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, 2019 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, 2019 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, 2019 at 10:57
• @Artelius -- a time signature is not a fraction, and irrational time signature has an entirely different meaning than irrational number.
– user39614
Mar 28, 2019 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. Mar 28, 2019 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 :-)? Mar 28, 2019 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. Mar 28, 2019 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. Mar 28, 2019 at 17:22
• Um, yes there are such symbols: tuplets. Mar 28, 2019 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. Mar 28, 2019 at 19:16

According to 4/2 (four two) time signature bottom number 2 is a relative value of the Whole note representing two Half notes that are equal to a Semibreve or a Whole note. Upper number says how many of the bottom numbers, so there are four Half notes in a bar and Half note becomes the Beat unit which is equivalent to one beat thus Whole note is 2 beats long.

Triplet is the most common type of Tuplet is a group of notes played in the space of other notes basically two of the same rhythmic value. Since every measure here is made up of 4 standard Half notes, two Triplet groups can be played in which a total of six Triplet Half notes can be found in a Bar.

So 4/3 is not considered as a regular time signature used in Western music where 3rd note(doesn't exist) gets the beat, it tells simply there are 4 of the Triplet Half notes in the bar indicated by 3 implying an incomplete 4/2 bar with 2 triplet half notes missing to be played at a faster pace than the 2nd Bar that makes it an irrational measure.