Master This Scale: Unlock Music Theory (Newsletter 13)

There I was with my classmates, recorder in hand.

“Do Re Mi Fa Sol La Ti Do.. Again!” instructed our middle school music teacher.

At the time, as a know-it-all little kid, I thought this was all pretty lame.

“Okay, I got it. Can we move on now?”

Of course, the public school system must cater to the lowest common denominator. There was plenty of overblown whistling coming from these small plastic woodwind instruments.

And so we drilled the major scale and Hot Cross Buns until everyone got it down, which took about the entire course.

I didn’t know it then, but those repetitions set the stage for learning everything else in Western music theory.

Yes, the most important scale to learn and understand is…

…the major scale!

Let’s dive into why.

The Standard For Scale Degrees

Let’s begin with the fact that the western octave is split into 12 equal divisions. Each division has its own note name and these names repeat every octave.

Because of the repeating nature of notes across octaves, we can visualize them along a circle:

Each note is separated from its neighbouring notes by an interval called a semitone (also called a “half step”, “half tone” or half step”). An interval is simply the distance between notes.

Notice how there are 7 letter names that represent the 12 notes (A through G). That comes as a result of the major scale being heptatonic (it has seven notes). We end up having one letter name per note with the major scale (and the other heptatonic scales and modes).

The pattern of intervals between the seven notes of the major scale is always the same, regardless of what note we start on.

W-W-H-W-W-W-H-repeat

W means whole tone (an interval of two semitones)

H means half tone

This set of intervals, starting with two whole tones, then a half tone, then three whole tones, then a half tone, is unique to the major scale.

And in terms of the seven scale degrees, the major scale has the original, unaltered degrees, which can be written as:

1 – 2 – 3 – 4 – 5 – 6 – 7 –

Inserting the intervals into these scale degrees gives us the following:

1 -W- 2 -W- 3 -H- 4 -W- 5 -W- 6 -W- 7 -H

The classic example of C major has “only white keys” (no alterations). In this case, we have the following notes for each scale degree:

1: C
whole step
2: D
whole step
3: E
half step
4: F
whole step
5: G
whole step
6: A
whole step
7: B
half step
1: C (the octave)

But we can start on any note. Let’s move a tritone away (we’ll get into the larger intervals, like tritone, shortly) to F♯ major:

1: F♯
whole step
2: G♯
whole step
3: A♯
half step
4: B
whole step
5: C♯
whole step
6: D♯
whole step
7: E♯
half step
1: F♯ (the octave)

The ♯ symbol is called “sharp” and raises the given note upward by one semitone.

We’ll soon see the opposite symbol ♭, which is called “flat” and lowers the given note downward by one semitone.

You may be privy to the fact that the seventh degree of the F♯ major scale, which is an E♯ note, is the same thing as an F note. These are called enharmonic equivalents—the reason we use E♯ instead of the objectively simpler “F” is because we’re dealing with a heptatonic scale that wants each of its seven degrees on its own note letter name.

It’s also worth discussing the intervals between the root of the major scale and each of its scale degrees. Every other scale’s degrees will be in reference to (and alterations) of these intervals:

1 = root (no interval)

2 = major second (2 semitones)

3 = major third (4 semitones)

4 = perfect fourth (5 semitones)

5 = perfect fifth (7 semitones)

6 = major sixth (9 semitones)

7 = major seventh (11 semitones)

As we’ll see, these scale degrees can be altered with sharps or flats, too. All other scales can be (and are) written as alterations of the major scale. The differences in scale degrees are noted with sharps and flats.

I want to share the Natural minor scale degrees as an example before moving on. It’s one of the most common scales (you may already know it) and a great way to examine how all scales can be related to the major scale.

The natural minor scale has the following scale degrees:

1 – 2 – ♭3 – 4 – 5 – ♭6 – ♭7

So the natural minor scale is a “major scale with flattened third, sixth and seventh degrees”:

♭3 = minor third (3 semitones)

♭6 = minor sixth (8 semitones)

♭7 = minor seventh (10 semitones)

Inserting the intervals into these scale degrees gives us the following:

1 -W- 2 -H- ♭3 -W- 4 -W- 5 -H- ♭6 -W- ♭7 -W

These alterations can be visualized with the C natural minor scale:

1: C
whole step
2: D
half step
♭3: E♭
whole step
4: F
whole step
5: G
half step
♭6: A♭
whole step
♭7: B♭
whole step
1: C (the octave)

