Working with Scales¶
A scale is an ordered set of tones spanning an octave, defined by a pattern of intervals. Scales are the foundation of melody and harmony — they determine which notes “belong” in a piece of music and shape its emotional character.
Scale Construction¶
Every scale is defined by its interval pattern — the sequence of whole steps (W = 2 semitones) and half steps (H = 1 semitone) between consecutive tones.
The major scale:
W W H W W W H
C D E F G A B C
2 2 1 2 2 2 1 ← semitones between each note
The natural minor scale:
W H W W H W W
C D Eb F G Ab Bb C
2 1 2 2 1 2 2
Building Scales¶
Use TonedScale to generate scales in any key:
from pytheory import TonedScale
c = TonedScale(tonic="C4")
major = c["major"]
minor = c["minor"]
harmonic_minor = c["harmonic minor"]
print(major.note_names)
# ['C', 'D', 'E', 'F', 'G', 'A', 'B', 'C']
Major and Minor¶
The major scale (Ionian mode) is the foundation of Western tonal music. Its pattern of whole and half steps creates a bright, resolved sound. Every major key has a relative minor that shares the same notes but starts from the 6th degree:
C major → A minor (both use only white keys)
G major → E minor (both have one sharp: F#)
F major → D minor (both have one flat: Bb)
c_major = TonedScale(tonic="C4")["major"]
a_minor = TonedScale(tonic="A4")["minor"]
# Same notes, different starting point
set(c_major.note_names) == set(a_minor.note_names) # True
The harmonic minor raises the 7th degree of the natural minor, creating an augmented 2nd interval (3 semitones) between the 6th and 7th degrees. This gives it a distinctive “Middle Eastern” or “classical” sound and provides the leading tone needed for dominant harmony:
Natural minor: C D Eb F G Ab Bb C
Harmonic minor: C D Eb F G Ab B C
↑ raised 7th
Modes¶
The seven modes of the major scale are rotations of the same interval pattern, each starting from a different degree. Each mode has a distinct emotional character:
c = TonedScale(tonic="C4")
Ionian (I) — the major scale itself. Bright, happy, resolved:
c["ionian"] # C D E F G A B C
Dorian (ii) — minor with a raised 6th. Jazzy, soulful (So What, Scarborough Fair):
c["dorian"] # C D Eb F G A Bb C
Phrygian (iii) — minor with a flat 2nd. Spanish, flamenco, dark (White Rabbit):
c["phrygian"] # C Db Eb F G Ab Bb C
Lydian (IV) — major with a raised 4th. Dreamy, floating, ethereal (The Simpsons theme, Flying by ET):
c["lydian"] # C D E F# G A B C
Mixolydian (V) — major with a flat 7th. Bluesy, rock, dominant (Norwegian Wood, Sweet Home Alabama):
c["mixolydian"] # C D E F G A Bb C
Aeolian (vi) — the natural minor scale. Sad, dark, introspective (Stairway to Heaven, Losing My Religion):
c["aeolian"] # C D Eb F G Ab Bb C
Locrian (vii) — minor with flat 2nd and flat 5th. Unstable, rarely used as a home key (used in metal and jazz over diminished chords):
c["locrian"] # C Db Eb F Gb Ab Bb C
Scale Degrees¶
Each note in a scale has a degree name that describes its function:
Degree |
Number |
Function |
|---|---|---|
Tonic |
I |
Home base — the key center |
Supertonic |
II |
One step above tonic |
Mediant |
III |
Halfway between tonic and dominant |
Subdominant |
IV |
A fifth below tonic (or fourth above) |
Dominant |
V |
The strongest pull back to tonic |
Submediant |
VI |
Root of the relative minor (or major) |
Leading Tone |
VII |
One semitone below tonic — pulls upward |
Access degrees by index, Roman numeral, or name:
major = TonedScale(tonic="C4")["major"]
major[0] # C4 (by index)
major["I"] # C4 (by Roman numeral)
major["tonic"] # C4 (by degree name)
major["V"] # G4 (dominant)
major["dominant"] # G4
major[0:3] # (C4, D4, E4) — slicing works too
Iteration¶
Scales are iterable and support len() and in:
for tone in major:
print(f"{tone.name}: {tone.frequency:.1f} Hz")
len(major) # 8 (7 notes + octave)
"C" in major # True
"C#" in major # False
Building Chords from Scales¶
Diatonic harmony builds chords by stacking every other note of the scale. A triad takes the 1st, 3rd, and 5th; a seventh chord adds the 7th.
In the C major scale, the diatonic triads are:
I C E G = C major
ii D F A = D minor
iii E G B = E minor
IV F A C = F major
V G B D = G major
vi A C E = A minor
vii° B D F = B diminished
Notice the pattern: major triads on I, IV, V; minor triads on ii, iii, vi; diminished on vii°. This pattern holds for every major key.
major = TonedScale(tonic="C4")["major"]
# Build diatonic triads
I = major.triad(0) # C E G (C major)
ii = major.triad(1) # D F A (D minor)
iii = major.triad(2) # E G B (E minor)
IV = major.triad(3) # F A C (F major)
V = major.triad(4) # G B D (G major)
vi = major.triad(5) # A C E (A minor)
# Build seventh chords
Imaj7 = major.chord(0, 2, 4, 6) # C E G B = Cmaj7
V7 = major.chord(4, 6, 8, 10) # G B D F = G7 (dominant 7th)
Common Progressions¶
Some of the most-used chord progressions in Western music:
I–IV–V–I — the foundation of blues, rock, country, folk
I–V–vi–IV — the “pop progression” (Let It Be, No Woman No Cry, With or Without You, Someone Like You)
ii–V–I — the backbone of jazz harmony
I–vi–IV–V — the “50s progression” (Stand By Me, Every Breath You Take)
i–bVI–bIII–bVII — the “epic” minor progression (Stairway to Heaven, My Heart Will Go On)
I–IV–vi–V — axis of awesome (many, many pop songs)
The 12-Bar Blues¶
The 12-bar blues is the most influential chord progression in American music. It’s 12 measures long and uses only three chords (I, IV, V):
| I | I | I | I |
| IV | IV | I | I |
| V | IV | I | V |
Every blues, early rock and roll, and much of jazz is built on this structure. In the key of A:
| A | A | A | A |
| D | D | A | A |
| E | D | A | E |
from pytheory import TonedScale
a = TonedScale(tonic="A4")["major"]
I = a.triad(0) # A major
IV = a.triad(3) # D major
V = a.triad(4) # E major
# The 12-bar blues progression
blues_12 = [I, I, I, I, IV, IV, I, I, V, IV, I, V]
Parallel Major and Minor¶
Two scales are relative if they share the same notes (C major and A minor). Two scales are parallel if they share the same tonic but have different notes (C major and C minor).
Mixing parallel major and minor is a powerful compositional tool — borrowing chords from the parallel minor in a major key creates dramatic color shifts. The bVI and bVII chords (Ab and Bb in C major) are borrowed from C minor and appear constantly in rock and film music.
c_major = TonedScale(tonic="C4")["major"]
c_minor = TonedScale(tonic="C4")["minor"]
# Compare: same tonic, different notes
c_major.note_names # ['C', 'D', 'E', 'F', 'G', 'A', 'B', 'C']
c_minor.note_names # ['C', 'D', 'D#', 'F', 'G', 'G#', 'A#', 'C']
