Non-power-of-two time signatures

Hi all - new to Dorico here. I am currently making use of a workflow that begins by generating compositional material in a programming language called Opusmodus, which is capable of non-power-of-two time signatures like 4/5 or 4/6. I then want to import that material to Dorico as an XML so that I can tweak it. I just purchased the crossgrade after reading in Dorico’s online reference guide that such time signatures are supported. However, after trying it out, I can’t figure out how to make it work. If I use, for instance, 4/6, it just creates a 4/4 bar with the text “4/6” as the time signature.

I then tried importing an XML with such a time signature, and Dorico got pretty confused. Example below:

Is there a way I’m not seeing to make it recognize these kinds of time signatures? I’m not as concerned about playback, but at the very least I’d need the option to see the actual durations of the notes. E.g. a bar with 2/3 should visually contain two half note triplets for a full duration of 1/3 of a whole note. Ideally, though, I am looking for a way to work off of an XML containing such time signatures.

All best,
Jack

Welcome to the forum, @manifesto-sauce (Jack)!

I’m not familiar with this type of notation but I’m reasonably certain someone will chime in sometime in the next few hours with some advice.

One thing: I have a feeling there won’t be a way to have automatic triplets based on a time signature. As far as I know, all tuplets need to be entered manually. I might be wrong.

Dorico will display other numbers on the denominator, and it will use the next smallest ‘real’ value for the duration.

If you need a different duration in the bar, then you’ll have to either use pickup bars for every bar, e.g. 4/3,3 as here:

or use tuplets.

There have been a few discussions about “irrational” time sigs before, as they are sometimes called.

@DanielMuzMurray It’d be fine to enter the tuplets manually. The issue is with the duration of the bar; a 4/3 bar would be divided into 4 notes, each 1/3 of a normal 4/4 bar.

Ben - that’s a helpful tip, but I don’t think it works with tuplets. Correct me if I’m wrong, though!

To be clear, what I mean is something like the image below with incomplete tuplets. I know that contemporary composers will often write 4/6 and use quarter notes as Dorico allows. In a context such as below, at least when a conductor isn’t involved, incomplete tuplets seem a lot clearer to read. A quarter note in a triplet has the same duration regardless of whether three eighth notes, quarter notes, or half notes fit in that triplet (unless you use ratios). That notation with a 2/4 + 1/6 time signature could also work.

I am getting the sense that this is outside of Dorico’s wheelhouse without a lot of headache, which is fine…in my opinion, it’d be a killer feature to implement in the future. Even if you had to turn off playback for scores that use such notation, there are a lot of contemporary composers I could see being excited about it, for better or worse.

Best,
Jack

Here’s a small Thomas Adès test I did a long time ago.

Jesper

Ades.dorico (1.5 MB)

Here is what jesele’s Thomas Adès example looks like when notated in traditional dyadic time signatures. Which version is easier to read?

Since I am not used to reading any of such music, both of them give me quite some headaches :wink:

I use Jesele’s technique above, and then I insert hidden tempo changes to make playback work correctly. PeterThomsen, very interesting, especially at bar 11-13!

I have hidden tempo changes in mine, too.

Jesper

@jesele Nice, I checked out the file, very helpful reference example! That doesn’t look as much of a headache to notate as I thought it’d be.

@PeterThomsen I think “traditional” is a stretch, haha! Or maybe I missed something in music history classes…

I think it’d heavily depend on what you are used to. For me, as is, your version is harder to read. When I read jesper’s version I subdivide into eighth notes and count a 3/4 polyrhythm that ends early when dealing with the triplets. However, to your point, notating the 5/e. bars as 15/16 could work well in that example, at least out of context. But, it would stop working if you have irrational time signatures with multiple divisions (e.g. 3/7 and 3/5) as Ades often does. I don’t know what piece that’s from but in the scores I’ve seen Ades usually just changes the value of a quarter note like I was complaining about above.

I think it’s understandable for these to be a headache at first—I also don’t think it’s all that intense in comparison with many things musicians and contemporary musicians are regularly invited to do. Sure, you could make a stupid mess out of it really easily. But there’s also an extent to which I think it can be musically intuitive with practice. It’s relatively easy when improvising to stop in the middle of a tuplet, even though most musicians haven’t developed the ability to read that notation yet.

