Simple and Compound Intervals

You already know how to name an interval by counting its degrees. Now let's sort intervals into two families: the ones that fit within an octave, and the ones that go beyond it.

Simple intervals

A simple interval spans an octave or less. The simple intervals are the second, the third, the fourth, the fifth, the sixth, the seventh and the octave.

Compound intervals

A compound interval is larger than an octave: the ninth, the tenth, the eleventh, the twelfth, and so on. Danhauser's French term is “intervalle redoublé”, a “doubled” interval, and he also gives “composé”, which is the word English uses. A compound interval can lie one, two or more octaves above the simple interval it comes from.

Finding the simple form of a compound interval

Subtract 7 from the interval number as many times as you need, until what's left is 8 or less. That remainder is your simple interval.

Let's try Danhauser's own example, the 16th. 16 minus 14, which is twice 7, leaves 2. So a 16th is a second plus two octaves.

Compounding a simple interval

To go the other way, add 7 to the interval number once for every octave you want to add. A third plus one octave gives 3 plus 7, which is a 10th. A third plus two octaves gives 3 plus 14, which is a 17th.

So two intervals can share a simple form. But even two intervals with the same number are not always the same size, and that is what the next lesson is about.