The Unison Octave Inversion

The Unison Octave Inversion

This is something that confuses most people.
How can you possibly invert… a unison?
After all: a unison is 2 versions of the exact same note.

Ask musicians what you get when you invert a unison, and most will reply: “a unison”.

A unison is technically speaking not an interval, because there is no distance between the 2 sounds.
It is 2 versions of the same note sounding simultaneously. Only players of stringed instruments can play this.
This poses a bit of a dilemma here: How do you invert “the same note”?

Well you want to be consistent with how you invert all other intervals.

When you invert an interval, you switch the 2 notes around.
The lower note becomes the higher note, and the higher note becomes the lower note.

How do you switch 2 notes around?
You invert an interval when you bring the lower note up an octave, or when you lower the higher note down an octave.
The lower note “jumps” over the higher note when you bring it up an octave.
The higher note jumps below the lower note when you bring it down an octave.

For example the notes C to F from low to high is a 4th.
When I want to invert that invertal, I can bring C up an octave or drop F down an octave. In either case I now get F to C, which is a 5th.

Notice how the sum of an interval and its inversion always equals 9: 3rds become 6ths, 4ths become 5ths, etc.

Applying all this to the unison and octave:
When both notes are the same note, it does not matter which of the 2 you raise or drop an octave: either way, you get an octave.

A unison inverted becomes an octave.

unison-inverted-becomes-an-octave

An octave inverted becomes a unison.

In following example, whether you drop the higher C down an octave, or bring the lower C up an octave, you get a unison.

octave-inverted-becomes-unison

Unisons and octaves are perfect intervals, and a perfect interval inverted becomes another perfect interval.
Also in this case the sum of the interval and its inversion equals 9. (1 + 8)

Keeping in mind that the sum of an interval and its inversion always adds up to 9, it wouldn’t make sense that a unison inverted would become another unison. 1 + 1 is 2, not 9.

Conclusion

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