And let’s get a bit more complex with F♯ minor (remember we’re flatting the third, sixth and seventh degrees, even if that means simply removing the sharp):

1: F♯
whole step
2: G♯
half step
♭3: A
whole step
4: B
whole step
5: C♯
half step
♭6: D
whole step
♭7: E
whole step
1: F♯ (the octave)

If we look at the series of intervals of the natural minor extended over 2 octaves, we can see something interesting:

1 -W- 2 -H- ♭3 -W- 4 -W- 5 -H- ♭6 -W- ♭7 -W- 1 -W- 2 -H- ♭3 -W- 4 -W- 5 -H- ♭6 -W- ♭7 -W

I bolded the series of intervals from the ♭3 to ♭3 and octave above.

This series of intervals is exactly the same as the major scale: W-W-H-W-W-W-H

So we have the same sequence of intervals but with a different starting point: a different “root” or “1”.

This is what we refer to as a mode. In this case, the major scale is the “parent scale” and the natural minor is a “mode of the major scale”.

More specifically, the natural minor is the 6th mode of the major scale because it starts on the 6th scale degree of the major scale. Let’s look at the series of intervals of the major scale extended over 2 octaves to see this more clearly:

1 -W- 2 -W- 3 -H- 4 -W- 5 -W- 6 -W- 7 -H- 1 -W- 2 -W- 3 -H- 4 -W- 5 -W- 6 -W- 7 -H

Remember that the natural minor has the intervals of W-H-W-W-H-W-W-

With this knowledge, we can state the following:

• The major scale starting a minor third (3 semitones) up will have the same notes as its corresponding natural minor scale.  

• Example: C major is the same as A natural minor
• The major scale starting a major sixth (9 semitones) down will have the same notes as its corresponding natural minor scale.  

• Example: C major is the same as A natural minor

• The natural minor scale starting a minor third (3 semitones) down will have the same notes as its corresponding major scale.  

• Example: C natural minor is the same as E♭ natural minor

• The natural minor scale starting a major sixth (9 semitones) up will have the same notes as its corresponding major scale.  

• Example: C natural minor is the same as E♭ natural minor

These are called “relative minors/majors” and every major scale will have its own relative minor, and vice versa.

As you might guess, there are seven modes of the major scale—one starting on each of the 7 notes. We’ll get to these shortly.

We have 12 distinct notes per octave in Western music theory, which means we have 12 distinct major scales (and 12 distinct minor scales), each starting from its respective note. Here are all twelve in a table to help simplify things (I’ll include the relative minor scales for reference):

Scale degree:	1	2	3	4	5	6	7
C major scale: (A minor scale)	C	D	E	F	G	A	B
D♭ major scale: (B♭ minor scale)	D♭	E♭	F	G♭	A♭	B♭	C
D major scale: (B minor scale)	D	E	F♯	G	A	B	C♯
E♭ major scale: (C minor scale)	E♭	F	G	A♭	B♭	C	D
E major scale: (C♯ minor scale)	E	F♯	G♯	A	B	C♯	D♯
F major scale: (D minor scale)	F	G	A	B♭	C	D	E
F♯ major scale: (D♯ minor scale)	F♯	G♯	A♯	B	C♯	D♯	E♯
G major scale: (E minor scale)	G	A	B	C	D	E	F♯
A♭ major scale: (F minor scale)	A♭	B♭	C	D♭	E♭	F	G
A major scale: (F♯ minor scale)	A	B	C♯	D	E	F♯	G♯
B♭ major scale: (G minor scale)	B♭	C	D	E♭	F	G	A
B major scale: (G♯ minor scale)	B	C♯	D♯	E	F♯	G♯	A♯

The F♯ could also be written as a G♭ (they’re enharmonic equivalents). If we were to call the scale G♭ major, we’d technically have all the same notes as F♯ major, though they’d be written like this:

Scale degree:	1	2	3	4	5	6	7
G♭ major scale:	G♭	A♭	B♭	C♭	D♭	E♭	F

By that, we can write out each major scale with its number of sharps or flats:

C major	0 sharps/flats
Db major	5 flats
D major	2 sharps
Eb major	3 flats
E major	4 sharps
F major	1 flat
F# major Gb major	6 sharps 6 flats
G major	1 sharp
Ab major	4 flats
A major	3 sharps
Bb major	2 flats
B major	5 sharps

The 12 Major Scales And The 12 Keys

Each major scale makes up its own major key (and relative minor key). The scale and key go by the same name.

