[SOLVED] Irrational time signatures?

• Jun 28, 2016 - 02:22

Could there possibly be the ability to add irrational time signatures?

For those who don't know, a irrational time signature would look something like 4/3. The 3 corresponds to a dotted quarter note, like 4 corresponds to a quarter note. I have a song that I could use this time signature in, but since I can't use it I have to stick to 12/8. It works, but I'd like to have it in 4/3.


Wait, what? A "1/3" note isn't a dotted quarter note—there's no such thing. 12/8 is normally counted as four dotted quarter notes. Look up compound meter.

Jun 28, 2016 - 02:55

In reply to by Isaac Weiss

I know what a compound meter is.

It's called an "irrational" time signature for a reason, but it's not -that- irrational to me.

1/3 does correspond to a dotted quarter note. A dotted quarter note falls between a quarter note and a half note. 3 falls between 4 and 2. 4 means the note is a quarter note, and 2 means it's the half note. So logically, the 3 means it's the dotted quarter note.

I've seen it used in other pieces of music, but I was just wondering if we could do it in MuseScore.

In reply to by Anonymous

That's not how math works. A dotted quarter note falls between a quarter note and half note, but so does a double-dotted quarter note. A dotted quarter note is 3/8; a double-dotted quarter note is 7/16. Neither is equal to 1/3. A quarter note tied to a dotted sixteenth note is also between a quarter note and a half note, and that duration is actually very close to 1/3 (it's 11/32), but it's still not 1/3.

If you're not comfortable with math, a simpler way to think about it is that three 1/3 notes have to equal a whole note. There's no way to come up with a value that works, therefore the note value does not exist.

In reply to by Isaac Weiss

I have realized many do not know what a dotted note actually is. A dot on a note means it is halfway to the next longest note(as in a duplicate of 2), so a quarter note is a third note, a dotted eighth note is a sixth note, a dotted sixteenth note is a twelfth note, etc.

All that being said, you kind of can get what you want.

As you mentioned yourself, the correct time signature is 12/8, so use that one to enter the score. Then right-click it and open up the time signature properties. These allow you to set custom numbers for the signature.

In reply to by GeoDasher36

Depends on what you actually are trying to indicate - from a "correctness" standpoint, those simply are not valid time signatures. Taken literally, x/12 that would indicate a measure in which the eighth note triplet was the basic beat, and 2/12 would mean two of them per measure. In what way would you intend for this to be different than simply writing 2/8? Depending on your answer to that, then we can figure out the best way of accomplishing the goal.

In reply to by Marc Sabatella

x/12 time signatures do appear in several songs, even if it is a strange rhythm. I have realized many do not know what a dotted note actually is. A dot on a note means it is halfway to the next longest note(as in a duplicate of 2), so a quarter note is a third note, a dotted eighth note is a sixth note, a dotted sixteenth note is a twelfth note, etc.

Are you aiming for one instrument in 4/3 and another in a more conventional time signature playing simultaneously or just trying to write for one instrument alone?

In reply to by underquark

I asked this feature some time ago, but nobody said any about this.

Why not to add the capability to use two different time signatures into the same music piece?

Let's say: the melody line (flute, per example), into 4/4; the bass and rhythm section into 12/8 (to get the typical swing style without to use triplets).

It is just an idea, not absolutely necessary (because we can get this with some artifacts), but... Why not to include it? ???

Just an idea.

Wikipedia has some interesting information about irrational time signatures. Apparently there is always an equivalent "rational" time signature, so irrational time signatures are only useful for indicating a transition. However, even in such cases it is always possible to achieve the same effect using tuplets, tempo changes or metric modulation (expressing a new tempo in terms of the old tempo, or "crotchet equals minim"). The average musician is far more likely to be familiar with any of those concepts than with irrational time signatures, so it would probably be a good idea to use one of the alternatives.

Like Jojo indicated with his tuplet example, 3 beats in 4/3 lasts the same as 4 beats in 4/4.

Jun 28, 2016 - 17:54

In reply to by shoogle

If I were to use 4/4 I would need to use so many tuplets that it becomes excessive. The orchestra I'm writing this piece for would not have too much trouble playing it. We've seen many other uncommon time signatures like 9/8, 7/8, and even 6+4/8.

In reply to by Anonymous

Those aren't irrational though. I would say 99.99% of professional musicians are accustomed to seeing unusual but rational time sginatures like 7/8. I would say 0.000000001% have even heard of something like 4/3, much less being accustomed to it or comfortable with it.

