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I learned recently that time signatures can be fractional in the top number. For example, 2.5/4 meter.

For normal time signatures, they have integer grouping structures. For example,

  • 4/4 meter has a grouping 1-1-1-1
  • 3/4 meter has a grouping 1-1-1
  • 6/8 meter has a grouping 3-3

and so forth.

Notice, in each case for these common meters, the groups contain integers.

Can beats in fractional meters be grouped? If so, are the numbers used in the groupings integers or can they involve non-integers (e.g. fractions)?

So might 2.5/5 be grouped like 1-1-1/2?

Stan Shunpike
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    Note: I'm pretty sure that the bottom number of a time signature must be some sort of power of 2 (2, 4, 8, etc.). X/5 is nonsensical. – John Doe Jan 04 '21 at 19:22
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    X/5 is not nonsensical. An X/5 bar would contain X ("quarter note") 5-tuplets. – Edward Jan 05 '21 at 00:50

3 Answers3

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The 8 in 6/8 is not a beat. The groupings of three are the beats.

I learned recently that time signatures can be fractional in the top number. For example, 2.5/4 meter.

"Can" in this context just means "a moderately well-informed musician is likely to know what it means", it's not standard. Traditionally, this "two beats then a beat cut short" feel would be notated in 5/8, and the quavers would be beamed either in groups of 2 and 3, or possibly 2-2-1.

The entire point of writing it in this non-standard way is to avoid making the performer consciously think about and interpret groupings for themself. You'll very occasionally see 2/♩. as an equivalent work-around for 6/8.

Esther
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  • So then a measure in 2.5/4 would be grouped, 1-1-0.5, where the 0.5 is the beat cut short? – Stan Shunpike Jan 04 '21 at 16:13
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    @StanShunpike; A measure in 2.5/4 would be grouped however the composer wants it grouped in order to communicate to the performer the desired effect. Maybe .5-1-.5-.5 is what the composer is after. – jwvh Jan 04 '21 at 17:58
  • @jwvh I can't promise nobody's ever done that, but it would be misleading at-best and I'd personally go as far as to call it wrong. It would be like writing simple quadruple with a quaver beat in 2/4, with the argument that it "can" be grouped .5-.5-.5-.5. – Esther Jan 05 '21 at 02:34
  • @StanShunpike I can't really give you any reasonable guarantees about how rarely-used time signatures "would" be grouped, they don't have the same conventions built around them that signatures like 4/4 do. But yes, I would tend to assume that it's two-and-a-half (short, really) beats in that two-then-a-short order barring strong evidence to the contrary. The most likely alternatives are the short beat going at the start or in the middle of the bar, beaming or possibly consistent accents should make it clear if this is what's meant; but I would personally just notate these in 5/8. – Esther Jan 05 '21 at 02:40
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Yes, beats in fractional meters can be grouped in integers, but in integers based on subdivisions of the beat. For example, a bar of (2.5)/4 could be treated as a bar of 5/8, then grouped as 2+3 or 3+2 according to an eighth-note pulse.

In the below excerpt from Percy Grainger's "Lord Melbourne (War Song)" (Lincolnshire Posy, fifth movement), I would conduct the (2.5)/4 measure as 1/4 + 3/8, and the (1.5)/4 measure as 3/8.

Percy Grainger, "Lord Melbourne", mm. 2-4

The 1/4 "pulse" would accommodate the triplet comprising the first portion of the measure. The 3/8 pulse(s) would handle the quarter-note + eighth-note second part of the measure.

Aaron
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    I can't help thinking this could be written - and read - better is a standard time sig. - x/8, with accents on what are now the 1st beats of each 'bar'. – Tim Jan 04 '21 at 09:18
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    @Tim I had the same thought and can only speculate: In the case of the 2.5 bar, the triplet at the beginning is most clearly written in quarter-note time, and the remainder of the bar, in 3/8, would require an "unnatural" accent on beat 3 -- similarly the 1.5 bar. – Aaron Jan 04 '21 at 12:00
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    Stravinski seemed happy with that sort of arrangement. – Tim Jan 04 '21 at 14:56
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Agreed with the other answers. I'd just opine that since how beats are grouped depends on the particular music involved, and that any note value or combination of note values can be considered the beat, and since any fractional meter is simply the equivalent of some integral meter (if we exclude irrational fractional meters, which are silly anyway), then fractional meters are unnecessary and a notational affectation.

Scott Wallace
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    fractional meters are rare these days, they were more common in the 1920’s (Ives, Cowell, Antheil) until the 50’s (Boulez, Takemitsu). Since then it has been more common (and less confusing) to use additive meters for the same effect - i.e. 2/4 + 1/8 where Ives might have had 2.5/4 –  Jan 05 '21 at 10:43
  • @DamianleGassick Thanks for the examples. I would still be inclined, just to keep things simple, to notate 2/4 + 1/8 as simply 5/8, and let the ways the rhythms are grouped in the score speak for themselves about how they should be performed. After all, we don't notate the time signature 6/8 as 3/8 + 3/8. But suum cuique. – Scott Wallace Jan 05 '21 at 11:07
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    personally, so would I, and it’s certainly clearer. If you ‘really’ want the 2/4 + 1/8 feel you can also put a dotted barline before the last eighth. –  Jan 05 '21 at 13:05
  • Agreed. After all, notation is just a means to an end, and whatever works to get the music performed as intended is fine. – Scott Wallace Jan 05 '21 at 13:07