Harmony - NORDISC Music

Harmony

Table of Contents

INTERVALS ........................................................................................................... 7

THE HORIZONTAL AND VERTICAL MUSIC CONCEPTS ............................................................................. 7 INTERVALS (SOUND-ASPECT) .................................................................................................................... 8 NATURAL INTERVALS .................................................................................................................................. 9

Sound-Aspect within Intervals................................................................................................................................. 9

Neutral .................................................................................................................................... 9

Consonant .............................................................................................................................. 9

Dissonant ................................................................................................................................ 9 Neutral Intervals ..................................................................................................................................................... 10

Neutral .................................................................................................................................. 10

Consonant ............................................................................................................................ 10

Dissonant .............................................................................................................................. 10

SIMPLE HARMONY............................................................................................. 11

SUGGESTIONS FOR MOVEMENTS ........................................................................................................... 11 HARMONIZING ........................................................................................................................................... 11

Add 2nd

Voice ......................................................................................................................................................... 11 Add 3

rd voice........................................................................................................................................................... 11

Add 4th voice ........................................................................................................................................................... 12

Inversions ............................................................................................................................................................... 12 THE OVERTONES ...................................................................................................................................... 12

The Temperated Tonal System ............................................................................................................................ 13 The Overtones and The Major Triad .................................................................................................................... 13

CHORDS .............................................................................................................. 14

TRIADS........................................................................................................................................................ 14 THE CONSTITUTION OF CHORDS ............................................................................................................ 15

Paragraph 1 ............................................................................................................................................................ 15 Paragraph 2 ............................................................................................................................................................ 15 Paragraph 3 ............................................................................................................................................................ 15 Paragraph 4 ............................................................................................................................................................ 15 Paragraph 5 ............................................................................................................................................................ 15 Paragraph 6 ............................................................................................................................................................ 15 Paragraph 7 ............................................................................................................................................................ 15

TURNS AND ARPEGGIO ............................................................................................................................ 16 Determination of Chords ....................................................................................................................................... 16

MODAL ASPECTS ....................................................................................................................................... 17 Modal Aspects of the 6 basic triad chords ........................................................................................................... 17

SOUND-ASPECTS ...................................................................................................................................... 18

NORDISC

This file is locked and caanot be copied or printed..

Chapter 2, Harmony, Intervals

All Aspects of ROCK & JAZZ /1 Music Theory 2

Sound-aspects within chords ................................................................................................................................ 18

Consonant ............................................................................................................................ 18

Neutral .................................................................................................................................. 18

Dissonant .............................................................................................................................. 18 DESCRIPTION OF CHORDS ...................................................................................................................... 19

3 Part Chords ......................................................................................................................................................... 19 4 Part Chords ......................................................................................................................................................... 19 5 Part Chords ......................................................................................................................................................... 20 6 Part Chords ......................................................................................................................................................... 21 7 Part Chords ......................................................................................................................................................... 21

CHORD TABLE............................................................................................................................................ 22 Other Chord Symbols ............................................................................................................................................ 25

Translation of the French Note Names ............................................................................. 26 JAZZ CHORD SYMBOLS ............................................................................................................................ 27

Special Problems in Chord Notation..................................................................................................................... 27 Changes in the Chord Reflected in Notation ....................................................................................................... 28

Alternative bass note (other than prim): ............................................................................ 28

Added Notes......................................................................................................................... 28

Accidentals ........................................................................................................................... 28

Shorthand Chord Symbols .................................................................................................. 28 Temporary Pause In Third Based Harmony ........................................................................................................ 28 Bitonal Chords ........................................................................................................................................................ 28 Various Peculiarities .............................................................................................................................................. 28

CHORD BOXES (FRET DIAGRAMS) ................................................................. 30

MAJOR CHORD BOXES ............................................................................................................................. 30 MINOR CHORD BOXES .............................................................................................................................. 34 MOVABLE CHORD BOXES, ADVANCED JAZZ .......................................................................................... 38

OTHER CHORD FORMS ..................................................................................... 39

CLUSTERS OF 1/1 NOTES ......................................................................................................................... 39 CLUSTERS OF 1/2 NOTES ......................................................................................................................... 39 ALTERNATIVE CHORDS ............................................................................................................................ 40

Stacks of Quarters ................................................................................................................................................. 40

“Spontaneous” fourth stacks .............................................................................................. 40 Stacks of Fifths ...................................................................................................................................................... 41

FUNCTIONAL HARMONY ................................................................................... 42

BASIC PRINCIPLES OF FUNCTIONAL HARMONY .................................................................................... 43 THE CONSTITUTION OF FUNCTIONAL HARMONY .................................................................................. 43

