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Harmony: Scales 🎶

Diatonic scales

A diatonic scale is a scale of 7 tones (heptatonal) that has 2 semitones steps and 5 tone steps where the semitones are separated at least by two full tones

In summary: any rotation or transposition of the CMajor scale

Diatonic Modes:

| N   | Name       | Pattern       | On C                | Natural notes | AKA
|-----|------------|---------------|---------------------|---------------|----------
| I   | Ionian     | 2 2 1 2 2 2 1 | C D  E  F  G  A  B  | C D E F G A B | Major
| II  | Dorian     | 2 1 2 2 2 1 2 | C D  Eb F  G  A  Bb | D E F G A B C | 
| III | Phrygian   | 1 2 2 2 1 2 2 | C Db Eb F  G  Ab Bb | E F G A B C D | 
| IV  | Lydian     | 2 2 2 1 2 2 1 | C D  E  F# G  A  B  | F G A B C D E | 
| V   | Mixolydian | 2 2 1 2 2 1 2 | C D  E  F  G  A  Bb | G A B C D E F | 
| VI  | Aeolian    | 2 1 2 2 1 2 2 | C D  Eb F  G  Ab Bb | A B C D E F G | Natural Minor
| VII | Locrian    | 1 2 2 1 2 2 2 | C Db Eb F  Gb Ab Bb | B C D E F G A |

Insights:

  • We can get any mode with white keys just by stressing the proper root.
  • Keeping the root in C, we can obtain all the modes by adding progresivelly flats (or sharps)

A mechanical way of learning modes on C,

  • as we jump to the next 5th mode, we just add a flat.
  • flats are chosen interleaving one from the 3 blacks and next from 2 blacks group
  • pick the flat on the right
  • to obtain IV we sharp instead flat and pick from left

In action:

_x_x__x_x_x_
o o o Xo o o IV  #4 Lydian (Exception from major sharps F)
o o oo o o o I      Ionian (Major, the reference, all whites)
o o oo o oX  V   b7 Mixolydian (flats B)
o oX o o ox  II  b3 Dorian (flats E)
o ox o oX x  VI  b6 Aeolian (flats A)
oX x o ox x  III b2 Phrygian (flats D)
ox x oX x x  VII b5 Locrian (flats G)
_x_x__x_x_x_
 4 2  5 3 1  (Order to add flats)

Note

If we extend the method we will get the other 5 tonalities, but they do not include the root (C) so they are not modes of the scale.

Each mode has their chords:

| N   | Name       | Natural notes | Tonic | 7th | Dom  | Dom7th |
|-----|------------|---------------|-------|-----|------|--------|
| I   | Ionian     | C D E F G A B | CMaj  | CM7 | GMaj | G7     |
| II  | Dorian     | D E F G A B C | Dmin  | Dm7 | Amin | Am7    |
| III | Phrygian   | E F G A B C D | Emin  | Em7 | Bdim | B∅7    |
| IV  | Lydian     | F G A B C D E | FMaj  | FM7 | GMaj | GM7    |
| V   | Mixolydian | G A B C D E F | GMaj  | GM7 | Dmin | Gm7    |
| VI  | Aeolian    | A B C D E F G | Amin  | Am7 | Emin | Em7    |
| VII | Locrian    | B C D E F G A | Bdim  | B∅7 | FMaj | FM7    |
  • The tonic (rest) chord: I III V
  • The dominant (tension) chord: V VII II
  • The 7th: I III V VII
  • The dominant 7th: V VII II IV

The tonic chord provides the majority or minority or neither (locrian) character of the mode.

