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​The Circle of ALL the Intervals​

​The Circle of Fifths is one of the most popular elements in music theory. If you do a google search about that exact keyword, you get around 8,180,000 results. So, without any doubt, it's essential, and as a music creator, you should know about it! It shows many connections in the Diatonic world, and a lot of pages give you some necessary information about that. Still, you probably won't find any sufficient information about how the Circle of Fifths applies to the intervals in general. You know by now that our approach to writing music is efficient, so let's jump right into this topic and see what secrets we can extract by looking for all the intervals on the Circle of Fifths.

The Circle of Fifths (or Circle of Fourths) is an essential building block in Western music theory and even Western culture. It organizes the twelve tones, key signatures, the most common chord progressions, and even connects to the seven Church modes and the Harmonic series. But it's also very precious in the world of Interval Theory. This perspective doesn't get any attention from a traditional point of view as it leaves the Diatonic system. Still, there are so many secrets to unlock, as you'll find out in this article.


​Relevancy in Western Music

​The Circle of Fifths or the Root Cycle 5 (RC5) is an excellent and most universal tool that holds Western music together. In Interval Theory, we refer to it as the RC5, in which the 5 represents the number of chromatic steps or half steps between two adjacent tones.

It was during the Baroque era (at around 1650) when the composers understood how the RC5 connects to all kinds of different tonal centers. As a result, modulation became quite popular. If you want to learn more about tonal centers or how to move elegantly through various tonal centers via dominant intervals, we've already discussed these subjects in dedicated articles.

​Before we dive into the individual circles of the intervals, here's a quick illustration that shows some of the connections of the Circle of Fifths to other parts of music theory.

​Since then, the Circle of Fifths almost works as a synonym for the Diatonic system. All the Folk music in Western culture, including lullabies or Christmas carols, is derived from it. Even whole musical genres, just like Blues, Jazz, Classic Rock, or Pop, originated by following the step-wise movement on that element.

It just sounds familiar to our ears, and we are used to listening to those progressions and harmonies, it's a beautiful musical language. But you know all of this already so, let's switch to Interval Theory and find out more about those intervallic secrets and how they can brighten up and color the concepts of composition.


The Circle of the Intervals

​In Interval Theory, we use chromatic steps or half steps as our grid to explain the distances between two notes (horizontally and vertically). The RC5 is an excellent starting point for further explorations as it covers all of the 12 tones available to us! ​We can start all the various cycles on any note. However, we are going to stick to the C as our starting point throughout all the examples.

​If we move step-wise through the RC5, we end up with authentic or plagal cadences, depending on the direction we go. We already showed the application of these cadences and how they work in composition, so let's move on to the next interval.


​The Root Cycle 2

If we skipped every other step, we just created what we call the RC2, depending on the direction, it becomes either an ascending or a descending movement. Please note that "2" describes the chromatic distance between all tones involved and not the steps on the Circle of Fifths!

​We've just created the whole-tone scale, and in composition, this scale very often won't be the first choice because of the following two reasons.

  1. ​You can't reinforce your tonal center via authentic or plagal cadences as there are no perfect Diatonic fifths (that's a 7) or perfect fourths (that's a 5) available on that scale. That gives you some harmonic problems that will need your attention as every possible tone in that succession of notes can act as a tonic.
  2. As there are no half-steps available, there are no leading tones for melody. You can't define melodic rest points, and therefore, your line will seem to go nowhere, which is not satisfying for the listener.

But still, we can use this sequence of tones very elegantly in composition. Below, you see an example of line-writing that goes through the RC2 descending as temporary tonal centers.

Let's switch gears a bit.

When we think of harmony based on the RC2, we actually get very close to Bitonality. The first three notes define one tonal center, and the remaining tones describe a second tonal center. It's almost like playing two major thirds with an added scale tone 2. And those major thirds are exactly 6 chromatic steps apart from each other, see it?

Just for the sake of bringing in a bit more vertical complexity, it can also be a C dominant 9th against a Gb dominant 9th. All of these tones come from the whole-tone scale. We even could have added scale tone -5.

​You see that the RC2 can guide us towards some advanced concepts of music theory, but let's stay practical and straightforward for now.

It won't often happen that you come across a composition that is mainly written on an RC2 as the whole-tone scale sounds a bit too exotic for most people, but temporarily, you can go in and out of it for a few steps, and you won't create any musical problems.

