The Two Octave Chromatic Scale

The basis of all scales and modes is the chromatic scale. Having all the intervals literally at your fingertips will help you to create the flavor of sound you’re looking for.

What Is The Deal With All Of These Numbers?!

When I was first learning scales, I would learn which notes to play. C Major was C, D, F, G, A, and B. G Major was G, A, B, C, D, E, F#. This continued for ten more scales. I quickly found myself frustrated and overwhelmed by the amount of memorization required. Eventually I came across some online resources that described the major scale by the numbered degrees 1, 2, 3, 4, 5, 6, and 7 no matter what notes were used. This was a revelation to me. It helped me to understand what I was playing relative to the first note in the scale. This helped until we started talking about modes. What is a b3? Where is the #11? How can a #4 be the same thing as a b5 and why are they called two different things? Frustration crept in once again.

Using numbered degrees of a scale made more sense to me, so I struck with it and began to learn two main points. The first is that all scales use portions of these numbered degrees, which are all shown in the above diagram. You can talk about Ionian, which is the same as the major scale, and use only natural degrees. This means you wouldn’t use any altered degrees that would make an interval sharp or flat. You could also talk about a scale like the Dorian mode, which is 1, 2, b3, 4, 5, 6, and b7. Using the altered degrees of b3 and b7 you can then compare it to Ionian to get a better sense of what Dorian is and how it functions. With this compare-and-contrast approach, you can take any scale/mode and alter one degree to learn how that one change effects your sound.

The other point is that once you extend these numbered degrees across two octaves, you can then see patterns extend further and see why certain degrees like #11 and b13 are used in specific modes or scales. A quick example would be to build a chord in alternating thirds.

Using a major third (2 whole steps) followed by a minor third (one and a half steps) and repeating is how we build a major chord, but what happens if we just keep building that chord? Starting from C we get C, E, G, B, D, F#, and A. These are the notes of the Lydian mode because it is Ionian with a #4 instead of a natural 4th degree. If you continue this pattern of alternating thirds you will add on Db, E, Ab, B, Eb, Gb, Bb, Db, and F which are notes of the Dorian mode starting at Db.

I stopped at F because at this point because we have used all twelve tones that are found in any octave. Yes, we had to go through 16 notes. And we did use several notes twice. We also used F# and called it Gb. The point is that building such a structure allows us to move through multiple sets of intervals that all treat these notes as different degrees. If you want to learn more about the above Lydian structure, then look up the Lydian Chromatic Concept. There’s a ton of material about George Russell’s Tonal Gravitational Concept out there along with a 257-page PDF found HERE.

I’ll cover some of Russell’s concept in another post. For now, l want you to view the above diagram that uses alternating thirds as the framework for a major chord. If you were to start on a minor third (like from E to G), then you also have the framework for a minor chord. The diagram above goes way beyond two octaves and is just an example of what building a chord in alternating thirds can do for you.

This is also an example of how you can use any interval from the chromatic scale in any chord. In the above diagram we started with C, E, G, and B for a CMaj7 chord. Way above that was Eb. This is the b3, which would make the chord minor. This sounds counterintuitive to play a chord that is major and minor, but it can work. Here’s an example of a CMaj7 with the note Ab from the third octave and the notes Eb, Gb, and Bb in the fourth octave. Listen for the flavor of the sound to change with some bright dissonance.

Putting It In Perspective

Above is a diagram of the key of C and its modes. You can think of the term “key” as meaning, “where Ionian starts,” so the key of C starts with C Ionian. By starting with Ionian, you can quickly find all the notes in your key by remembering one simple rule: degrees 1 and 4 do not have flats. Since Ionian is only the natural degrees, we can stop using whole steps and half steps and start counting degrees. Here’s how you can count this out in your head. Feel free to use the highlighted degrees in the above diagram for Ionian.

1 is C, skip b2, 2 is D, skip b3, 3 is E, there is no flat 4, 4 is F, skip b5, 5 is G, skip b6, 6 is A, skip b7, 7 is B, and return to 1. By knowing that there are flat degrees to skip, you can be aware of those degrees from the Chromatic Scale. You don’t always play them, but they are always available to you.

You may have noticed that I have a degree labeled #4/b5. This is because if you have a 4th degree, then you cannot have a #4. The same can be said for the 5th degree, so if you have a 5th degree then you can‘t use a b5 degree. Look at Lydian and Locrian. Lydian has a #4 and a 5th degree, so I’ve highlighted only the #4. Locrian has a 4th and b5 degree, so I’ve highlighted only the b5.

If you’re having a hard time memorizing the degrees of all seven modes, then check out my post on the modes. I have a way for you to learn the modes in fifths that really helped me to understand the modes by comparing them.

The First Octave And Naming The Degrees

The first diagram with the yellow highlights put all our modes in relative order. Relative means that you use the same notes across all your modes. Now I’ll display the modes in parallel, which means that the modes still have the same degrees, but each mode starts on the same note. Feel free to compare the yellow and green highlights so you can see how the modes retain their degrees.

