Irrational meter - why the mark of a triplet in 4 half notes

Can someone please explain to me why the mark of a triplet in this 4 half notes? I understood how to play it but from what i read you can only write triplets on 3 notes like 3 eighths 3 quarters etc... See picture

• There are whole, half, quarter etc. notes, but nothing that shows third. So, to me, the 4/3 time signature is somewhat pointless, as to show 'proper' notes, they need to have the 'triplet' sign. I reckon it could be written out in standard form and make more sense. – Tim Mar 28 at 7:48
• Because there is no notehead shape that alone depicts 1/3 note. there's 1/2, 1/4,1/8, but no 1/3. Same reason as triplets themselves. – Tim Mar 28 at 8:11
• I'm fairly certain that there are better ways to show what needs playing rather than use irrational meters. Judging by the question, I'm not alone. – Tim Mar 28 at 10:57
• @Artelius -- a time signature is not a fraction, and irrational time signature has an entirely different meaning than irrational number. – ex nihilo Mar 28 at 12:02
• My comment was tongue in cheek. Music and mathematics go hand in hand, though, and I think this is somewhat of an unfortunate (dare I say, irrational?) terminology. Also, in my view a time signature is a fraction (but it is not just a fraction). As a fraction it indicates how many whole notes fit in a bar. Of course it has other, perhaps more important meanings. – Artelius Mar 28 at 12:48

The problem is, that tuplet just means some note length modification takes place. Mathematically you require a standard fraction with numerator and denominator and there seem to be different opinions which of those to put into the tuplet bracket.

Wikipedia suggest under Tuplet Notation a full fraction representation in the form 2:3 for exotic cases, but I have never seen one.

So counting the note values and looking at the current time signature may be necessary for resolution.

To answer your last question: the use of 'triplet' indicator is allowable for any length note. It tells you to play the three marked notes so that each takes up 1/3 the meter-time that would have normally been covered by two of the notes in question. Thus, in quarter time meter, a one-beat triplet is written with eighth notes (normally two per quarter note), a two-beat triplet is written with quarter notes, etc.

The use of anything other than 2,4,8,16 as the denominator of the designated meter is highly discouraged, especially among those of us who have to perform the piece.

• So if it was 6/5 time signature and there were 5 half notes i would but the number 5 benith the notes? Even if it does not makes sense :-)? – LoveIsHere Mar 28 at 13:39
• “highly discouraged” – that seems a bit of a fogyish attitude, no? Normal odd time signatures like 5/4 were probably also highly discouraged at some point, but I'd argue that it's very much a good thing that they eventually become widespread for where it makes sense. Sure you could denote that all in 4/4 with silly incompletely meters, but with a 5/4 signature it can get more directly to the musical intention. I don't see why that would be fundamentally different with irrational signatures. – leftaroundabout Mar 28 at 15:16
• @leftaroundabout It is different because there are no symbols for notes that have anything other than 2^(-k) duration. Thus no point in an N/3 time signature. – Carl Witthoft Mar 28 at 17:22
• Um, yes there are such symbols: tuplets. – leftaroundabout Mar 28 at 17:23
• For one thing, you can also have non-triplet (or other tuplets but 3) notes in such a bar. But even if you don't have them in the bar, it can be an effect to put single 4/3 bar in a piece in 4/4 – writing the same thing without an irrational signature would require two awkward tempo-change marks. – leftaroundabout Mar 28 at 19:16