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"]
>>> 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"]
>>> 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"].note_names
['C', 'D', 'E', 'F', 'G', 'A', 'B', 'C']

Dorian (ii) — minor with a raised 6th. Jazzy, soulful (So What, Scarborough Fair):

>>> c["dorian"].note_names
['C', 'D', 'Eb', 'F', 'G', 'A', 'Bb', 'C']

Phrygian (iii) — minor with a flat 2nd. Spanish, flamenco, dark (White Rabbit):

>>> c["phrygian"].note_names
['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"].note_names
['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"].note_names
['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"].note_names
['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"].note_names
['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
>>> major["I"]
C4
>>> major["tonic"]
C4
>>> major["V"]
G4
>>> major["dominant"]
G4
>>> major[0:3]
(<Tone C4>, <Tone D4>, <Tone E4>)

Iteration

Scales are iterable and support len() and in:

>>> for tone in major:
...     print(f"{tone.name}: {tone.frequency:.1f} Hz")
C: 261.6 Hz
D: 293.7 Hz
E: 329.6 Hz
F: 349.2 Hz
G: 392.0 Hz
A: 440.0 Hz
B: 493.9 Hz
C: 523.3 Hz
>>> len(major)
8
>>> "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"]
>>> major.triad(0)
C major
>>> major.triad(1)
D minor
>>> major.triad(2)
E minor
>>> major.triad(3)
F major
>>> major.triad(4)
G major
>>> major.triad(5)
A minor
>>> major.chord(0, 2, 4, 6)
C major 7th
>>> major.chord(4, 6, 8, 10)
G 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 Key class makes working with progressions easy:

>>> from pytheory import Key
>>> key = Key("G", "major")
>>> chords = key.progression("I", "V", "vi", "IV")
>>> for c in chords:
...     print(c.identify())
G major
D major
E minor
C major
>>> key.nashville(1, 5, 6, 4)
[<Chord G major>, <Chord D major>, <Chord E minor>, <Chord C major>]
>>> key.chords
['G major', 'A minor', 'B minor', 'C major', 'D major', 'E minor', 'F# diminished']
>>> key.seventh_chords
['G major 7th', 'A minor 7th', 'B minor 7th', 'C major 7th', 'D dominant 7th', 'E minor 7th', 'F# half-diminished 7th']

Build a seventh chord on any individual degree with seventh():

>>> key.seventh(0)   # I7
G major 7th
>>> key.seventh(4)   # V7
D dominant 7th
>>> key.seventh(6)   # vii7
F# half-diminished 7th

This is the single-degree version of seventh_chords — useful when you need one specific chord rather than the full list.

>>> Key.detect("C", "E", "G", "A", "D")
C major

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)
>>> IV = a.triad(3)
>>> V  = a.triad(4)
>>> blues_12 = [I, I, I, I, IV, IV, I, I, V, IV, I, V]

Key Signatures

The signature property tells you how many sharps or flats a key has:

>>> Key("G", "major").signature
{'sharps': 1, 'flats': 0, 'accidentals': ['F#']}
>>> Key("F", "major").signature
{'sharps': 0, 'flats': 1, 'accidentals': ['Bb']}
>>> Key("C", "major").signature
{'sharps': 0, 'flats': 0, 'accidentals': []}

Relative and Parallel Keys

Two keys are relative if they share the same notes (C major and A minor). Two keys are parallel if they share the same tonic but have different notes (C major and C minor):

>>> Key("C", "major").relative
A minor
>>> Key("A", "minor").relative
C major
>>> Key("C", "major").parallel
C minor

Borrowed Chords

Modal interchange — borrowing chords from the parallel key — is one of the most powerful tools in songwriting. The bVI and bVII chords (Ab and Bb in C major) are borrowed from C minor and appear constantly in rock and film music:

>>> Key("C", "major").borrowed_chords
['C minor', 'D diminished', 'Eb major', 'F minor', 'G minor', 'Ab major', 'Bb major']

Secondary Dominants

A secondary dominant is the V chord of a non-tonic chord. It creates a momentary pull toward that chord, adding harmonic color:

>>> key = Key("C", "major")
>>> key.secondary_dominant(5)
D dominant 7th
>>> key.secondary_dominant(2)
A dominant 7th

Random Progressions

Need inspiration? Generate weighted random progressions. The weights favor common chord functions (I and vi most likely, vii least):

>>> key = Key("C", "major")
>>> chords = key.random_progression(4)
>>> [c.identify() for c in chords]
['C major', 'F major', 'A minor', 'G major']

All Keys

Enumerate all 24 major and minor keys:

>>> Key.all_keys()
[<Key C major>, <Key C minor>, <Key C# major>, <Key C# minor>, ...]

