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2.6 Interval Inversion and Compound Intervals

4 min readjanuary 3, 2023

Mickey Hansen

Mickey Hansen

Mickey Hansen

Mickey Hansen

Now that we have a basic understanding of interval size and quality, let’s learn some skills that will later help us use intervals to construct chord progressions and interpret harmonies. In this section, we will go over and compound intervals. 

Interval Inversions

When we talk about intervals, we are always talking about ascending intervals. For example, a C to an E is a Major 3rd. But what about an E to a C? Sure, we could figure out by looking at the notes that an E to a C is a minor 6th. What interval would a descending minor 3rd be? There must be some relation between a descending interval and an ascending interval.

Interval inversion is the process of taking an interval (the distance between two pitches) and flipping it upside down!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-DdD0OYQVBXZJ.gif?alt=media&token=d30fae3a-c8a6-437e-9337-9481d1b7ea69

For example, the inversion of a perfect fifth (an interval consisting of seven half steps) is a (an interval consisting of five half steps). The inversion of a (an interval consisting of four half steps) is a (an interval consisting of eight half steps).

All you have to do to invert an interval is subtract the interval by 9, and then give the inverted interval the opposite quality as the original interval. For example, the inversion of an A5 would be a d4, and the inversion of an M3 would be a m6. The inversions of perfect intervals are also perfect. 

Here's an example of a (F-A) being inverted:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-W1We4BYW7Quz.png?alt=media&token=4448de38-091c-4344-b33c-81304fd48b42

Let's look at a few more examples of inversions on a staff:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-HhF5ZorWrhSz.png?alt=media&token=aef0ac58-52ae-4105-9bbb-da89703b373c

Your turn! Practice inverting these intervals by using the tricks above (answers at the end of the chapter):

There are two ways to interpret an interval inversion. First is that if you have two notes that are some interval apart, switching around those two notes gives the interval inversion. A common example that you should remember is the P5 and P4 inversions. If you have a , say G to D, and you switch the notes around, you get a perfect 4th. 

The other way to interpret is that they are the . Let’s take the same example. We know that the inversion of a is a perfect 4th. If I want to go up by fifths starting at G, I get G, D, A, etc. What if I want to go down by perfect 5ths? Based on the inversion, going down by perfect fifths is the same thing as going up by perfect 4ths. So, I get G, C, F, etc. 

Compound Intervals 

Compound intervals are intervals that span more than one octave. In music, we sometimes have very big intervals, but saying that two notes are a 24th apart is not as meaningful as saying that two notes are 3 octaves and a 3rd apart. The 3rd creates the unique sound of the interval – moving a note up or down an octave doesn’t really matter too much in terms of interpreting , , and interval quality. 

Here are a few compound intervals:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3Ivt6vnO1xxt.png?alt=media&token=53d19529-27a0-4621-b212-09de7ed3eadf

Why is a 24th three octaves and a 3rd and not just 3 octaves? One octave is 8 notes, right? To answer this question, try considering an octave and a 1st. That’s still just an octave, since a P1 is a . So, a 9th is actually an octave and a 2nd. 

This happens every time you add an octave. You might want to remember that P1 is a , and the octaves are 1 + 7n, where n > 0. An 8th, 15th, 22nd, 29th, etc. are all perfect octaves. From there, you can figure out the compound interval by subtracting your interval from the largest possible octave and adding 1. For example, a 13th is an octave plus a 6th. You might also refer to this as a “compound 6th.” 

The interval quality stays the same when you compound intervals. If you have a minor 13th, it will be a , and if you have a Major 13th, you have a

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-EXAkGTdR0Yd9.png?alt=media&token=21c9d569-949b-4270-adde-d26036803433

🦜 Polly wants a progress tracker: Can you identify the interval that spans from an F# to the B an octave above? What about a G that reaches to the Db two octaves above?

Answers:

  • augmented 5th

  • minor 3rd

  • perfect 4th

  • diminished 5th

Key Terms to Review (17)

Augmented 4th

: An augmented 4th is an interval that spans four letter names but eight half steps. It creates tension due to its dissonant nature.

Compound Major 6th

: A compound major 6th is an interval that spans nine semitones or twelve half steps. It consists of two major 6ths stacked on top of each other.

Compound Minor 6th

: A compound minor 6th refers to an interval larger than an octave plus a minor 6th. It consists of more than twelve letter names plus one additional note.

