[SOLVED] Irrational time signatures?

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.

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.

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?

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.

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.

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.

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)

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.

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.

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.