But you can construct little musical building blocks that come out of the RC2. You can insert those blocks quickly in your sketches and combine them with other elements vertically. This will give you some exciting sounds and colors.

Another great application of this scale is to write runs. Most composers rely on the usual 7-tone scales, but this 6-tone scale creates an exciting flavor. The video below shows an excerpt from the piece "Into the Abyss", which is part of the Composition Course (Lesson 41). Please pay attention to this short moment when the run shows up. It's a quick transition, but still, every moment you can add these small nuances to a composition will help to make it stand out better from the pack. So, don't underestimate the power of accumulation.


​The Root Cycle 3

​Next, let's go to every third step on the Circle of Fifths, and you'll see that we create a distance of three chromatic steps between all the tones.

Even if you are not familiar with concepts of Polytonality, please remember that the RC3 and the Octatonic scale belong strongly together. When we bring up this 8-tone-scale, we deal with four possible root tones, which are totally equal. Those root tones fall precisely on the RC3, and they work perfectly in composition. ​

​Below, there's a little piano exercise that let your fingers move through the Octatonic scale while switching through the various roots in the bass.

Just by listening to the polytonal sound and the various root tones involved, you instantly hear the exotic flavor. However, it also sounds familiar to our ears, and here is why:

​The vertical structures that we use in Polytonality are actually not complex. It's all about major triads, minor triads, and pure dominant structures on each tonal center. What makes it sound sophisticated, though, is the combination of sound.

​We'll go deeper into those polytonal concepts in other materials. For now, let's come back to the Circle of Fifths and how it suggests we use the various intervals. But if you are a piano player, then these types of fingering exercises are very beneficial to your performing skills. And because we want you to have this exercise available at all times, don't miss to download the PDF of the complete full training right now!

​Get full access to the PDF of this piano exercise. This is perfect training for piano players and gives a good insight into how you can use the various root tones of the Octatonic scale.


​The Root Cycle 4

​You know the method by now. Let's go to every fourth step and have a look at the tones that we end up with.

​When we play those notes in succession, we only get three different tones, which give the impression of an augmented triad. Actually, this 4+4 connects to many different musical places, such as Minor Major 7ths or even 9ths, Equivalents, Chromatic Harmony, Polytonality again.

We also refer to this structure as a Portal, which is very helpful and versatile in composition. Using Portals, you will be able to control the chromatic movement of your lines, modulate elegantly to new tonal centers or simply add more flavor and color to common chord progressions.

​​If you are curious about how YOU can benefit from using Portals in your writing, then we invite you to have a look at our "Portals workshop". It's a 5-day video training that teaches you all the secrets of this technique.

​But in addition to a 4+4, the RC4 also works excellently in composition, especially when you set up the tonal centers via Secondary Dominants. Please have a more in-depth look at our interval analysis of "Giant Steps" by John Coltrane, and you'll realize that he based the whole tune on an RC4.

​Behind many complex artistic works, you'll start seeing simple patterns that hold everything together. That's why we dwell a little bit on why you should have a process for writing music as your starting point. Feel free to leave or alter the formula at any time, but make sure that you don't turn to random actions. You won't be able to build your career on randomness (or luck).


The Root Cycle 6

​The RC6 is unique in that it doesn't have a direction. It splits the Circle of Fifths in half, and the distance between the two tones involved always remains six chromatic steps, no matter the direction.

​The most apparent use case for this RC is what the Diatonic system calls "Tritone Substitution", but it connects to many more musical options.

The first thing you should keep in mind is that we've got some freedom with voice-leading as the distance between the tones always remains six, no matter the direction. In other words, the RC6 has no Harmonic Weight, and we can decide by ear which type of voice-leading we want to use (regular or substitute).

​Now that we know some of the properties of the other RCs already, we can connect the RC6 to Polytonality very easily. It's quite apparent that it lines up perfectly with some of the other RCs, which live in the polytonal world. Hence, all of their characteristics apply to the RC6 as well.

​Also, the RC6 appeared quite prominently when we discussed the Dominant Intervals and their behavior. This all will give you a lot of inspiration on how you can use this RC in your writing to spice up some changes.


