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Interval inversion

To invert an interval consists to put an octave higher the interval lowest note. This gives a new interval, complementary to the first one.

Principles

To invert an interval consists to put an octave higher the interval lowest note. An interval and its inversion are complementary and always form an octave.

FIGURE 1 - Examples of intervals with their inversion
Interval(d-f) Reversed interval(f-d at the octave) Interval(g-c sharp) Reversed interval(c sharp-g at the octave)

Be careful not to confuse the interval inversion with the change in direction of the interval (ascending to descending, for example).

Name of an inverted interval

To find the name of the inverted interval, simply perform the following operation: 9 - interval = inverted interval.

For example, the inversion of a third is a sixth (9 - 3 = 6).

The following table summarizes the equivalences between interval and inversion.

Tableau - Interval inversion
IntervalInversion
UnisonOctave
SecondSeventh
ThirdSixth
FourthFifth
FifthFourth
SixthThird
SeventhSecond
OctaveUnison

Note that this table is symmetrical. The first 4 lines are enough to find the last 4 lines, since the intervals are complementary two by two. An inverted second gives a seventh, which inverted itself, gives back a second.

Qualification of a inverted interval

The qualification of an inverted interval is always the opposite of the qualification of the original interval.

Tableau - Inversion and qualification
QualificationInversion qualification
DiminishedAugmented
MinorMajor
PerfectPerfect
MajorMinor
AugmentedDiminished
Another way to find the name and the qualification of an interval is therefore to rely on its inversion. If you are facing a large interval (greater than a fifth), you only need to reverse the interval, find its name and qualification, and then assign the inversed name and inversed qualification to the original interval.

Some inversion examples

FIGURE 2 - Intervals and inversions

The interval D-C becomes C-D when inversed. The latter is a major second. The interval D-C is therefore a minor seventh (9 - 2 = 7, minor opposite to major).

The interval F-D becomes D-F when inversed. The latter is a major third. The interval F-D is therefore a minor sixth (9 - 3 = 6, minor opposite to major).

The interval C-G becomes G-C when inversed. The latter is a diminished fourth. The interval C-G is therefore an augmented fifth (9 - 4 = 5, augmented opposite to diminished).

It is sometimes more complicated to go through the inversion than to look directly for the initial interval. However, it is always useful to know how to do this gymnastics. This method allows you to check the result from another method. This method is also useful in the construction of chord inversions.

Last update on 2018/12/03

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