Talk:Dotted note

Chopin's Nocturnes Op. 55 (Chopin)
I think there should be some mention of the use of dotted notes as used by Chopin in his Nocturne in F minor (Op. 55, No. 1). In the seventh measure, there is a rather unusual chord, in my opinion. It actually consists of two dotted notes with a detached quarter note above. I have not found any definition of this particular usage in any music theory or music definition book. This may not be Chopin's own notation, but rather that of Schirmer's Library of Musical Classics. I am not sure.

This chord seems to be played as a thirty-second note (B-flat), followed by a dotted thirty-second (E), followed by the quarter note (A-flat), ascending. The first two notes are actually played in the second beat, whereas the final A-flat is played in the third, where the chord is written. It is like an arpeggio with a pause before the last note in the run.

I apologize for my lack of proper music terminology. Hopefully my explanation is sufficient.

If anyone has a concrete definition for this, I think it (along with the source of the definition) would make a nice addition to the dotted note page.

Marc321 22:57, 1 June 2007 (UTC)
 * It must be a weirdness of Schirmer's. My Henle edition has nothing like that. Rather, it has a stem-up quarter note on A flat, above a stem-down dotted quarter with B flat and E natural, with a wavy vertical line indicating to roll the chord.
 * P.S. We usually don't count partial measures at the beginning of a piece when numbering, so the feature you mention is in measure 7, not 8. &mdash;Wahoofive (talk) 18:14, 2 June 2007 (UTC)

Is this the measure you mean? My Henle edition has only single dots rather than double dots in the lower voice of the top staff, but that's insignificant for this discussion. &mdash;Wahoofive (talk) 18:56, 2 June 2007 (UTC)
 * Thank you for replying and for the picture. That is the measure I'm talking about. Thank you for correcting me on counting the measures. I was not sure about that when I posted.


 * The version in your book makes a lot more sense. I've uploaded a scan from my book just for comparison. Now that I've seen another perspective, I do not think this is important enough to be included in the main dotted note page. Interesting, nonetheless. Marc321 00:49, 5 June 2007 (UTC)

why do people not like the oboe?? it is amazing!!

Formula
Rather a silly formula in the generalisation section. In the first place it contains two errors, hence cannot function. In the second, and maybe most important place, it doesn't tell you anything you need to know and will not be used by anyone.130.89.218.91 (talk) 21:33, 24 February 2008 (UTC)
 * I replaced the formula with a correct one (took it from the dutch wiki). Of interest to music theorists and scholars too. Be aware that many aspects of music have mathematical aspects too. Pls keep the formula. regards, DTBone (talk) 11:37, 25 February 2008 (UTC)

The formula still does not work. I did change the wording (and, incidentally, spelling) of the previous editor so the subsection actually makes sense. Please fix the actual math, though.

69.54.28.201 (talk) 03:43, 8 March 2008 (UTC)

Another less complicated formula that would work is $$a_n=2a-\frac a{2^n}$$. — Insanity Incarnat  e  21:19, 23 March 2008 (UTC)

I think the formula should actually be $$a_n=2n-\frac n{2^a}$$. I've tried graphing them both and this seems more accurate. ONEder Boy (talk) 20:41, 2 May 2010 (UTC)

Formula

 * Although notes with more than three dots do not occur often, one can determine the length of any given note a with n dots: $$a_n=a\left(1+\tfrac 12+\tfrac 14+ \cdots + \tfrac 1{2^n}\right)=2a-\frac a{2^n}$$.


 * This makes it clear that continuous dotting does give a continuous prolongation of the original note, but it will never get as long as twice the original value.

