Interval Inversion and Compound Intervals

Interval Inversion and Compound Intervals: AP Music Theory Study Guide

Get ready to dive into the world of music theory as we explore interval inversions and compound intervals. In this guide, we’ll flip intervals upside down (like a musical acrobat!) and stretch them out to cover multiple octaves. Let’s make these musical concepts as clear (and fun) as a day at the opera!

When we talk about intervals, we typically mean ascending intervals. So, from C up to E is a Major 3rd, but what happens if we flip it and go from E down to C? Spoiler alert: it’s not the same interval! This flipping process is called an interval inversion.

Here’s how it works:

For example, if we take a perfect fifth (which spans seven half steps) and flip it, we get a perfect fourth (an interval with five half steps). Likewise, a major third (four half steps) becomes a minor sixth (eight half steps) when inverted.

To invert any interval, subtract the interval number from 9 and flip its quality. So, an A5 (augmented fifth) inverts to a d4 (diminished fourth), and an M3 (major third) inverts to an m6 (minor sixth). Perfect intervals simply stay perfect because they’re just that awesome (they’re the superheroes of intervals 🦸‍♂️).

Let's take another example. The inversion of a Major 3rd like F to A (F-A) results in a minor 6th (A-F).

Try it for yourself! Take these intervals and flip them using the tricks above (keys and answers are below):

• Diminished 4th
• Major 6th
• Minor 7th
• Perfect 5th
• Major 2nd
• Augmented 4th

Remember, there are two main interpretations of interval inversions:

1. Switch the notes around: A perfect 5th (G to D) flipped becomes a perfect 4th (D to G).
2. Descending intervals: If ascending a perfect 5th from G gets us to D, descending a perfect 5th from G would land us at C (which is an ascending perfect 4th).

Sometimes, musical intervals are so large they span more than one octave. These are compound intervals, and they sound just as grand as they look.

To explain why a 24th is three octaves plus a 3rd and not just three octaves (like adding 2 and 2 is always 4), think of an octave as including a "1st." So, a 9th is an octave plus a 2nd. This repeats for every added octave:

If you have a minor 13th, it’s an octave plus a minor 6th (we like to call this a "compound minor 6th"). The interval quality (major, minor, perfect, etc.) doesn’t change as you extend it beyond a single octave.

Let's stretch those intervals! Here are some examples:

• Why is a 24th three octaves and a 3rd? One octave is like a fancy musical elevator that goes eight floors (notes). So, you go up eight notes and add in a 1st. Hence, a 9th is actually an octave and a 2nd.

Question: Can you identify the interval from F# to the B an octave above? Answer: An augmented 5th.

Question: What about a G to the Db two octaves above? Answer: A minor 3rd.

• Augmented 4th: An interval that spans four letter names and eight half steps, creating more tension than your favorite thriller movie.
• Compound Major 6th: Goes beyond an octave to say, “I’m double the fun!”
• Consonance: Harmonious sounds that make your ears and soul high-five each other.
• Diminished 4th: Also known as a tritone, making it the musical cousin of “nails on a chalkboard.”
• Dissonance: Musical tension that begs for resolution – like the cliffhanger at the end of your binge-worthy TV show.
• Perfect 5th/Fourth/Unison: Intervals that scream stability and consonance. They’re the Avengers of intervals – reliable and strong!

So, whether you're flipping intervals upside down or stretching them into compound intervals, understand that these concepts are the building blocks of advanced harmony and musical expression. Take these tricks and turn your next composition into an orchestral masterpiece! 🎶

Now, go forth and conquer the world of music theory – one interval at a time. Rock on! 🎤🎷