• # Explained: The Relationship Between The Octave And The Inversion Of Intervals

In this lesson, Ill be showing you the relationship between the octave and the inversion of intervals.

There is need for anyone who is interested in learning and mastering the inversion of intervals to understand the relationship between the octave and the inversion of intervals because it deepens your knowledge of the inversion of intervals.

Attention: Although a vast majority of those who will read this lesson are familiar with the octave, we’ll be starting out with a quick review on the concept of the octave just to refresh our minds and for the sake of those who do not have a proper understanding of the term.

So, give me your undivided attention and in the next few minutes you’ll have a new perspective to the inversion of intervals.

## A Short Note On The Octave

The term octave is associated with the number “eight.” Therefore, whenever you come across the term octave, your mind should be occupied with the number eight.

“But There’s More To The Octave Than Eight”

The reason why “number eight” is important in music theory is because all the notes that have the same letter name on the keyboard are octaves apart from each other.

All the C’s on the keyboard:

…are octaves apart from each other:

From this C:

…to that C:

…is an octave.

It’s also important to note that the reason why the major scale starts out and ends on the same note is because of the octave equivalence between notes.

The C major scale:

…starts on C and ends on C:

C (starts from this C):

C (ends on this C):

“Here Are Octave Examples On The Keyboard…”

C octave:

Db octave:

D octave:

Eb octave:

E octave:

F octave:

Gb octave:

V
G octave:

Ab octave:

A octave:

Bb octave:

B octave:

## The Inversion Of Intervals — Explained

Before I show you the relationship between the octave and the inversion of intervals, which is our goal in this lesson, permit me to briefly share with you on the concept of inversion.

This basic information will prepare your mind before we delve into an advanced perspective to the inversion of intervals.

### “Here’s A Basic Explanation On The Concept Of Inversion”

An interval consists of two notes — strictly two. So the following are intervals:

C-D:

E-Bb:

A-E:

Each of the intervals consist of a lower note and an upper note. In the case of “C-D”:

…C is the lower note, while D is the upper note.

“So, What Is Inversion?”

An interval is said to be inverted when the order or position of the notes of an interval are changed in such a way that the lower note becomes the upper note and the upper note becomes the lower note.

The inversion of “C-D”:

…produces “D-C”:

…and you can clearly see a change of the order or position of the notes.

The two other interval examples given are “E-Bb” and “A-E”:

E-Bb:

A-E:

When inverted, “E-Bb” becomes “Bb-E”:

E-Bb:

Bb-E:

…while “A-E” becomes “E-A”:

A-E:

E-A:

That, ladies and gentlemen, is inversion. ;)

### The Relationship Between The Octave And The Inversion Of Intervals

It will interest you to know that the inversion of intervals and the concept of the octave are related.

Let’s explore these theories:

1. Only intervals that are within the compass of the octave can be inverted.
2. Adding a given interval and its inversion together produces an octave.

…because they form the basis of this relationship.

Relationship #1 – “Only intervals that are within the compass of the octave can be inverted.”

An interval may be categorized as simple or compound, and the octave is the reference that is used to determine if an interval is simple or compound.

Simple intervals are within the compass of an octave, while compound intervals are bigger than an octave.

Simple intervals (which are within the compass of an octave) belong to the category of intervals that can be inverted.

Take a look at “C-D” in simple and compound forms:

C-D (simple):

C-D (compound):

“C-D” in its simple form can be inverted:

C-D:

…to D-C:

…but its compound form cannot be inverted.

Relationship #2 – “Adding a given interval and its inversion together produces an octave.”

Also, when “C-D” and “D-C” are summed up:

C-D:

D-C:

…we’ll have “C-D-C”:

…which spans an interval of a eighth or octave (from C to C):

The inversion of “D-F#” produces “F#-D:

D-F#:

F#-D:

…and when both intervals are added together, we have “D-F#-D”:

…which spans an interval of a eighth or octave (from D to D):

Submission: This is true for every other simple interval.

## A Breakdown Of The Concept Of Inversion Using The Octave

In the inversion of intervals, it’s important to keep the following changes in mind:

Change of Size

Change of Quality

…and we’ll be focusing on both changes in this segment.

### The Change Of Size — Explained

In an octave (let’s use C-C):

If you take a second interval (C-D) away:

…you’ll have a seventh interval (D-C) remaining:

If you take a third interval (C-E) away:

…you’ll have a sixth interval (E-C) remaining:

If you take a fourth interval (C-F) away:

…you’ll have a fifth interval (F-C) remaining:

If you take a fifth interval (C-G) away:

…you’ll have a fourth interval (G-C) remaining:

If you take a sixth interval (C-A) away:

…you’ll have a third interval (A-C) remaining:

If you take a seventh interval (C-B) away:

…you’ll have a second interval (B-C) remaining:

So, for each interval taken away from the octave, the remaining interval is the inversion of the interval taken away from the octave.

### The Change Of Quality — Explained

If you take a minor interval away from any given octave, you’ll be left with a major interval:

If C-Db (a minor interval):

…is taken away from the C octave:

…the interval we’re left with (which is Db-C):

…is a major interval.

Taking a major interval away from any given octave, would leave you with a minor interval:

For example, when C-D (a major interval):

…is taken away from the C octave:

…what we have left (D-C):

…is a minor interval.

If you take a diminished interval away from any given octave, you’ll be left with an augmented interval:

If C-Gb (a diminished interval):

…is taken away from the C octave:

…the interval we’re left with (which is Gb-C):

…is an augmented interval.

Taking an augmented interval away from any given octave, would leave you with a diminished interval:

For example, when C-D# (an augmented interval):

…is taken away from the C octave:

…what we have left (D#-C):

…is a diminished interval.

I hope this helps.

## Final Words

Please note that perfect intervals remain don’t change their quality when inverted.

For example, taking a perfect fourth (C-F):

…away from the C octave:

…leaves us with yet another perfect interval — “F-C” (a perfect fifth interval):

Thank you for your time and see you in another lesson.

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#### Chuku Onyemachi

Head of Education at HearandPlay Music Group
Hello, I'm Chuku Onyemachi (aka - "Dr. Pokey") - a musicologist, pianist, author, clinician and Nigerian. Inspired by my role model Jermaine Griggs, I started teaching musicians in my neighborhood in April 2005. Today, I'm privileged to work as the head of education, music consultant, and chief content creator with HearandPlay Music Group sharing my wealth of knowledge with hundreds of thousands of musicians across the world.