Harmony

  • Definition
  • Chords I – Triads
  • Chords II – Seventh Chords
  • Progressions I – Diatonic Chords
  • Progressions II – Classical Progressions
  • Progressions III – Pop Schemas
  • Progressions IV – Triadic Transformations
  • Progressions V – Combinations, Extended Harmony, Lehman Terms, and Other Harmonies

Definition of “Harmony” from The Oxford Dictionary of Music

“At its simplest, the simultaneous sounding of 2 or more notes; in this sense synonymous with chord. More broadly, however, harmony refers to organization and arrangement of chords and their relationships to one another. It therefore concerns not only music’s vertical, synchronic dimension, but also its horizontal, diachronic progress.”

Chords I – Triads

Major (no annotation)

  • 1st, 3rd, and 5th from the major scale, or…
  • Root + 4 semitones = Third (and) Third plus 3 semitones = Fifth; 7 Overall
  • Semitone 4 + 3 = Major Chord

Minor (min, – )

  • 1st, lowered 3rd, 5th, or…
  • Semitone 3 + 4

Diminished (o, dim)

  • 1st, lowered 3rd, lowered 5th, or…
  • Semitone 3 + 3 (6 Overall)

Augmented (+, aug)

  • •1st, 3rd, raised 5th, or…
  • Semitone 4 + 4 (8 Overall)

Chords II – Seventh Chords

(b = lowered, # = raised)

Major 7th (maj7)

  • 1 – 3 – 5 – 7
  • Semitone 4 + 3 + 4

Dominant 7th (7)

  • •1 – 3 – 5 – b7
  • •Semitone 4 + 3 + 3

Minor 7th (m7, min7)

  • 1 – b3 – 5 – b7
  • Semitone 3 + 4 + 3

Half Diminished 7th (m7(b5))

  • 1 – b3 – b5 – b7
  • Semitone 3 + 3 + 4

Fully Diminished 7th (o7, dim7)

  • 1 – b3 – b5 – bb7
  • Semitone 3 + 3 + 3

Augmented 7th (+7, aug7)

  • 1 – 3 – #5 – b7
  • Semitone 4 + 4 + 2

Progressions I – Diatonic Chords

Diatonic – within a key

Major

  • Diatonic Triads = C, Dm, Em, F, G, Am, Bdim
  • Roman Numerals = I, ii, iii, IV, V, vi, viio
  • Diatonic Seventh Chords = Cmaj7, Dm7, Em7, Fmaj7, G7, Am7, Bm7(b5)

Minor

  • Diatonic Triads = Am, Bdim, C, Dm, E(!), F, G#dim (!!)
  • Roman Numerals = i, iio, III, iv, V, VI, viio
  • Diatonic Seventh Chords = Am7, Bmin7(b5), Cmaj7, Dm7, E7, Fmaj7, G#dim7

Progressions II – Classical Progressions

Classical Functions = Tonic, Predominant, and Dominant

Tonic (I) can go to and from any form

  • Other types include Mediant (iii) and Subtonic (vi)

Predominant (ii or IV) usually goes to Dominant

Dominant (V or viio) wants to go to Tonic

  • V always major because of leading tone (or 7th scale degree)
  • Ending on dominant is a great way to loop

Seventh Chords have the same function as their diatonic triadic counterparts

Progressions III – Pop Schemas

From Open Music Theory – link

Schemas: Progressions that represent typical movement in popular music with allowance for substitutes (such as using ii instead of IV) and rotations (or starting on a different chord)

  • 12-bar Blues: I – I – I – I – IV – IV – I – I – V – IV – I – V
  • Double Plagal: bVII – IV – I
  • Doo-Wop: I – vi – IV – V
  • Singer/Songwriter: vi – IV – I – V
  • Hopscotch: IV – V – vi – I
  • Lament: i – bVII – bVI – V
  • Circle of Fifths: i – iv – VII – III etc.
  • Puff: I – iii – IV

Progressions IV – Triadic Transformations

Triadic Transformations: A theory on harmony developed over the last 160 years (originating from Hugo Riemann) to explain non-diatonic triadic movement. Operations are represented by a single letter, and R, P, and L can be used in combination of up to four letters with no sequential repetition. Practically, operations such as these are often explored in film music.