In reply to by Anonymous

Yes, but the point is, the mere fact that someone might be accustomed to playing uncommon "rational" time signatures in no way implies they would be equally playing in uncommon "irrational" time signatuires/ Like I said, the vast majorioty of musicians have never heard of such a thing and would be completyely flummoxed by it.

In reply to by Anonymous

Those are perfectly reasonable time signatures. You didn't notice that they all have a denominator of 8?

If you consistently have three beats per measure, there are other options than tuplets in 4/4 or irrationality—use a time signature with the numerator based on 3. If you want three dotted quarter beats per measure, that's 9/8. (If a dotted quarter note were equal to a "1/3" note, then three dotted quarters would equal 4/4 or 8/8.)

In reply to by Anonymous

Here "rational" means that the denominator is a power of 2, corresponding to a whole/half/quarter/eighth/etc. note getting one beat. You can also represent the time signature as the number of beats to a measure over the graphic for the note that gets one beat - which could even be dotted, so e.g. 6/8 would be a 2 over a dotted quarter.

Very uncommon to use 3 for dotted quarter notes. Never seen this ever before. Lets examine this system:
If 3= dotted quarter then
6 = dotted eight and
12= dotted sixteenth.
A dotted whole note would be 1.5.
The clearest way without having to invent new note value names would be to write the counter number as usual and place a dotted note symbol as denominator.

In reply to by musikai

The real problem is "how to indicate a rate of 2, 3 or 4 times with a unit that is a dotted half"? Jean-Philippe Rameau has encountered this problem but I am aware that there is a problem with the denominator (3) which does not really represent the subdivision of a whole note as 2, 4, 8, 16, etc. ..
Besides Saint-Saëns had in his re-edition works by Rameau transformed 2/3 to 3/2 ... but a rate 3 times with half note for unity is not a rate 2 times that the dotted half note is unity, even if, ultimately, the account is good. So I prefer the solution of Rameau... lack of a better ; )

In reply to by Miré

I think the real problem here is that nobody seems to agree about what the 'Y' in an an X/Y irrational time signature actually means, and therefore irrational time signatures are not a good way to represent music unambiguously. In fact, given that there is always an equivalent "rational" way to notate whatever you wanted from the irrational time signature it would appear that irrational time signatures are rather pointless.

In reply to by Miré

If you turn off your math brain for a second you could also argue that "quarter notes" is the NAME of the note that is one beat. In Rameau's example he gave the dotted half note the NAME "3". He wasn't thinking about fractions at all. Because at the end of the day a time signature is not a fraction; it tells you the size of a measure by indicating how many of what kind of notes fill a whole measure.
Why he chose not to use the perfectly reasonable 12/8 which was widely used in his day I wouldn't know; maybe he wanted this music played slowly, not like a gigue?
BTW the term "compound meter" is not in use in German. I think it confuses more than it clarifies by suggesting something far more complicated than it is. We just learned that 6/8 is almost always counted in dotted crotchets.

In reply to by musikai

And indeed, in Brouwer's Preludios Epigrammaticos #2 this is exactly what was done. It looks exactly like an A minor chord (8 over a dotted crotchet) and I puzzled over it for some time. Personally I would prefer 8 over 3.

Judging from the discussion here, "irrational" is a good name.

There is a simple workaround. You can always just ignore the denominator and just look at the notes. I believe they used to write music without any time signature, so in a way it's superfluous.

But a dotted quarter is 1.5, while a 1/3 note would be 1.3333.... They're not the same.

If you try to figure out what a conductor's beats mean, though, a 4/3 time signature is not very helpful, because 1/3 notes would be triplets, and there are no triplets in the examples that Miré posted. Now, musicians do not always mark the beat according to the denominator anyway. If you want to subdivide each beat into three, then the numerator is a multiple of 3. For example, 6/8 is in 2, 12/8 is in 4, etc. For your example with 4 dotted halves, I would notate that as 12/4. It's not our fault if Rameau couldn't do arithmetic. It was a fairly new concept when he lived.

In reply to by RexC

I do not think Rameau is concerned arithmetic. He just wanted to point out that the chosen unit of time was the dotted half and in the absence of an agreement ( which, even today, remains to find) he thought n/3 would be a solution. In music it's all about practice, his idea was not good does it seem.

In reply to by RexC

Arithmetic dates back to the ancient Greeks (actually even before), that's why we call it by a Greek name. And I do not think Rameau was a fool who did not know arithmetic. He just had other priorities.
Seriously though, any kind of notation that is not in general use will cause problems with performers. The music has to come with a user's manual and composers who do things like that generally provide one.
The specific example of 4/3 is of course just compound meter with crotchets substituted for quavers (a hybrid of compound meter and cut time if you want). I still fail to understand why it is so important to have those dotted halfs and why dotted quarters won't do. Rameau could have said that it signals a slow tempo, but since the invention of the metronome one can signal this with a beats pre minute number.

