## Interval Inversion

Much has already been said on intervals. They have been topic of another blog entry, too. Intervals are of particular importance because they constitute basic elements for building more advanced melodic structures. However, there are some other things one should know about intervals, among others also interval inversion.

Performing interval inversions is really easy, as long as we: 1) have learned how to build an interval and 2) can add numbers up till 9 :) If we want to turn something upside down, which is the colloquial term for “invert”, we must proceed so that what first was “up” would now be “down” and the other way round. For example, let us imagine that we are sleeping on our belly, and it is our back that is “up”. When we turn over, it is our belly that is now the “upper” element. In other words, we could say we have “inverted” ourselves – do not forget to train a little before you fall asleep! ;)

Interval inversion is simply a change in the sound order within an interval. The originally “upper” sound will now be the “lower” one, and the other one will now be called “upper”.

HOWEVER,

certain things are not to be forgotten. First, we change the position of only one sound at a time. Moreover, it is to be moved so that the order of sounds changes. If we are supposed to perform an inversion upward, we move the lower sound up so that it is placed higher than (or at least on equal altitude with) the originally “upper” sound. Of course, the note should remain the same, i.e. a C remains a C: it is just the octave that changes. In case of performing of a downward inversion, the originally “upper” sound is moved “beneath” the lower sound of the original interval. Main (simple) intervals (i.e. intervals smaller than or equal with an octave) are always added up within an octave, so while inverting them we move notes to the neighbor octaves (up or down). Compound intervals (up to the fifteenth which equals two octaves) are added up within a fifteenth, so while inverting them notes are moved two octaves higher or lower. In other words, a compound interval inversion is the same interval as that resulting from inverting of a simple interval. Please take a look at the following examples:

Why are you supposed to know how to count to 9? The answer is simple: mathematically, when added, the basic interval and its inversion will always make 9. If we know this, it is easy to tell what interval the perfect fourth (4) inversion is. 4 + ? = 9, thus 9 - 4 = 5 → the perfect fourth inversion is the perfect fifth!
Now, let us try it with another interval: 9 - 7 = 2 → so, the inversion of a seventh is a second. But if we want to invert a “non-perfect” (i.e. major or minor, augmented or diminished) interval, we must remember that:

- inverted minor interval results in a major, and inverted major results in a minor interval,
inverted diminished interval results in an augmented, and inverted augmented results in diminished interval.

It means that the second words (major, minor, augmented, diminished) in the compound names of an interval and its inversion must be opposites. An exception is constituted by perfect intervals: an inverted perfect interval always results in a perfect interval! :)

To practice your intervals try out our on-line exercises: Intervals Recognition and Intervals Comparison. You can also make Intervals Test and check yourself :)