Musical intervals: The compound intervals

7 min readApr 10, 2021

In this article you will be looking at the compound intervals.

If you haven’t already seen my previous article ‘Musical Intervals: The building blocks of music’ I would recommend you read that first.

Introduction to compound intervals

So far we have looked at simple intervals that are no larger than an octave. Now we will look at compound intervals that are larger than an octave.

Finding a compound intervals number property

To find a compound interval’s number property you count all the notes that the interval contains. This includes the starting and finishing notes but excludes any chromatic notes. You always count upwards from the scale’s starting note. In the key of C, this will be the C note.

Counting the notes of the C major scale

Counting the interval from ‘C’, past the octave to ‘D’ gives 9 notes. These are C, D, E, F, G, A, B, C, and D. Thus this interval’s number quality is a ‘ninth’. This interval is an octave higher than the ‘second’ interval.

Counting the interval from ‘C’, past the octave to ‘E’ gives 10 notes. These are C, D, E, F, G, A, B, C, D, and E. Thus this interval’s number quality is a ‘tenth’. This interval is an octave higher than the ‘third’ interval.

Counting the interval from ‘C’, past the octave to ‘F’ gives 11 notes. These are C, D, E, F, G, A, B, C, D, E, and F. Thus this interval’s number quality is an ‘eleventh’. This interval is an octave higher than the ‘fourth’ interval.

Counting the interval from ‘C’, past the octave to ‘G’ gives 12 notes. These are C, D, E, F, G, A, B, C, D, E, F, and G. Thus this interval’s number quality is a ‘twelfth. This interval is an octave higher than the ‘fifth’ interval.

Counting the interval from ‘C’, past the octave to ‘A’ gives 13 notes. These are C, D, E, F, G, A, B, C, D, E, F, G, and A. Thus this interval’s number quality is a ‘thirteenth’. This interval is an octave higher than the ‘sixth’ interval.

Counting the interval from ‘C’, past the octave to ‘B’ gives 14 notes. These are C, D, E, F, G, A, B, C, D, E, F, G, A, and B. Thus this interval’s number quality is a ‘fourteenth’. This interval is an octave higher than the ‘seventh’ interval.

Counting this interval from ‘C’, past the octave to ‘C’ gives 15 notes. These are C, D, E, F, G, A, B, C, D, E, F, G, A, B, and C. Thus this interval’s number quality is a ‘Fifthteenth’. But it has its own name, the ‘double octave’. This interval is an octave higher than the ‘perfect octave’ interval.

You’ve now finished counting the major scales’ compound intervals. This gives you the number quality for each compound interval.

ninth
tenth
eleventh
twelfth
thirteenth
fourteenth
fifteenth

A quick review of what we previously covered

From my previous article ‘Musical Intervals: The building blocks of music’ we learned:

That a major scale only has major and perfect intervals.
That its unison, fourth, fifth, and octave are all perfect intervals.
That it's second, third, sixth, and seventh are all major intervals.
That if you lower a major interval by a semitone it becomes a minor interval. This gives you the minor second, minor third, minor sixth, and minor seventh intervals.
That if you lower a perfect fifth interval by a semitone it becomes a diminished interval. This gives us a diminished fifth interval.
That if you raise a perfect fourth interval by a semitone it becomes an augmented interval. This gives you an augmented fourth interval.
That the diminished fifth and augmented fourth intervals are identical. The only difference is their names.

Observations from counting the compound intervals

Whilst counting the notes of the compound intervals you will have noted:

That the ‘ninth’ interval is an octave higher than the ‘second’ interval.
That the ‘tenth’ interval is an octave higher than the ‘third’ interval.
That the ‘eleventh’ interval is an octave higher than the ‘fourth’ interval.
That the ‘twelfth’ interval is an octave higher than the ‘fifth’ interval.
That the ‘thirteenth’ interval is an octave higher than the ‘sixth’ interval.
That the ‘fourteenth’ interval is an octave higher than the ‘seventh’ interval.
That the ‘fifteenth’ or ‘double octave’ interval is an octave higher than the ‘perfect octave’ interval.