Consonance

: Consonance refers to harmonious sounds that are pleasing and stable. It occurs when two or more pitches played together sound agreeable and resolved.

Descending Intervals

: Descending intervals are musical intervals that move from a higher pitch to a lower pitch. They can be identified by the distance between two notes in terms of steps or half steps.

Diminished 4th

: A diminished 4th is an interval that spans four half steps. It is also known as a tritone, and it creates a dissonant and tense sound.

Dissonance

: Dissonance refers to the combination of musical notes that sound tense, unstable, or harsh when played together. It creates a sense of tension and usually resolves to a more stable and consonant sound.

Interval Inversions

: Interval inversions refer to the process of flipping the order of notes within an interval. For example, if a C to E is a major third, its inversion would be an E to C, which is a minor sixth.

Major 2nd

: A major 2nd is an interval consisting of two adjacent notes with one whole step (two half steps) between them.

Major 6th

: A major 6th is an interval that spans nine half steps. It has a bright and uplifting sound, often associated with happiness or triumph.

Major Third

: A major third is an interval that spans three letter names and four half steps. It has a bright, happy, and uplifting sound.

Minor 7th

: A minor 7th is a musical interval that spans 10 half steps or semitones. It consists of a root note and the note seven half steps above it, flattened by one half step.

Minor Sixth

: A minor sixth is an interval that spans six letter names but eight half steps. It has a somewhat dark or mysterious quality to its sound.

Octave plus a 2nd (9th)

: An octave plus a 2nd, also known as a 9th, refers to an interval consisting of eight letter names plus one additional note. For example, C to D is an octave plus a 2nd because there are eight letter names (C, D, E, F, G, A, B, C) and one additional note (D).

Perfect 5th

: A perfect 5th is a musical interval that spans seven half steps or semitones. It consists of five whole tones plus one additional half step.

Perfect Fourth

: A perfect fourth is an interval that spans four letter names and five half steps. It is considered consonant and has a strong, stable sound.

Perfect Unison

: A perfect unison refers to two notes that are played or sung at the same pitch. It is the smallest interval in Western music.

2.6 Interval Inversion and Compound Intervals

4 min readjanuary 3, 2023

Mickey Hansen

Mickey Hansen

Mickey Hansen

Mickey Hansen

Now that we have a basic understanding of interval size and quality, let’s learn some skills that will later help us use intervals to construct chord progressions and interpret harmonies. In this section, we will go over and compound intervals. 

Interval Inversions

When we talk about intervals, we are always talking about ascending intervals. For example, a C to an E is a Major 3rd. But what about an E to a C? Sure, we could figure out by looking at the notes that an E to a C is a minor 6th. What interval would a descending minor 3rd be? There must be some relation between a descending interval and an ascending interval.

Interval inversion is the process of taking an interval (the distance between two pitches) and flipping it upside down!

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-DdD0OYQVBXZJ.gif?alt=media&token=d30fae3a-c8a6-437e-9337-9481d1b7ea69

For example, the inversion of a perfect fifth (an interval consisting of seven half steps) is a (an interval consisting of five half steps). The inversion of a (an interval consisting of four half steps) is a (an interval consisting of eight half steps).

All you have to do to invert an interval is subtract the interval by 9, and then give the inverted interval the opposite quality as the original interval. For example, the inversion of an A5 would be a d4, and the inversion of an M3 would be a m6. The inversions of perfect intervals are also perfect. 

Here's an example of a (F-A) being inverted:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-W1We4BYW7Quz.png?alt=media&token=4448de38-091c-4344-b33c-81304fd48b42

Let's look at a few more examples of inversions on a staff:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-HhF5ZorWrhSz.png?alt=media&token=aef0ac58-52ae-4105-9bbb-da89703b373c

Your turn! Practice inverting these intervals by using the tricks above (answers at the end of the chapter):

There are two ways to interpret an interval inversion. First is that if you have two notes that are some interval apart, switching around those two notes gives the interval inversion. A common example that you should remember is the P5 and P4 inversions. If you have a , say G to D, and you switch the notes around, you get a perfect 4th. 

