Advanced Harmony

This document covers advanced music theory concepts for experienced musicians and those looking to explore jazz, modern classical, and experimental harmony in Relanote.

Church Modes

What are Modes?

Modes are scales derived by starting on different degrees of a parent scale. The seven church modes (or diatonic modes) come from the major scale:

Mode	Degree	Pattern	Character
Ionian	1st	W-W-H-W-W-W-H	Bright, happy (= Major)
Dorian	2nd	W-H-W-W-W-H-W	Minor with bright 6th
Phrygian	3rd	H-W-W-W-H-W-W	Dark, Spanish/Middle Eastern
Lydian	4th	W-W-W-H-W-W-H	Dreamy, floating
Mixolydian	5th	W-W-H-W-W-H-W	Dominant, bluesy
Aeolian	6th	W-H-W-W-H-W-W	Natural minor
Locrian	7th	H-W-W-H-W-W-W	Diminished, unstable

Each mode has a characteristic tone that distinguishes it from major or natural minor:

Mode	vs Major/Minor	Characteristic Tone
Dorian	Minor + M6	Raised 6th (M6 vs m6)
Phrygian	Minor + m2	Lowered 2nd (m2 vs M2)
Lydian	Major + A4	Raised 4th (#4)
Mixolydian	Major + m7	Lowered 7th (b7)
Locrian	Minor + d5	Diminished 5th (b5)

Modes in Relanote

rela

; Church modes as interval sets
scale Ionian     = { R, M2, M3, P4, P5, M6, M7 }  ; = Major
scale Dorian     = { R, M2, m3, P4, P5, M6, m7 }
scale Phrygian   = { R, m2, m3, P4, P5, m6, m7 }
scale Lydian     = { R, M2, M3, A4, P5, M6, M7 }
scale Mixolydian = { R, M2, M3, P4, P5, M6, m7 }
scale Aeolian    = { R, M2, m3, P4, P5, m6, m7 }  ; = Natural Minor
scale Locrian    = { R, m2, m3, P4, d5, m6, m7 }

Modal Rotation with `rotate`

You can think of modes as rotations. The rotate builtin shifts elements:

rela

; rotate shifts block elements
; rotate 1 moves first element to end
| C4 D4 E4 F4 G4 A4 B4 | |> rotate 1  ; => | D4 E4 F4 G4 A4 B4 C4 |

; C Ionian rotated by 1 = D Dorian (starting from D)
; C Ionian rotated by 2 = E Phrygian (starting from E)
; ...and so on for all 7 modes

Diatonic Harmony

Diatonic Chords

Diatonic chords are built using only notes from a single scale. In major:

Degree	Triad	Seventh	Function
I	Major	Maj7	Tonic
ii	minor	min7	Subdominant
iii	minor	min7	Tonic substitute
IV	Major	Maj7	Subdominant
V	Major	Dom7	Dominant
vi	minor	min7	Tonic substitute
vii°	dim	min7(b5)	Dominant substitute

rela

; Diatonic triads in C major
scale Major = { R, M2, M3, P4, P5, M6, M7 }

chord IMaj   = [ R, M3, P5 ]       ; C
chord IImin  = [ R, m3, P5 ]       ; Dm  (built on 2nd degree)
chord IIImin = [ R, m3, P5 ]       ; Em
chord IVMaj  = [ R, M3, P5 ]       ; F
chord VMaj   = [ R, M3, P5 ]       ; G
chord VImin  = [ R, m3, P5 ]       ; Am
chord VIIdim = [ R, m3, d5 ]       ; Bdim

; Diatonic 7th chords
chord IMaj7   = [ R, M3, P5, M7 ]      ; Cmaj7
chord IImin7  = [ R, m3, P5, m7 ]      ; Dm7
chord IIImin7 = [ R, m3, P5, m7 ]      ; Em7
chord IVMaj7  = [ R, M3, P5, M7 ]      ; Fmaj7
chord V7      = [ R, M3, P5, m7 ]      ; G7 (dominant)
chord VImin7  = [ R, m3, P5, m7 ]      ; Am7
chord VIIm7b5 = [ R, m3, d5, m7 ]      ; Bm7(b5)