​Root Cycle 1

We've made it to the last RC, the RC1. And this one really brings us back to where we started this journey, that's the Circle of Fifths, and here's how they are connected.

​The RC5 and the RC1 are the only cycles that go through all of the 12 tones available to us!

​If you are a member of our Academy, you probably heard me say, "Everybody can follow a chromatic line!" already. Chromatic lines are not only easy to listen to but also very powerful and even inspirational in composition. We'll come across those lines quite often in other materials and go way deeper into how you can use them.

​Right now, we just want to hint their power by showing you an excerpt from our e-book "Root Cycles I", which is available to all members inside the membership. This will give you a more precise picture of how musical they can sound.

We will come back to this e-book in a minute and show you a musical demonstration that was written using only the various Root Cycles that we've discussed in this article. 


​Why is there no RC7 to RC11?

By going through the RCs 1 to 6, we've covered all possible movements between two root tones. Let me explain. When we talk about roots and their progressions, we always refer to the shortest distance between two adjacent notes.

Here's an example: From C to E can be 4 chromatic steps up or 8 down. Both movements are perfectly fine, but why do we refer to this movement being an RC4 ascending and not an RC8 descending?

​The shortest distance sets the direction of the Harmonic Weight between two neighboring root tones. The physical movement does not represent the Harmonic Weight!

​We want to know the direction of the Harmonic Weight because it tells us how to apply voice-leading in Interval Theory. For that reason, you should focus on the RCs 1 to 5 and their attached direction; that's the Harmonic Weight and all you need to know to use proper voice-leading.


​What about unequal Root Progressions?

Most of the time, we will write root progressions that bring in all the various intervals. We encourage you to look at a root progression as a combination of little fragments of the RCs explained above. It's just a matter of where do you enter and where do you leave.

​This way of thinking provides a fresh perspective that lets you create tonal centers on the fly, modulations that are interesting to listen to, or even polytonal structures. Using a musical key would limit your choice of notes automatically to seven, and you will have to make some efforts to find your way out of that cage first before defining a new one. And still, chances are very high that the music that comes out of that will sound very common and ordinary.

And if you want to create a Diatonic sound, you can always start in a key and analyze the distances in half steps later to determine the closest distance and the direction of the movement. We don't want you to unlearn anything but to enhance your existing knowledge with Interval Theory!


​Showing the RCs in Action

If you made it to this point in the article, you know more about how the intervals relate to the Circle of Fifths than somebody who graduated from music university! :)

But let's shift the focus to the application and see how we can use that knowledge to write some orchestral music! In the video below, we are showing another excerpt from the "Root Cycles I" e-book materials that demonstrates the creative process of putting the RCs into actual music.

Please enjoy this presentation of the orchestral piece named "Torn Sky".

​As you can tell from the video, the gathering follows simple steps, and those gathered building blocks make up almost the whole sketch. However, the final result sounds very sophisticated and exciting. That's one of the main advantages which come with Interval Theory. The shift of the perspective opens up many new musical doors that (probably) would have stayed hidden from a Diatonic-point of view, even for an experienced composer.


Summary

​Now you hopefully agree that it's not just the Circle of Fifths but really the Circle of ALL the Intervals! It can be quite fascinating and freeing at the same time to realize that all of these sounds and combinations of sounds are available right in front of us - all the time.

Here's a quick list of the main takeaways from this article.

  • ​The Circle of Fifths is highly relevant to the Diatonic system and Western Culture
  • ​The RC5 and 1 are the only ones that go through all twelve tones available to us
  • ​The RC2 seems a bit rough to use but connects smoothly to Bitonality
  • ​The RC3 shows all the various roots of the Octatonic scale, and therefore, works nicely in Polytonality
  • ​The RC4 connects to Portals and opens up the door to chromatic harmony
  • All the RCs have a direction, and it's either ascending or descending. The RC6 has no direction
  • The RCs 1 to 6 cover all possible root movements and show the direction of the Harmonic Weight which is important for voice-leading
  • Root progressions consist of combined Root Cycle fragments

​Advice

​Although the various Root Cycles are straightforward in their construction, they can provide an infinite source of inspiration for the composer. Be creative and combine smaller fragments from the different cycles into longer progressions and let your ear decide whether or not you like the sound of it.


Frank Herrlinger​

Co-founder and instructor at Music Interval Theory Academy