What Is The Music Theory RULE OF 9? | Q + A

The Rule Of 9 For Inverting Intervals

Tommaso Zillio

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nine rule interval inversion

One thing that many guitar students find very confusing is intervals. Especially the topic of inverting intervals.

That is: “If a C to an A is a major sixth, then how the %!@# A to C is a minor third? Why does everything change if we turn the notes around?!?”

Well, I hope to be able to clear some of that up for you right now :-)

First of all, if you don’t know what an “interval” is or what “inversion” means, then scroll down to the second video on this page and watch it right now.

Otherwise, keep reading:

The Rule of 9

What I want to share with you here is the “theory trick” to invert an interval. That is: when we invert an interval, how do we go (for instance) from a major 6th to a minor 3rd?

Easy. Just remember these two “rules” to invert any interval:

  1. To get the “number” part, subtract from 9. That is: to invert a 6th, do 9-6 = 3 (a 6th inverts to a 3rd). To invert a 5th, do 9-5 = 4 (a 5th inverts to a 4th)

  2. Major becomes minor and vice versa. Perfect stay perfect. Augmented becomes diminished and vice versa.


  • A major 6th becomes a minor 3rd…
  • …while a minor 6th becomes a major 3rd.
  • A perfect 5th becomes a perfect 4th.
  • A diminished 5th becomes an augmented 4th.

At this point, {subtag:name|part:first|ucfirst}, you may say: “Ok, Tommaso, but if you give away the trick here in the email, then why should I watch the video that you will undoubtedly link below?”

Well, first of all, I’m expecting people would like to have more details on this explanation, and those are in the videos :-)

But hey, you may have a point here! Curse my mission of informing people. I should have written just some clickbait here and left the real answer for the video!

Or should I?

Because you see, the question that prompted me to record the video below (and the question that you probably still have right now) is NOT “How do you invert intervals?”.

The question is: “Why 9? Where does the 9 come from?”

(Is it because there are 9 planets in the solar system? But they are 9 only if you count Pluto. But Pluto isn’t even a planet! And what do planets have to do with music??)

And THAT, my dear reader, is what I’m answering in the video below:

In this video, we also talk about:

  • Seeing the fretboard as 6 pianos
  • Appreciating Classical Music
  • The #BeardofKnowledge
  • And more!

Confused By Intervals?

Now, if you are confused by intervals, that is:

  • You don’t know what an interval is
  • You don’t know what an inversion is
  • You have an idea what intervals are, but they make no sense to you

Then here’s a video that explains them clearly from the very beginning:

Of course, music theory does not stop at intervals. Indeed, intervals by themselves are not that useful! But if you use intervals to build chords, then you can start evoking any kind of emotion in your music.

To become a master of emotions using chords and chord progressions, check out the Complete Chord Mastery guitar course

Video Transcription

Hello, internet, So nice to see you! Today I’m going to answer a lot more of your questions.

Visualize the fretboard as pianos stacked on top of each other.

Wait, what? Are you serious? It’s not a joke. You know what? This idea of visualizing all the strings as piano, to me is completely backward, honestly, because I get that for a piano player, The piano is more intuitive because it’s linear. But guys, those are strings. The string is an actual line, it’s more linear. If anything, I will tell you visualize the piano as a string.

Okay, I would go completely the opposite. But I mean, if you find that visualizing the six strings as six different pianos, okay, one on top of each other, shifted by a fourth or whatever, it’s easier for you, I mean, more power to you. But I think it’s making it too complex. Okay, every string is really intuitive. Every time you go up a fret, you go up a half step in pitch.

This is simpler than a piano because the piano has all the black and white keys, etc, etc. This is way more linear.

I think I think we should do the opposite.

Why do you subtract nine?

This is a question on how to invert interval. Okay. So whenever we have an interval, and you change the order of the note, the notes, the interval changes.