Functional Harmony

Chords serve three main functions:

Function	Chords	Character
Tonic	I, iii, vi	Stable, home
Subdominant	ii, IV	Moving away
Dominant	V, vii°	Tension, wants to resolve

rela

; ii - V - I progression (jazz standard)
let twoFiveOne =
  | [<2> <4> <6> <8>]:2 |    ; IImin7
  ++ | [<5> <7> <9> <11>]:2 | ; V7
  ++ | [<1> <3> <5> <7>]:1 |  ; IMaj7

Tension Chords

What are Tensions?

Tensions are chord tones beyond the 7th: 9th, 11th, and 13th. They add color and complexity.

Tension	Interval	Semitones from Root
9	M9 (= M2 + octave)	14
b9	m9	13
#9	A9	15
11	P11 (= P4 + octave)	17
#11	A11	18
13	M13 (= M6 + octave)	21
b13	m13	20

Available Tensions

Not all tensions work with all chord types:

Chord Type	Available Tensions
Maj7	9, #11, 13
min7	9, 11, 13
Dom7	9, #11, 13 (natural)
Dom7	b9, #9, #11, b13 (altered)
min7(b5)	9, 11, b13

Tension Chords in Relanote

rela

; Extended chords
chord Maj9   = [ R, M3, P5, M7, M9 ]
chord Maj13  = [ R, M3, P5, M7, M9, M13 ]

chord min9   = [ R, m3, P5, m7, M9 ]
chord min11  = [ R, m3, P5, m7, M9, P11 ]

chord Dom9   = [ R, M3, P5, m7, M9 ]
chord Dom13  = [ R, M3, P5, m7, M9, M13 ]

; Altered dominant tensions
chord Dom7b9     = [ R, M3, P5, m7, m9 ]
chord Dom7sharp9 = [ R, M3, P5, m7, A9 ]
chord Dom7b13    = [ R, M3, P5, m7, m13 ]

; The "Hendrix chord" - 7#9
chord HendrixChord = [ R, M3, P5, m7, A9 ]  ; E7#9 in Purple Haze

Voice Leading with Tensions

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; Smooth voice leading: tensions resolve down by step
let smoothTwoFive =
  | [<2> <4> <6> <8> <9>]:2 |       ; Dm9
  ++ | [<5> <7> <9> <11> <13>]:2 |  ; G13
  ++ | [<1> <3> <5> <7> <9>]:1 |    ; Cmaj9

Altered Scale

What is the Altered Scale?

The altered scale (also called "super locrian" or "diminished whole-tone") contains all four altered tensions: b9, #9, #11 (= b5), and b13 (= #5).

Degree	1	b2	#2	3	#4	#5	b7
Interval	R	m2	A2	M3	A4	A5	m7

Altered = Melodic Minor `rotate 6`

The altered scale is the 7th mode of melodic minor. Think of it as melodic minor rotated by 6 positions:

rela

; Melodic minor scale
scale MelodicMinor = { R, M2, m3, P4, P5, M6, M7 }

; Play Ab melodic minor as a block, then rotate 6
; Ab Bb Cb Db Eb F G => rotated by 6 => G Ab Bb Cb Db Eb F
; This gives us G Altered!

let abMelodicMinor = | Ab4 Bb4 Cb5 Db5 Eb5 F5 G5 |
let gAltered = abMelodicMinor |> rotate 6  ; => | G5 Ab4 Bb4 Cb5 Db5 Eb5 F5 |

Melodic Minor Modes

All seven modes of melodic minor are useful (each is a rotate of the parent):

