Is 41/16 a proper time signature?

Question

I know nothing about music theory so please forgive my terminology.

I made a pattern that I've counted off as having 41 16th notes. I'm counting 1-e-and-a-2-e-and-a...etc and the pattern ends on ...10-e-and-a-11.

I only understand time signatures as fractions so it seems to me that since this can't be reduced then it can only be expressed as 41/16. Intuitively though that seems too weird to be correct.

The way the pattern sounds is as three measures of 5/8 and one measure of 11/16, and this does work for my purposes better than 41/16, but is still clumsy.

Is there another way of expressing this or is 41/16 correct?

sound file (pattern repeated 4 times):

Answer 1

There aren't really rules around "proper" time signatures, so much as practical considerations. "Is there another way of expressing this?" Yes, there is almost certainly a better way.

The first thing to understand is that a time signature doesn't tell you how many notes are in a measure, or even simply how long the measure it is. It also makes implications about meter, the idea that these notes and beats are organized into recurring structures. This idea of meter inherits from the same idea in poetry, in which you organize words by strong or weak syllables and into lines of a certain number of syllables. Consider:

Twinkle twinkle little star
How I wonder what you are

The strong and weak syllables are arranged into trochees—Twinkle twinkle. And there are four such groups in each line. Compare:

Hey diddle diddle
The cat and the fiddle

This time, the pattern is one strong syllable followed by two weak syllables: Hey did-dle did-dle / the (yes, we cheat a little by printing "The" on the second line, but it really belongs with the first metric line). Here the foot is dactyllic; we have syllables grouped in sets of three, and two such groups in a line.

Musical meters work similarly. There are many questions/answers on here already highlighting the fact that 6/8 is really "compound duple" meter, two beats subdivided into three.

Whew! That's a lot of setup to say:

1. Your group of notes probably has some internal groupings. You said you counted them out as "1-e-and-a 2-e-and-a"; this suggests that they fall into beats that subdivide into four. Now, do you find the beats grouping themselves in regular ways? Perhaps the first 32 sixteenth notes are actually two measures of four quarter notes? As others have hinted, if you do in fact have some "irregular" measures, chances are that either they're a number of much more mundane measures with a single irregular one appended, or, even if they do group into more exotic subdivisions like 5 or 7, they still form meaningful groups and phrases.
2. I can't help questioning the count of 41. For one thing, it's a big number to count to! But secondly—forgive me if this is something you already totally understand—beat and meter make no claims about "how many notes" are in a measure. There might be 16 sixteenth notes, or 4 quarter notes—or a single sixteenth note, a dotted eighth note, a quarter note, and a half rest. If you are counting actual notes, make quite sure that they're all the same length and that there are no rests involved. Your final "10-e-and-a 11-" ends the bar only if we need the next bar to begin immediately. Is there a chance that the phrase really finishes off "10-e-and-a 11[rests: -e-and-a 12-e-and-a]"? Or that the final note is longer than a sixteenth note?

TLDR:

1. Choose a time signature on the basis of how the notes fall together into beats and phrases, and
2. It's not just about "the notes"; silences and held notes take up time too!

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UPDATE:

Since the audio link has been posted, a few things are clear: No, my fears that you were confusing "how many notes" with "how many beats" were unfounded. You've got notes of several different durations mixed in there, and yes, you counted through them accurately. (Or, maybe you did? I keep making it two full bars of 4/4 followed by 2 and a half beats, which would be a total of 42 16th notes. But I'm not at all sure I'm keeping up with the count.) Also, yes, this is definitely an irregular-length phrase. It's far from cut-and-dried how you should organize the beats into measures, and yes, you'll have some kind of unusual time signature at some point.

The first grouping that occurs to me is simply to start in 4/4. If we proceeded with this, we could get two full measures in, and then if I'm hearing the remainder correctly, it would just be a solitary measure of 5/8. A case could also be made for some more unusual groupings, but let's look at what musical elements suggest this 4/4 conclusion.

First of all, in the beginning, the ride cymbal is recurring regularly; this leads us strongly to perceive this as "the beat." If those are quarter notes, then everything the drums do in the first 7 beats is just 8th notes. Another thing suggesting 4/4 is the descending series of four tom notes, which would take up the second four-beat measure.

A case could be made for other groupings within those first 7 quarter-note beats—is it actually 3/4? Maybe 5/4? The only difference in that case is where you want the "strong beat" of a downbeat to be felt.

I would take a "subtractive" approach to explaining what's left over; it's as if there "would have been" a longer bar (and maybe another bar beyond that) but it got interrupted. This is where some unusual time signature will come in handy (but I think it's actually a whole number of 8th notes, in which case I'd use that rather than 16ths).

Answer 2

Notation is meant to make reading easier by representing the structure of the music.

