# Is there a 2/3 time signature, or "cut-time" equivalent for 3/4?

Here's a passage written in 3/4 time:

(The composer uses an ambiguous shorthand after the first measure, but assume that where he wrote dotted-half tremolos he intended for the passage to be played 3 beats per measure with bow changes as spelled out in the first measure.)

Now suppose that along the way the composer wants to change the emphasis to two beats per measure, like this:

If this were a 4/4 ("common time") passage, something like this could be indicated with a change to 2/2 ("cut time"). But is there a time signature for this case of going from 3 quarter notes to 2 dotted-quarters?

My first guess was that the second example could be indicated with a time signature of 2/3. But I can't find any examples of such a time signature, and would any musician understand that – especially if it weren't demonstrated explicitly in the first measure?

• 6/8 should do what you’re asking, if I’m understanding you correctly. Feb 17 '20 at 18:32

The lower number in time signatures basically is used for crotchets - 4, quavers - 8, and semiquavers -16. It reflects that a 'full bar' contains a semibreve, and the number tells how many of the notes will fill that bar.

So, even in compound time, the lower number will be 4,8 or 16. Having a 3 at the bottom wouldn't make sense. Cut time is really 4/4 with a 2/4 feel. Same bottom number.

The 3/4 in the top example does give a 1-2-3 feel, as it should. But the second example becomes 6/8, or 12/16 - a duple time sig., which often gets counted as a slow 1-2, 1-2. The time sig. exists already, and is quite appropriate.

Out of interest, check Bernstein's 'America' - where 3/4 gets morphed into 6/8, both conveniently having the same number of beats per bar, with the feel changing.

• The second example should only become 12/16 if every 3rd 16th note is supposed to be emphasized (which I doubt given the beaming in the question). Feb 18 '20 at 6:59
• @Dekkadeci - given only that sample, yes, 6/8 is more feasible.
– Tim
Feb 18 '20 at 7:16

2/3 is not considered a valid time signature. The top number is the number of beats in a bar. The bottom number is the duration associated with 1 beat. 2/3 could be parsed as 2 half-note-triplets per bar, but that's ridiculous. You'll only ever see powers of 2 (2, 4, 8, 16...) in the bottom position.

The time signature change you're showing in your examples is from 3/4 to 6/8. (While 6/8 has 6 8th notes per bar, it has 2 pulses per bar.)

This notation is a little unclear. Have you seen this in an actual score, or is this just a theoretical question? The top note, which follows the pulse in both examples, isn't really part of the tremolo, so I personally wouldn't notate it as such. I'd notate the 2-note tremolo with stems down and actually write out 3 quarter notes (3/4) or 2 dotted quarter notes (6/8) above the tremolo with stems up.

This sort of change in pulse, where 3/4 can morph into 6/8 and vice versa, is called hemiola. If the change of pulse is only temporary, a change in time signature wouldn't be necessary since 3 quarters and 2 dotted quarters both make sense and mean the same thing in both time signatures.

• @jjmusicnotes Yes, 2/3 is ridiculous. It is purposefully obtuse and hard to understand. The notation required to make it work would be very difficult to read. Whatever musical idea you think you're conveying, I guarantee you there is a conventional time signature which conveys the same idea and is easier to read. Sure, no rules and anything goes. I'm on board with wacky stuff like Nancarrow, Cage, Feldman, etc, but telling beginners that 2/3 is valid is only going to confuse them. By convention, 2/3 is invalid. You can't seriously be refuting this? Feb 17 '20 at 19:43
• @jjmusicnotes - ridiculous - open to ridicule. When people do 'strange' things, that's what happens. It may be very clever - or it may just throw 'normal' into chaos. Still a valid word. Watered down - 'not normal'...
– Tim
Feb 17 '20 at 20:24
• Is there a standard convention for a third note? As mentioned sever times in several answers the bottom note represents the "type" of note that gets a beat. Another way of looking at 4/4 it is 4 *(1/4) 4 quarter notes, 3/4 = 3 quarter notes, 3/2 = 3 half notes. What is being challenged is the definition of a 1/3 note. Someone mentioned half note triplet (if I'm correct) but that doesn't necessarily motivate a 1/3 note definition as the 1/2 note is being used to demarcate time intervals. What would a 1/3 note be?
– user50691
Feb 17 '20 at 20:57
• @jjmusicnotes The composers you cite are essentially getting their rocks off to no good end. Time signatures like that do nothing to change the rhythm of the piece. Feb 18 '20 at 15:37
• @jjmusicnotes Nowhere did I say it was ridiculous because it is invalid. If there were any causality at all, I would presume it is the other way around. I describe it as invalid because a) most music software (that I have access to) won't even allow it, b) it has no defined meaning (how many pulses per bar? says who?), c) I have personally never seen it or anything like it used in real life. I describe it as ridiculous because it offers no functional meaning which cannot be conveyed using normal TSs. It would only ever be used to confuse, or perhaps out of confusion on the composer's part. Feb 18 '20 at 20:53

Since you mention bowing, presumably this is for strings and the part is played in double stops.