Mode	Name	rotate	Formula	Use
I	Melodic Minor	0	R M2 m3 P4 P5 M6 M7	min(maj7) chords
II	Dorian b2	1	R m2 m3 P4 P5 M6 m7	sus(b9) chords
III	Lydian Augmented	2	R M2 M3 A4 A5 M6 M7	Maj7(#5) chords
IV	Lydian Dominant	3	R M2 M3 A4 P5 M6 m7	7(#11) chords
V	Mixolydian b6	4	R M2 M3 P4 P5 m6 m7	7(b13) chords
VI	Locrian #2	5	R M2 m3 P4 d5 m6 m7	min7(b5) chords
VII	Altered	6	R m2 A2 M3 A4 A5 m7	7alt chords

In Relanote

rela

; Melodic minor and its modes
scale MelodicMinor    = { R, M2, m3, P4, P5, M6, M7 }
scale DorianFlat2     = { R, m2, m3, P4, P5, M6, m7 }
scale LydianAugmented = { R, M2, M3, A4, A5, M6, M7 }
scale LydianDominant  = { R, M2, M3, A4, P5, M6, m7 }
scale MixolydianFlat6 = { R, M2, M3, P4, P5, m6, m7 }
scale LocrianNat2     = { R, M2, m3, P4, d5, m6, m7 }
scale Altered         = { R, m2, A2, M3, A4, A5, m7 }

; Altered dominant chord
chord Alt7 = [ R, M3, A5, m7, m9 ]  ; 7(#5b9)

; ii-V-I with altered dominant
let alteredTwoFive =
  | [<2> <4> <6> <8>]:2 |               ; Dm7
  ++ | G4 B4 Eb5 F5 Ab5 |:2             ; G7alt (absolute pitches for clarity)
  ++ | [<1> <3> <5> <7>]:1 |            ; Cmaj7

Harmonic Minor P5 Below (HMP5b)

What is HMP5b?

HMP5b (Harmonic Minor Perfect 5th Below), also called Phrygian Dominant or Spanish Phrygian, is the 5th mode of harmonic minor (= rotate 4).

rela

; A Harmonic Minor rotated by 4 = E Phrygian Dominant
let aHarmonicMinor = | A4 B4 C5 D5 E5 F5 G#5 |
let ePhrygianDom = aHarmonicMinor |> rotate 4  ; => | E5 F5 G#5 A4 B4 C5 D5 |

The Characteristic Sound

HMP5b combines:

Phrygian b2 (Spanish/Arabic sound)
Major 3rd (dominant chord quality)

This creates the classic flamenco/Middle Eastern dominant sound.

Interval	R	m2	M3	P4	P5	m6	m7
Character	Root	b9 tension	Major 3rd	11	5	b13	Dominant 7

In Relanote

rela

; Harmonic minor modes (each is rotate N of harmonic minor)
scale HarmonicMinor   = { R, M2, m3, P4, P5, m6, M7 }  ; rotate 0
scale LocrianNat6     = { R, m2, m3, P4, d5, M6, m7 }  ; rotate 1
scale IonianAug       = { R, M2, M3, P4, A5, M6, M7 }  ; rotate 2
scale DorianSharp4    = { R, M2, m3, A4, P5, M6, m7 }  ; rotate 3
scale PhrygianDom     = { R, m2, M3, P4, P5, m6, m7 }  ; rotate 4 = HMP5b
scale LydianSharp2    = { R, A2, M3, A4, P5, M6, M7 }  ; rotate 5
scale SuperLocrianbb7 = { R, m2, m3, d4, d5, m6, d7 }  ; rotate 6

; Flamenco-style progression
let flamenco =
  | [<1> <3> <5>] |:4           ; Am
  ++ | [<7> <2> <4>] |:4        ; G
  ++ | [<6> <1> <3>] |:4        ; F
  ++ | E4 G#4 B4 D5 |:4         ; E7(b9) - Phrygian Dominant

Messiaen's Modes of Limited Transposition

What are Symmetrical Scales?

Olivier Messiaen identified scales that repeat at intervals smaller than an octave. These modes of limited transposition have only 2, 3, 4, or 6 unique transpositions (unlike the 12 of normal scales).

