Compound Intervals

A Guide To Intervals That Span Beyond An Octave

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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.

C-D Major Ninth Interval
C-D Major Ninth Interval

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.

G-C Perfect Eleventh Interval
G-C Perfect Eleventh Interval

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.

C-C sharp Augmented Octave
C-C sharp Augmented Octave

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.

C-D Flat Minor Ninth Interval
C-D Flat Minor Ninth Interval

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.

Perfect Compound Intervals

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.

Major Compound Intervals

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.

Minor Compound Intervals

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.

Augmented Compound Intervals

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.

Diminished Compound Intervals

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.

 

 

 

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