Scale Transposition

Transpose an entire scale by a number of semitones:

>>> c_major = TonedScale(tonic="C4")["major"]
>>> d_major = c_major.transpose(2)
>>> d_major.note_names
['D', 'E', 'F#', 'G', 'A', 'B', 'C#', 'D']

Degree Names

Get the traditional function name for any scale degree:

>>> major = TonedScale(tonic="C4")["major"]
>>> major.degree_name(0)
'tonic'
>>> major.degree_name(4)
'dominant'
>>> major.degree_name(6)
'leading tone'
>>> major.degree_name(6, minor=True)
'subtonic'

Scale Fitness

Score how well a set of notes fits a scale (0.0–1.0). Useful for melody analysis or detecting which scale a phrase belongs to:

>>> major = TonedScale(tonic="C4")["major"]
>>> major.fitness("C", "D", "E", "G")
1.0
>>> major.fitness("C", "D", "F#", "G")
0.75

Scale Recommendation

Given a melody or set of notes, find the best-matching scales ranked by fitness. Useful for figuring out what key you’re in or finding alternative scales to improvise over:

>>> from pytheory.scales import Scale

>>> Scale.recommend("C", "D", "E", "G", "A", top=3)
[('C', 'major', 1.0), ('A', 'aeolian', 1.0), ...]

>>> Scale.recommend("C", "Eb", "F", "Gb", "G", "Bb", top=3)
[('C', 'blues', 1.0), ...]

How it works: recommend() tests your notes against every scale in every key (all 12 tonics times all scale types in the Western system). Each candidate is scored using fitness() — the fraction of your notes that belong to that scale (1.0 = perfect match). Results are ranked by fitness, with chromatic scales deprioritized since they match everything. Scales whose length is closer to the number of input notes are preferred when fitness scores tie.

Returns a list of (tonic, scale_name, fitness) tuples. Pass top= to control how many results you get back (default 5).

Parallel Modes

See all 7 modes that share the same notes as a scale:

>>> major = TonedScale(tonic="C4")["major"]
>>> for name, notes in major.parallel_modes().items():
...     print(f"{name}: {' '.join(notes)}")
C ionian: C D E F G A B C
D dorian: D E F G A B C D
E phrygian: E F G A B C D E
...

Common Progressions

Get all named progressions realized in a key with chord symbols:

>>> key = Key("C", "major")
>>> progs = key.common_progressions()
>>> for name, chords in list(progs.items())[:3]:
...     symbols = [c.symbol for c in chords]
...     print(f"{name}: {' → '.join(symbols)}")
I-IV-V-I: C → F → G → C
I-V-vi-IV: C → G → Am → F
I-vi-IV-V: C → Am → F → G

Chord Suggestions

Given a chord in a key, suggest_next() returns likely next chords based on functional harmony voice-leading rules:

>>> key = Key("C", "major")
>>> g_major = key.triad(4)   # V chord
>>> [c.symbol for c in key.suggest_next(g_major)]
['C', 'Am', 'F']

Modulation

modulation_path() suggests a chord-by-chord route from one key to another, using pivot chords when available:

>>> path = Key("C", "major").modulation_path(Key("G", "major"))
>>> [c.symbol for c in path]
['C', 'Em', 'D', 'G']

pivot_chords() shows which chords are shared between two keys:

>>> Key("C", "major").pivot_chords(Key("G", "major"))
['A minor', 'B minor', 'C major', 'D major', 'E minor', 'G major']

Scales are the map; the key is the territory. Once you know the landscape, you can wander freely – and you’ll always know how to get home.