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2.6 Interval Inversion and Compound Intervals

#inversions

#intervals

#compound-intervals

#harmony

โฑ๏ธย ย 3 min read

written by

Mickey Hansen

mickey hansen

Caroline Koffke

caroline koffke

(editor)

November 2, 2020


2.6: Interval Inversion and Compound Intervals

Now that we know what intervals are and understand how they work, let's switch things up and try inverting some intervals! ๐Ÿฅณ Wait...but what does that mean? In simple terms, interval inversion is basically just an interval that has been flipped 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

To invert an interval, the lower of the two notes is moved up an octave so that it is above the former top note. Or vice versa, take the upper note and bump it down an octave, then it'll be below the former lower note.

Here's an example of a major third (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

Notice how we now have a new interval? By applying the interval identification skills you learned in the last chapter, you can tell that this interval must be a minor sixth because it spans 6 lines and spaces, and 8 semitones! However, this isn't the only way to reach this conclusion, and it is not the quickest either. There are a few rules of interval inversion that you can follow to determine the inversion more efficiently.

The Rules of Interval Inversion ๐Ÿ™ƒ:

โžก๏ธthe two interval sizes will add up to nine (eg. a major 3rd inverts to a minor 6th, 3+6=9)

โžก๏ธmajor intervals invert to minor intervals, and vice versa

โžก๏ธaugmented intervals invert to diminished intervals, and vice versa

โžก๏ธperfect intervals invert to perfect intervals

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):

  • diminished 4th

  • major 6th

  • minor 7th

  • perfect 5th

  • major 2nd

  • augmented 4th

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-0PLZfA9XElkT.gif?alt=media&token=6af917b7-c9c5-482e-826e-330cb02901dc

Next up: Compound Intervals!

So far we have learned about simple intervals, which are intervals within an octave. But now we are going to venture past the octave and dive into compound intervals. These are the intervals that are larger than an octave.

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

Compound intervals can be a bit tricky to identify because it's difficult to quickly recognize or count them. Instead we can break them into octaves and simple intervals so that they are much easier to handle.

Let's take the perfect 13th in the example above and go through the process of identification together.

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

This diagram displays the process of identification step-by-step. Firstly we need to divide the interval at the octave, which in this case is the D. We can now see that this compound interval is made up of an octave (D-D) and a perfect 5th (D-A). The value of these intervals are then added together to find the size of the compound interval (8+5=13). And finally, the quality of this interval is determined by the quality of the simple interval. So the 13th must be a perfect 13th!

๐Ÿฆœ 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

  • major 2nd

  • perfect 4th

  • minor 7th

  • diminished 5th

continue learning

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