Now we’ll put the chromatic scale to work. You always have a 1st degree because you must start somewhere when building chords and scales. Your starting point is never flat because this first degree is your anchor point to bult intervals from. The name for this degree depends on how you are using it. If you are using this as the first note in a chord, then it is your root note. If you are using this note as what you resolve to, then it is called the tonic. Here’s an example.

If you are playing Am, Dm, G, and C then you have Am with a root note of A, Dm with a root note of D, G major with a root note of G, and C major with a root note of C that happens to also be the tonic note since that is where this chord progression resolves to.

But what if you are talking about a melody? Maybe something that just uses notes A, F, G, and then D? Well, it depends on what you are resolving to in the end. If you are using the C Ionian scale and finish on a C chord, then a melody that ends on D is ending on the 2nd degree, which is called the super tonic. Super just mean above, so this is the degree that is above the tonic.

The other natural degrees also have names that have specific meanings. The 3rd degree is the mediant, which is the note that is between the tonic and the dominant. The 4th degree is the sub-dominant or pre-dominant. Either name works as it is the degree that leads into the dominant. The 5th degree is the dominant, which means that it leads back to the tonic with a strong, dominant, pull. The 6th degree is the sub-mediant. This time the term mediant still means between the tonic and dominant, but the term sub means below the tonic. The 7th degree is the leading tone because it literally leads you up (or down) to the tonic.

Looking at the first octave of the chromatic scale we have all those degrees, but we also have five flattened degrees. Let’s take a moment to cover those as well. The b2 is called the minor second or the Neapolitan. Minor second is the most common name but thinking of this as the Neapolitan can help you to remember that this degree has a special function outside of the standard use. Normally when you use a scale like C Phrygian you start with the chord Cm7 and follow that with DbMaj7. This DbMaj7 starts on the b2 degree of Phrygian, but if you play a major chord here like Db major then you are using a Neapolitan chord. Another alternative is to play Db7. This is the Tri-Tone Substitution for G7, which is the dominant 5th chord to C major or C minor. I’ll talk more about Neapolitans and Tri-Tone Subs in other posts, so for now just know that the “minor second” has some useful options when using different chords based on tension.

The b3 is the minor third or the chromatic mediant. Now please do not get this confused with Chromatic Mediant Chords. Those chords can fit into more than one position in the chromatic scale. What we are talking about is the b3 note. Think of it like the mediant, which can help you move to and from chords and modes. The difference here is that the b3 is half a step above the super tonic, so it moves very easily to the 2nd degree note. I like to think of this degree as the “chromatic” mediant because it reminds me that I can use this degree to build or borrow chords that really help my 2nd and 3rd degrees. For example, I could play Em7, Em7, Dm7, CMaj7. That’s fine, but what if I played a chord off the b3 degree between Em and Dm? I could play Em7, EbMaj7, Dm7, CMaj7 and it would sound so much better. That b3 is still a mediant, but it reminds me that there is a chromatic option here.

The b5 or #4 is called the diminished fifth or the augmented fourth. It’s the same note. The difference is in the name, but both names have the same use. Let’s start with the use of this degree. The interval from the 1st degree to this b5/#4 is three whole steps, which is why it is called the Tri-Tone. It’s literally three whole tones. This interval has a lot of tension which helps you to lead to a tonic chord. But we can also use this degree to build a chord that helps use move chromatically. Let’s try CMaj7, G7, G7, CMaj7. It works but is very bland. If we build a half-diminished chord on the b5 degree, then we can improve our progression and play CMaj7, F#m7b5, G7, CMaj7. This works because the F#m7b5 feels like a leading tone chord and moves up half a step just like the leading tone should, but since it is built on the b5 degree we can move up half a step to the G7 and then continue our progression.

The other part of the b5/#4 is the degree used. If your scale has a #4 like Lydian, then you sharpen the note. That sounds simple but think of it like this. C Lydian has a #4 so you have the note F# and not Gb. If you used Gb, then you would also have the G note as well and would cause some confusion because you can only have one note that is named with a G. The other problem is that you wouldn’t have the notes F or F#, so now you would have the note E followed by two notes that use G in their name.

The same thing happens in Locrian with a b5. C Locrian has a 4th degree note of F, so F# can’t be used. We then use Gb as our G note that fits the b5 degree position. Check out the green highlighted notes above for Lydian and Locrian and you’ll see how each note letter is only used once. Whether it is flat or sharp depends on the mode used. There are some scales/modes that use a bb7 or double-flat 7. This is the same thing as the 6th degree, but it is a bb7 because there is already a 6th degree accounted for. Scales like C Locrian bb7 have degrees 1, b2, b3, 4, b5, b6, bb7 and notes C, Db, Eb, F, Gb, Ab, Bbb (B double-flat). Again, each degree number is used once, and each letter is used once.

The b6 is the minor 6th or the chromatic sub-mediant. It can also be called the augmented fifth when using an augmented chord or scale since it would have a #5 degree. I like to think of this as the chromatic sub-mediant because it is a great place to add in a chord for some great movement. Using the progression Am7, Am7, G7, CMaj7 we can move down and have it sound alright. These are just chords built on degrees 6, 5, and 1. Now we can use a chord like AbMaj7 built on the b6 degree and play Am7, AbMaj7, G7, CMaj7. Like the chromatic mediant built on our b3 degree, this chord also helps add some color to our progression.