Paragraph 1 ............................................................................................................................................................ 43 Paragraph 2 ............................................................................................................................................................ 43 Paragraph 3 ............................................................................................................................................................ 43

DOMINANT .................................................................................................................................................. 44 SUBDOMINANT........................................................................................................................................... 44 DOUBLE DOMINANT / SUBDOMINANT...................................................................................................... 45

Harmonic double functions .................................................................................................................................... 45 MAJOR / MINOR PARALLEL FUNCTIONS ................................................................................................. 45



BLUES FUNCTIONS.................................................................................................................................... 46 Harmonic blues functions ...................................................................................................................................... 46

NEAPOLITAN CHORDS .............................................................................................................................. 47 The Neapolitan function family.............................................................................................................................. 47

HARMONIC FUNCTIONS IN ONE KEY ....................................................................................................... 48 Table of Functions ................................................................................................................................................. 48

Shorthand Acronyms ........................................................................................................... 49 TABLE OF MODAL ASPECTS ..................................................................................................................... 49

Modal examples within functional harmony ...................................................................... 50

Comments ............................................................................................................................ 50 CHARACTERISTICS OF CHORD FUNCTIONS .......................................................................................... 50

TONIC ..................................................................................................................................................................... 50 DOMINANT ............................................................................................................................................................ 50 SUBDOMINANT .................................................................................................................................................... 50 Double Functions ................................................................................................................................................... 51 Dim Functions ........................................................................................................................................................ 51 Blues Functions...................................................................................................................................................... 51 Functions within Purely Modal Scales .................................................................................................................. 51 Functions within modal scales classified on scale steps .................................................................................... 52 Other Functional Terms......................................................................................................................................... 52 The Number System .............................................................................................................................................. 53 The Classical System ............................................................................................................................................ 53 My Suggestion ....................................................................................................................................................... 53 A Special Problem in Functional Harmony .......................................................................................................... 54

HARMONIC CADENCES .................................................................................... 55

TENSION LEVELS OF CHORD FUNCTIONS.............................................................................................. 55 STANDARD CADENCES ............................................................................................................................. 55 CADENCE OSTINATOS .............................................................................................................................. 57

"Simple 5-member Cadence of the Subdominant Type" .................................................................................... 57 OTHER CADENCES .................................................................................................................................... 58

Fade ........................................................................................................................................................................ 58 Rhythmical Cadence .............................................................................................................................................. 58 Rhythmical Cadences ............................................................................................................................................ 59 Linear Cadence ...................................................................................................................................................... 59

ADVANCED JAZZ CHORDS ............................................................................... 60

REHEARSING THE CHORDS ..................................................................................................................... 60 ROCK AND JAZZ TERMINOLOGY .............................................................................................................. 60 FUNCTIONAL HARMONY / DIATONIC TRIADS .......................................................................................... 60 SEVENTH CHORDS (4 PARTS) .................................................................................................................. 62 SIXTH CHORDS (4 / 5 PARTS) ................................................................................................................... 63 SUS CHORDS ............................................................................................................................................. 63 CHORDS WITH ADDED NOTES ................................................................................................................. 64 EXTENDED CHORDS ................................................................................................................................. 64 NINTH CHORDS (5 PARTS) ........................................................................................................................ 65 DOUBLE-ALTERED CHORDS ..................................................................................................................... 66 ELEVENTH CHORDS (6 PARTS) ................................................................................................................ 66 THIRTEENTH CHORDS (7 PARTS) ............................................................................................................ 67 STACKED CHORDS .................................................................................................................................... 67



POLYCHORDS ............................................................................................................................................ 67

A TRANSITION .................................................................................................... 68

TRANSITIVE HARMONY (MODULATION) ......................................................... 69

POSSIBLE MODULATIONS BETWEEN 2 KEYS ......................................................................................... 70 Function Shift ......................................................................................................................................................... 70 Non-Functional Steps ............................................................................................................................................ 70 Major to Minor ........................................................................................................................................................ 70

THE TRANSITIVE PRINCIPLES .................................................................................................................. 70 Function Shift ......................................................................................................................................................... 70

FUNCTION SHIFTS (TRANSITIVE HARMONY) .......................................................................................... 71 NON-FUNCTIONAL STEPS ......................................................................................................................... 73

Lower or raise ........................................................................................................................................................ 73 Guidelines Function Shift ...................................................................................................................................... 74

Find the First Key ................................................................................................................ 74

Compare Intervals in Key I and Key Ii ............................................................................... 74

Find the Function Shifts ...................................................................................................... 74

Search both Forwards and Backwards in the Melody ..................................................... 74 Blues Chords .......................................................................................................................................................... 75 "The Ravel Step" – "# Minor 3" ............................................................................................................................ 75

