Building Major and Natural Minor Scales

In our last lesson, we established the fundamental components of pitch in Western music: the twelve notes of the chromatic scale and the intervals of semitones and tones that separate them. We also explored the precise mathematical relationship between octaves and frequency. Now, we'll begin to assemble these individual notes into the structured patterns that form the backbone of melody and harmony.

Today's lesson focuses on constructing the two most important scales in Western music: the major scale and the natural minor scale. The learning outcome is for you to be able to build these scales starting from any of the twelve root notes. A scale is essentially a formula—a specific sequence of intervals—that defines a set of notes that sound cohesive together. Mastering these formulas is a critical step toward composing the chord progressions and melodies characteristic of the deadmau5 sound.

The Anatomy of a Scale

Before we build our first scale, let's revisit our key interval units from the last lesson:

• A semitone (or half step) is the distance from one key to the very next, e.g., from C to C♯.
• A tone (or whole step) is the distance of two semitones, e.g., from C to D.

A scale is simply a selection of seven of the twelve available notes within an octave, arranged in a specific order according to a pattern of tones and semitones. This pattern is what gives each type of scale its unique sonic character.

The Major Scale: The Formula for Brightness

The major scale is often associated with bright, happy, or triumphant emotions. Its structure is one of the most foundational patterns in music theory. The easiest way to see this pattern is by starting on the note C, as the C major scale conveniently uses only the white keys on the piano.

C Major Scale: C - D - E - F - G - A - B - C

If we analyze the intervals between these notes, a clear pattern emerges:

• C to D: Tone (T)
• D to E: Tone (T)
• E to F: Semitone (S)
• F to G: Tone (T)
• G to A: Tone (T)
• A to B: Tone (T)
• B to C: Semitone (S)

This gives us the universal formula for any major scale: Tone-Tone-Semitone-Tone-Tone-Tone-Semitone, or T-T-S-T-T-T-S. In the common producer vernacular of whole and half steps, this is W-W-H-W-W-W-H.

The following video provides a clear, practical demonstration of this formula on the keyboard.

A Mathematical Perspective on Scales

Given your background, you may appreciate a more abstract, mathematical way to represent this pattern. We can think of the 12 notes of the chromatic scale as integers on a "clock" from 0 to 11 (e.g., C=0, C♯=1, D=2, ... B=11).

In this system:

• A semitone is a "1-step".
• A tone is a "2-step".

The major scale formula (T-T-S-T-T-T-S) can thus be written as an interval sequence:
$[2,2,1,2,2,2,1]$
Notice that the sum of these intervals is $2+2+1+2+2+2+1=12$, the total number of semitones in an octave. A scale is therefore a journey around the 12-note clock that returns to its starting point.

Any scale can be fully defined by two pieces of information: its starting note (the tonic) and its interval sequence. This means we can use this single integer sequence as an algorithm to construct a major scale from any starting note.

Let's apply this to construct the G major scale:

1. Tonic: G
2. Add 2 (Tone): G → A
3. Add 2 (Tone): A → B
4. Add 1 (Semitone): B → C
5. Add 2 (Tone): C → D
6. Add 2 (Tone): D → E
7. Add 2 (Tone): E → F♯ (Note: This requires a black key)
8. Add 1 (Semitone): F♯ → G (completes the octave)

The resulting G Major scale is: G - A - B - C - D - E - F♯ - G.

The following video provides a more formal explanation of this concept, defining scales via their tonic and interval sequence.

The Natural Minor Scale: The Formula for Seriousness

The natural minor scale is the other essential scale type. It's often used to create darker, sadder, or more pensive moods, and it's a staple in progressive house. deadmau5 tracks are frequently in minor keys.

The formula for the natural minor scale is: Tone-Semitone-Tone-Tone-Semitone-Tone-Tone, or W-H-W-W-H-W-W.

Using our integer-based interval sequence notation, this becomes:
$[2,1,2,2,1,2,2]$
Again, the intervals sum to 12.

Let's watch the same producer-focused video to see how this is applied.

Let's use this formula to build the E natural minor scale:

1. Tonic: E
2. Add 2 (Tone): E → F♯
3. Add 1 (Semitone): F♯ → G
4. Add 2 (Tone): G → A
5. Add 2 (Tone): A → B
6. Add 1 (Semitone): B → C
7. Add 2 (Tone): C → D
8. Add 2 (Tone): D → E (completes the octave)

The E minor scale is: E - F♯ - G - A - B - C - D - E.

Relative Keys: Two Scales for the Price of One

You might have noticed something interesting.

• C Major: C - D - E - F - G - A - B
• A Minor: A - B - C - D - E - F - G

Both scales use the exact same set of seven notes (all the white keys), but they start on a different tonic and thus have a different interval sequence and a different emotional feel. These two scales are called relative keys.

Every major scale has a relative minor scale whose tonic is the 6th note of the major scale. Conversely, every minor scale has a relative major whose tonic is the 3rd note of the minor scale.

• The relative minor of G major (G-A-B-C-D-E-F♯) is E minor.
• The relative major of C minor (C-D-E♭-F-G-A♭-B♭) is E♭ major.

This relationship is a powerful shortcut. If you know the notes of a major scale, you automatically know the notes of its relative minor. This will become extremely important when we start building chord progressions, as progressions often move between relative major and minor chords.

Practical Application

It's time to put this into practice and train your ear.

1. Open Ableton Live and load an instrument (like a Simpler with a basic waveform or an instance of Analog) onto a MIDI track.
2. Create a new MIDI clip and open the piano roll.
3. Program the following scales, one after the other. Pay attention to the pattern of whole and half steps on the grid.
   • C Major: C3, D3, E3, F3, G3, A3, B3, C4
   • G Major: G3, A3, B3, C4, D4, E4, F#4, G4
   • A Minor: A3, B3, C4, D4, E4, F4, G4, A4
   • E Minor: E3, F#3, G3, A3, B3, C4, D4, E4
4. Listen to the playback of each scale. Can you hear the difference in character between the major and minor scales? The major scales should sound brighter, while the minor scales sound more somber or driven.

Conclusion

In this lesson, we translated the abstract concepts of tones and semitones into concrete, usable formulas for building major and minor scales. These patterns are not arbitrary rules but are the very DNA of Western harmony.

Here are the key takeaways:

• A scale is defined by its tonic (starting note) and its interval sequence.
• The major scale formula is T-T-S-T-T-T-S, or the interval sequence [2, 2, 1, 2, 2, 2, 1]. It generally sounds bright or happy.
• The natural minor scale formula is T-S-T-T-S-T-T, or the interval sequence [2, 1, 2, 2, 1, 2, 2]. It generally sounds dark or serious.
• Every major scale has a relative minor (starting on its 6th degree) that shares the exact same notes.

Now that you can generate the primary note palettes for any key, our next step will be to use these notes to build chords. In the next lesson, we will construct major, minor, and diminished triads, the three-note chords that form the fundamental building blocks of harmony.