Music Theory
Intervals, chord construction, modes, and harmonic analysis — the grammar of music.
Pitch and the Chromatic Scale
The twelve notes
Chromatic scale (all 12 notes, ascending):
C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B (C)
1 2 3 4 5 6 7 8 9 10 11 12
Enharmonic equivalents: C# = Db (same pitch, different name)
Sharp (#): raises pitch by one half step
Flat (b): lowers pitch by one half step
Half step (semitone): smallest interval in Western music (C→C#)
Whole step (tone): two half steps (C→D)
Concert pitch: A4 = 440 Hz
Each octave doubles the frequency: A3=220, A4=440, A5=880
Each semitone: multiply by 2^(1/12) ≈ 1.05946Intervals
Interval names
Semitones Name Example (from C) Sound
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0 Unison C→C same note
1 Minor 2nd (m2) C→Db dissonant, tense
2 Major 2nd (M2) C→D whole step
3 Minor 3rd (m3) C→Eb sad, dark
4 Major 3rd (M3) C→E happy, bright
5 Perfect 4th (P4) C→F strong, open
6 Tritone (A4/d5) C→F# unstable, "devil"
7 Perfect 5th (P5) C→G stable, power chord
8 Minor 6th (m6) C→Ab
9 Major 6th (M6) C→A
10 Minor 7th (m7) C→Bb bluesy tension
11 Major 7th (M7) C→B jazzy tension
12 Octave (P8) C→C same note, higher
Inversion: interval + inversion = 12 semitones (octave)
M3 (4) + m6 (8) = 12
P4 (5) + P5 (7) = 12Keys and Key Signatures
Circle of fifths
C (0 sharps/flats)
F (1b) G (1#)
Bb (2b) D (2#)
Eb (3b) A (3#)
Ab (4b) E (4#)
Db (5b) B (5#)
Gb/F# (6b/6#)
Moving clockwise: add one sharp (fifths: C→G→D→A→E→B→F#)
Moving counterclockwise: add one flat (fourths: C→F→Bb→Eb→Ab→Db→Gb)
Order of sharps: F C G D A E B ("Father Charles Goes Down And Ends Battle")
Order of flats: B E A D G C F (reverse)Relative major/minor
Every major key has a relative minor (same key signature):
C major ↔ A minor (0 accidentals)
G major ↔ E minor (1 sharp)
D major ↔ B minor (2 sharps)
A major ↔ F# minor (3 sharps)
E major ↔ C# minor (4 sharps)
B major ↔ G# minor (5 sharps)
F# major ↔ D# minor (6 sharps)
F major ↔ D minor (1 flat)
Bb major ↔ G minor (2 flats)
Eb major ↔ C minor (3 flats)
Ab major ↔ F minor (4 flats)
Db major ↔ Bb minor (5 flats)
Gb major ↔ Eb minor (6 flats)
Relative minor is 3 semitones below the major
C major → down 3 → A minor
Eb major → down 3 → C minorChords
Triad types
Type Formula Intervals Example Sound
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Major 1-3-5 M3 + m3 C-E-G happy, stable
Minor 1-b3-5 m3 + M3 C-Eb-G sad, dark
Diminished 1-b3-b5 m3 + m3 C-Eb-Gb tense, unstable
Augmented 1-3-#5 M3 + M3 C-E-G# dreamy, unresolved
Suspended 4 1-4-5 P4 + M2 C-F-G open, unresolved
Suspended 2 1-2-5 M2 + P4 C-D-G open, ambiguousSeventh chords
