Compound intervals are intervals spanning more than one octave.

## Compound Intervals

So far, you have learned about simple intervals that span at most one octave. Compound means something consists of two or more elements. In this case, we can describe compound intervals as they consist of one or more octaves and simple intervals. So, we can build a compound interval either by counting the intervals between notes by half steps or first putting the notes in the same octave and then figuring out the size of the remaining simple interval. The qualities of simple intervals were perfect, major, minor, augmented and diminished. We name compound intervals just like the simple intervals. Let’s see an example.

In this example, you can see a major ninth (M9) interval between C and D. Notice that this D is not the one right after C. It is one octave higher in pitch. So this interval spans more than an octave and it is a compound interval. These notes are 14 half steps away from each other. If we analyze this interval, we can see that it consists of an octave plus a major second interval (a simple interval). So twelve of the half steps come from the octave and the remaining two half steps come from the major second that spans beyond an octave. Let’s see another example.

In this example, you can see a perfect eleventh (P11) interval between G and C. Notice that C is again one octave higher in pitch. So this is a compound interval too. It consists of an octave plus a perfect fourth interval.

### Naming Compound Intervals

Just like simple intervals, we can name two compound intervals that have same half steps differently. Let’s see some examples.

In this example, there is an augmented octave (A8) between C and C sharp. It consists of an octave plus a half step. Remember when I mentioned that augmented intervals are one half step wider than perfect and major intervals. An octave is a perfect interval too. So if we widen it a half step like this, this will be an augmented interval too. Because we augmented an octave, we call it an augmented octave.

As you can see, there is a minor ninth (m9) interval between C and D flat here. It consists of an octave plus a half step too. But notice that this interval has nine note names between C and D flat, not eight like the one above. It sounds exactly like an augmented octave, and yet it is a minor ninth interval.

### Perfect Compound Intervals

If we build a compound interval that has an octave (or octaves) plus a simple perfect interval, we call it a perfect compound interval. Here is a figure that shows all perfect compound intervals up to fifteenth built on the note C.

Let’s have a look at their details.

INTERVAL NAME | SYMBOL | NUMBER OF HALF STEPS | BASIC FORMULA |
---|---|---|---|

Perfect Eleventh | P11 | 17 | Octave+Perfect Fourth |

Perfect Twelfth or Tritave | P12 | 19 | Octave+Perfect Fifth |

Perfect Fifteenth or Double Octave | P15 | 24 | Octave+Octave |

This table shows the names and symbols of the perfect compound intervals, the number of half steps they contain, and the basic formulas to build them.

### Major Compound Intervals

If we build a compound interval that has an octave (or octaves) plus a simple major interval, we call it a major compound interval. Here is a figure that shows all major compound intervals up to fifteenth built on the note C.

Let’s have a look at their details.

INTERVAL NAME | SYMBOL | NUMBER OF HALF STEPS | BASIC FORMULA |
---|---|---|---|

Major Ninth | M9 | 14 | Octave+Major Second |

Major Tenth | M10 | 16 | Octave+Major Third |

Major Thirteenth | M13 | 21 | Octave+Major Sixth |

Major Fourteenth | M14 | 23 | Octave+Major Seventh |

This table shows the names and symbols of the major compound intervals, the number of half steps they contain, and the basic formulas to build them.

### Minor Compound Intervals

If we build a compound interval that has an octave (or octaves) plus a simple minor interval, we call it a minor compound interval. Here is a figure that shows all minor compound intervals up to fifteenth built on the note C.

Let’s have a look at their details.

INTERVAL NAME | SYMBOL | NUMBER OF HALF STEPS | BASIC FORMULA |
---|---|---|---|

Minor Ninth | m9 | 13 | Octave+Minor Second |

Minor Tenth | m10 | 15 | Octave+Minor Third |

Minor Thirteenth | m13 | 20 | Octave+Minor Sixth |

Minor Fourteenth | m14 | 22 | Octave+Minor Seventh |

This table shows the names and symbols of the minor compound intervals, the number of half steps they contain, and the basic formulas to build them.

### Augmented Compound Intervals

If we enlarge a perfect or major compound interval by a half step, we build an augmented compound interval. Here is a figure that shows all augmented compound intervals up to fifteenth built on the note C.

Let’s have a look at their details.

INTERVAL NAME | SYMBOL | NUMBER OF HALF STEPS | BASIC FORMULA |
---|---|---|---|

Augmented Octave | A8 | 13 | Octave+Augmented Unison |

Augmented Ninth | A9 | 15 | Octave+Augmented Second |

Augmented Tenth | A10 | 17 | Octave+Augmented Third |

Augmented Eleventh | A11 | 18 | Octave+Augmented Fourth |

Augmented Twelfth | A12 | 20 | Octave+Augmented Fifth |

Augmented Thirteenth | A13 | 22 | Octave+Augmented Sixth |

Augmented Fourteenth | A14 | 24 | Octave+Augmented Seventh |

Augmented Fifteenth | A15 | 25 | Octave+Augmented Octave |

This table shows the names and symbols of the augmented compound intervals, the number of half steps they contain, and the basic formulas to build them.

### Diminished Compound Intervals

If we narrow down a minor compound interval by a half step, we build a diminished compound interval. Here is a figure that shows all augmented compound intervals up to fifteenth built on the note C.

Let’s have a look at their details.

INTERVAL NAME | SYMBOL | NUMBER OF HALF STEPS | BASIC FORMULA |
---|---|---|---|

Diminished Ninth | d9 | 12 | Octave+Diminished Second |

Diminished Tenth | d10 | 14 | Octave+Diminished Third |

Diminished Eleventh | d11 | 16 | Octave+Diminished Fourth |

Diminished Twelfth | d12 | 18 | Octave+Diminished Fifth |

Diminished Thirteenth | d13 | 19 | Octave+Diminished Sixth |

Diminished Fourteenth | d14 | 21 | Octave+Diminished Seventh |

Diminished Fifteenth | d15 | 23 | Octave+Diminished Octave |

This table shows the names and symbols of the diminished compound intervals, the number of half steps they contain, and the basic formulas to build them.