The b7 is the dominant 7th or the sub-tonic and has several functions. As a note it is the sub-tonic meaning below the tonic. It still wants to move up to the tonic, but not with the strength of the leading tone. It still has pull, which can be found in a dominant chord, which a major triad with the b7 degree note. The b7 wants to move toward the tonic and this is helped by the interval from the major triad’s 3rd degree to the b7. This distance is a Tri-Tone and once again it is leading us. In this case, it leads down a fifth, meaning that a dominant chord acts as the 5th degree chord and wants to resolve to the 1st degree chord. This means that you can play a progression like A7, Dm, G7, C. The A7 is a fifth above D so it resolves to Dm. We can keep playing our progression and then use another dominant chord and use G7 to resolve a fifth down to C.

The other function is with m7 chords. Dm7, Em7, and Am7 all have a b7 degree note in them because of the way they are built. What happens with the b7 note of each of these chords is that relative to C major they are notes that easily resolve to C. Dm7’s b7 is C, so we are already back at C as the tonic note. Em7’s b7 is D, which is the super tonic and moves nicely to the tonic just like when you play Csus2 to C major. Am7’s b7 is G, which is a perfect fifth above our tonic. This dominant pull let’s Am7’s b7 move to tonic as well. Of course, you don’t have to go straight to your tonic chord. You always have creative freedom to play what sounds good to you.

The Second Octave and Degree Number Changes

The names of the degrees remain the same, but the numbers change because of the way they function. Now start with degrees 1, b3, 3, 5, b7 and 7. These degrees do not change because they are the foundation for your Maj7 and m7 chords. Think of them as the framework of any structures you make that span more than one octave. This framework can be found in our diagram that used alternating thirds.

That leaves degrees b2, 2, 4, #4, b6, and 6. Notice how these are the even numbered degrees. Now add 7 to them figure out what the new number is. Our b2 and 2 become b9 and 9. 4 and #4 become 11 and #11. Our b6 and 6 become b13 and 13. If you continue into the third octave, then you still use the 9s, 11s, and 13s because they function the same way in all higher octaves.

Multiple Functions For Even Degrees

Playing a chord like C add2 has me play C, D, E, and G which the D note causes some tension and a bit of a clash. If I play a chord like Cadd9, then I use D in the next octave as a 9th degree. This removes the tension and adds a bit brightness rather than a clash. We can do the same with Esus b2 and Esus b9. The b2 clashes against the root note, while the b9 has some breathing room for the notes to be heard and felt.

The same thing happens with a Lydian style chord like Csus#4 and Csus#11. We have the notes C and G for both but putting the F# in the #4 position causes a unique tension that can work. The alternative is to use Csus#11 and put the F# in the next octave to create a bit of mystery or vagueness. You can continue to use examples like Csus4 vs Csus11, Em b6 vs Em b13, and C6 vs Cadd13 to highlight how these even numbered degrees can drop their tension by being playing in the next octave.

Now you may have been wondering why I keep saying, “the next octave” and not the second or third octave. Well, I don’t know which octave you are using notes from, but I do know that the notes and intervals function the same way once you leave the first octave. The only functional difference between higher octaves is that as the pitch increases, the function decreases. Think of the audio example from earlier. That b3 should not work in a major chord, but a b3 with a high enough pitch can loose enough of its function to be used in a melody. This does require a bit of interpretation but try it out and I’m sure you’ll find uses for mis-matched intervals when the pitch is high enough.

How To Use This Concept

After reading all this and trying out some of it you may be wondering how you can apply this to your own compositions. Think of it like this: using C Ionian gives you the chord Dm7. This chord is built on the second degree or super-tonic and contains the degrees 1, 2, b3, 4, 5, 6, and b7. You have access to the b3 and b7 even though you are playing C Ionian. Using our modes in relative order with they yellow highlights (because the green highlighted diagram put the modes in parallel order), we can see that the notes used in Ionian are the first notes in each subsequent mode.

This also means that if were playing an Am chord you could use the degrees of Aeolian to color that chord in a different way. You could use an Am7 b13, which would be the notes A, C, E, G, and F in the next octave. You could also try a more complex chord like Am7 #5/E, which would be E, A, C, F, and G. You can even use a simple chord like Asus2 or Asus4, which are A, B, E and A, D, E.

Another way is to use the Chromatic Scale over any mode so that you can use intervals that don’t belong, but work. You could use the b2 in Aeolian to give your chord or melody a Phrygian flavor. You could take a Dom7 and play the b3 in a higher octave for a tension note in your melody. You can even use the 6th degree as your bb7 in Locrian to create a fully diminished chord. Its all up to you.

Try out different voices of chords to add color to your own compositions. If you want to know more about borrowing chords, Tri-Tone subs, and other out-of-the-box concepts then keep checking out my posts. I’ll be sure to cover as much as I can in due time.