Fractional/Tuplet Time Signatures

• Jul 23, 2011 - 22:12


As discussed in I think it would be extremely beneficial for MuseScore to better support fractional and tuplet time signatures. Tuplet time signatures (4/3 or 4/6 etc, which would be four half notes from a half note triplet or four quarter notes from a quarter note triplet, respectively), although technically supported, are impossible to notate because you cannot split the bar into the desired space. Thus, if you were to place a quarter note in a bar of say, 5/6 (which would be 3 and a third quarter notes per measure) you would have that third of space showing, except with an infinite number rests as anything one third is not divisible by anything (1/2)^2.

Fractional time signatures would make this easier, as for example:

4/4 one. . . two. . . three. . . four. . . 5/6| one. . two. . three. . four. . five. . 4/4| one. . . two. . . three. . . four. . . | ||

is typically harder to understand than

4/4 one. . . two. . . three. . . four. . . 3+1/3/4| One. . Tri. . plet. . Three. . Tri. . 4/4| one. . . two. . . three. . . four. . . | ||

As triplets are used much more commonly than bars with a time signature denominator of six.

One option without this addition would be to find the lowest common multiple of the denominators of the two time signatures. For example, using the previous example above.

12/8 one. . . four. . . se'en. . . ten. . . 10/8| one. . three. . five. . se'en. . nine. . 12/8| one. . . four. . . se'en. . . ten. . . | ||

The only problem with that is that it might get lengthy, and be confusing. For a new example, with eleven-uplets. Say I want seven 11:4 quarter note eleven-uplets in a bar. Without fractional or tuplet time signatures, you'd have to write the song like this, even if just for one bar.

44/32 one...........12...........23...........34........... 28/32| one....5....9....13....17....21....24.... 44/32| one...........12........... etc

I think that is extremely difficult to comprehend (it took me at least ten minutes to figure out how to write it, plus a bit of paper and a calculator). Not to mention that every other bar in the song would have to have a quarter tied to a dotted 16th note for the traditional quarter in 4/4 (like the dotted quarter in 12/8 is equal to the quarter in 4/4 in the previous example).

Thank you for anything you can do to make a musician's life easier, and thank you for making MuseScore the incredible and probably best notation program in the world today.



To me, if you can't notate something in normal time (note) lengths (half, quarter, eighth, etc) then there's no way you can explain it properly for counting it out to play it. Can you show present-day examples of such time sigs?

In reply to by [DELETED] 12786

A quick scan of the page you provided did not show a single piece that used a denominator other than established note lengths: whole, half, quarter, etc. Yes, some have strange numerator lengths, but none had the kind of time you mentioned (4/3, 4/6).

So, you didn't answer the most basic question I asked: if the denominator of the time sig is _not_ based on a note length, how do you establish the rules to play it, esp for a group such as an orchestra?

In reply to by schepers

I'm sorry, I don't recall you mentioning needing examples of ones with a specific denominator, I thought you just asked for example of which normal note lengths aren't used. Hmm.

Well, what is a "quarter note"? A whole note divided in four. Hence the 'four' used in the denominator. Then wouldn't "4/6" be four parts of a whole note that was divided into six? That's a six in the denominator. 4/4 is four quarters of a whole note per measure, so 4/6 is four sixths of a measure. In other words, four quarter notes of a quarter note triplet. Isn't that a note length?

Here's an example for you, again.
I really suggest you read it this time. But if it is too much (even though it's five paragraphs), the point is that an example of one piece that uses such denominators is ' Henry Cowell's piano piece "Fabric" '. That's right, it says it uses denominators from 1 - 9.

If you finish reading that, please realize that I am not only requesting better support for these odd denominator bars but also for fractional numerator time signatures as well.

You know, professional performers go to college for a reason. It's to learn this sort of stuff, learn about quarter tones, enharmonics, music history, music theory, and especially things they might come across someday like this. This isn't a new idea, people HAVE used these bars before, and people WILL write in them again. I only ask that MuseScore assist them, and me.

