Talk:Dotted note

message: 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)
replies: text: 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)

text: 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)
replies: text: Which bar? Tjako (talk) 22:06, 23 August 2010 (UTC)
replies: text: 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)

text: Quadruple-dotted notes appear in Schumann's string quartet, Op. 41 No. 1. Double sharp (talk) 10:31, 12 September 2012 (UTC)

text: 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)
thread_title: Formula

message: *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)
replies: text: 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)
replies: text: Which bar? Tjako (talk) 22:06, 23 August 2010 (UTC)
replies: text: 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)

text: Quadruple-dotted notes appear in Schumann's string quartet, Op. 41 No. 1. Double sharp (talk) 10:31, 12 September 2012 (UTC)

text: 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)
thread_title: Formula

message: 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)
thread_title: Accuracy

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

message: 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. —Wahoofive (talk) 04:26, 7 January 2015 (UTC)
replies: text: 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)
thread_title:  Too much detail in lede