In reply to by RexC

I have realized many do not know what a dotted note actually is. A dot on a note means it is halfway to the next longest note(as in a duplicate of 2), so a quarter note is a third note, a dotted eighth note is a sixth note, a dotted sixteenth note is a twelfth note, etc.

4/3 is rational. Maybe you should go back to eight grade. What it is not is a fraction with a terminating decimal form. Using time signatures that have a repeating decimal form sounds like it just messes everything up. The 3 would not correspond to a dotted quarter note. I think 12/8 is great. 6/8 is often conducted with the 2 beat pattern add counted as such. Thus, 12/8 can be conducted and counted as of with four beats-exactly what I believe you need. If not, equivalent time signatures are: 6/4, 3/2, and 4/2.6666666666666666666666... (technically this last one is the one you want. This is absolutely stupid to write so just stick with 12/8)

In reply to by ♪𝔔𝔲𝔞𝔳𝔢𝔯 ℭ𝔯𝔞𝔣𝔱𝔢𝔯♪

"Rational" has a different meaning in music to the usual mathematical meaning. You are correct that "rational" in maths means "any number that can be expressed as a fraction in the form N/D where N and D are integer numbers (and D is greater than zero)", so 4/3 is, by definition rational in a mathematical sense.

The same condition for rationality also applies to time signatures in a musical context, but here there is also an extra condition: D (the denominator) must be a power of 2. If the denominator is not a power of 2 then the time signature is considered to be "irrational". 3 is not a power of 2, so 4/3 is indeed irrational in a musical context.

What about a time signature consisting of e.g. a 4 over a dotted half note? The upper element is the number of beats, the lower element is the graphic for the element getting a beat. Thus 6/8 would become 2 over a dotted quarter, distinguishing it unambiguously from 3/4, which is a 3 over a non-dotted quarter.

In reply to by Marc Sabatella

I'm not sure about that - it seems to me that it resolves the original question, if you put a literal dotted note as the bottom element of a time signature, instead of an integer.

I may have asked this question before, but is there support in MS for doing this?

In reply to by dhfx

Well, the idea of an "irrational time signature" goes way beyond this, Sure, in the special case where the denominator is 3, compound time signatures like 6/8 are basically the same as 2/3. But what about a denominator of, say, 5 - so the basic beat is the quarter note quintuplet? We have no means of supporting that at all. Merely making 6/8 display as 2/3 is already possible, and adding support for 2/(dotted quarter) would be trivial. But having a time signature of 7/5 is simply not possible at all.

In reply to by dhfx

And it still wouldn't notate the same as 7/5. There is no way in MuseScore have a measure that actually displays seven quarter note quintuplets. Which is my point. It's not just about the appearance of the time signature - it's about having the measure itself actually look and play the way a true 7/5 measure would look and play.

In reply to by Marc Sabatella

Would you mind elaborating on why this is a matter of technical impossibility? I am not in the least knowledgeable about computing or software design, so maybe I should just keep silence because of my ignorange. That said, I can't help but wonder why it's any less feasible to create a measure of, as you suggest, 7/5, than anything else. I'm mostly wondering about this considering that, were one to disregard the conventions of western musical notation, simply playing one's instrument, it is certainly possible to play the equivalent rhtyhm of seven quarter note quintuplets, followed immediately, for example, by a measure of 4/4. Admitedly, it should require a high level of musicianship to do so, but it is conceivable.

In reply to by smrlongman1


for example: 3/4
3 is a nominator (or numerator) and 4 is a denominator.

The nominator shows how many notes are in one measure

The denominator indicates the base note value.
Base note value, should be exponent of the 2, like: 1, 2, 4, 8, 16, 32, 64, 128, 256.
note: (2^0=1)

In general: musicians don't understand a time signature like 8/5.
Because they cannot predict what the value and appearance of the 5th note should be.

In reply to by Ziya Mete Demircan

Further, there is actually a growing number of musicians in contemporary avant-garde who are familiar with this, and it is becoming common even with younger composers to incorporate this element into their music. I would add, also, that Finale has a time consuming, although workable solution built into the program for the purpose of representing non-dyadic (so called "irrational") time signatures. So, again, considering my ignorance about Musescore's technical specs, by speaking further I may reveal not only my ignorance, but my stupidity, but it would seem to me that unless there are incomparable differences between Musescore and, for example, Finale, then I should fail to understand why it is a technical impossibility for support of this feature to be incorporated into the program, for those composers or hobbyists, such as myself, who may wish to experiment or incorporate such techniques themselves. My question is simply to understand if it is reasonably possible to incorporate this feature into the program. Thank you.