For example, the notes of C major make up the key of C major just like the notes of A major make up the key of A major.

When you see a key signature in written music (the clef followed by a series of sharps), you’re being told what the key is. See the chart above for the number of flats or sharps that apply to each key.

Like the intervals I illustrated earlier, the 12 keys can also be visually represented via a circle. The circle of fifths is perhaps the most important music theory resource you’ll ever come across:

We can see that, as the name suggests, we move clockwise through fifths (or counterclockwise through fourths). We add sharps/remove flats going clockwise (or add flats/remove sharps going counterclockwise). To me, it’s easier to envision the number of flats or sharps a key has via the circle of fifths than it is in the table I shared earlier.

Note the order of unaltered notes in the circle of fifth (that make up C major): F → C → G → D → A → E → B

These are the order of sharps as they appear in our keys (F → C → G → D → A → E → B)

• The key of G has one sharp: F♯

• The key of D has two sharp: F♯ and C♯

• The key of A has three sharp: F♯, C♯, and G♯

• The key of E has four sharp: F♯, C♯, G♯, and D♯

• The key of B has five sharp: F♯, C♯, G♯, D♯ and A♯

• The key of F♯ has two sharp: F♯, C♯, G♯, D♯, A♯ and E♯

• Bonus: The key of C♯ has two sharp: F♯, C♯, G♯, D♯, A♯, E♯ and B♯

To find the key of a written key signature, we can identify the last sharp, go up a semitone to the following letter name, and that will be our key.

Example of G major (1 sharp)—with F♯ as the last sharp:

Example of B major (5 sharp)—with A♯ as the last sharp:

And the order of flats (moving counterclockwise) is the opposite (B → E → A → D → G → C → F):

• The key of F has one flat: B♭

• The key of B♭ has two flats: B♭ and E♭

• The key of E♭ has three flats: B♭, E♭ and A♭

• The key of A♭ has four flats: B♭, E♭, A♭ and D♭

• The key of D♭ has five flats: B♭, E♭, A♭, D♭ and G♭

• The key of G♭ has six flats: B♭, E♭, A♭, D♭, G♭ and C♭

• Bonus: The key of C♭ has seven flats: B♭, E♭, A♭, D♭, G♭, C♭ and F♭

To find the key of a written key signature, we can identify the second-to-last flat, and that will be our key.

Example of B♭ major (2 flats)—ending with B♭ and E♭:

Example of A♭ major (4 flats)—ending with A♭ and D♭:

You'll have to remember that F major has 1 flat.

I use the following mnemonic device for remembering these orders:

Order of sharps + clockwise movement: [F]ather [C]harles [G]oes [D]own [A]nd [E]nds [B]attle

Order of flats + counterclockwise movement: [B]attle [E]nds [A]nd [D]own [G]oes [C]harles’ [F]ather

You can remember these however you’d like (and I’d strongly recommend committing the circle of fifths to memory).

The Modes And Chords Of The Major Scale

Moving onto the modes and harmonizing the major scale. This is where things get fun!

Most musicians start with the chords/harmony of the major scale. However, since we’ve been focusing on the major scale, its intervals and scale degrees, let’s start with the modes.

Once again, a mode of a scale has the same repeating sequence of intervals but the starting point (root) and intervals relative to the root are different.

I showed this with the major scale and the natural minor (the 6th mode). They both have the same sequence of intervals (W-W-H-W-W-W-H), they just start at different points:

• Major scale: W-W-H-W-W-W-H-repeat

• Natural Minor scale: W-H-W-W-H-W-W-repeat

This gives us different scale degrees (remember that each scale has its own unique scale degrees):

• Major scale: 1 – 2 – 3 – 4 – 5 – 6 – 7 –

• Natural Minor scale: 1 – 2 – ♭3 – 4 – 5 – ♭6 – ♭7 –

And we can start a mode on any of the scale degrees of the major scale.

In terms of the names of the modes, each has a Greek name. The major scale’s first mode is also known as the Ionian mode (they are the same scale). The natural minor (6th mode) is known as the Aeolian mode.

