Advanced Intervals

Now that we have looked at the intervals in the major and minor scales, we have covered almost all of the intervals possible within an octave. The chart below includes the minor 2nd and tritone to round out the collection.

A minor second is simply one half step away from the starting note, and a tritone is an interval of three whole steps (or three tones, hence the name 'tritone'). The tritone falls between the perfect 4th and perfect 5th, so it can also be called an augmented 4th or diminished 5th. Also, the tritone is significant because it is 6 half steps and thus divides the octave exactly in half.

Half Steps Interval Name Abbreviation
0 (Perfect) Unison -
1 minor 2nd, half step m2, h
2 Major 2nd, whole step M2, W
3 minor 3rd m3
4 Major 3rd M3
5 Perfect 4th P4
6 tritone
(augmented 4th, diminished 5th)
(aug4, dim5)
7 Perfect 5th P5
8 minor 6th m6
9 Major 6th M6
10 minor 7th m7
11 Major 7th M7
12 (Perfect) Octave Oct, 8ve

When intervals occur that are greater than an octave, you simply keep counting up as if the scale continued. The trick is that you can't simply add intervals together numerically by the interval names: an octave plus a major 3rd is not a major 11th as you might expect, but a major 10th. But, you can add intervals if you think of them in half steps: 12 half steps + 4 half steps = 16 half steps.

Half Steps Interval Name Abbreviation
12 (Perfect) Octave Oct, 8ve
13 minor 9th m9
14 Major 9th M9
15 minor 10th m10
16 Major 10th M10
... ... ...

Complimentary Intervals

Two intervals are considered complimentary when they add up to an octave. If you think of the intervals in terms of their half-steps, any two intervals that add up to 12 are considered complimentary. On the other hand, if you think of them in terms of their scale degrees, they should add up to 9, and minor intervals should be paired with major intervals. For example, a minor 3rd (3 half steps) and a major 6th (9 half steps) are complimentary, as are a major 7th (11 half steps) and a minor 2nd (1 half step). A perfect 4th and a perfect 5th are complimentary, and the tritone is its own compliment because it divides the octave in half.

Complimentary Intervals

"Music is nothing else but wild sounds civilized into time and tune." - Thomas Fuller

"After silence, that which comes nearest to expressing the inexpressible is music." - Aldous Huxley

"Music in the soul can be heard by the universe." - Lao Tzu

"Music is a higher revelation than all wisdom and philosophy." - Ludwig van Beethoven

"Music is the movement of sound to reach the soul for the education of its virtue." - Plato

"Music expresses that which cannot be said and on which it is impossible to be silent." - Victor Hugo

"Music is nothing else but wild sounds civilized into time and tune." - Thomas Fuller

Copyright © Sienna M. Wood, 2015-2016