Moods of modes: https://www.youtube.com/watch?v=8i7K9GYzbIY

Major modes (Ionian, Lydian, Mixolydian)

  • Modes with a major third (+4) are called major.
  • Resting chord (tonic) is Major: I
  • They bring a happy mood

Which are

  • I Ionian:
    • Major key
    • The dominant 7th is the only dominant minor 7th
    • Contains B and F that lead to C and G
    • G7 C is a perfect closure (Chinpon)
    • Happy + Ritmic
  • IV Lydian
    • F -> F# (augmented 4th)
    • Happy + Brilliant, magic
  • V Mixolydian
    • Dominant 7th is minor with minor 7th
    • Sounds milder but also epic
    • Also epic because bVII BbMaj
    • Happy + Epic

Minor modes (Aeolian, Dorian, Phrygian)

  • Modes with a minor third (+3) are called major.
  • Resting chord (tonic) is a minor triad: ia
  • They bring a sad mood

Which are

  • VI Aeolian:
    • Mood: Sad + epic
    • Dominant vii
  • II Dorian
    • In between Aeolean and Mixolyidian
    • Has the Epic chord of Mixolydian bVII BbMaj
    • IVMaj FMaj is also a happy/force contrast
  • III Phrygian
    • Domminant is a B∅7
    • Inquietante

Neither major neither minor

VII Locrian mode is quite special as the resting triad is a dim chord, neither major nor minor.

  • VII Locrian tonic chord is neither Major nor minor, it is a dim chord
    • Weird mood
    • Resting chord is a diminished 5th chord
    • The only one with the bV

Pentatonic scale

Pentatonic scale is used by many cultures. An octave has 5 notes a fifth away (7 semitones).

C3 -(+7)-> G3 -(+7)-> D4 -(+7)-> A4 -(+7)-> E5

Folded in a octave and sorted: C D E G A, resulting in +2 +2+ 3 +2 +3 interval pattern.

Among the 12 existing transpositions, 4 are specially useful:

The ones that fit into natural notes:

  • C: C D E G A
  • G: G A B D E
  • F: F G A C D

And the one that uses all and only altered notes:

  • F#: F# G# A# C# D#

Yep, the black piano keys conforms a pentatonic scale! A melody that you can transpose in order to use just black keys is using a pentatonic scale.

Songs in pentatonics

  • Starway to heaven - Led Zeppelin
  • Sunshine Of Your Love – Cream
  • Under the bridge - Red Hot
  • My Girl - The Temptations
  • Wandrin' Star - Lee Marvin (Western)
  • Hoochie Coochie - Muddy Waters
  • Don't worry be happy - McFerri

Modes:

| N   | Western             | Intervals | On C         | CMaj Rot  |
|-----|---------------------|-----------|--------------|-----------|
| I   | Major pentatonic    | 2 2 3 2 3 | C D  E G  A  | C D E G A |
| II  | Egyptian, suspended | 2 3 2 3 2 | C D  F G  A# | D E G A C |
| III | Blues minor         | 3 2 3 2 2 | C D# F G# A# | E G A C D |
| IV  | Blues major         | 2 3 2 2 3 | C D  F G  A  | G A C D E |
| V   | Minor pentatonic    | 3 2 2 3 2 | C D# F G  A# | A C D E G |

| N   | Western             | CMaj Rot  | Natural transpositions | Altered trans. |
|-----|---------------------|-----------|------------------------|----------------|
| I   | Major pentatonic    | C D E G A | F G A C D - G A B D E  | Gb Ab Bb Db Eb |
| II  | Egyptian, suspended | D E G A C | G A C D F - A B D E G  | Ab Bb Db Eb Gb |
| III | Blues minor         | E G A C D | A C D F G - B D E G A  | Bb Db Eb Gb Ab |
| IV  | Blues major         | G A C D E | C D F G A - D E G A B  | Db Eb Gb Ab Bb |
| V   | Minor pentatonic    | A C D E G | D F G A C - E G A B D  | Eb Gb Ab Bb Db |
  • Major: es la unica que puede construir un acorde mayor en C (C E G), es la unica que tiene E, construida con dos segundas
  • Menor: es la única que puede construir un acorde menor en C (C D# G)
  • Minor blues: Incluye la 3a menor pero no la 5a???
  • Major blues: ???