Here are the 7 modes of the major scale laid out in order with their intervals:

1. Ionian: W-W-H-W-W-W-H-repeat

1. Dorian: W-H-W-W-W-H-W-repeat

1. Phrygian: H-W-W-W-H-W-W-repeat

1. Lydian: W-W-W-H-W-W-H-repeat

1. Mixolydian: W-W-H-W-W-H-W-repeat

1. Aeolian: W-H-W-W-H-W-W-repeat

1. Locrian: H-W-W-H-W-W-W-repeat

Now let’s incorporate their scale degrees (the interval between each successive note and the root) as they compare to the major scale:

1. Ionian: 1 -W- 2 -W- 3 -H- 4 -W- 5 -W- 6 -W- 7 -H-repeat  
   • No alterations! It’s the same as the major scale
     
2. Dorian: 1 -W- 2 -H- ♭3 -W- 4 -W- 5 -W- 6 -H- ♭7 -W-repeat
   • Flatted third and seventh degrees compared to the major scale
     
3. Phrygian: 1 -H- ♭2 -W- ♭3 -W- 4 -W- 5 -H- ♭6 -W- ♭7 -W-repeat  
   • Flatted second, third, sixth and seventh degrees compared to the major scale
     
4. Lydian: 1 -W- 2 -W- 3 -W- ♯4 -H- 5 -W- 6 -W- 7 -H-repeat  
   • Sharped fourth degree compared to the major scale
     
5. Mixolydian: 1 -W- 2-W- 3- H- 4 -W- 5 -W- 6 -H- ♭7 -W-repeat  
   • Flatted seventh degree compared to the major scale
     
6. Aeolian: 1 -W- 2 -H- ♭3 -W- 4 -W- 5 -H- ♭6 -W- ♭7 -W-repeat  
   • Flatted third, sixth and seventh degrees compared to the major scale, as we had discussed previously
     
7. Locrian: 1 -H- ♭2 -W- ♭3 -W- 4 -H- ♭5 -W- ♭6 -W- ♭7 -W-repeat  
   • Flatted second, third, fifth, sixth and seventh degrees compared to the major scale

Let’s revisit each of the potential scale degree intervals we’ll encounter in major diatonic harmony (there are more to know for other scales, but this will cover the majority of what we’ll find in music):

1 = root (no interval)

2 = minor second (1 semitone)

2 = major second (2 semitones)

♭3 = minor third (3 semitones)

3 = major third (4 semitones)

4 = perfect fourth (5 semitones)

♯4 = augmented fourth (6 semitones)*

♭5 = diminished fifth (6 semitones)*

5 = perfect fifth (7 semitones)

♭6 = minor sixth (8 semitones)

6 = major sixth (9 semitones)

♭7 = minor seventh (10 semitones)

7 = major seventh (11 semitones)

*The ♯4 and ♭5 are enharmonic equivalents (the same note) but are labelled differently depending on which note they refer to in the sequence.

In our classic C major scale, our modes would be as follows:

Scale degree:	1	2	3	4	5	6	7
C Ionian:	C	D	E	F	G	A	B
D Dorian:	D	E	F	G	A	B	C
E Phrygian:	E	F	G	A	B	C	D
F Lydian:	F	G	A	B	C	D	E
G Mixolydian:	G	A	B	C	D	E	F
A Aeolian:	A	B	C	D	E	F	G
B Locrian:	B	C	D	E	F	G	A

And because the modes only “clicked” for me once I started practicing them all from the same root, here are the 7 modes of the major scale all starting on C (here, we can really notice the differences):

Scale degree:	1	2	3	4	5	6	7
C Ionian:	C	D	E	F	G	A	B
C Dorian:	C	D	E♭	F	G	A	B♭
C Phrygian:	C	D♭	E♭	F	G	A♭	B♭
C Lydian:	C	D	E	F♯	G	A	B
C Mixolydian:	C	D	E	F	G	A	B♭
C Aeolian:	C	D	E♭	F	G	A♭	B♭
C Locrian:	C	D♭	E♭	F	G♭	A♭	B♭

 

Let’s move on to diatonic harmony and the chords of our major keys by starting with our 4 triads.

Triads are built by stacking thirds (the root, third and fifth degrees of our scales).

Here are the triads:

• Major triad: 1 – 3 – 5

• Minor triad 1 – ♭3 – 5

• Diminished triad: 1 – ♭3 – ♭5

• Augmented triad: 1 – 3 – ♯5

We won’t encounter the augmented triad in major scale harmony, but I wanted to make you aware of it anyway.