The Seven Modes

Mode	Pattern	Transpositions	Notes
1	W-W-W-W-W-W	2	Whole tone scale
2	H-W-H-W-H-W-H-W	3	Octatonic (diminished)
3	W-H-H-W-H-H-W-H-H	4	9 notes
4	H-H-m3-H-H-H-m3-H	6	8 notes
5	H-M3-H-H-M3-H	6	6 notes
6	W-W-H-H-W-W-H-H	6	8 notes
7	H-H-H-W-H-H-H-H-W-H	6	10 notes

Mode 2: Octatonic (Diminished Scale)

The most commonly used symmetrical scale in jazz:

Half-Whole: H-W-H-W-H-W-H-W (starts with half step)
Whole-Half: W-H-W-H-W-H-W-H (starts with whole step)

C Half-Whole: C - Db - Eb - E - F# - G - A - Bb - C
C Whole-Half: C - D  - Eb - F - Gb - Ab - A - B  - C

In Relanote

rela

; Messiaen's Modes of Limited Transposition
scale WholeTone    = { R, M2, M3, A4, A5, A6 }          ; Mode 1
scale Diminished   = { R, m2, m3, M3, A4, P5, M6, m7 }  ; Mode 2 (H-W)
scale DiminishedWH = { R, M2, m3, P4, d5, m6, M6, M7 }  ; Mode 2 (W-H)

; Mode 3
scale Messiaen3 = { R, M2, m3, M3, A4, P5, m6, M6, M7 }

; Whole tone dominant
chord Aug7 = [ R, M3, A5, m7 ]  ; Works with whole tone scale

; Diminished 7th chord (symmetrical - same chord every m3)
chord Dim7 = [ R, m3, d5, M6 ]  ; M6 = d7 enharmonically

Symmetry and Transposition

rela

; Diminished scale has only 3 transpositions:
; C dim = Eb dim = F# dim = A dim
; Db dim = E dim = G dim = Bb dim
; D dim = F dim = Ab dim = B dim

; Whole tone has only 2 transpositions:
; C whole tone = D = E = F# = G# = A#
; Db whole tone = Eb = F = G = A = B

Lydian Chromatic Concept

George Russell's Theory

The Lydian Chromatic Concept of Tonal Organization (1953) proposes that the Lydian scale (not Ionian/Major) is the most consonant scale relative to a major chord.

Why Lydian?

The major scale has a dissonance: the 4th degree (F in C major) creates an "avoid note" against the major chord. Lydian's #4 eliminates this:

C Major chord: C - E - G

C Ionian:  C - D - E - F - G - A - B    (F clashes with E)
C Lydian:  C - D - E - F# - G - A - B   (F# = #11, no clash)

The Lydian Chromatic Scale

Russell extended Lydian to include all 12 chromatic notes, ordered by consonance:

Order	Notes	Relationship
1-7	C D E F# G A B	Lydian scale (most consonant)
8	F	Lydian b7 (Mixolydian character)
9	Bb	Blues note
10	Eb	Minor character
11	Ab	Further removed
12	Db	Most distant

Chord-Scale Unity

Russell's concept: every chord implies a scale, and vice versa. The parent scale defines "in" and "out" notes:

Chord	Parent Scale
Cmaj7	C Lydian
Cmaj7#11	C Lydian
C7	C Lydian Dominant (mode IV of G melodic minor)
Cm7	C Dorian
Cm(maj7)	C Melodic Minor
C7alt	C Altered (mode VII of Db melodic minor)

In Relanote

rela

; Lydian as the primary scale
scale Lydian = { R, M2, M3, A4, P5, M6, M7 }

; Lydian Chromatic extensions
scale LydianDominant = { R, M2, M3, A4, P5, M6, m7 }     ; add b7
scale LydianAugmented = { R, M2, M3, A4, A5, M6, M7 }    ; add #5
scale LydianDimished = { R, M2, M3, A4, P5, M6, m7, M7 } ; add both 7ths