EPILOGUE TO TRANSITIVE HARMONY .................................................................................................... 75

ORCHESTRATION TUTOR ................................................................................. 76

THE SYMPHONY ORCHESTRA SCORE .................................................................................................... 77 A Very Simple Score Layout ................................................................................................................................. 78

THE INSTRUMENTS OF THE SYMPHONY ORCHESTRA ......................................................................... 79 Woodwinds ............................................................................................................................................................. 80

Transverse Flute .................................................................................................................. 80

Piccolo Flute......................................................................................................................... 81

Oboe ..................................................................................................................................... 81

English Horn ......................................................................................................................... 82

Clarinet ................................................................................................................................. 83

Bass Clarinet ........................................................................................................................ 84

Bassoon ................................................................................................................................ 85

Saxophone ........................................................................................................................... 86 Brass ....................................................................................................................................................................... 87

French Horn ......................................................................................................................... 87

Trumpet................................................................................................................................. 88

Trombone ............................................................................................................................. 89

Tuba ...................................................................................................................................... 90 Percussion .............................................................................................................................................................. 91 Other ....................................................................................................................................................................... 92

Harp ...................................................................................................................................... 92

Piano ..................................................................................................................................... 93 Strings ..................................................................................................................................................................... 94



Violin ..................................................................................................................................... 94

Viola ...................................................................................................................................... 95

Cello ...................................................................................................................................... 96

Double Bass ......................................................................................................................... 97 GOOD ORCHESTRATION PRACTICES ..................................................................................................... 98

Number of Duplicate Instruments ......................................................................................................................... 98

Woodwinds ........................................................................................................................... 98

Brass ..................................................................................................................................... 98

Percussion ............................................................................................................................ 98

Strings ................................................................................................................................... 98 Strings and Woodwinds ......................................................................................................................................... 99 String Chord Texture ........................................................................................................................................... 107 Arpeggio Strings................................................................................................................................................... 108 Woodwinds and Brass ......................................................................................................................................... 108 Fat and Thin Textures ......................................................................................................................................... 113 Tutti ....................................................................................................................................................................... 116 A “Floating” Score without a pulse...................................................................................................................... 122

OTHER HARMONIC SYSTEMS ........................................................................ 126

PARALLELISM........................................................................................................................................... 126 Parallelism non-functional, parallel chord movements ...................................................................................... 126

Main rules ............................................................................................................................126 POLYHARMONY / BITONALITY ................................................................................................................ 127

Polyharmony (bitonal chord relations) ................................................................................................................ 127

Bitonality - example ............................................................................................................128 CHORD ROWS.......................................................................................................................................... 129

Fourth Rows ......................................................................................................................................................... 129 Fifth Rows ............................................................................................................................................................ 129

NON-FUNCTIONAL HARMONY / COLOUR CHORDS .............................................................................. 129

INDEX HARMONY ............................................................................................. 131



All Aspects of ROCK & JAZZ

Volume 1 – Music Theory

4 of 5 documents

ISBN 9788791995071 4

th Edition, 1

st Issue

Autumn 2007 Produced in Denmark

Digital Books™ is a trademark of NORDISC Music & Text, DK-2700 Broenshoej, Denmark

www.nordisc-music.com

Text, notes, musical examples Illustrations, layout and concept © Copyright H.W. Gade 1984-2007

http://www.nordisc-music.com/



Absolute Harmony

Intervals

THE HORIZONTAL AND VERTICAL MUSIC CONCEPTS

Until now we have only mentioned of music moving in linear direction, i.e. on a horizon-

tal level. But 2 or more melodies moving on separate tonal levels create a linear move-

ment and a sound, i.e. a horizontal and a vertical sound. We distinguish between two

sorts of classical music; polyphonic (multiple-part) and homophonic (single part) mu-

sic. The fugues of Bach are polyphonic music, where the interplay between individual

voices is the predominant feature. Homophonic music on the contrary consists of one sin-

gle melody with harmonies, and the last 100 years and more have been, by and large,

purely homophonic. We live in the centuries of the chords.

To understand what a vertical sound, a "chord" is, you must understand what an interval is. If you have

studied classical Musical Theory before, you might have to consider the whole consonance/dissonance

concept anew. Especially in this field, classical Musical Theory does fall short compared to the reality of

the music of the living.

Interval An interval is a given distance between 2 notes either

played simultaneously or in a row.

The following examples show all the common intervals. The examples are divided into 3 levels: neu-

tral, consonant and dissonant. These "sound-aspects" will be explained in details in the next sec-

tions. The intervals marked with a red box are “natural” (see Overtones).



