An earlier tutorial showed
how the distance between two notes (called an interval) can be
named depending on its size (i.e. the number of semitones between
the notes). For example, an interval of 7 semitones can be called
a "perfect fifth", such as the interval between C and
G:

However, it is not totally correct to say that the interval
between C and G will always be 7 semitones, a perfect fifth. This
is only true where C is the lower of the two notes. The interval may
be inverted by moving C up by an octave (or, conversely, moving G
down by an octave):

This interval is a perfect fourth, 5 semitones.

Bear in mind here that we are talking only about moving pairs of
notes around within the octave, not extending an interval
beyond an octave by moving the higher note up by 12 semiones, or the
lower note down by 12 semitones. Such extended intervals will be the
subject of a future tutorial.

The following table shows the intervals within an octave, with
their inversions. Note that when the size of the first interval
increases, the size of the inverted interval decreases. NB, the
interval of a diminished fifth contains the same number of semitones
as its inversion, an augmented fourth.

0 / 12 semitones

1 / 11 semitones

2 / 10 semitones

3 / 9 semitones

4 / 8 semitones

5 / 7 semitones

6 / 6 semitones

7 / 5 semitones

8 / 4 semitones

9 / 3 semitones

10 / 2 semitones

11 / 1 semitones

It really is worth taking some time to get comfortable with the concepts
discussed here. In particular, it will make life a lot easier for you when you
come to consider chord construction.

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