In reply to by astromath

"Fabric" is public domain in the USA. However, upon reviewing the score, I find that I was incorrect; Cowell simply uses elaborate series of noteheads in stead of placing tuplets over all beats. It seems to be more of a study of note value than time signatures (reviewing the basis that a "quarter note quintuplet" is truly "five fifth notes"). The other pieces mentioned on the page are NOT public domain (Thomas Adès' works). Therefore, it is not possible to attain copies of these works.

The public domain for "Fabric" can be seen here:…

I continue my search for an example to show you; however, my guess is that writing in this manner is so new and avant-garde that there won't be many examples to show, just readings on how it is done.

In reply to by [DELETED] 12786

I still am caught by your analysis of what the denominator expresses.

If the denominator was 3, for example, how would one know that it was specifically related to half notes, which is what it seems you are saying when you say, "Tuplet time signatures (4/3 or 4/6 etc, which would be four half notes from a half note triplet or four quarter notes from a quarter note triplet, respectively),"

Nothing in 4/3 suggests that the common denominator is a half note. To follow your thoughts, the "3" would mean that the bar is divided into 3 equal sections. How would one know the value of the bar that is divided?

These alternate schemes may have a use as a graphic element, but I can't see how this clearly expresses what one wants, time-wise without having to explain the concept, which defeats the purpose of having a Common Music Notation system.

I am eager to understand how this would add functionality to Standard Musical Notation, so please explain more if you think I have missed the point.


In reply to by ChurchOrganist

I think what you are asking for (?) is the ability to write a 4 division in a bar of 3. I wrote something to this affect a number of years ago, and I notated it (by hand) as a "four-tuplet"(4 in the time of 3). I'm not sure if MS can do this. Is that what you mean?


In reply to by xavierjazz

No. I am discussing something completely different, although, yes, MuseScore has that functionality.

A denominator in a time signature is based of the fractional division from a whole note. A quarter note is called such due to the fact that it is on quarter (1/4) of a whole note. In 4/4 time, you have four quarters of a whole note with an emphasis ("beat") on each quarter. An eighth note is called such due to the fact that it is one eighth of a whole note (1/8). in 5/8 time, you have five of those fractions, five parts of that whole note divided into eight, per bar.

Therefore, the same should follow dividing into non-multiple of 2 denominators: for example, consider a bar in four four time with two quarter note triplets. Those triplets are truly sixth notes (a whole note divided into six equal pieces) felt at a tempo (due to the time signature) of four equal pieces. Therefore, it is not necessary (and generally confusing) to write entire songs in these patterns such as six/six time ... six/six time has the same "amount" or "stuff" in the bar as four/four, but is divided and felt and most importantly READ differently. However, it can arguably be more sanely written as 6/4.

So if I was in 4/4 time and that was my melody and for one bar in the middle of a song I wanted to write FIVE parts of that whole note divided into SIX (five quarter notes of a typical six quarter note triplet) I would need to write in 3-1/3 / 4 time or write in 5/6 time, both of which can be easily understood in this manner. No, I am NOT talking about a quintuplet (dividing a normal space into five beats), I am talking about subdividing an ABNORMAL space into five beats.

As I lengthily described in the original question, in five six time, the five notes would have the same duration as five notes in two quarter note triplets (where instead there is just six).

In reply to by xavierjazz

In 4/3 time, your denominator would NOT be a half note. It would be a THIRD note, or, in other words, a half note in a half note triplet.

I think you are understanding a time signature incorrectly - 4/3 implies the bar would be split into FOUR equal parts, the equal parts being each equal to one third of a whole note.

In "Fabric" by Henry Cowell, Cowell decides to notate this strangeness by using different noteheads: squares, triangles, diamonds. They replace the tuplet by simply creating a "new note", if you will.