In reply to by dhfx

The only real purpose of value for, say, 7/5 would be as a transition between rational time signatures. As an example, if you were writing a melody in 6/4 which was grouped in 4 quarter notes followed by 2, then that would become the subdivision which defined that piece. However, if you were to interject a measure of 7/5, it works as a way to throw off the listener. If we group 7/5 as 5+2/5, then the 4+2 quarter note pulse of the 6/4 melody would be turned into subdivisions of 5/5 (equal to the length of 4 quarter notes) and 2/5 (which would be the length of two quarter note quintuplets). This is only a specific example, and the uses can vary from this, but you are right in that it would not make any difference from 7/4 unless contrasted with rational time.

In reply to by starrgate16

In other words, a transition from 6/4 to 7/5, which almost nobody understands...


Is completely equivalent to a transition from 6/4 to 7/4 with a metric modulation of "old whole note equals new whole + quarter note" (or "5 in the space of 4") which nearly everybody understands.


So not only are irrational time signatures completely redundant, they are also abuse the very definitation of a time signature in two ways:

  • Irrational time sigatures affect tempo as well as meter
  • Their interpretation is dependent on the preceding time signature

In reply to by shoogle

In a purely metric sense, irrational time signatures do not affect the tempo or depend on the preceding time signature. A bar of 7/5 consists of 7 fifth-notes. A fifth-note is the length of 1/5 of a 1/1 (whole) note. That would mean that a fifth-note is a quarter-note quintuplet. However, there is no way to notate a fifth note without using tuplet notation. A bar of 7/5 does not consist of 7 "quarter notes" that are faster in tempo as opposed to 6/4. Writing a bar of 7/5 using quarter notes is musically incorrect - and that's where confusion stems from - because people will assume that the quarter note of 7/5 is equal to the quarter note of 6/4, affecting the tempo of the quarter note - but 7/5 is split into fifth-notes, not quarter notes.

I wouldn't write a whole piece in an irrational time signature. I've used them very rarely for literally one bar out of an entire piece. They're not hard for one to wrap their head around, but I wouldn't use them too religiously. I've used them mainly to clean up bars when I only want a certain number of tuplet notes, and then return to a standard rhythmic pattern. Completely arbitrary, but nice to have them when you need them. Inserting a metric modulation indicating the beat in reference to a tuplet is another method, but I find a quick irrational bar like a 4/6 often does the trick just fine. Not terribly confusing, and when used sparingly, are very effective, in my opinion. I'd say stick to the 12/8, and if the use of a 4/3 is justified, use it. It doesn't really sound like your piece requires a huge amount of 4/3, Then again, I'm not the composer, so what do I know ?

I would argue this issue is far from solved. There is a substantial ammount of contemporary orchestral music that is starting to explore the use of such idiosyncratic rhymic ideas. The contemporary practice of using "irrational" (non dyadic) time signatures seems to be for the purpose of implementing rhythmic units which are the equivalent of incomplete tuplets of "y" value, or also as a sort of short hand for metric modultion. I am no expert, but I have listened to several contemporary composers discuss how they have implemented such an approach in their own compositions. It may not be something that is especially pallatable to most, or that even has a straightforward indication of how to utilize such a tool. However, it is something that composers are going to start exploring more, by all indication, and thus far, I know of no notation software that offers this as a possibility for playback, but only such as with the "local" time signature feature already implemented in musescore. Whether it is in the realm of those composers whose interest it is to try and reverse engineer some of the rhythms of modern hip hop and electronic music, or, as for myself, someone just interested in experimenting with weird rhythms, there are people who would be very interested to see this implemented more fully in a music notation program.

In reply to by smrlongman1

Can you name some examples of such scores?

One way to reverse-engineer real irrational rhythms is to record the sound and process it to get a time-frequency spectrogram, then just mark off the attacks and durations of the notes and see how closely they can be represented in a conventional human-musician-friendly form - or by defining an idiom like swing that involves a deliberate anticipation/hesitation of attack times while staying attached to the underlying meter.

In reply to by dhfx

Thanks for your reply in earnest. Yes, one composer I've been made aware of is Brian Krock, with his small ensemble, Big Heart Machine. If you look up the youtube channel for Adam Neely, and look for his video called "irrational time signatures" you can find a few more examples, such as the composer Tomas Ades, or Bryan Ferneyhough (there's some videos on youtube with the accompanying score). I haven't seen any score itself from the music of these composers, aside from excerpts on youtube videos, but perhaps you would be able to find it on imslp(dot)org or elsewhere.

