Scale & Mode Formulas
The interval formula for every common scale and mode — as whole/half steps, as semitones from the root, and spelled out in C. The major scale, all seven modes, harmonic & melodic minor, pentatonic, blues and more.
| Scale / mode | Notes | Formula (W/H) | Intervals | Example in C |
|---|---|---|---|---|
| Major (Ionian) | 7 | W–W–H–W–W–W–H | 0, 2, 4, 5, 7, 9, 11 | C D E F G A B |
| Natural minor (Aeolian) | 7 | W–H–W–W–H–W–W | 0, 2, 3, 5, 7, 8, 10 | C D E♭ F G A♭ B♭ |
| Harmonic minor | 7 | W–H–W–W–H–W½–H | 0, 2, 3, 5, 7, 8, 11 | C D E♭ F G A♭ B |
| Melodic minor | 7 | W–H–W–W–W–W–H | 0, 2, 3, 5, 7, 9, 11 | C D E♭ F G A B |
| Dorian | 7 | W–H–W–W–W–H–W | 0, 2, 3, 5, 7, 9, 10 | C D E♭ F G A B♭ |
| Phrygian | 7 | H–W–W–W–H–W–W | 0, 1, 3, 5, 7, 8, 10 | C D♭ E♭ F G A♭ B♭ |
| Lydian | 7 | W–W–W–H–W–W–H | 0, 2, 4, 6, 7, 9, 11 | C D E G♭ G A B |
| Mixolydian | 7 | W–W–H–W–W–H–W | 0, 2, 4, 5, 7, 9, 10 | C D E F G A B♭ |
| Locrian | 7 | H–W–W–H–W–W–W | 0, 1, 3, 5, 6, 8, 10 | C D♭ E♭ F G♭ A♭ B♭ |
| Major pentatonic | 5 | W–W–W½–W–W½ | 0, 2, 4, 7, 9 | C D E G A |
| Minor pentatonic | 5 | W½–W–W–W½–W | 0, 3, 5, 7, 10 | C E♭ F G B♭ |
| Blues | 6 | W½–W–H–H–W½–W | 0, 3, 5, 6, 7, 10 | C E♭ F G♭ G B♭ |
| Phrygian dominant | 7 | H–W½–H–W–H–W–W | 0, 1, 4, 5, 7, 8, 10 | C D♭ E F G A♭ B♭ |
| Harmonic major | 7 | W–W–H–W–H–W½–H | 0, 2, 4, 5, 7, 8, 11 | C D E F G A♭ B |
| Hungarian minor | 7 | W–H–W½–H–H–W½–H | 0, 2, 3, 6, 7, 8, 11 | C D E♭ G♭ G A♭ B |
| Whole tone | 6 | W–W–W–W–W–W | 0, 2, 4, 6, 8, 10 | C D E G♭ A♭ B♭ |
| Diminished (whole–half) | 8 | W–H–W–H–W–H–W–H | 0, 2, 3, 5, 6, 8, 9, 11 | C D E♭ F G♭ A♭ A B |
| Diminished (half–whole) | 8 | H–W–H–W–H–W–H–W | 0, 1, 3, 4, 6, 7, 9, 10 | C D♭ E♭ E G♭ G A B♭ |
| Chromatic | 12 | H–H–H–H–H–H–H–H–H–H–H–H | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 | C D♭ D E♭ E F G♭ G A♭ A B♭ B |
Build any of these on a chosen root with the interactive scale finder. W = whole step (2 semitones), H = half step (1), W½ = three semitones.
How to read this
A scale is a pattern of semitone steps from a root. The pattern is the scale; the root just moves it.
major 2 2 1 2 2 2 1
natural minor 2 1 2 2 1 2 2
harmonic minor 2 1 2 2 1 3 1
melodic minor 2 1 2 2 2 2 1
major pentatonic 2 2 3 2 3
minor pentatonic 3 2 2 3 2
blues 3 2 1 1 3 2Notes & gotchas
- The modes are one scale, seven starting points. Dorian is the major scale from its second degree, Mixolydian from its fifth.
- What makes a mode audible is the harmony under it, not the notes themselves — C major over a D bass is Dorian.
- Harmonic minor's augmented second between degrees 6 and 7 is the three-semitone jump that gives it its distinctive sound.
- Pentatonics omit the semitone clashes, which is precisely why they are so forgiving to improvise over.
- In code, keep scales as interval lists and apply them to a root — never hard-code note names.