However, in 4/3 time (four of three-parts of a whole note) you could arguably have four half notes as which:
-the first three are a tuplet written as "3:4"
-the last half note is a tuplet written as "1 : 4/3"

This WOULD follow common music notation. The issue is getting it into MuseScore correctly. You see, a quarter note still = a quarter note. An eighth note still = an eighth note. You're just subdividing the bar and feeling the beat differently.

a bar of 5/6 in the middle of a 4/4 song CANNOT be written any other except one of these ways.

4/4 | 5/6 |4/4
4/4 | 3-1/3 / 4 | 4/4
4/4 |10/8 | 4/4

The last of which requiring a tempo change of quarter equals dotted quarter going into the bar and dotted quarter equals quarter leaving the bar.

Thank you for reading!

In reply to by [DELETED] 12786

DJ_Dude wrote:

> a bar of 5/6 in the middle of a 4/4 song CANNOT be written any other except one of these ways.

> 4/4 | 5/6 |4/4
> 4/4 | 3-1/3 / 4 | 4/4
> 4/4 |10/8 | 4/4

> The last of which requiring a tempo change of quarter equals dotted quarter going
> into the bar and dotted quarter equals quarter leaving the bar.

Well, that sounds like a challenge, so let's find another way.

The first point to make is that 5/6 has no conventional interpretation, because the "denominator" of a time signature isn't, really, it's an indication of which note symbol we are using to represent "one beat". There are only note symbols for binary divisions of a breve (from the Latin for "longest note" ), and therefore any conventional time signature has a power of 2 at the bottom. In compound time, when the beat is to be divided into thirds, instead of using a basic symbol for the beat, we use a dotted symbol (e.g. 1.5 x 1/4), and write the time signature as 12/8 or whatever, in the well-known way. So this is somewhat wonky, because 12/8 time is not "in 12" at all, it's in 4, but if you try to write the fraction with 4 on top you get in a mess. (Strictly the denominator would be 8/3) The best suggestion for avoiding this was given by Carl Orff (as the Wikipedia article reminded me, though I have sung Carmina Burana, and encountered this totally intuitive system) -- he puts the beat note symbol itself under the number of beats.

Anyway, here's what you do. You want a tune with a combination of 4/4 and 5/6 bars, so the latter are 5/6 the length of the former, right?

* 4/4 + 5/6

Find the LCD of the fractions and rewrite:

4/4 => 12/12
5/6 => 10/12

* 12/12 + 10/12

We don't have a symbol for 1/12, but we can choose any symbol. Let's use semiquavers.

* 12/8 + 10/8

We now have conventional time signatures, immediately understandable by musicians (which is the important thing, after all). Funny times like 10/8 are fairly common, and you always have to look at the notes to see how they are divided, in this case perhaps 5 beats, but more likely irregularly.

Brian Chandler

In reply to by Imaginatorium

Mr. Chandler,

Yes, I missed that version in my little post there, but if you scan yourself up back to the original question I posted you can see that I have already posted this exact example and shown it's problems - my mistake, sorry. I was figuring someone was going to post that argument or that the entire song could be written in 8/8 and then the 10/8 bar with the whole changing tempos ordeal or something of that likeness ...

Yes, 12/8 and 10/8 would be good in this situation, but what if I was working with a bar like 7/11 or something like that? The LCD would be slightly bigger and the problem would be slightly more difficult to deal with ... I believe the example I showed (scroll back up yonder and read the original question!) would require a quarter note tied to a dotted sixteenth note for the typical bar to be felt in four (which is not only ridiculous but makes notation of tuplets in MuseScore next to impossible for a single beat).

The point being, that all this nonsense could be eliminated with the addition of being able to add fractions to numerators (or denominators, for that matter) and being able to split a bar into those parts (tuplets) easily, AND/OR making division of that bar into the currently possible non-two-to-the-power-of-x more supported and easier to notate in.