There is nothing ambiguous about the notation in your first example. It is absolutely clear: after the first bar, the top note is held for the whole of each bar. The slurs in the first bar are superfluous, but harmless.

If you want to assume the composer and/or editor and/or publisher didn't understand standard music notation, then of course you are entitled to that opinion. But you can't expect anyone else to guess what you think the notation should have been, unless you provide some evidence or context for your ideas.

The first bar of the second example is clear enough for any practical purpose. The following bars are identical to the first example and mean the same thing, of course.

2/3 is a perfectly acceptable time signature, though it doesn't mean anything that is relevant to your example. It means that one bar consists of two-thirds of a triplet of quarter notes. In some contexts, that sort of notation is clearer than a complex mess of tuplets that span bar lines, or tempo changes at every barline.

I don't understand why you think the relation between common time and cut time is relevant to the example either.

• I see this sort of short-hand frequently in violin sheet music, usually with segue written after the illustration of how the short-hand should be played out. My reference to common vs. cut time was by analogy: in both cases the notation is otherwise the same, but the beat emphasis is changed. Feb 17 '20 at 19:40
• @feetwet I would expect simile, not segue. Feb 18 '20 at 5:58
• I wouldn't say that 2/3 is an "acceptable" time signature, as us musicians work exclusively with powers of 2 in the denominator. Otherwise, you're right on. Feb 18 '20 at 15:36

Two things: I would assume that if there were a switch from 3/4 to 6/8, the 8th note would be consistent, and the pulse duration would change, but if one were wise, you'd simply indicate that with a little parenthetical marking above that says (in symbols I can't make here) 8th note = 8th note.

Best to err on the side of clarity and even redundancy. You want your performers spending time on making music, not figuring out what you mean. Also, 2/3 means something very specific, though many folks (as we've seen here) think it's not "valid." We call 8th notes 8th notes, or 1/4 notes 1/4 notes, because of how many of them there'd be in a whole note.

So 2/3 time would be a measure of 2 1/3 notes. Now, what's a 1/3 note? Well, it'd be ONE note that lasts as long as one of the notes in a half note triplet. So, 2/3 time would be launching into half note triplets, but only doing two of them. These are called irrational time signatures, and they're great.

Normally, if we want regular 1/8 note triplets (which would be 12th notes, wouldn't they?) we have to have them in packs of three. But what if you wanted 5 of them? You'd use the time signature of 5/12 time. Not a big deal, but you find plenty of old-fashioned people (who still think poetry has to rhyme) who think that's not cool.

My understanding is cut time is a matter of changing common time (with 4 beats) to a feel with only two beats played at a faster tempo.

But you are talking about taking a triple meter with 3 beats and changing the pulse to 2 with no change in the total time. That's changing to compound meter. In other words you want two beats with subdivisions of 3.

If you want to alternate the meters, but keep the sixteenth subdivisions at the same speed, you could do like Berstein did in America list the meters together...

There is no single time signature for representing the change from 3 quarter-notes to two dotted-quarters in a measure (with the tempo per measure unchanged.) However it's common enough to have a name (and is known from some centuries.) The term "hemiola" has this change a one of its meanings. (Another meaning is a succession of 2-beat phrases in a 3-beat piece, typical in waltzes but usually just notated with half-notes and ties.)

There are two different time signatures that represent this grouping: 3/4 and 6/8. The first represents. Some composers (I think Leonard Bernstein in West Side Story) used alternating time signatures of 3/4 and 6/8. It's a bit "wordy" (or at least "signature heavy") but hard to misread. (So simple, even a computer can do it.)

I've seen three other methods. If the prevailing rhythm is 3/4 and only a few measures are 6/8 style, one could used dotting, beaming and slurring to make things clear. (It would be 3/4 beamed as 6/8.) A second method is the reverse if the piece is mostly 6/8. These are pretty easy to read. The other thing is to write something like 3/4+6/8 as the time signature and let the players figure it out. (Brahms wrote 3/4+2/4 to represent 7/4 in one piece.)

Personally I've found (not much experience) that most musicians can interpret a pair of dotted quarters (in a 3/4 measure) correctly. (Note that the 6/8 interpretation is dotted-quarter followed by eighth tied to quarter.)

• Time signatures don't represent changes. They indicate two things: 1.) how many unit pulses there are in a given measure and 2.) what symbol represents a single unit pulse. Feb 17 '20 at 18:53
• 3/4 +2/4 doesn't equal 7/4..!
– Tim
Feb 17 '20 at 20:18
• True. That's why it's so interesting. I would have expected 3/4+2/4+2/4 or again, just write 7/4 beaming as 3+2+2.
– ttw
Feb 17 '20 at 21:04