Major 7th (Maj7): 1-3-5-7 C-E-G-B jazzy, warm
Dominant 7th (7): 1-3-5-b7 C-E-G-Bb bluesy, wants to resolve
Minor 7th (m7): 1-b3-5-b7 C-Eb-G-Bb mellow, smooth
Minor-major 7th (mM7): 1-b3-5-7 C-Eb-G-B dark, dramatic
Diminished 7th (dim7): 1-b3-b5-bb7 C-Eb-Gb-A spooky, symmetrical
Half-dim 7th (m7b5): 1-b3-b5-b7 C-Eb-Gb-Bb sad, jazzy
Extended chords:
9th: add 2nd an octave up (C-E-G-Bb-D = C9)
11th: add 4th an octave up (C-E-G-Bb-D-F = C11)
13th: add 6th an octave up (C-E-G-Bb-D-F-A = C13)Chord inversions
Root position: 1 - 3 - 5 (C-E-G) most stable
First inversion: 3 - 5 - 1 (E-G-C) lighter
Second inversion: 5 - 1 - 3 (G-C-E) unstable, passing
Seventh chord inversions:
Root: 1 - 3 - 5 - 7 (C-E-G-B)
1st inv: 3 - 5 - 7 - 1 (E-G-B-C)
2nd inv: 5 - 7 - 1 - 3 (G-B-C-E)
3rd inv: 7 - 1 - 3 - 5 (B-C-E-G)
Figured bass shorthand:
Root = 5/3 1st inv = 6/3 (or just 6) 2nd inv = 6/4Diatonic Chords — All Major Keys
Formula: I - ii - iii - IV - V - vi - vii°
Uppercase = major, lowercase = minor, ° = diminished
Key I ii iii IV V vi vii°
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C: C Dm Em F G Am Bdim
G: G Am Bm C D Em F#dim
D: D Em F#m G A Bm C#dim
A: A Bm C#m D E F#m G#dim
E: E F#m G#m A B C#m D#dim
B: B C#m D#m E F# G#m A#dim
F#: F# G#m A#m B C# D#m E#dim
F: F Gm Am Bb C Dm Edim
Bb: Bb Cm Dm Eb F Gm Adim
Eb: Eb Fm Gm Ab Bb Cm Ddim
Ab: Ab Bbm Cm Db Eb Fm Gdim
Db: Db Ebm Fm Gb Ab Bbm CdimDiatonic seventh chords: IMaj7 - ii7 - iii7 - IVMaj7 - V7 - vi7 - viiø7
Key IMaj7 ii7 iii7 IVMaj7 V7 vi7 viiø7
──────────────────────────────────────────────────────────────────
C: CMaj7 Dm7 Em7 FMaj7 G7 Am7 Bø7
G: GMaj7 Am7 Bm7 CMaj7 D7 Em7 F#ø7
D: DMaj7 Em7 F#m7 GMaj7 A7 Bm7 C#ø7
A: AMaj7 Bm7 C#m7 DMaj7 E7 F#m7 G#ø7
E: EMaj7 F#m7 G#m7 AMaj7 B7 C#m7 D#ø7
B: BMaj7 C#m7 D#m7 EMaj7 F#7 G#m7 A#ø7
F: FMaj7 Gm7 Am7 BbMaj7 C7 Dm7 Eø7
Bb: BbMaj7 Cm7 Dm7 EbMaj7 F7 Gm7 Aø7
Eb: EbMaj7 Fm7 Gm7 AbMaj7 Bb7 Cm7 Dø7
Ab: AbMaj7 Bbm7 Cm7 DbMaj7 Eb7 Fm7 Gø7
Db: DbMaj7 Ebm7 Fm7 GbMaj7 Ab7 Bbm7 Cø7Diatonic Chords — All Minor Keys
Natural minor: i - ii° - III - iv - v - VI - VII
Key i ii° III iv v VI VII
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Am: Am Bdim C Dm Em F G
Em: Em F#dim G Am Bm C D
Bm: Bm C#dim D Em F#m G A
F#m: F#m G#dim A Bm C#m D E
C#m: C#m D#dim E F#m G#m A B
G#m: G#m A#dim B C#m D#m E F#
D#m: D#m E#dim F# G#m A#m B C#
Dm: Dm Edim F Gm Am Bb C
Gm: Gm Adim Bb Cm Dm Eb F
Cm: Cm Ddim Eb Fm Gm Ab Bb
Fm: Fm Gdim Ab Bbm Cm Db Eb
Bbm: Bbm Cdim Db Ebm Fm Gb AbHarmonic minor: i - ii° - III+ - iv - V - VI - vii°
Raised 7th changes v→V (major!) and VII→vii° (diminished)
This is why harmonic minor exists: to create a strong V→i cadence.
