I understand how interval inversions add up to 9. (up a 3rd, down a 6th etc...) Now suppose I take the interval of F to A and then find the inversion of a descending 6th to the A below. (3+6=9)

Here's where my confusion lies. I also have heard that an inversion is simply in the opposite direction of the original interval. So a descending 3rd from F to D is the inversion of ascending third F to A.

Now let's take that D and throw it on top of the initial pitch F. Now we have another interval of an ascending 6th. Is that ascending 6th from F to D another type of inversion which could be related to our ascending interval of F to A? Or am I just making this more difficult than it really is?

  • This questions seems very unclear. What is a descending interval? You always count intervals from the lowest note up.
    – Neil Meyer
    Commented Jun 8, 2016 at 19:03
  • 7
    @NeilMeyer intervals are described as descending all the time especially in melodies. For example if in a melody you were singing you went down from a E to a C you would be descending by a Major third.
    – Dom
    Commented Jun 8, 2016 at 19:36

5 Answers 5


The confusion lies here:

I also have heard that an inversion is simply in the opposite direction of the original interval. So a descending 3rd from F to D is the inversion of ascending third F to A.

This should instead read "a descending third from F to D is the inversion of an ascending sixth from F to D." The problem really lies in the wording of that original sentence; something about it is misconstrued, it seems to me.

The one instance where an interval inverts to itself is the tritone, but even that's not exactly correct; an augmented fourth inverts to a diminished fifth, and vice-versa. Even though the pitches used are the same on the piano, the interval is technically different.

Edit: One way the original sentence makes sense is if the individual is thinking of the concept of inversion at its most general. Bach, as a textbook example, would occasionally "invert" motives and just move pitches in the opposite direction. Thus if a motive began with an ascending fifth, he would simply write a descending fifth.

But when we're talking about actual interval sizes—likes 3rds and 6ths—that original sentence is incorrect.

  • 1
    I think you got it with your edit. Inversion can have a different meaning in music that is concerned with manipulating sets of notes, see: Bach, 12 tone music/serialism, etc. Inverting a rising third means going down a third in that context.
    – bfootdav
    Commented Jun 8, 2016 at 23:05
  • Yep. Sorry for being unclear, but my question was answered! I was just confused as to how an interval can mean 2 slightly different things. Thanx a lot. And also thanx for your username compliment. 😃Any green in your blood? ☺ Commented Jun 10, 2016 at 6:48
  • @CavieVibes2003 Yep, 06-08.
    – Richard
    Commented Jun 10, 2016 at 7:48

The confusion here is natural, because the "inversion" of an interval, in classical harmony, does not mean the same interval in the other direction from a given note, but rather means to move the upper note down an octave, or the lower note up an octave. Thus, the "inversion" of the interval C up to E, which is a major third, is not C down to A flat, also a major third, but rather C down to E below it, which is a minor sixth. It's actually a pretty silly convention if you ask me.


Actually the inversion of a third will always be a sixth - not a third as posited in the title of your question. 3 + 6 = 9.

The inversion of a fifth will be a fourth 5 + 4 = 9. The inversion of a fourth will be a fifth 4 + 5 = 9 and so on.

An inversion of an interval (by definition) is simply flipping (inverting) the two notes comprising the interval so that the note on top is now on bottom and vice versa. It amounts to turning the interval upside down (inverting it).

One of the notes will always move by an octave which results in the two intervals adding up to contain 9 notes because each interval (the original and inversion of the original) contains both original notes (resulting in them being counted twice - once in each of two interval depictions).

In a true inversion, the notes will always be the same - only the order will change.

The picture below shows how to create an inversion of an interval by moving one of the notes up an octave.

enter image description here

Similarly you can invert the opposite way by moving the highest note an octave lower. But the two notes will be the same and the interval value will change so that the two will add up to nine.

It is certainly valid to define a descending third as an interval of a third and an ascending third an interval of a third. They are just not technically considered true "inversions" in accordance with the understanding of that term in music teaching.


You are making it slightly more difficult. Don't forget that inverted intervals change name, too. Thus, C to E is a major 3rd, whilst E to C is a minor 6th. Yes, the 'rule of nine' applies, but the interval becomes the opposite. Take C to Eb, it's a minor 3rd; invert it, Eb to C, and it's major 6th. C to G# is aug.5th, while G# to C is dim.4th.

We generally count and call intervals from the lower note, as it's easier to see. BUT - your concept of taking an interval of whatever, and using the same interval backwards is a misconception. As in - C to E (maj.3rd), a backwards maj.3rd would be Ab to C. Inversion is using the SAME TWO NOTES, and naming them as intervals counted from the bottom, for simplicity. So C to E AND Ab to C ARE both maj.3rds. No inversion in sight.


I think you are mixing up several different concepts, all called "inversion".

https://en.wikipedia.org/wiki/Inversion_(music) gives a short explanation of the difference between

  • inverted intervals
  • inverted melodies
  • inverted voices (in counterpoint)
  • inverted chords (in common practice harmony)

Some of these concepts might be better described as "reflection" (i.e. "reading the score viewed in a mirror"), but even then, the "mirror" could be either horizontal, changing the relative pitch of the notes, or vertical, reversing the order of the notes in time.

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