Working out the quality property for each compound interval

We know the ‘eleventh’, ‘twelfth’, and ‘double octave’ intervals are all an octave higher than the perfect fourth (P4), the perfect fifth (P5), and the perfect eighth (octave) (P8) intervals. Thus these intervals must be perfect as well.

This gives us the:

perfect eleventh (P11)
perfect twelfth (P12)
double octave (P15)

We know the ‘ninth’, ‘tenth’, ‘thirteenth’, and ‘fourteenth’ intervals are an octave higher than the major second (M2), major third (M3), major sixth (M6), and major seventh (M7) intervals. Thus these intervals must be major as well.

This gives us the:

major ninth (M9)
major tenth (M10)
major thirteenth (M13)
major fourteenth (M14)

We know a major interval has a smaller version, the minor interval. This is the same for compound intervals. This gives us the:

minor ninth (m9)
minor tenth (m10)
minor thirteenth (m13)
minor fourteenth (m14)

We learnt in my previous article that there is an interval that doesn’t occur naturally in the major scale or natural minor scale. We learnt it had 2 different names depending on whether you lower or raise a note to get it.

It was called either the augmented fourth interval or the diminished fifth interval depending if you raised the fourth a semitone or lowered the fifth a semitone.

We learnt that if you lower a perfect interval by a semitone it becomes a diminished interval. We know that the perfect twelfth interval is an octave higher than the perfect fifth interval. The perfect twelfth interval (P12) lowered by a semitone becomes a Diminished twelfth interval. (dim12, d12, or o12).

We also learnt that if you raise a perfect interval by a semitone it becomes an augmented interval. We know that the perfect eleventh interval is an octave higher than the perfect fourth interval. The perfect eleventh (P11) raised by a semitone becomes an augmented eleventh interval. (A11 or +11)

So the last interval is named either as:

The Diminished twelfth (dim12, d12, or o12).
or the Augmented eleventh (A11 or +11)

You now have all 13 intervals of the Chromatic scale.

List of all the compound intervals

minor ninth (m9)
major ninth (M9)
minor tenth (m10)
major tenth (M10)
perfect eleventh (P11)
augmented eleventh (A11 or +11) or diminished twelfth (dim12, d12, or o12).
perfect twelfth (P12)
minor thirteenth (m13)
major thirteenth (M13)
minor fourteenth (m14)
major fourteenth (M14)
double octave

Using the ‘compound’ notation

The easiest way to name compound intervals is to work out what the interval would be if it were a simple interval and then put the word ‘compound’ in front.

For example, the interval from C to E is a major 3rd. If we made it C to E (an octave higher) we can call it a compound major 3rd instead of a major tenth.

The minor ninth = compound minor 2nd
The major ninth = compound major 2nd
The minor tenth = compound minor 3rd
The major tenth = compound major 3rd
The perfect eleventh = compound perfect 4th
The perfect twelfth = compound perfect 5th
The minor thirteenth = compound minor 6th
The major thirteenth = compound major 6th
The minor fourteenth = compound minor 7th
The major fourteenth = compound major 7th

Some more stuff about compound intervals

A compound perfect interval raised by a semitone becomes augmented.
A compound perfect interval lowered by a semitone becomes diminished.
A compound major interval raised by a semitone becomes augmented.
A compound major interval lowered by a semitone becomes minor.
A compound major interval lowered by two semitones becomes diminished.

You should never lower or raise the double octave as this will change the starting or ending note of the scale. This in turn would result in you having a different scale than what you started off with. (For example C#, D, E, F, G, A, B, and C#).

If you made it too here I’d like to thank you for reading my article. I hope you have got something from it. If you found this useful please let me know.