Key i ii° III+ iv V VI vii°
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Am: Am Bdim C+ Dm E F G#dim
Em: Em F#dim G+ Am B C D#dim
Bm: Bm C#dim D+ Em F# G A#dim
F#m: F#m G#dim A+ Bm C# D E#dim
Dm: Dm Edim F+ Gm A Bb C#dim
Gm: Gm Adim Bb+ Cm D Eb F#dim
Cm: Cm Ddim Eb+ Fm G Ab Bdim
The V chord being MAJOR in minor keys is the foundation
of classical harmony. Wieniawski exploits this constantly:
D minor: A major (not Am) resolving to Dm
G minor: D major (not Dm) resolving to GmChord Progressions
Common progressions (with examples in multiple keys)
I - V - vi - IV "pop/rock"
C: C - G - Am - F
G: G - D - Em - C
D: D - A - Bm - G
A: A - E - F#m - D
I - IV - V - I "classical cadence"
C: C - F - G - C
G: G - C - D - G
D: D - G - A - D
ii - V - I "jazz turnaround"
C: Dm7 - G7 - CMaj7
G: Am7 - D7 - GMaj7
F: Gm7 - C7 - FMaj7
Bb: Cm7 - F7 - BbMaj7
i - iv - V - i "minor classical"
Am: Am - Dm - E - Am
Dm: Dm - Gm - A - Dm
Gm: Gm - Cm - D - Gm
Em: Em - Am - B - Em
vi - IV - I - V "emotional/dramatic"
C: Am - F - C - G
G: Em - C - G - D
12-bar blues:
I - I - I - I / IV - IV - I - I / V - IV - I - V
In A: A-A-A-A / D-D-A-A / E-D-A-E
Circle of fifths progression:
iii - vi - ii - V - I
C: Em - Am - Dm - G - CClassical minor key progressions (Romantic era — Wieniawski’s language)
i - iv - V7 - i standard minor cadence
i - VI - III - VII - III - V minor key circle (Baroque)
i - V/V - V - i secondary dominant approach
i - N6 - V - i Neapolitan 6th (Romantic signature)
i - It+6 - V - i Italian augmented 6th
i - Ger+6 - V - i German augmented 6th
In D minor (Wieniawski Concerto No. 2):
Dm - Gm - A7 - Dm (i-iv-V7-i)
Dm - Bb - F - C - F - A (i-VI-III-VII-III-V)
Dm - Eb/G - A - Dm (i-N6-V-i — Neapolitan)
Dm - Bb/D# - A - Dm (i-Ger+6-V-i)Harmony Concepts
Consonance and dissonance
Consonant (stable):
Unison, octave, perfect 5th, major/minor 3rd, major/minor 6th
Dissonant (tension):
Minor 2nd, major 7th, tritone
Tension → resolution is the engine of music
Dominant (V) → Tonic (I) is the strongest resolution
G7 → C (tritone B-F resolves inward to C-E)Cadences
Authentic cadence: V → I (strongest resolution)
Perfect authentic: V → I (both in root position, melody on tonic)
Half cadence: ? → V (ends on dominant — sounds incomplete)
Plagal cadence: IV → I ("Amen" cadence)
Deceptive cadence: V → vi (surprise — expected I, got vi)
In D minor:
Authentic: A → Dm (V → i)
Half: Dm → A (i → V)
Plagal: Gm → Dm (iv → i)
Deceptive: A → Bb (V → VI)Secondary dominants
Any chord can be preceded by ITS dominant:
V/V: D7 → G → C (D7 is V of G, which is V of C)
V/ii: A7 → Dm → C (A7 is V of Dm)
V/vi: E7 → Am → C (E7 is V of Am)
V/IV: C7 → F → C (C7 is V of F)
Secondary dominants create chromatic color and forward motion.
Wieniawski uses these constantly — modulations via secondary dominants
are a hallmark of Romantic violin writing.Modes (scales built on each degree)
Mode Start on Character Example
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Ionian 1st (C) Major, happy standard major
Dorian 2nd (D) Minor, cool jazz, funk
Phrygian 3rd (E) Dark, Spanish metal, flamenco
Lydian 4th (F) Dreamy, floating film scores
Mixolydian 5th (G) Major, bluesy rock, blues
Aeolian 6th (A) Natural minor sad, dark
Locrian 7th (B) Diminished, rare unstable, theoretical