# Is it possible to have a note that is both dotted and a triplet?

Basically, I am coding a C# function that returns a number of milliseconds depending on the given note. I was wondering if it's possible to have a note that is both dotted and a triplet, it would be easier not to accommodate this in my code but I wouldn't want to leave it out if it was indeed something that might be needed.

• As a software developer, if it's tricky to implement and you don't think people will use it, don't do it. Simple. – corsiKa Sep 23 '15 at 21:21

Yes it is possible to have a note that is part of a triplet and dotted for example:

In this we're using quarter note triplets. Instead of having them all be 3 even quarter note triplets the first one is dotted and the second one is shortened giving us a triplet consisting of a dotted quarter note followed by an eigth note followed by a quarter note to fulfill the triplet.

• The interesting bit is that those dotted-triplet quarters should be indistinguishable from regular quarter notes. Marking a note as tripletted merely gives it 2/3 of the regular duration. Dotting a note gives it 3/2 of its usual duration. 2/3 * 3/2 = 1, so those eighth notes should be firing exactly on beats 2 and 4. You should also be able to remove the triplet/dot marks from those first quarter notes of each set, so that what you're left with, on beats 2 and 4, two short-long pairs. If those notes switched places, you'd have "swung" eighths, btw. – Jemenake Nov 23 '15 at 3:28
• @Jemenake But that would indicate a wrong metrical pattern, as user33027 pointed out in their answer. It would indicate something equivalent to 6/8 rather than something equivalent to 3/4. Moreover, it is reasonable to have a group with a dotted note which is not at the start of the group, e.g. \times 2/3 { c'4 d'4. e'8 } – Rosie F Oct 17 '19 at 13:18

This should be easy to support in code, as what lilypond calls generically "tuplets" (\times 2/3, \times 4/5, etc.) merely means the notes they enclose have some fractional duration, and the presence of dots simply extends the duration of the previous (possibly already dotted) note duration by half.

% atonal-util notes2time --tempo=60 c4. d8 e4
1s 500ms
500ms
1s
= 3s
% atonal-util notes2time --tempo=60 --fraction=2/3 c4. d8 e4
1s
333ms
666ms
= 2s


This can lead to support for very silly things that should never appear in notation.

% atonal-util notes2time c4. c4.. c4... c4.... c4.....
1s 500ms
1s 750ms
1s 875ms
1s 937ms
1s 968ms
= 9s 31ms


Hopefully my numbers aren't buggy, so it would be good to have another implementation to check them against....

• "silly things that should never appear..." - are you familiar with Conlon Nancarrow? – user13202 Sep 23 '15 at 22:18

You can certainly write it, and the computer will play it. For example, in Finale (notation software from Make Music Inc.), you can enter three consecutive dotted eighth notes and then use the Triplet tool on them: a dialog box will pop up with the suggested option of putting the three dotted eighth notes in the "space" of two dotted eighth notes. At the beginning of a 4/4 measure that leaves an eighth rest and a half rest.

Of course this means that the result of this ridiculous charade is that you have three "normal" eighth notes written in a needlessly confusing way. It is of much greater use to have just one dotted note within a triplet, such as for example, a quarter note, a dotted quarter note and an eighth note "tripleted" into the "space" of half note.

If you're writing notation software, then you definitely need to accommodate all possible combinations of dotted notes and triplets. How Finale does it is by using "Enigma Duration Units" (or EDUs, something that you might find mildly amusing if you find the Enigma Variations mildly enjoyable). A "normal" quarter note is equal to 1,024 EDUs.

So, in the example of a quarter note, a dotted quarter note and an eighth note "tripleted" into the "space" of half note, the quarter note probably takes up 683 EDUs, the dotted quarter note 1,023 EDUs and the eighth note 342 EDUs. Then to obtain milliseconds it's a simple matter of arithmetic with the metronome marking.

Others pointed out that formally a triplet with a dot has the same length as a non-triplet note without a dot. That's sort of a red herring since the musical accents of the two phrases LilyPond sets as

\new RhythmicStaff { \tuplet 3/2 { 4. 8 4 } 4 \tuplet 3/2 { 8 4 } }


are completely different. In particular, the first eighth triplet is unaccented and may not be exactly on-beat (particularly in dances) since only the first note carries the "weight of the step" and first and second note form a unit. In contrast, the second eighth triplet is very much accented and a syncopated note strongly on-beat (which sounds contradictory but is due to it being too short for a regular on-beat accent).

All blues picking rhythm with triplets has a dotted quarter-note in it, but it is just not written as it looks fussy and complicated. You play the quarter-note timing nonetheless to get the blues "groove".

Listen to a good blues picker and you can hear it. Without the dotted quarter-note timing, it just ain't blues!

Here is Mary Flower picking blues (plenty of triplets in there and if written, they would be written as straight triplets):

• Sorry, what's a "quarter-note"? I thought that was the American equivalent of a "crotchet". I'm actually referring to triplets. – Robbie Coyne Sep 28 '15 at 8:19