Unusual/Abstract Time Signatures

I’m working on a piece and want to use some Henry Cowell-inspired meters (for example 5/6, 4/5). I know that Dorico supports using such meters.

The piece I’m using has encountered a problem, though!
In previous attempts at experimenting with such a meter (5/6), I get what’s expected: space for 5 quarter notes. The metric playback isn’t correct, but at least it looks correct:
Screen Shot 2017-10-09 at 11.20.18 AM.png
However, in the project I’m currently working on, it’s only giving space for 4 quarters:
Screen Shot 2017-10-09 at 11.20.08 AM.png
What’s happening? How can I get this to work correctly (WITHOUT pulling a Finale/Sibelius backdoor of making a Tuplet and hiding all the stuff)? I know Dorico supports this function - why is it failing in THIS project?

Related question: Are there plans to get the software to natively support the correct playback of such meters? At the end of the day, it’s a simple multiplication/division equation to occur in the background.


How would you count a 5/6 or 4/5 meter? Can this be replaced by the more general used meters? Just wondering.

your example doesn’t look correct.
unless indicated otherwise, a change in time signature doesn’t indicate a tempo change.
a quarter-note in: 4/4, 5/8 or 5/6 has the same duration.

5/6 indicates a bar length of 5 quarter-note sextuplets, which is less than 4/4.
It won’t fit 5 regular quarters.

Let’s consider simpler examples:
one bar in 6/6 = one bar in 4/4
can fit 4 quarter notes or 6 quarter sextuplets

4/4 q=q 6/4
in this case, 6/4 has the same tempo, longer metric length and longer duration

4/4 q=>q. 6/4
6/4 would have faster tempo, longer metric length and the same duration

4/4 q=q 6/6
6/6 has the same tempo, the same metric length (of 4 quarter-notes) and the same duration

4/4 qT=>q 6/6
6/6 has faster tempo, the same metric length (of 4 quarter-notes) and shorter duration
the same as
4/4 qT=>q 4/4

A bar of 5/6 would feel like quarter note triplets against 4/4 time, but it would only have 5 notes, not 6. It leaves out the last 2/3 of a beat.

Likewise for 4/5. Image a quarter note 5-tuplet pulse, but with only 4 notes, not 5.

Sugar -
You are correct.
However - Dorico doesn’t (yet?) understand the abstract/irrational durations natively.
In the first example (allowing for 5 quarter notes in a bar of 5/6) - it allows for the notes to be entered. But for playback to work correctly (metrically), you need to insert a new Metronome Marking for 150% of the original tempo. It’s a little clunky - hence my follow-up question.
In order to correctly insert 5 sixth notes, you would use the Notehead change under the Edit menu and select the triangle noteheads. However, that doesn’t change the understood length of the note - only the graphic image for what’s displayed. It’s a conflict created by composers using Cowell’s other notehead shapes for things other than fifth notes, sixth notes, etc.

As Dorico functions currently, inserting a bar of X/6 allows you to put X quarter notes in the measure - but it doesn’t reinterpret tempo. Same applies for other denominators (/5, /7, /9, etc. – although the /7 and /9 switch to 8th notes).

perhaps I wasn’t clear.

Dorico shouldn’t allow you to enter 5 quarters in 5/6.
A bar in 5/6 only has room for 5 quarter-note sextuplets.

If you need a bar of 5 quarter-notes at faster tempo, it should be 5/4 + tempo change marking (e.g. q => q.)

If you need a bar of 5 quarter-note sextuplets, it would be 5/6 without any tempo change marking AND the 5 quarter-note sextuplets would need to be notated as tuplets, not as regular quarters.

Cowell, Ferneyhough, Adès and many others use the 5/6 time signature to mean that the quarter note is the same as the quarter-note sextuplet; in other words, it’s exactly the same as marking the tempo a little faster in 5/4. The reason composers like to write 5/6 instead of a metric modulation is that the player can keep thinking in the same base tempo, with tuplets; and you can switch tuplets very quickly. I think of it as mixed meter (5/8 etc.) that’s not limited to 8ths, 16ths, 32nds, etc. One of my pieces goes 2/4, 5/12, 6/14, 4/4, etc. That would be really cumbersome with constant metric modulations. So ryanwms is asking for something reasonable.