So for instance, if I have a third, a major third, so from C to E, okay, C to E. It’s a major third. These if I play the C lower and the E higher, but if I play the E lower and the C higher, okay, always in the same octave, this interval is sixth, not a third anymore.

So E, then C. C higher, is an interval of a sixth, but C lower and E higher, it’s an interval of a third, okay. Kind of a formal thing, okay. But it’s important to know those intervals because later they become important, and they help you make music.

Why do I subtract nine? Well, and here’s the answer that sounds like a joke at the beginning, because a third plus a six is an octave, which means eight. Right? Sounds like a joke, right?

But that’s the thing in the strange way, we have to count the intervals. And we are counting the beginning note and the end note. So for instance, in the scale, C to E is a third because it contains the notes C, D, and E. In between C and E there are C, D and E notes. So it’s a third because there are three notes. While E to C, it’s E, F, G, A, B, C, there are six notes.

Now, in theory, we should have eight notes from C to C, but we are counting the E twice because of this strange way of counting the intervals. So whenever you invert an interval, the two interval sum to the number nine, which, or a musician will say they sum to an octave.

I know it’s confusing, I didn’t make the system, the nine, subtract from nine. It’s a mnemonic way that it’s easy to remember. And it works every time. When you invert an interval, subtract the number from nine, a fifth becomes a fourth, a second becomes a seven, a third becomes a six, and vice versa.

The only few people I know who play guitar and also appreciate music theory in the classical genre. A lot of the modern day musicians I know just disregard the classical genre and think of all of them to be boring as if they were all beginner level Mozart esque music.

Well, let’s say that the answer is yes, no, and maybe it depends who you ask. Okay. I consider myself a modern musician. I don’t play much classical music. But I really love theory, and I know a lot of people who are exactly the same and they do appreciate classical music.

I mean, just because I don’t play classical music doesn’t mean I don’t listen to classical music. Okay, or I cannot appreciate it.

What I see is that there are definitely some specific groups or cliques of people were people who listen only to classical music or listen only to Jazz, people who listen only to extreme death metal. People who listen only to the free jazz, English free jazz punk. Okay, or stuff like that.

I like all music. I know a lot of people who like all music. I don’t know if it’s really true. That modern musicians don’t appreciate theory. It’s true that many modern players, many non-professional modern players want to be able to play everything immediately without going through theory.

It is true that if you go on Facebook or Twitter or places like that right now, it’s full of teachers telling you that you don’t have to learn theory. That is true. It’s unfortunate because you have to learn theory. I’m sorry, the but it’s a great clickbait today to say you don’t have to learn theory. So I agree with you on that. But I think as several modern musician making great music that like the theory, they’re really competent in that and they’re using it to make great music

Only with a very interesting and well explained content is it possible to bear such an awful English. The concepts learned are worth the tremendous effort for the ear, thanks.

The backhanded compliment. only the most clever can pull this off successfully.

Hashtag beard of knowledge.

That’s because at the beginning of times, I make a vow. And I said I will never shave. Until I can explain music theory to all the world and also actually I actually like the beard, so I’m gonna keep it anyway.

I can’t begin to tell you how much you’ve changed my playing over the past few months since I started watching your videos. Thank you so much.

Well, thank you. I really love this kind of feedback. And I think you mentioned a very important thing here, is that it took some time. Okay, so here’s the thing, guys, you’re gonna watch this video. Sometimes you understand the everything I say in this video. Sometimes you don’t. And sometimes it takes a little bit of practice.

The important thing is do one small thing every day, keep practicing those things. If you need help, I have courses, I can help you further. Just send me an email and we can find what works for you. Otherwise, just keep watching the free videos on my channel. There’s nothing wrong in that. I mean, I’m putting them out as free videos because I want you guys to watch them. So no problem either way. The important point is stick to it. Give it a little bit of time. It takes time to get better, but then you do get better. Okay, so keep practicing and kudos for your improvement.

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