Triads in Pentatonics are limited as not all diatonic notes are available.

  • I, IIsus4, IIIsus4, Vsus4, vi (expressed in diatonic intervals)
  • C, Dsus4, Esus4, Gsus4, Amin (C transposition)

Because of these limitations pentatonic melodies are usually harmonized with diatonic chords.

Also, pentatonics on C can be considered by the notes shared by three Diatonic Scales on C

I IV V -> Major
I II V -> Blues Major
II V VI -> Suspended
II III VI -> Minor
III VI VII - Blues Minor


| Ionian I | Lydian IV | Mixolydian V | CD_F_GA | Major Pentatonic I 
| Ionian I | Dorian II | Mixolydian V | CD*E*G_A_ | Blues Major Pentatonic IV
| Aeolian VI | Dorian II | Mixolydian V | C_D_EG*B* | Suspended Pentatonic II
| Aeolian VI | Dorian II | Mixolydian V | CE*F*GA | Minor Pentatonic VI

|-----|------------|---------------|---------------------|---------------|-------|-----|------|--------|----------
| I   | Ionian     | 2 2 1 2 2 2 1 | C D  E  F  G  A  B  | C D E F G A B | CMaj  | CM7 | GMaj | G7     | Major
| II  | Dorian     | 2 1 2 2 2 1 2 | C D  Eb F  G  A  Bb | D E F G A B C | Dmin  | Dm7 | Amin | Am7    | 
| III | Phrygian   | 1 2 2 2 1 2 2 | C Db Eb F  G  Ab Bb | E F G A B C D | Emin  | Em7 | Bdim | B∅7    | 
| IV  | Lydian     | 2 2 2 1 2 2 1 | C D  E  F# G  A  B  | F G A B C D E | FMaj  | FM7 | GMaj | GM7    | 
| V   | Mixolydian | 2 2 1 2 2 1 2 | C D  E  F  G  A  Bb | G A B C D E F | GMaj  | GM7 | Dmin | Gm7    | 
| VI  | Aeolian    | 2 1 2 2 1 2 2 | C D  Eb F  G  Ab Bb | A B C D E F G | Amin  | Am7 | Emin | Em7    | Natural Minor
| VII | Locrian    | 1 2 2 1 2 2 2 | C Db Eb F  Gb Ab Bb | B C D E F G A | Bdim  | B∅7 | FMaj | FM7    |

Chromatic scale

Dodecatonic. Uses all piano keys, so 12 semitone intervals. No modes available.

Whole-tone hexatonic

  • Whole-tone hexatonic scale has just whole-tone intervals (6*2semitones=12)
  • Because the intervals are uniform, has no sense to talk about diferent modes
  • Just has two transpositions:
    • The one with the lower keys of the scale in natural keys
      • C D E F# G# A#
    • The one with the lower keys of the scale in altered keys
      • Db Eb F G A B
    • On the semitone of the major scale switches from black to white keys and viceversa
  • Only two triads are available.
    • In C:
      • Caug (Eaug and G#aug are just inversions)
      • Daug (F#aug and A#aug are just inversions)
    • In F:
      • Faug (Aaug and Dbaug are just inversions)
      • Gaug (Baug and Ebaug are just inversions)
  • Function and mood
    • Because all the intervals are the same, a listener used to diatonic scale will not find the patterns and leading tones
    • So, the scale has an unsettling and weird mood
    • Also gives the sensation of being lost
    • Used in horror movies, in the dream carrillion
    • A root can be built upon repetition or stress

Melodic Minor scales

Jazz scales: Melodic, Harmonic, Augmented, Diminished...

