# What is this time signature?

I am working through an exercise which has me determining the time signature of measures, and I'm stumped on this one:

In determining the value of the septuplet, I need to first determine whether the answer will be in compound time or simple time, based on this page where it was defined:

This is in the section titled Hybrid Meters, where we were introduced to

the hybrid duple times 5/2, 5/4, 5/8, and 5/16,

the hybrid triple times 7/2, 7/4, 7/8, 7/16

and the hybrid quadruple times which can be formed by taking the upper number to be 9,10, or 11, and the lower number to be 2, 4, 8, or 16.

Now I'm guessing there are infinitely many more possibilities, but these are the only ones we've covered so far, and my question is: am I wrong to say that it is impossible to classify this measure as one of the time signatures listed above, using one of the interpretations of septuplets' values stated in the second image?

• Only glancing right now, so I don’t feel sure enough to provide an answer, but I think I disagree with the definition of septuplets in that second image. By my understanding, a septuplet in simple time takes the place of 4 sixteenths as shown, but would take the place of six sixteenths in compound time, not three. At any rate, I think you’re technically correct that you can’t 100% guess the difference between this being a relatively normal 9/8 or a relatively abnormal 8/8 (3+2+3 subdivision), but the former seems far more likely absent further evidence. Has 8/8 been discussed? Commented Nov 29, 2017 at 4:01
• @PatMuchmore This is entirely right. It is far more likely that the septuplet takes the space of six notes than four. Consider converting this to an answer. Commented Nov 29, 2017 at 7:38
• I agree with Pat and Kilian here - since the measure's beaming (and therefore metric subdivision) implies compound meter, if the septuplet did not occur within the same metrical grouping, it would need to be specified with a ratio (e.g. 7:4) Commented Nov 29, 2017 at 13:59
• 8/8 hasn't been discussed yet. I'm going to take the answer to be 9/8 by treating the septuplets as 7:6. Thanks so much for clarifying! This one threw me for a loop.
– user45413
Commented Nov 29, 2017 at 17:30

I disagree with the definition of septuplets in that second image. By my understanding, a septuplet in simple time takes the place of 4 sixteenths as shown, but would take the place of six sixteenths in compound time, not three. At any rate, the beaming together of three eighth notes after the septuplet and the dotted-quarter before makes it clear that this septuplet comes between two compound beats. I think you’re technically correct that you can’t 100% guess the difference between this being a relatively normal 9/8 or a relatively abnormal 8/8 (3+2+3 subdivision), but the former seems far more likely absent further evidence. As a hybridization of 4/4 time, it seems possible that 8/8 has come up in the book, but it isn’t in the list you’ve provided.

• Yes, I'd agree -- my "internal" rule, which I am pretty sure is correct, is that a triplet/quintuplet/septuplet, etc. takes up the time that a standard group of notes of the same beaming would take to fill one beat. <-- that's probably incomprehensible to anyone but me :-) Commented Nov 29, 2017 at 12:41
• OK, I'll disagree with @PatMuchmore's disagreement :-) Caveat, that I've played a lot of strange rhythms in musical theater, but don't have a strong theoretical background. I would play this as the septuplet takes a single eighth note. Wouldn't a 16th note Triplet take the space of a single eighth in compound time? That would make the example 7/8 time. And.. I think the examples in the text are poorly written.
– Greg
Commented Nov 29, 2017 at 13:53
• @PatMuchmore thanks for the answer! I was careful to list every time signature that has come up.
– user45413
Commented Nov 29, 2017 at 17:25
• @Greg I wouldn't be surprised if your interpretation is the one the author intended. But I agree the book is not as great as I thought it was. It depends heavily on the teacher to not just elaborate on topics, but to clarify actual problematic ambiguities which frequently arise. The exercises are great, but I would not recommend this book to someone for independent study.
– user45413
Commented Nov 29, 2017 at 18:14
• Actually, I'd say 7:4 or 7:8 in simple time, and 7:6 for compound time. Commented Dec 7, 2017 at 2:56

The book's definition of a 7-tet is misleading. OK - more than misleading, when stated as a 'rule' it's plain wrong! That's a '7 in the time of 6' tuplet. So the 'hybrid' idea isn't required. It's a straightforward compound-triple 9/8.

(And it's the first time I've heard of 'hybrid' meters. Not a bad concept, but don't assume anyone else will know what you're talking about!)

In the contest of a theory exercise, there's room for confusion. In real music, which WILL have a time signature, it should be clear. Though a '7:8' notation rather than just plain '7' might have been helpful.

• Yeah the term seems to only be used in my book. Other places seem to call them complex or irregular time signatures. Is this correct?
– user45413
Commented Nov 29, 2017 at 17:26
• 'Complex' perhaps. I don't see how, foir instance, a consistent 3+2 5/8 could be called 'irregular'. Commented Nov 29, 2017 at 17:56
• I learned it as "hybrid" meters as well, but my book also called it mixed meters. Commented Dec 7, 2017 at 2:58

...is 9/8.

### But it's hard to figure out, because...

...the book is almost entirely wrong in defining tuplets.

### Here is a better way to think about tuplets

Tuplets are always relative to the "next higher" note value within the time signature.

• For simple time that means the "usual" binary relationships: whole note, half note, quarter note, eighth note, etc.

• For compound time tuplets are relative to dotted half notes, dotted quarter notes, eighth notes, sixteenth notes, etc.

### A look at sixteenth-note tuplets

In simple time

• 1 regular sixteenth = 1/4 beat
• 2 regular or 3-tuplet sixteenths = 1/2 beat
• 4 regular or 5-to-7-tuplet sixteenths = 1 beat
• 8 regular or 9-to-15-tuplet sixteenths = 2 beats

For x=0 to n, 2x to 2x-1 sixteenths = (2x)/4 beats = 2x-2 beats.

In compound time

Taking the eighth note as the basic pulse. (Equivalents based on the dotted quarter "large pulse" are given in parentheses.)

• 1 regular sixteenth = 1/2 beat (= 1/6 of a dotted quarter)
• 2 regular or 3-tuplet sixteenths = 1 beat (= 1/3 of a dotted quarter)
• 4-to-7-tuplet sixteenths = 3 beats (= 1 dotted quarter)
• 8-to-15-tuplet sixteenths = 6 beats (= 1 dotted half)

Note that the relationships aren't quite as consistent as in simple time, because the subdivisions of the beat are 3-based down to the eighth note but 2-based beyond that.