I removed the above according to the citation added to the info that more than three dots are note used. Thus unless a source is found showing they have since become common or infrequent but notable, the formula is unnecessary. Hyacinth (talk) 23:40, 15 May 2010 (UTC)


 * I have seen quadrupole-dotted notes in Bruckner's symphonies (specifically No. 9). So, that source that says they aren't used is incorrect or improperly cited. Justin Tokke (talk) 19:12, 23 August 2010 (UTC)
 * Which bar? Tjako (talk) 22:06, 23 August 2010 (UTC)
 * Movement 1, the passage at bars 355-373 is permeated by quadruple dots. (pp. 60-64 in the Eulenburg study score) Anotherak (talk) 18:27, 9 April 2014 (UTC)
 * Quadruple-dotted notes appear in Schumann's string quartet, Op. 41 No. 1. Double sharp (talk) 10:31, 12 September 2012 (UTC)
 * Quadruple-dotted notes appear in Verdi's Requiem, Rex tremendae majestatis section, (pp. 88-89 in the Eulenburg study score) BudgieJane (talk) 22:58, 15 July 2022 (UTC)

The article now has this version. Hyacinth (talk) 12:08, 12 September 2012 (UTC)
 * Any number of dots may be added to a note; n dots serve to lengthen the note by $$1 - \tfrac{1}{2^n}$$ of its original duration.

Accuracy
The article gives the current meaning of a dot, "The dot adds a half as much again to the basic note's duration," but fails to tell us when this usage became invariant. My guess is that someone published a John Thompson-type primer midway through the nineteenth century codifying this usage and that some time thereafter the professionals, having all learned from this primer as youths, internalized it. But there are many examples of usage where the dot does not mean "half as much again", from the baroque (where often the dot added more than half as much again) at least through Verdi (who, like other composers of the time, commonly used a dot to add 1/3 as much again, because this notation was easier to read than changing the time signature to 6/8 or 12/8).

A neophyte who reads this article as is, and is otherwise uninstructed, will sing the "Battle Hymn of the Republic" incorrectly: in a rhythm never actually performed. Ccerf (talk) 22:57, 5 December 2008 (UTC)

Since no one seems to disagree, I've added the words "in modern practice" to the second sentence of the article. C. Cerf (talk) 02:59, 27 November 2012 (UTC)

Wrong uses of dotted note
Does anyone think about this??

Sometimes, a dotted eighth note plus a sixteenth note is wrongly used to mean a quarter note triplet plus an eighth note triplet. Any Google search I can use to find a forum about this?? Georgia guy (talk) 17:40, 22 June 2009 (UTC)
 * Sometimes in baroque music there is debate on this, e.g. when you have a gigue in triplets, where dotted notation might be meant like a quarter+eight in the ternary rhythm (especially when one voice has ongoing ternary eightsm and another voice has the dotted eight+sixteenth notation simultaneous). On the other side of the spectrum there is the jazz, where simple eight notes be played with swing (like triplets consisting of a quarter+eight). Btw amateur musicians sometimes play the dotted eight+sixteenth like a triplet with quarter+eight, usually due to lack of sufficiently developed rhythmical feeling of the music. regards, DTBone (talk) 22:47, 24 June 2009 (UTC)


 * It appears to me that "Georgia guy" hasn't read the immediately preceding section, in which I intended to make plain that the use "Georgia guy" describes in the first sentence as "wrongly" is often "correctly." After sixty years of hearing "Battle Hymn of the Republic", I've invariably heard the dotted rhythm sung as a "quarter note triplet plus an eighth note triplet" (above).  I did hear once that the Army Band plays it with the dots interpreted the twentieth-century way, but I haven't personally heard that, and doubt that the Army Chorus would accompany them in the same rhythm.


 * And what "Dutch T-bone" says about baroque music is applicable to the nineteenth century as well; Verdi, for example, wrote commonly in 12/8 but marked it 4/4, notating the ternary quarter+eighth with dots. Given the difference between candlelight and modern electrical light, it is hardly surprising that composers used dots, which are much easier to discern in a dimly lit pit, rather than ternary notation.C. Cerf (talk) 15:06, 6 June 2014 (UTC)

See: Swing (jazz performance style). Hyacinth (talk) 09:54, 28 November 2019 (UTC)

Correction to Formula
I am a neophyte, but have a good understanding of math. So I have a few questions for those more knowledgeable about music to clarify the formula.