Simply for my education, what is the purpose of this since there are no 1/3, 1/5, 1/7 notes?

In terms of duration, there are 1/3 and 1/5 notes. Four 1/4 notes fit in a 4/4 bar. A 1/3 note means three would fit in a 4/4 bar; 1/3 note = half-note triplets. The purpose is if you would like to notate something as in the example I posted, or in the music of composers like Ades. You count as if you are counting a tuplet and then stop in the middle. 1-2-3-1-2-3-1-2- (on 3: ) 1-2-3-4

It’s a logical extension of the notion of quarters, eighths, sixteenths and so on.

A time signature like 4/4 is expressing a bar of four beats, each lasting 1/4 of a whole note/semibreve. A time signature like 4/6 extends that fractional idea: the bar is 4 beats, each lasting 1/6 of a whole note, or one triplet quarter note (1/4 * 2/3 = 1/6).

A more extreme example, a 7/10 time signature means a bar of 7 beats each lasting 1/10 of a whole note, or 4/5 of an eighth note (i.e. a quintuplet 8th note).

Why would you want to do that? Well in some pieces it serves to allow quick metric modulation back and forth. Other music might want to more systematically explore different ratios of bar lengths and pulses. Could you do that with, say, frequent tempo shifts instead? Sure, but it might not communicate the intended structures and concepts as well.

But in short, contra to what you said, there are 1/3, 1/5 or 1/7 notes, it’s just usually we only encounter them as subdivisions of a beat based on 1/2, 1/4 or 1/8 notes (1/3 = triplet half note, 1/5 = quintuplet quarter, 1/7 = septuplet quarter, …). Some composers choose to use them as pulse elements in their own right, and use time signatures that reflect that.

I understand the logic, but fail to understand why it is needed, as tuplets can notate the same.

To me it looks like a lazy composer’s shorthand, when the composer should really focus on making it simple for the performer…

You still use tuplets, as in the example above. You can’t notate something like the example above (which was a proof of concept for explanatory purposes) with multiple tuplet divisions without using notation that is unusual in some way. The idea is to make it as simple to read as possible while keeping the same musical idea. The best solution will likely change for different musical contexts.

“The composer should focus on xyz for the performer” is performer-dependent. Some performers like playing music that is rhythmically complex. Some hate it. Don’t write it for performers that you know will hate it. I write music for performers that I know will enjoy it.

I for one find the irrational TS easier to understand than your incomplete tuplets, but I would never say you are lazy.

Suum cuique

That depends perhaps on how one defines simple. Another notation might make it simpler for a performer to realize individual rhythmic elements, but harder for them to grasp the broader structures they’re part of. (And let’s not discount, in complex music, anything that obfuscates compositional structure, may make it harder to identify notational errors, both for composers and performers.)

As a performer for decades, I remain unconvinced. (but will bow out of the discussion)

I mean, obviously, you do you, and I hope that as a performer you don’t often find yourself in the position of having to play music that creates what feel like artificial and unnecessary difficulties for you.

But given that performers can differ in how they prefer to approach rhythmic complexities, maybe it’s understandable that some composers prefer to notate their music in a way that best aligns with how they see it, and trust that players will find the ways to break down (and where helpful, rewrite) the material that best suit their own needs?

BTW, I ought to mention: the only notation software I’m aware of that really, properly supports these time signatures is Lilypond, where they automatically work out of the box, presumably because (IIRC) Lilypond considers all note durations as rational numbers, and cases like 1/3, 1/5, 1/7, 1/10 etc. are just another case of that.

Not only that, but if you tweak barline engraving from operating at a score-level context to a staff-level one, you can also get support for independent time signatures and bar lines in different staves. Here’s a little extract of something I put together years ago, not with performance in mind, just to see what the software could be made to do:

No clever tweaks, just standard Lilypond-style music entry and the aforementioned config change for barline engraving (which is necessary only if you want separate time signatures in different parts, not to support so-called “irrational” time signatures themselves). Layout and MIDI playback “just work”. All a consequence of the underlying data model.

I assume there are different tradeoffs for Dorico, which has to process tweaks to the score and layout in real time, which may make it hard to fully support such time signatures. But “Enter whatever fraction you like, we’ll display the time signature with these numbers and interpret the denominator as the closest rounded down power of two” is a much better out-of-the-box compromise than any other UI-based notation software I am familiar with.