In reply to by [DELETED] 12786

I don't really want to repeat myself, but:

(1) Normal time signatures indicate what note symbols will be used for the basic unit (a beat in simple time; 2/3 of a beat in "compound time"; some part of a beat in more complex cases). Fundamentally, if Musescore supported 2/3 time, what number of what note symbols would it be supposed to allow in each bar?

As Marc Sabatella just said, it seems extremely reasonable to be able to construct whatever string of notes, barlines, and so on that you want -- much less reasonable to expect Musescore to do any more than just allow the symbols.

(2) As far as the example I discussed goes (4/4 and 5/6), you claimed it couldn't be done any other way; I pointed out that it can. What's more, such a combination of 12/8 (quadruple compound time) and 10/8 ("other") is barely unusual at all. You will find such things in Ravel, for example, and it's not anything that a reasonably competent musician would even find difficult to understand.

Of course you are right that you can easily find numbers so the dots and ties get unmanageable. But "working with a bar in 7/11" has to be in the context of some other time signature. Suppose you have alternating bars of 7/11 and 5/2 -- one is expected to feel a seven-rhythm (hard enough in itelf), and be able to group 5-1/2 of these notes together and feel them as a secondary beat. Hmm.

In reply to by [DELETED] 12786

I think MuseScore is able to notate "Fabric" by Henry Cowell. I took a closer look to the space and I wonder about something.
Check measures 3 and 4, right hand. Why the second note on the lower voice is after the first triplet in measure 3 and before the last note of the last tuplet in measure 4 ? It looks like a typesetting error to me... Am I wrong?

In reply to by Nicolas

I note that Cowell's proposal (on the first page of the "Fabric" PDF) to use a different notation didn't exactly catch on, presumably because few musicians had much need for it. It seems to me that, while it might be nice to make MuseScore so flexible that it can handle "fractional and tuplet time signatures", it is something that only a tiny fraction of MuseScore users would find useful. Is there enough demand for this to make it worthwhile implementing better support for this? If you like, I am questioning whether this would really be "extremely beneficial" as DJ_Dude suggested in his original post.

In reply to by Jon Foote

I look at it this way: it would be extrmely beneficial if MuseScore made it possible to do all sorts of experimental notations graphcially, but expecting any sort of automation or "correct" playback is probably unreasonale for non-standard notations. I haven't completely followed this discussion, but am guessing that MuseScore could be used to create something that looks just like the desired notation. It might just take use of invisible rests and other elements, manual spacing adjustments, etc, to get there, and of course it would not play ack anything reasonable. If there are specific things that are preventing this from happening (like, say it would work perfectly if only you could hide tuplet brackets), I think it would be worth looking into addressing those. But given that every new feature means something else gets left out, it's hard to see how direct support for non-metric time signatures could possibly be worth the effort it would take to implement.

In reply to by Marc Sabatella

Henry Cowell system can be handled by MuseScore 1.1 and I'm not following all this discussion about time signature. The notation in Cowell sheet is pretty standard, except he removed the tuplet bracket and uses different noteheads... I made a transcription. Check it here :
Edit: with a video score :
Please put a comment there if you find mistakes in the transcription.

Hi folks -

I just stumbled across this thread, so I apologize for the (really) late post.

I too would like to use odd meters like 9/5, 9/3, 6/3 etc. in my music. Essentially, I'm thinking of them as divisions of a bar, based on 1/1 time (where there is one whole note per bar in music). This is the normal method of devising a time signature in music today, but (as was noted earlier) only multiples of two are indicated (x/1, x/2, x/4, x/8, etc.). My way of thinking is to "fill in" the gaps skipped over by this process - x/3 = 3 divisions of a bar (the triplet half note becomes the beat), x/5 = 5 divisions of a bar (the quintuple quarter note is the beat), etc.

