There is so much music-theoretical information that it makes strong sense to find ways to reduce redundant parts of it wherever possible. In this episode we are going to reduce the number of relevant intervals by 50%. This is possible because there is a musical phenomenon, called octave equivalence.

# What is octave equivalence?

While comparing different tones one will find that tones an octave apart sound extremely similar. Played together these tones easily fuse into each other. The reason is that the second tone has the double frequency as the first. The waves of both tones fit perfectly into each other. And exactly that can be used to reduce the amount of relevant intervals.

# Complementary Intervals

Imagine we have the three tones g2, c3 and g3. If the tones g2 and g3 are virtually the same, then it is not so important if we have the interval g2-c3 or c3-g3. Both intervals complement each other to an octave and therefore are called *complementary intervals*. Other complementary intervals are …

- Prime and octave
- Minor second and major seventh
- Major second and minor seventh
- Minor third and major sixth
- Major third and minor sixth
- Perfect fourth and perfect fifth
- Augmented fourth and diminished fifth

# How can we use that?

There are several music theoretical aspects where it does not matter if we have one or the other interval, for example a minor third or its complement, the major sixth. A model of thirds describes sixths at the same time. That is the reason why the three music theoretical models presented in the first episode do only contain primes, seconds, thirds and fifths. The other intervals are therefore contained as well.

# Video demonstration

The following video summarizes the things said before by some sound examples.

# Summary

- Tones with an octave distance are sounding very similar. Therefore also intervals sound similar that consists of tones octaves apart.
- Such intervals, e.g. fourth and fifth or third and sixth are called complementary intervals.
- The symmetry model utilizes that by containing only seconds, thirds and fifths. The complementary intervals are neglected.

I see that your video has more of the intervals than your list has (major third/minor sixth was left off). Good to see. I’m enjoying the series so far!

O, thanks! I’ve fixed that.