# Is “divide into” in this sentence equivalent to “be divided by”?

When the beats divide into twos, the music is said to be in simple time;

Source: The AB Guide to Music Theory, page 19, in the last paragraph

But I don't understand why is the 3/4 time signature also in simple time, since 3 can not be divided by two.

In this answer it says that:

idiomatic alternative...
divide 2 into 4, giving the answer 2

And in this definition:

(of a number) be contained in a number without a remainder.
"3 divides into 15"

Then I guess that "divide 2 into 4 without a remainder" amounts to "2 divides into 4", and hence "the beats divide into twos" means "twos can be divided by the beats with no remainder". But does that statement make sense?

• 3/4 time has 3 beats in a bar, but 2 quavers in a beat – Aric Aug 18 '17 at 13:55

You are misunderstanding the use of "divide into" in the music example.

In common 4/4 time, the beats can be divided into 2. This is not because 4 is divisible by 2, but because each individual beat has two quavers in it. In 3/4 this is the same. Each beat has 2 quavers in it.

In compound time, the beats cannot be divided into 2. 6/8, for example, has 2 beats, each beat with 3 quavers.

The sentence is saying that the individual beats can be divided into two, not the number of beats in a bar.

The meaning of "divide into" in this sentence is the same, you just applied it to the wrong thing.

• Could you please paraphrase "When the beats divide into twos" using "divided by"? – Lerner Zhang Aug 18 '17 at 14:03
• "When every beat in a bar can be divided by two(quavers)"? – Lerner Zhang Aug 18 '17 at 14:07
• Then is "when the beats divide into twos" equivalent to "when one beat can be divided by two(quavers)", and hence "when one beat divides into two"? – Lerner Zhang Aug 18 '17 at 14:09
• And hence "divide into" is the same as "be divided into"? In this scenario? – Lerner Zhang Aug 18 '17 at 14:11
• @Lerner Correct. Simple time is simple because each beat has two subdivisions (beats can be divided into 2). Compound time is compound because each beat has three. – Aric Aug 18 '17 at 14:11