; Chord-scale approach: define chord with its scale
let cmaj7_sound = {
  chord: [ R, M3, P5, M7 ],
  scale: Lydian,
  avoid: []  ; no avoid notes in Lydian!
}

; Vertical vs Horizontal
; Vertical: chord tones (arpeggios)
; Horizontal: scale tones (melody)
let lydianMelody =
  | <1> <2> <3> <#4> <5> <6> <7> <8> |

Practical Applications

Jazz ii-V-I with Extensions

rela

scale Major = { R, M2, M3, P4, P5, M6, M7 }
set key C4
set tempo 120

; Rich ii-V-I voicings
let jazzTwoFiveOne =
  ; Dm9
  | D3 A3 C4 E4 F4 |:2
  ; G13(b9) - altered dominant
  ++ | G2 B3 E4 F4 Ab4 |:2
  ; Cmaj9
  ++ | C3 E3 B3 D4 |:1

rela

; Borrowing chords from parallel modes
set key C4

; I - bVII - IV - I (borrowing bVII from C Mixolydian)
let modalInterchange =
  | [<1> <3> <5>] |:4     ; C
  ++ | Bb3 D4 F4 |:4       ; Bb (from C Mixolydian)
  ++ | [<4> <6> <8>] |:4   ; F
  ++ | [<1> <3> <5>] |:4   ; C

Symmetrical Scale Application

rela

; Using diminished scale over dominant 7th
set key G4  ; G7 resolving to C

; G diminished (H-W) for G7(b9) sound
let dimDominant =
  | G4 Ab4 Bb4 B4 Db5 D5 E5 F5 |:4
  ++ | C4 E4 G4 |:1  ; resolve to C

Advanced Harmony ​

Church Modes ​

What are Modes? ​

Modal Characteristics ​

Modes in Relanote ​

Modal Rotation with rotate ​

Diatonic Harmony ​

Diatonic Chords ​

Functional Harmony ​

Tension Chords ​

What are Tensions? ​

Available Tensions ​

Tension Chords in Relanote ​

Voice Leading with Tensions ​

Altered Scale ​

What is the Altered Scale? ​

Altered = Melodic Minor rotate 6 ​

Melodic Minor Modes ​

In Relanote ​

Harmonic Minor P5 Below (HMP5b) ​

What is HMP5b? ​

The Characteristic Sound ​

In Relanote ​

Messiaen's Modes of Limited Transposition ​

What are Symmetrical Scales? ​

The Seven Modes ​

Mode 2: Octatonic (Diminished Scale) ​

In Relanote ​

Symmetry and Transposition ​

Lydian Chromatic Concept ​

George Russell's Theory ​

Why Lydian? ​

The Lydian Chromatic Scale ​

Chord-Scale Unity ​

In Relanote ​

Practical Applications ​

Jazz ii-V-I with Extensions ​

Modal Interchange ​

Symmetrical Scale Application ​

Further Reading ​

Advanced Harmony

Church Modes

What are Modes?

Modal Characteristics

Modes in Relanote

Modal Rotation with `rotate`

Diatonic Harmony

Diatonic Chords

Functional Harmony

Tension Chords

What are Tensions?

Available Tensions

Tension Chords in Relanote

Voice Leading with Tensions

Altered Scale

What is the Altered Scale?

Altered = Melodic Minor `rotate 6`

Melodic Minor Modes

In Relanote

Harmonic Minor P5 Below (HMP5b)

What is HMP5b?

The Characteristic Sound

In Relanote

Messiaen's Modes of Limited Transposition

What are Symmetrical Scales?

The Seven Modes

Mode 2: Octatonic (Diminished Scale)

In Relanote

Symmetry and Transposition

Lydian Chromatic Concept

George Russell's Theory

Why Lydian?

The Lydian Chromatic Scale

Chord-Scale Unity

In Relanote

Practical Applications

Jazz ii-V-I with Extensions

Modal Interchange

Symmetrical Scale Application

Further Reading