What is this time signature?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

The correct time signature...

...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, 2^x to 2^x-1 sixteenths = (2^x)/4 beats = 2^x-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.