Characteristics of intervals – Inversions


Let me start with the example of the perfect 5th interval from C to G, as indicated on the next keyboard:

perfect fifth C to G

You can make an inversion of this perfect 5th interval by either taking the highest note and move it an octave down, or by taking the lowest note and move it an octave up. In the keyboard below, you see the highest note that was moved an octave down. Whether you move the highest note an octave down, or the lowest note an octave up, the result is the same: the inversion of the perfect 5th interval from C to G is a perfect 4th interval from G to C.

perfect fourth G to C

So, a perfect 4th interval is the inversion of a perfect 5th interval. The reverse is also true: a perfect 5th interval is the inversion of a perfect 4th interval. Together they add up to an octave, because a perfect 5th (7 semitones) plus a perfect 4th (5 semitones) make together 12 semitones, an octave.

You can also see it the following way: when you want to go from C to G, you can either go up a 5th, or go down a 4th.

Inversions of other intervals

Now, this is not only true for the ‘perfect 5th-perfect 4th pair’. Other pairs of intervals exist that act the same way. In fact, every interval has its inversion. For example, the inversion of the major 3rd interval from –let’s say- E to G# is the minor 6th interval from G# to E. Also here, the intervals add up to an octave, because 4 semitones (major 3rd) plus 8 semitones (minor 6th) equals 12 semitones (an octave).

A special case is the tritone interval. The tritone doesn’t need a partner, it just needs itself! A tritone splits an octave exactly in two equal parts, so a tritone just needs another tritone to make an octave.

A tritone consists of 6 semitones, so: 6+6=12, an octave!

Here’s a list of intervals with their inversions:

Intervals with their inversion:
Perfect unison + perfect octave

Semitone (or minor second) + major seventh

Whole tone (or major second) + minor seventh

Minor third + major sixth

Major third + minor sixth

Perfect fourth + perfect fifth

Tritone + tritone


Notice that a perfect interval always goes together with another perfect interval and a minor interval always goes together with a major interval (and, of course, vice versa).


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Martin Cohen

Martin Cohen is a science and piano teacher. He is also a jazz musician and composer.

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