Heptatonic scales which are chromatic transpositions or rotations of the C Melodic minor scale Like diatonic scales, also has 2 halftones and 5 fulltones, but now the two halftones are separated one fulltone.

| N   | Name        | Pattern       | Transposed on C      | Rotations            |
|-----|-------------|---------------|----------------------|----------------------|
| I   | Melodic Min | 2 1 2 2 2 2 1 | C  D  Eb F  G  A  B  | C  D  Eb F  G  A  B  |
| II  | Dorian b2   | 1 2 2 2 2 1 2 | C  Db Eb F  G  A  Bb | D  Eb F  G  A  B  C  |
| III | Lydian Aug  | 2 2 2 2 1 2 1 | C  D  E  F# G# A  B  | Eb F  G  A  B  C  D  |
| IV  | Lydian Dom  | 2 2 2 1 2 1 2 | C  D  E  F# G  A  Bb | F  G  A  B  C  D  E  |
| V   | Aeolian Dom | 2 2 1 2 1 2 2 | C  D  E  F  G  Ab Bb | G  A  B  C  D  Eb F  |
| VI  | Half Dimin. | 2 1 2 1 2 2 2 | C  D  Eb F  Gb Ab Bb | A  B  C  D  Eb F  G  |
| VII | Altered     | 1 2 1 2 2 2 2 | C  Db Eb E  Gb Ab Bb | B  C  D  Eb F  G  A  |

Harmonic Minor scales

Heptatonic scale an harmonic sequence 1 3 1 and a minor sequence 2 1 2 2

| N   | Name         | Pattern       | Transposed on C      | Rotations            |
|-----|--------------|---------------|----------------------|----------------------|
| I   | Harmonic Min | 2 1 2 2 1 3 1 | C  D  Eb F  G  Ab B  | C  D  Eb F  G  Ab B  |
| II  | Locrian 6    | 1 2 2 1 3 1 2 | C  Db Eb F  Gb A  Bb | D  Eb F  G  Ab B  C  |
| III | Major #5     | 2 2 1 3 1 2 1 | C  D  E  F  G# A  B  | Eb F  G  Ab B  C  D  | 
| IV  | Dorian #4    | 2 1 3 1 2 1 2 | C  D  Eb F# G  A  Bb | F  G  Ab B  C  D  Eb | 
| V   | Phrygian Dom | 1 3 1 2 1 2 2 | C  Db E  F  G  Ab Bb | G  Ab B  C  D  Eb F  | 
| VI  | Lydian #2    | 3 1 2 1 2 2 1 | C  D# E  F# G  A  B  | Ab B  C  D  Eb F  G  |
| VII | Altered bb7  | 1 2 1 2 2 1 3 | C  Db Eb Fb Gb Ab A  | B  C  D  Eb F  G  Ab |

Harmonic Major scales

Heptatonic scale an harmonic sequence 1 3 1 and a major sequence 2 2 1 2

| N   | Name        | Pattern       | Transposed on C      | Rotations            |
|-----|-------------|---------------|----------------------|----------------------|
| I   | Melodic Maj | 2 2 1 2 1 3 1 | C  D  E  F  G  Ab B  | C  D  E  F  G  Ab B  |
| II  | Dorian b5   | 2 1 2 1 3 1 2 | C  D  Eb F  Gb A  Bb | D  E  F  G  Ab B  C  |
| III | Phrygian b4 | 1 2 1 3 1 2 2 | C  Db Eb E  G  Ab Bb | E  F  G  Ab B  C  D  |
| IV  | Lydian b3   | 2 1 3 1 2 2 1 | C  D  Eb F# G  A  B  | F  G  Ab B  C  D  E  |
| V   | Myxolyd. b2 | 1 3 1 2 2 1 2 | C  Db E  F  G  A  Bb | G  Ab B  C  D  E  F  |
| VI  | Lyd. aug#2  | 3 1 2 2 1 2 1 | C  D# E  F# G# A  B  | Ab B  C  D  E  F  G  |
| VII | Locryan bb7 | 1 2 2 1 2 1 3 | C  Db Eb F  Gb Ab A  | B  C  D  E  F  G  Ab |

