MUSIC THEORY FUNDAMENTALS - Chapter 6, Exercise 1 Solution
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Analyzing the 9/8 Time Signature

PROBLEM
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In the time signature 9/8, identify the real beat unit, how many beats
are in a measure, and whether this meter is simple or compound - and
name its duple/triple/quadruple classification.

SOLUTION
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Step 1 - Determine whether it's simple or compound. The chapter's own
compound-meter examples (6/8, 9/8, 12/8) all use an 8 as the bottom
number with a numerator that's a multiple of 3. Since 9 is a multiple of
3, 9/8 is a COMPOUND meter, meaning each beat subdivides into 3 eighth
notes rather than 2.

Step 2 - Determine the beat unit. In compound meter, three eighth notes
group together to form one beat, and three eighth notes tied together
equal one dotted quarter note. So the real beat unit in 9/8 is the
DOTTED QUARTER NOTE.

Step 3 - Determine beats per measure. There are 9 eighth notes total in
the measure, and each beat uses 3 of them (9 / 3 = 3), so there are 3
beats per measure.

Step 4 - Classify by beats per measure. 3 beats per measure is TRIPLE,
per this chapter's own duple/triple/quadruple table.

ANSWER: 9/8 has a dotted quarter note as its beat unit, 3 beats per
measure, is a compound meter, and is classified as compound triple.

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WHY THIS WORKS AS AN ANSWER

This matches the chapter's own compare-table exactly, which lists 9/8
under the "Compound / Triple" cell. The reasoning generalizes directly:
in any compound meter written with an 8 denominator, the top number
divided by 3 always gives the real number of beats, and 3 grouped eighth
notes always form one dotted-quarter beat.