The other way to interpret is that they are the . Let’s take the same example. We know that the inversion of a is a perfect 4th. If I want to go up by fifths starting at G, I get G, D, A, etc. What if I want to go down by perfect 5ths? Based on the inversion, going down by perfect fifths is the same thing as going up by perfect 4ths. So, I get G, C, F, etc. 

Compound Intervals 

Compound intervals are intervals that span more than one octave. In music, we sometimes have very big intervals, but saying that two notes are a 24th apart is not as meaningful as saying that two notes are 3 octaves and a 3rd apart. The 3rd creates the unique sound of the interval – moving a note up or down an octave doesn’t really matter too much in terms of interpreting , , and interval quality. 

Here are a few compound intervals:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3Ivt6vnO1xxt.png?alt=media&token=53d19529-27a0-4621-b212-09de7ed3eadf

Why is a 24th three octaves and a 3rd and not just 3 octaves? One octave is 8 notes, right? To answer this question, try considering an octave and a 1st. That’s still just an octave, since a P1 is a . So, a 9th is actually an octave and a 2nd. 

This happens every time you add an octave. You might want to remember that P1 is a , and the octaves are 1 + 7n, where n > 0. An 8th, 15th, 22nd, 29th, etc. are all perfect octaves. From there, you can figure out the compound interval by subtracting your interval from the largest possible octave and adding 1. For example, a 13th is an octave plus a 6th. You might also refer to this as a “compound 6th.” 

The interval quality stays the same when you compound intervals. If you have a minor 13th, it will be a , and if you have a Major 13th, you have a

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-EXAkGTdR0Yd9.png?alt=media&token=21c9d569-949b-4270-adde-d26036803433

🦜 Polly wants a progress tracker: Can you identify the interval that spans from an F# to the B an octave above? What about a G that reaches to the Db two octaves above?

Answers:

  • augmented 5th

  • minor 3rd

  • perfect 4th

  • diminished 5th

Key Terms to Review (17)

Augmented 4th

: An augmented 4th is an interval that spans four letter names but eight half steps. It creates tension due to its dissonant nature.

Compound Major 6th

: A compound major 6th is an interval that spans nine semitones or twelve half steps. It consists of two major 6ths stacked on top of each other.

Compound Minor 6th

: A compound minor 6th refers to an interval larger than an octave plus a minor 6th. It consists of more than twelve letter names plus one additional note.

Consonance

: Consonance refers to harmonious sounds that are pleasing and stable. It occurs when two or more pitches played together sound agreeable and resolved.

Descending Intervals

: Descending intervals are musical intervals that move from a higher pitch to a lower pitch. They can be identified by the distance between two notes in terms of steps or half steps.

Diminished 4th

: A diminished 4th is an interval that spans four half steps. It is also known as a tritone, and it creates a dissonant and tense sound.

Dissonance

: Dissonance refers to the combination of musical notes that sound tense, unstable, or harsh when played together. It creates a sense of tension and usually resolves to a more stable and consonant sound.

Interval Inversions

: Interval inversions refer to the process of flipping the order of notes within an interval. For example, if a C to E is a major third, its inversion would be an E to C, which is a minor sixth.

Major 2nd

: A major 2nd is an interval consisting of two adjacent notes with one whole step (two half steps) between them.

Major 6th

: A major 6th is an interval that spans nine half steps. It has a bright and uplifting sound, often associated with happiness or triumph.

Major Third

: A major third is an interval that spans three letter names and four half steps. It has a bright, happy, and uplifting sound.

Minor 7th

: A minor 7th is a musical interval that spans 10 half steps or semitones. It consists of a root note and the note seven half steps above it, flattened by one half step.

Minor Sixth

: A minor sixth is an interval that spans six letter names but eight half steps. It has a somewhat dark or mysterious quality to its sound.

Octave plus a 2nd (9th)

: An octave plus a 2nd, also known as a 9th, refers to an interval consisting of eight letter names plus one additional note. For example, C to D is an octave plus a 2nd because there are eight letter names (C, D, E, F, G, A, B, C) and one additional note (D).

Perfect 5th

: A perfect 5th is a musical interval that spans seven half steps or semitones. It consists of five whole tones plus one additional half step.

Perfect Fourth

: A perfect fourth is an interval that spans four letter names and five half steps. It is considered consonant and has a strong, stable sound.

Perfect Unison

: A perfect unison refers to two notes that are played or sung at the same pitch. It is the smallest interval in Western music.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.