I'm doing this to more clearly show metric modulations in my music. For example, my latest piano piece uses x/4 values as quarter = 69 beats per minute, x/5 values as quarter = 86.25 BPM and x/3 values as 51.75 BPM. These oddball metronome values are derived as ratios against the original pulse of quarter = 69 BPM. Now I could just notate the changes in the score by keeping the meters 'normal' and showing the tempo changes as they happen, but I'd prefer to use the 'odd' meters, since they show the metric modulations in a clear and concise manner.

MuseScore kind of does this, but it crashes like crazy - I try to add a quintuple quarter note to a 9/5 measure and the program quits every time. Is there any way to fix the bug? Would the program allow me to count a quintuple quarter note as a beat in a measure of 9/5 or 6/5 time?

Having said this, the larger issue at play (for me) is that music notation programs like MuseScore (or Finale, or Sibelius, or most other programs) unintentionally limit composers' creative choices by forcing them to prescribe to methods of music notation which are more practical, commonplace, etc. etc. And I certainly understand why this is the case! But, advances in notation always happen through experimentation, mistake making, retooling the notating process, and trying repeatedly until an acceptable method is found for both composers and performers. Please don't overlook this vital component of the creative process! Sure, there are only "a few composers" who will want to notate things a certain way today, but who knows what will happen 100 years from now...

In reply to by Chris Auerbach-Brown

The whole reason for notation is to provide the ability to write down how a musician, who does not know what you want sonically, can approximate your meaning. That is what any language is for, communication. So, if you want to communicate with musicians, start by learning the common language. Common notation is flexible enough to allow you to communicate ANY musical gesture, understanding that there is a limit to how exact ANY translation can be.

I don't think that simply because you want to write in a different manner, an existing language should be expected to change to accommodate you.

If you have a new, useful addition, expose it and others will then use it.

In my case, I am simply too busy dealing with music itself to worry about odd approaches.

So, MuseScore is a Music Notation Program, not a graphics program, and is dedicated to providing a way to share MUSIC.

I'll see you in 100 years.

p.s.- There is no such thing in music notation as a 9/5 measure.

In reply to by xavierjazz

See this thread for more info and examples of pieces of music which use these types of time signatures:

Also, see Wikipedia's entry on Irrational Time Signatures:

It's clear that using these time signatures provides a cleaner, more effective way of notating metric modulations in music. It's not that I just "want to write in a different manner" or that I "don't understand the common language of music notation."

And, in case you think this music is "impossible to perform," check out this clip of the Ecstasio movement from Thomas Ades's work "Asyla" (which uses a 5/6 time signature):

In reply to by xavierjazz

ACTUALLY WITH ALL DUE RESPECT. 9/5 EXISTS!!! ITS ACTUALLY 9/10 AND I PLAY IT. irrational meters are the shizz!! Imagine you are playing quins for 2 quarternotes that means you have 10 notes to deal with. play the only 9 notes and start the next quarter a fraction of quin before the way it should have played.. you just played 9/10

I remember when I was a bassoonist way back in high school band we played a piece that started out in 9/12 time for many bars before changing to 3/4 later. It wasn't that hard of a piece rhythmically but I just wanted to add that this sort of notation is out there and being used.
As an aside, does anyone else, when hearing of irrational time, get the image of a time signature such as 5/sqrt(2) or 3/pi?

I read the thread and I absolutely agree with the need for more choices for the composer. And I see that most people don't get why the erroneously-called "irrational" time signatures are actually very much needed. They actually make things EASIER for the performer in some cases.

First of all, try reading Elaine Gould's book "Behind Bars", pages 180-181. You will see that this exists, and is not so uncommon today. And yes, there is a reason for it.

If we take as our counting basis NOT the quarter note, but the whole note, then we define our unit of time to be 1/1=1 (the whole note). So the whole note has a value of 1, and is the basis of our system.

So the half note is 1/2 of the whole note = 1/2 of 1 = 1/2.