Armed with these basic chords, we can harmonize our major scale and acquire the chords of any given key.

Allow me to write out the chords and then explain them with the knowledge we’ve accumulated thus far:

• I – major triad

• ii – minor triad

• iii – minor triad

• IV – major triad

• V – major triad

• vi – minor triad

• viiº – diminished triad

Major Scale Degree:	1	2	3	4	5	6	7
Chord:	I (major)	ii (minor)	iii (minor)	IV (major)	V (major)	vi (minor)	vii° (diminished)

First off, I love the use of Roman numerals here, since they immediately tell us the chord’s location within the key and the chord’s character.

Major = uppercase

• examples: I, IV and V

Minor = lowercase

• examples: ii, iii and vi

Diminished = lowercase with circle

• example: vii°

Augmented (not included) = uppercase with plus sign

• example: III+ (from Melodic Minor)

Let’s consider the triads of the trusty C major scale. Remember that triads are built on stacked thirds, so we’ll skip a letter for each successive note.

• I – major triad: C – E – G (1 – 3 – 5)

• ii – minor triad: D – F – A (1 – ♭3 – 5)

• iii – minor triad: E – G – B (1 – ♭3 – 5)

• IV – major triad: F – A – C (1 – 3 – 5)

• V – major triad: G – B – D (1 – 3 – 5)

• vi – minor triad: A – C – E (1 – ♭3 – 5)

• viiº – diminished triad: B – D – F (1 – ♭3 – ♭5)

And getting back to the modes, they directly correspond to the chords:

• C Ionian (1 – 2 – 3 – 4 – 5 – 6 – 7 -) → I – major triad: C – E – G (1 – 3 – 5)

• D Dorian (1 – 2 – ♭3 – 4 – 5 – 6 – ♭7 -) → ii – minor triad: D – F – A (1 – ♭3 – 5)

• E Phrygian (1 – ♭2 – ♭3 – 4 – 5 – ♭6 – ♭7 -) → iii – minor triad: E – G – B (1 – ♭3 – 5)

• F Lydian (1 – 2 – 3 – ♯4 – 5 – 6 – 7 -) → IV – major triad: F – A – C (1 – 3 – 5)

• G Mixolydian (1 – 2 – 3 – 4 – 5 – 6 – ♭7 -) → V – major triad: G – B – D (1 – 3 – 5)

• A Aeolian (1 – 2 – ♭3 – 4 – 5 – ♭6 – ♭7 -) → vi – minor triad: A – C – E (1 – ♭3 – 5)

• B Locrian (1 – ♭2 – ♭3 – 4 – ♭5 – ♭6 – ♭7 -) → viiº – diminished triad: B – D – F (1 – ♭3 – ♭5)

And because I love jazz so much, let's wrap things up by stacking another third above the fifth to get our seventh chords:

• I – major seventh: C – E – G (1 – 3 – 5 – 7)

• ii – minor seventh: D – F – A (1 – ♭3 – 5 – ♭7)

• iii – minor seventh: E – G – B (1 – ♭3 – 5 – ♭7)

• IV – major seventh: F – A – C (1 – 3 – 5 – 7)

• V – dominant seventh: G – B – D (1 – 3 – 5 – ♭7)

• vi – minor seventh: A – C – E (1 – ♭3 – 5 – ♭7)

• viiº – minor seven flat five: B – D – F (1 – ♭3 – ♭5 – ♭7)

Major Scale Degree:	1	2	3	4	5	6	7
Triad:	I (major)	ii (minor)	iii (minor)	IV (major)	V (major)	vi (minor)	vii° (diminished)
Mode:	Ionian	Dorian	Phrygian	Lydian	Mixolydian	Aeolian	Locrian
Seventh Chord:	I (major seventh)	ii (minor seventh)	iii (minor seventh)	IV (major seventh)	V7 (dominant seventh)	vi (minor seventh)	vii° (minor seven flat five)

And to think that all of this is based around the simple major chord!

That’s it for now (this one’s already long). Please don’t hesitate to reach out with questions—I’ve studied this for so long that I may take certain things for granted when teaching.

Always happy to help (and your questions help me with content ideas).

Master the major scale, and then unlock nearly everything in Western theory.

‘Til next week,

-Art