Relative (R)

  • Change to Relative (I > vi or i > III)
  • From Major: Raise 5th by 2 semitones
  • From Minor: Lower Root by 2 semitones
  • C > Am or Am > C
  • The Prelude from Final Fantasy series

Parallel (P)

  • Change to Parallel Mode (I > i or i > I)
  • From Major: Lower third by a semitone
  • From Minor: Raise third by a semitone
  • C > Cm or Am > A
  • Kass’s Final Song from The Legend of Zelda: Breath of the Wild
    • lead sheet – music
    • Uses P between Am and A at change between first and last section (mm. 16-19, 00:16-00:19)

Leading Tone (L)

  • From Major: Lower Root (1) by semitone to Leading Tone (7) or I > iii (C > Em)
  • From Minor: Raise 5th by a semitone or i > VI (Em > C)
  • •Velvet Room Theme (opening) from Persona series

Special Operation: SLIDE (S)

  • From Major: Raise Root and 5th by semitone or I > bii (A > Bbm)
  • From Minor: Lower Root and 5th by semitone or i > (#)VII (Cm > B)
  • Trisection from Final Fantasy Tactics
    • (music, occurs at 00:56-1:00, Db > Dm)

Progressions V – Combinations, Extended Harmony, Lehman Terms, and Other Harmonies

Combinations

  • Example. RP: C + R = Am + P = A
    • C > A
    • Brinstar from Metroid
  • Example LPL: E + L = G#m + P = Ab + L = Cm
    • E > Cm
  • Example RPRP: A + R = F#m + P = Gb + R = Ebm + P = Eb;
    • A > Eb

Extended Harmony (9ths, 11ths, and 13ths)

  • Ninth Chords
    • 9 = 4 + 3 + 3 + 4
    • maj9 = 4 + 3 + 4 + 3
    • min9 = 3 + 4 + 3 + 4
    • 7(b9) = 4 + 3 + 3 + 3
    • 7(#9) = 4 + 3 + 3 + 5
  • Eleventh Chords
    • 11 = 4 + 3 + 3 + 4 + 3
    • min11 = 3 + 4 + 3 + 4 + 3
    • maj9(#11) = 4 + 3 + 4 + 3 + 4
    • 9(#11) = 4 + 3 + 3 + 4 + 4
    • Can alter ninth as well with 7 basis (4 + 3 + 3…)
  • Thirteenth Chords
    • 13 = 4 + 3 + 3 + 4 + 3 + 4
    • 11(b13) = 4 + 3 + 3 + 4 + 3 + 3
    • Can alter ninth and eleventh as well with 7 basis

Lehman Terms (and Other Special Transformations)

  • Hollywood Harmony pp.90, 97-99
  • Tx = Transpose x amount of semitones up from first chord while retaining quality
    • Example C + T4 = E
    • Example Bm + T6 = Fm
  • N (Near Fifth)
    • If major, transpose up five semitones to the new root and switch modes
      • Example: A + N = Dm
      • Teardrop
    • If minor, transpose down five semitones to the new root and switch modes
      • Example Em + N = B
  • H (Hexatonic Pole)
    • If major, transpose down four semitones to new root and switch modes
      • Example D + H = Bbm
    • If minor, transpose up four semitones to new root and switch modes
      • Example Am + H = Db
  • ~y = “fuzzy transformation”, extended harmony (based on triad) and alternations covered

Other Harmonies

  • Quartel – based off of 5 semitones (5 + 5 + 5….)
  • Quintel – based off of 7 semitones (7 + 7 + 7…)
  • Clusters – based off of 1 or 2 semitones
    • Chromatic – based off of 1 semitone (1 +1 + 1…)
    • Whole-Tone – based of 2 semitones (2 + 2 + 2…)
    • Combination Clusters – mixture of 1 and 2 semitones
  • …Actually, anything is possible. We can utilize set theory to define all other brand of harmonies (and existing ones) for the equal temperament system. It can examine other systems with accommodations, but it is usually not the best tool for the job (many cultures have written theory and notation supporting other tuning and musical systems).