'' with ''n'' dots: <math>a_n=a\left(1+\tfrac 12+\tfrac 14+ \cdots + \tfrac 1{2^n}\right)=2a-\frac a{2^n}</math>.
			{\| align=right
			\|[[File:dotted notes.svg]]
			\|}

			==Notation==
			[[File:dotted notes3.svg\|right\|frame\|Example 1. Dotted notes and their equivalent durations. The curved lines, called [[Tie (music)\|ties]], add the note values together.]]
			If the note to be dotted is on a space, the dot also goes on the space, while if the note is on a line, the dot goes on the space above (this also goes for notes on ledger lines).<ref>Glen Rosencrans, ''Music Notation Primer''. New York: Passantino (1979): 29</ref> However, if a dotted note on a line is part of a [[chord (music)\|chord]] where a higher note is also on a line, the dot for the lower note is placed in the space below: [[File:Dotted chord.png\|14px]] <ref>Ted Ross. ''Teach Yourself The Art of Music Engraving & Processing'' Hansen Books, Florida.</ref>

			The dots on dotted notes, which are located to the right of the note, are not to be confused with the dots which indicate [[staccato]] [[articulation (music)\|articulation]], which are located above or below the note as shown in the 3rd and 4th notes of Example 2.

			Theoretically, any note value can be dotted, as can [[rest (music)\|rest]]s of any value. If the rest is in its normal position, dots are always placed in third staff space from the bottom.<ref>Read (1969): 119; 120, Example 8-28. The author points out the obvious fact "that it is impossible to tie rests."</ref>

			The use of a dot for [[Augmentation (music)\|augmentation]] of a note dates back at least to the 10th century, although the exact amount of augmentation is disputed; see [[Neume]].

			Dots can be used across [[bar (music)\|barlines]], such as in [[H. C. Robbins Landon]]'s edition of Joseph Haydn's [[Symphony No. 70 (Haydn)\|Symphony No. 70 in D major]], but most writers today regard this usage as obsolete and recommend using a tie across the barline instead.<ref>Read (1969): 117–118. "Ranging from Renaissance madrigals to the keyboard works of Johannes Brahms, one often finds such a notation as the one at the left below." (The next page shows an example labeled "older notation" of two measures of music in 4/4 of which the second measure contains, in order: an augmentation dot, a quarter note and a half note.</ref>

			More than one dot may be added; each dot adds half of the duration added by the previous dot, as shown in example 1.

			==Double dotting==
			A double-dotted note is a note with two small dots written after it. Its duration is 1¾ times (1x + ½x + ¼x = 2x − ¼x) its basic [[note value]].

			The double-dotted note is used less frequently than the dotted note. Typically, as in the example below, it is followed by a note whose duration is one-quarter the length of the basic note value, completing the next higher note value.

			Before the mid 18<sup>th</sup> century, double dots were not used. Until then, in some circumstances, single dots could mean double dots. <ref>{{cite book\|last=Taylor\|first=Eric\|title=The AB Guide to Music Theory Part I\|year=2011\|publisher=ABRSM\|isbn=978-1-85472-446-5\|page=18}}</ref>

			[[File:Double-dotted note.svg\|frame\|right\|Example 2. The first two notes show a double-dotted [[eighth note]] followed by a [[thirty-second note]], that are connected with a [[Beam (music)\|beam]].]]
			Example 2 is a fragment of the second movement of [[Joseph Haydn]]'s [[string quartet]], [[Opus number\|Op.]] 74, No. 2, a [[variation (music)\|theme and variations]]. The first note is double-dotted. Haydn's theme was adapted for piano by an unknown composer; the adapted version can be heard {{Audio\|Meditation -- Josef Haydn.mid\|here}} (3.7 [[Kilobyte\|KB]] [[MIDI]] file).

			In a [[French overture]] (and sometimes other [[Baroque music]]), notes written as dotted notes are often interpreted to mean double-dotted notes,<ref>Adam Carse, ''18th Century Symphonies: A Short History of the Symphony in the 18th Century''. London: Augener Ltd. (1951): 28. "Contemporary theorists made it clear that the dotted note should be sustained beyond its actual value (the double dot was not then in use), and that the short note or notes should be played as quickly as possible."</ref> and the following note is commensurately shortened; see [[Historically informed performance]].

			==Triple dotting==
			{{Redirect\|Triple dot\|the punctuation mark that usually indicates an intentional omission of a word or phrase from the original text\|Ellipsis}}
			[[File:triple-dotted note.gif\|frame\|right\|Example 3]]
			A triple-dotted note is a note with three dots written after it; its duration is 1⅞ times (1 + ½ + ¼ + ⅛ = 2 − ⅛) its basic note value. Use of a triple-dotted note value is not common in the Baroque and Classical periods, but quite common in the music of [[Richard Wagner]] and [[Anton Bruckner]], especially in their brass parts. See example 3.

			An example of the use of double- and triple-dotted notes is the Prelude in G major for piano, [[Preludes (Chopin)\|Op. 28]], No. 3, by [[Frédéric Chopin]]. The piece, in [[time signature\|common time]] (4/4), contains running [[Sixteenth note\|semiquavers]] in the left hand. Several times during the piece Chopin asks for the right hand to play a triple-dotted [[half note\|minim]] (lasting 15 semiquavers) simultaneously with the first left-hand semiquaver, then one semiquaver simultaneously with the 16th left-hand semiquaver.

			More than three dots are highly uncommon but theoretically possible;<ref>Bussler, Ludwig (1890). ''Elements of Notation and Harmony'', p. 14. 2010 edition: ISBN 1-152-45236-3.</ref> only quadruple dots have been attested.<ref name=CWMN>http://www.informatics.indiana.edu/donbyrd/CMNExtremesBody.htm</ref>

			==See also==
			[[File:Dotted eighth-sixteenth.png\|thumb\|120px\|"[[Swung note\|Hard swing]]" (3:1): dotted eighth-sixteenth.]]
			*[[Swung note]]
			*[[Notes inégales]]
			*[[Tuplet]]
			*[[1/2 + 1/4 + 1/8 + 1/16 + · · ·]]

			==References==
			<references />

			{{Musical note values}}
			{{Musical notation}}

			{{DEFAULTSORT:Dotted Note}}
			[[Category:Musical notation]]
			[[Category:Rhythm and meter]]

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2012-07-01T12:51:13Z

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