Music Theory

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) ≈ 1.05946

Semitones  Name              Example (from C)   Sound
──────────────────────────────────────────────────────────
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) = 12

                    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)

Every major key has a relative minor (same key signature):
  C major ↔ A minor     (0 accidentals)
  G major ↔ E minor     (1 sharp)
  F major ↔ D minor     (1 flat)

Relative minor is 3 semitones below the major
  C major → down 3 → A minor
  Eb major → down 3 → C minor

Type         Formula    Intervals        Example     Sound
────────────────────────────────────────────────────────────
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

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
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

Roman numerals: I=major, ii=minor, IV=major, V=major, vi=minor

Key of C:  I=C  ii=Dm  iii=Em  IV=F  V=G  vi=Am  vii°=Bdim

Common progressions:
  I - V - vi - IV     "pop progression" (C-G-Am-F)
  I - IV - V - I      "classical" (C-F-G-C)
  ii - V - I           "jazz turnaround" (Dm-G-C)
  I - vi - IV - V      "50s doo-wop" (C-Am-F-G)
  vi - IV - I - V      "emotional" (Am-F-C-G)
  12-bar blues:        I-I-I-I / IV-IV-I-I / V-IV-I-V

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)

Mode        Start on    Character         Example
─────────────────────────────────────────────────────
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