TonalityGUIDE - Tonal music basic theory for Undergraduates
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Inversions of intervals
An interval is inverted by moving the bottom note of the interval up an octave so that it is above what was previously the top note. It is called an inversion because by putting the bottom note at the top, you are turning the interval upsidedown. The example below shows the common diatonic intervals and their inversions (click here to see the inversions of all the other various intervals):

Inversions of triads
Triads can be also be inverted by moving the bottom note up an octave. Because triads consist of three notes, they can be inverted twice as in the example below. The bottom note of a triad in its original position, arranged as a stack of two thirds, is called the root and so is said to to be in root position. The names for the two inversions speak for themselves:

The inversions of the C major triad can be rearranged without necessarily changing the inversion. For example, the first C major triad below is arranged so that the three notes are as close together as possible. A triad arranged arranged like this is said to be in 'close position'). In the second example below, the C major triad is is spread out but the root is still at the bottom. While it is still in root position it is now said to be in 'open position'.

In all these examples the notes of a C major triad have been re-arranged in various ways and while this considerably changes their sound, they are all recognisably C major triads. This is clear if you compare the sound of them as as group with, for example, a C augmented or E flat minor triad.

TIP: if you want to know if a three-note chord is based on a triad constructed from thirds, and which triad it is, you can try re-arranging it as a stack of thirds