I’ve just tried out some of my Dorico pieces with 13/12 and 11/12, and created a new one in 5/6, and they all seem to work fine - so I’m not sure what the problem is with your file. Maybe try deleting the bar, and try again?

My understanding of how these “irrational” or non-power-of-two time signatures work is that a 5/6 bar would be 5/6ths of a sextuplet lasting for a whole note (semibreve), and Dorico will allow 5 quarter notes in that bar.

I agree with Stephen’s assessment that there must be some other reason why the fifth quarter note is not allowed in there: presumably the time signature for the following bar is in the “wrong” place, so try re-creating the 5/6 time signature with Insert mode on, which should push the following time signature to the right spot.

well…, if there is 5 quarter notes in a bar than it is 5/4 not 5/6.

Seriously though, I understand the concept of what you call “irrational” meters. I just think this practice is unnecessarily confusing.
Classical time signatures are consistent with what’s inside the bar. Even if you hide all time signatures, you can still perform music as intended, because the number of notes and their grouping in the bar tell you the correct time.

Now, if you try doing it with your irrational time signatures, there will be no way telling which bar is which.
The solution is very simple. 5/6 should hold 5 quarter note sextuplets, marked as sextuplets, not as regular 5 quarter notes.

As I am not a practitioner of these kinds of techniques myself, I am perhaps arguing from shaky ground, but I think that your approach, Sugar, is at odds with that employed by the composers who habitually use this kind of time signature, such as Adès. Although a 5/6 bar could be notated with five quarter notes, it is not the length of five regular quarter notes: instead, it would be the length of six and two thirds quarter notes, assuming a consistent quarter note pulse between (say) a preceding bar of 4/4, so the metric modulation would be 1 quarter of 4/4 equals 1 1/3 quarter in 5/6.

Now, where is that Henry Cowell plug-in?

Ahh! YouTube! :laughing:

I actually use a version of Sugar’s approach in my own pieces with these time signatures: in a 5/12 bar with 5 eighth notes, I will write (6) above the notes, as a way to show that these go at sextuplet speed. For 6/14, I’ll write (7); for 7/20 I’ll write (5), etc. That seems to help players understand the rhythm.

I never thought about using this kind of meters and still wondering if there isn’t a way to use the traditional meters instead. I wouldn’t even know how to play a piece lilke this. Isn’t this more used because it’s different and intresting instead of practical?

If you try to notate the example above (fountain1) in a more traditional way, you will soon see why this method is so clear and straightforward. Try to keep 2/4 all the way. You will end with extremely complex nested tuplets. Try to change meters, like from 2/4 to 5/8 to 6/8 - you will have to specify metronome numbers all along to make the relations right.

In theory yes. If you listen to a human player performing a piece like this it will simply sound like tempo changes or “ad libitum”. Nothing new or groundbreaking really.
This much complexity and implied precision looks more interesting on paper. The extra labor related to notation and rehearsal time doesn’t translate to a unique musical expression. In my personal opinion of course.

Yawn. Not this. Adès is the first to show how his music can be performed accurately and precisely — and not just alone on his piano, but also leading a large symphony orchestra. Both LAE and Stephen explained why this made its way into notation conventions. It’s hardly up to you to decide whether or not this is viable. Let the chips fall where they may.

Daniel - You’re correct in how you’re interpreting what Dorico is allowing.
I have done the “delete the bar” trick a few times, but I keep ending up with the same result. The measure preceding the 5/6 bar is 2/4. I’ve tried making that something greater (7/4), but still the same result. I’ve even Quit and restarted Dorico altogether. In this specific file, at this spot, I cannot get the 5/6 to work correctly.

If you’re going hard core Cowell and intermixing fifth notes, sixth notes, and others into one bar of some other meter - yes, it would take a lot of time and sound crazy. However, I’ve used a simple x/4 to x/6 motion within a piece, and it sounds brilliant. A slight speed-up through the line. Especially going x/4 to x/6 is very easy - in a grad class, we accurately “performed” (clapped), at sight, a rhythm that mixed 4/4 and 4/6 meters.

Did you try to create the time signature change with Insert mode toggled on as well?

Only of the human player doesn’t “get” how the rhythm is meant to go.

But there are human players (and some of them call themselves professionals!) who don’t even “get” J S Bach’s rhythms, let alone Cowell’s.