Is there a rhythmic substructure to the notes in the pattern? If you have units of 5/8 that repeat (at least roughly) three times, and one variation that is 1/16 longer, I would prefer to see it written as three bars of 5/8 alternating with one of 11/16, because that would convey this structure, is easier to read, and ties into something that people may have already seen (5/8 is exotic enough, but more comprehensible than 41/16).

If it's a long, winding phrase with no internal structure, nothing prevents you from writing it as 41/16. (Then again, you might be better served by streamlining the phrase to a simpler meter.)

Both versions will elicit raised eyebrows from fellow musicians; IMO, the 5/8-version signals "wannabe prog metal shredder", the 41/16 version screams "wannabe avantgarde composer".

Answer 3

The issue of whether 41/16 is "proper" notation is well dealt with.

Listening to the sample, were I conducting this, I would conduct it as
4/4 + 4/4 + 2/8 + (3+2)/16

However, there are some slight variations that also work.
4/4 + 4/4 + 2/8 + (2+3)/16
4/4 + 4/4 + 3/8 + 3/16

The variations are based on some ambiguity in the perception of strong/weak pulses in the final 9 sixteenths.

Answer 4

As a performer, I would without any doubt whatsoever prefer three measures of 5/8 plus one of 11/16 over a single measure of 41/16. But 5/8 suggests a different counting pattern than the one you describe, because 5/8 implies alternating groups of 3 and 2 sixteenth notes. Your description of the counting suggests that it's all groups of two, with only one group of three at the end, and that you're thinking of the quarter note as the beat. If that's the case, consider a series of 4/4, 3/4, and 2/4 measures, as appropriate, with 7/8, 5/8, or 3/8 at the end.

"As appropriate" here refers to the larger metrical grouping of your pattern. For example, a series of 48 sixteenth notes could be three measures of 4/4, six measures of 2/4, four measures of 3/4, four measures of 6/8, or any of several other possibilities. What makes the difference?

In the likely event that your pattern isn't actually nineteen groups of two followed by one group of three, first figure out the smaller-scale organization: where do the groups of two and three fall? This can be thought of as a series of eighth notes and dotted eighth notes. Then look at the larger-scale organization: group the groups of two and three into measures comprising two or more of these groups, where possible (the occasional measure of 3/16 is permissible, but is perhaps best avoided).

If the order of groups of two and three is not consistent in each iteration of the pattern, consider changing the time signatures accordingly. Also consider whether the music would be easier to write or read if you doubled the note lengths and wrote it as a pattern of 41 eighth notes.

Answer 5

Several good answers here. I'll provide one that takes more of a procedural approach.

To answer the question as it has been asked: yes, 41/16 is a completely valid time signature.

To answer the question in the context of your composition: no, 41/16 is not the most accurate way to state the time signature used in the clip you posted. The bottom number of the time signature specifies which note value is the basis for the beat. The first section of notes is comprised of exclusively eighth notes which appear on the same eighth note grid (i.e. no dotted notes or anything else that would shift the grid by a sixteenth note); no sixteenth notes are present that could affect the way the music is felt, therefore it has to be a split between an eighth-note base and a sixteenth-note base (5/8 and 11/16 as others have mentioned).

To stretch it even further, yes, 41/16 is a valid way to conceptualize what you have written regardless of how it is felt, since time signatures by nature are not required to be stated in terms of feel (or connected to it whatsoever). Additionally, sometimes there's not even a correct way to do that; for example, consider a rock beat that's stated as 15/16 and felt in 4-4-4-3. The beat would clearly be on each quarter note despite the bottom number. It would be unconventional to state this as 3.75/4, even though that's exactly what's happening, and saying "it's in 15/16 and felt in 4-4-4-3" is much easier than saying "it's in 4/4 but each bar is missing the last 16th note" (raises even more questions) or stating it as alternating bars of 3/4 and 3/16 (inaccurate in terms of feel). For your composition, this would apply if you have sections that are supposed to work together in a way that isn't supported by how you would state their time signatures.

But if that doesn't apply then this may need to be treated not as whether you can but whether you should, in which case, no, don't mark this composition as 41/16 unless you explicitly want the musicians to feel it...in 41. There is no way to subdivide that without combining different phrase sizes because 41 is a prime number, and even if it wasn't there could end up being multiple ways to subdivide it anyway since it's such a large number (e.g. 42, which could be 6 groups of 7, 14 groups of 3, etc.), thus requiring specification of a feel. Not to mention specifying the feel outright will save time, be easier to read, and reduce ambiguity for you and your performers.

...unless the ambiguity is the point of your composition or otherwise makes the process easier for the performers, in which case, yes, state the time signature as 41/16 and let your musicians feel it however they want.