I see only two possibilities (excluding the definition in question), neither of which involves the finite geometric series shown on the main page.

1. The dots are grouped first and then apply to the note. Note that a multiplicative nature is needed, since no note occurs in parentheses. Mathematically, consider N to be the given note duration, and a(k) the duration sequence: a(0) = N   a(1) = N·  = N(·) = N + (1/2)N = (1 + 1/2)N = (3/2)N a(2) = N·· = N(··) = N + (1/2)(1/2)N = (1 + 1/4)N a(3) = N··· = N(···) = (1 + 1/8)N etc.

Then we get the formula a(k) = ( 1 + 1/2^k )N, where 2^k equals 2 raised to the power k

2. The dots are applied recursively to the note. This would result in an additive behavior because of the recursivity is applied to the note. Using the above, b(0) = N   b(1) = N·  = (N·) = N + (1/2)N = (3/2)N b(2) = N·· = (N·)· = N· + (1/2)N· = (3/2)N· = (3/2)( (3/2)N )   replace N· with (3/2)N using b(1) b(3) = N··· = (N··)· = N·· + (1/2)N·· = (3/2)N·· = (3/2)( (3/2)N· )      replace N·· with (3/2)N· = (3/2)( (3/2)(3/2)N )  replace N· with (3/2)N The formula here is then  b(k) = (3/2)^k N    Note the additive nature is evident in: b(2) = N· + (1/2)N· = ( N + (1/2)N ) + (1/2)( N + (1/2)N ) =  [ 1 + 2(1/2) + (1/2)(1/2)]N       binomial which at first looks geometric, but in fact follows a binomial pattern in   powers of (1/2): b(k) = [ 1 + (1/2)]^k N   similar to the binomial   [ 1 + x ]^k

Neither of these yield a geometric series. The unquestioned definition on the main page is vague, but seems to imply the recursive definition (2) above, since for N··, the right is considered first, so the second dot applies to the note before it, N·.

There should be a rigorous definition out there somewhere. Are there two pieces for which the same double-dotted note has different beat durations? — Preceding unsigned comment added by 69.238.72.1 (talk) 07:11, 13 February 2013 (UTC)

No, the way it works is that the first dot adds 1/2 of the base note's value, the second adds 1/4, the third adds 1/8, and so on. Thus a whole note is 4 beats in common time: a dotted whole note is then 6 beats, and a double-dotted whole note is 7 beats. If you somehow added an infinite number of dots, you'd reach the next higher note value (since 1 + 1/2 + 1/4 + 1/8 + ⋯ = 2). Of course, this is mostly theoretical, as no one in their right mind would write something like ! Double sharp (talk) 07:52, 6 June 2016 (UTC)


 * We should just eliminate the formula from the article completely. It adds nothing to understanding and just provides opportunities for nerd arguments like this. &mdash;Wahoofive (talk) 05:49, 7 June 2016 (UTC)
 * – Yes, please! -- Michael Bednarek (talk) 12:58, 7 June 2016 (UTC)

Too much detail in lede
Although the mathematical formula is interesting for connoisseurs, it isn't really that central to the understanding of the term "dotted note" The same goes for the reference to notes inégales and the possibility that the notes of dotted rhythms might not be exactly 3:1. These items are worthy of inclusion in the article, but it seems a bit much to put such subsidiary topics in the lede paragraph. &mdash;Wahoofive (talk) 04:26, 7 January 2015 (UTC)
 * I don't mind the mention and links of notes inégales and "swing" nor the observation that playing practice is not always strictly metronomic (is that a word?), but that formula in the lead has been bugging me for some time. I even think the article would lose nothing if it were omitted entirely from the article; the prose explanation seems entirely sufficient. -- Michael Bednarek (talk) 06:28, 7 January 2015 (UTC)