In reply to by dhfx

I found a pretty cool video of analysis of a string trio by Brian Ferneyhough, on the youtube channel by Samuel Andreyev for one. And again, from the Finale forum I visited where they discuss the matter of implementing "irrational", or non-dyadic time signatures in that program, one user noted that the book "Principles of Rhythm" by Paul Creston. I have only just begun to read it, but purportedly, it deals at some length with rhythmic ideas of this sort. It's fairly rare, and out of print, but I was able to find a copy online for free, and there is also a simply read-able version through scribd.

I still say use the time-signature notation that replaces the bottom element by a representation of the note value that takes one beat. Thus 6/8 becomes 2 over a dotted quarter note. You could even have, say, a 7 over a group of five eighth notes, which would be one interpretation of 7/5, with each measure being 35 eighths in duration.

Is there a possibility to overlay the time signatures appearing in the score with an image showing something different - either an "irrational" time signature, or one with the denominator replaced with a representation of the note that gets one beat (e.g., 2 over a dotted quarter when 6/8 is used in the score)?
This could be done by marking the score time signatures "not visible" and overlaying each with a .gif with transparent background, or a vector-graphic image (is it possible to insert an image into a score?). That is, until MS is able to do something like this natively.

Hey guys. I'm both new to Musescore (finding it great so far) and late to this discussion it seems. I'd like to begin with a few words on irrational time signatures.

Like mr Jojo-Schmitz and others point out, there's little use for irrational measures if you can just have either tuplets divide a whole note into whatever parts you want, or if there's some further subdivision which matches the desired time values in standard dyad measures; after all, notation is meant to be as simple as possible, at least in my opinion, and the last thing you need is make performers do what they already know how to do but demand them to do so in a foreign language, instead of trying to convey a musical purpose. This being said, there's a not so obvious problem when dealing with, let's call it, tuplet irrational measure equivalencies: It only works when dealing with whole note values.

Of course, I'd be crazy if, in order to communicate 3 thirds of a whole note in a single measure I wrote 3/3 instead of a 4/4 triplet, but say I want to work with sevenths, and it's just the case that I don't want 7, but maybe 6 or 8 of those, now you see I have a problem. If I want a 6/7 measure and wrote a 4/4 seven beat tuplet, I'd be a seventh longer than intended; if I wanted a 8/7 measure and wrote a 4/4 seven beat tuplet, I'd be either one seventh short, or six sevenths longer in the next measure, which I couldn't aproximate back to standard dyadic beat value even with a thousand nested tuplets, and even if I could, would that be any easier for me or the performer than just writing 8/7? So as you can see, there is actual use, in specific contexts if you will, for irrational time signatures.

Now, there's a very easy way (kind of a formula) to bypass this problem without irrational time signature playback.

You need to figure out the real time value of your whole note, which is after all the thing you want to divide into non dyadic parts. For the sake of example, let's use a very easy Eighth = 80.

First we divide the minute (because we use BPM as our real time reference) by the number of beats: 60 (seconds)/80 (beats) = 0.75. This will tell us how many seconds the note value of our tempo indicator lasts, in this case, our eighth note. Since we know our eighth note is 0.75 seconds long, and that an eighth note is an eighth of a whole note, we can just multiply our result by 8: 0.75 * 8 = 6, and get our real time value for a whole note, and since we know our whole note real time value is 6 seconds, we just divide that by the desired fractional value; in this case, we want sevenths, so: 6/7 = 0.857142.

Finally, we divide our minute again, this time by our seventh's real time value: 60/0.857142 = 70; and by applying Eighth = 70 to the irrational measure (of course, you need to create a n/7 time signature with rythmic value n/8 and turn your Eighth = 70 indicator invisible) we transform our eighths into sevenths.

Unfortunately, there's another problem with this solution, maybe too specific but nonetheless frustrating for the adventurous composer, regarding playback. When working with polymeter, every measure has a number of beats corresponding to the longest simultaneous time signature, just like in real life handwritten scores; however, Musescore can't have two or more BPM indicators for different measures, in which case it would have to fit equal beats into all of them and calculate equivalencies between rational and any combination of irrational measures.

In other words, without irrational time signature playback, you can't have either rational and irrational, or multiple irrational time signatures perform simultaneously. Again, this may be too specific, but it would be very interesting and helpful to have, specially for musicians who want to get familiar with them.

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