The quarter note is 1/4 of the whole note = 1/4 of 1 = 1/4 itself.

Now this procedure of halves clearly creates the denominators in use today, which are all powers of two. And they can play most rhythms out there. BUT, only if the counting basis is always consistent. in other words, your basic subdivision must always be the same, or easily discernible from the previous bars to the current point in the score.

Things change when you want to change the subdivision. Since most of you need an example, please construct one yourselves using these easy to follow guidelines, and I think you will see the point of discussion.

For our example, you have two bars of 16 16th notes each, and the next bar you still want the very same two bars of 16 notes, but their durations have to change, for example become what is called 16-th note 5-plets. In effect, you have four bars, the first two are in 16/16, the next two in 16/20.

One will say "fine, use metric modulation!". Problem solved.



Imagine now that I have the very same two 16-note bars played 5 times:

  • the first time in 16th notes,
  • the second time in 16-th note 5-plets (in reality 20th notes),
  • the third time time in 16-note septuplets (in reality 28th notes),
  • the fourth time in slower 16-th note 9-plets (9 notes in the space of a half note, in reality 18th notes),
  • and the fifth in slower 11-plets (11 notes in the space of a half-note, in reality 22nd notes)

and the section is to be repeated, so the next is again the normal 16th notes.

Now there are two ways for one to do this.

1)The traditional way would be to use constant rhythmic modulation. Just write the exact same two bars five times, writing on top of the barline separating bars 2 and 3:
4 16-th notes = 5 16th notes = 7 16th notes. then
two bars later: 14 16 notes = 9 16th notes,
then two bars later, 9 16th notes = 11 16-notes,
then two bars later, 11 16-th notes = 16 16-th notes again

and you are done.
Upside: it can be handled by the notation programs.
Downside: it will be immensely difficult for the performer to actually keep the time in such a fashion so that when he/she returns to the first measure, the true 16th notes are on the same speed. Constant time modulation kill steady pulse for the performer.

2) What would be infinitely easier for the performer to do is simply count the subdivisions, and then add some little "extra" in the end.

The first two bars are 4/4 in 16th notes.
The next two bars can be translated as a 20/20 bar, and a 12/20 bars right after. The first of the two gives the performer the timing, and the second one the leftovers.
Next the performer switches from thinking in quintuplets to thinking in septuplets, reading 28/28 and 4/28.
After that, he switches to 3 bars of 9/9 and one of 5/9, and
finally to two bars of 11/11 and one of 10/11
and then back to 4/4 time.

Downside: Not supported by the notation programs.
Upside: The performer simply switches the subdivisions, and so the overall time is not compromised.

(The kind of playing where you can play the same phrase in different subdivisions is very well documented now, both in the Indian and jazz traditions, for example read the book "Rhythmic Illusions" by Gavin Garrison.)

By the way, PLEASE STOP using the stupid "irrational measures" idiocy. There is nothing irrational about these time signatures. If anything, they are VERY RATIONAL! They are fractions, as rational as rational can be. Irrational would involve irrational numbers.
If you wish to name them, use something like "non-binary time signarures", which would mean that the denominator is not a power of two, just as the binary counting system is based on the powers of two.

I hope this helps.…
Here is a song from my band. The verse is 3 bars of 4/4 and 1 bar of 8/12 or 4/6 or 2/3. It is convenient to write it in this manner, as after chorus 2, we swap from a triplet feel to sixteenths. So am I to do relative tempo changes? quarter -> dotted quarter? Am I to dot all the 16ths and write the song in 8 base? so 12/8 to 8/8 then back to 12/8 but with a bunch of dotted sixteenths for each measure. Or can I just make that one bar 8/12 and be done.

Here's what you do. Take a bar of common time. Divide it into pieces equal to your denominator. Multiply by your numerator. That's the duration of the bar. I'm actually just looking around for fractional tuples =/. 8+2/3 : 8

PS. Sorry for dragging up an old thread :P

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