Double Harmonic scales

Has two harmonic sequences 1 3 1 and a full tone.

| N   | Name        | Pattern       | Transposed on C      | Rotations            |
|-----|-------------|---------------|----------------------|----------------------|
| I   | D.Harm.Maj. | 1 3 1 2 1 3 1 | C  Db E  F  G  Ab B  | C  Db E  F  G  Ab B  | Bizantine
| II  | Lydian #2#6 | 3 1 2 1 3 1 1 | C  D# F  F# G  A# B  | Db E  F  G  Ab B  C  |
| III | UltraPhryg. | 1 2 1 3 1 1 3 | C  Db Eb E  G  Ab A  | E  F  G  Ab B  C  Db |
| IV  | Gypsy Minor | 2 1 3 1 1 3 1 | C  D  Eb F# G  Ab B  | F  G  Ab B  C  Db E  | Hungarian minor
| V   | Oriental    | 1 3 1 1 3 1 2 | C  Db E  F  Gb A  Bb | G  Ab B  C  Db E  F  |
| VI  | Ionian #2#5 | 3 1 1 3 1 2 1 | C  D# E  F  G# A  B  | Ab B  C  Db E  F  G  |
| VII | Loc. bb3bb7 | 1 1 3 1 2 1 3 | C  Db D  F  Gb Ab A  | B  C  Db E  F  G  Ab |

AKA

  • North Indian Thaat named Bhairav
  • South Indian (Carnatic) Melakarta named Mayamalavagowla.

Songs:

  • Misirlou E Double Harmonic

Diminished scales

Octatonic scale of altering half and full tones.

| N   | Name             | Pattern         | Transposed on C         | Rotations            |
|-----|------------------|-----------------|-------------------------|----------------------|
| I   | Diminished       | 2 1 2 1 2 1 2 1 | C  D  Eb F  Gb Ab A  B  | C  D  E  F  G  Ab B  |
| II  | Dimini. inverted | 1 2 1 2 1 2 1 2 | C  Db Eb E  Gb F  A Bb  | D  E  F  G  Ab B  C  |

Other scales

C  Eb F  Gb G  Bb - 3 2 1 1 3 2 - Blues (minor pentatonic plus a perfect 4th)

Non-western scales (Western classic view)

Taken from here Origins are western perspective on how it sounds. Indeed each of those culture use many scales including some of the considered "western scales".

Pentatonics

| Origin     | intervals           |               |                      |
|------------|---------------------|---------------|----------------------|
| Egyptian   | 1  2     4  5    b7 | 2 3 2 3 2     | C  D     F  G     Bb |
| Chinese    | 1     3 #4  5     7 | 4 2 1 4 1     | C     E  F# G     B  |
| Japanese   | 1 b2     4  5 b6    | 1 4 2 1 4     | C  Bb    F  G  Ab    |

Heptatonics: Egyptian, Persian,

| Origin     | intervals           |               |                      |
|------------|---------------------|---------------|----------------------|
| Persian    | 1 b2  3  4 #4 b6  7 | 1 3 1 1 2 3 1 | C  Db E  F  Gb Ab B  |
| Indian     | 1  2  3  4  5 b6 b7 | 2 2 1 2 1 2 2 | C  D  E  F  G  Ab Bb |
| Arabic     | 1  2  3  4 #4 b6 b7 | 2 2 1 1 2 2 2 | C  D  E  F  Gb Ab Bb |
| Jewish     | 1 b2  3  4  5 b6 b7 | 1 3 1 2 1 2 2 | C  Db E  F  G  Ab Bb |
| Gypsy      | 1  2 b3 #4  5 b6 b7 | 2 1 3 1 1 2 2 | C  D  Eb F# G  Ab Bb |

1 3 1 2 1 3 1

C Db E F G Ab B