INTERVALS (SOUND-ASPECT)



(Intervals, sound-aspect continued)

Listen to the Notes

NATURAL INTERVALS

A natural interval is traditionally the term for the two basic 2 intervals, the fifth (5) and the fourth (4),

i.e. the two principle elements of functional harmony, the dominant (the fifth) and the subdominant (the

fourth) (see Functional harmony). These two intervals also happen to be the original "mother intervals",

from which Western harmony emerged.

Sound-Aspect within Intervals

A very important property of intervals is their sound ("colour"). There are 3 aspects:

Neutral

Enharmonic notes (B / C and E# / F) Basic intervals prime and octave. Natural intervals

fourth and fifth (and eleventh). Second intervals seconds, (flat) seventh, ninth*) Fifth inter-

vals, natural, flat and sharp *)

Consonant

Third intervals, all forms major, minor, sixth, tenth, thirteenth.

Dissonant

Seconds, flat second, sharp seventh, flat ninth.

*) Belonged to the dissonant sound-aspect in the last century

A1FIG133.MID



Neutral Intervals

I have placed the second intervals and fifths, lowered as well as raised, under neutral scales. The

music historical development since Richard Wagner has changed the perception of consonance and

dissonance among the listeners. A development that has been going on since the middle ages where

only fifths and fourths were consonant (!), and the third was regarded as a repulsive dissonance

(!!!). The neutral lowered fifth, so extremely common in the music of our time was considered so

dangerous that the medieval theorists named it "The diabolic Tritonus".

Slowly, slowly the taste changed. The third became consonant. By the end of the 1900th century, the

sixth, the seventh and the ninth obtained their civil rights as neutral, "authorised" intervals, and the

other intervals quickly followed. And today you can divide the intervals in:

Neutral

Enharmonic, natural or intervals associated with the whole note scale

Consonant

Third intervals: the intervals to determine the tonal gender.

Dissonant

The half note intervals so frequently employed in modern music however "dissonant", they may

sound

Chapter 2, Harmony, Simple Harmony


Simple Harmony

The classical counter-point has ceased to exist. Today all intervals are allowed, though

short movements between the individual parts of the harmony are considered an advan-

tage due to instrumental technical reasons.

SUGGESTIONS FOR MOVEMENTS

1 Shortest possible movements.

2 If the melody part (the leading voice) needs a resting point, it is best to let the supporting part end

in a consonant interval.

3 Within whole note scales with mostly parallel thirds, lowered fifth or basic seconds, fourths or

small sevenths, all intervals are neutral or consonant (see the section about "Parallelism" and the

section about "Melodic doubling" in Scales)

4 Within chromatic, free tonal or mixed blues/modal neutral scales the 2-part harmonies de-

pend on the predominant tonality.

5 Main rule: within modern harmony all intervals (and harmonies) are allowed, the individual

use is however restricted by the tonal surroundings and the style.

HARMONIZING

Add 2nd

Voice

When harmonizing 2nd voices, you normally use thirds. Here is a little tune with a nice 2nd voice.

Add 3rd

voice

And here comes a third voice, complicating the matter a bit.



Add 4th

voice

The vocal score looks somewhat crowded, but it sounds ok.

Inversions

An inversion is an octave change in the pitch of one or more notes in a chord.

THE OVERTONES

A "single" note is not one, but many tones. The Greek philosopher Pythagoras, the father of all music

science, in the middle of the 600th century BC discovered this fundamental characteristic of tones. As

you strike a note on an instrument with a soundboard or strings, a spectrum of overtones discreetly fol-

lows the main note, nearly inaudible, but present. The overtones have a waste influence on the sound of

the instruments, especially when executing a chord. The overtones create the colour or timbre of the

note.

The C in the figure has been lowered two octaves (15va) to make the high notes easier to read. The

basic C note is shown in the blue rectangle. The notes marked with a red rectangle are “false” com-

pared to the temperated system. Listen to the Notes.

A1FIG136.MID



The Temperated Tonal System

The overtones marked with red in the treble clef are false, if compared to a piano. But in fact, it is

the piano that is “false” compared to nature's own tones.

For practical reasons, the piano and many other instruments are divided in equal 1/2-note steps,

although the nature tones are not evenly distributed. Therefore the so-called enharmonic notes (see

Note Writing and Scales) sound alike on the piano, but not on the violin, which is flexible enough to

use the nature tones. The difference is not shown in the written notes. This little "deception", a ba-

roque invention from the time of Bach, has been guilty of preserving the myth about "the absolute

monarchy of the twelve 1/2 notes", a myth that was terminated by the blues scales.

The Overtones and The Major Triad

The overtones determine the placing of the harmonics (overtones). Besides this you can conclude

another very important thing from the overtones:

Almost all the intervals turn up in the overtones. And the overtones contain a MAJOR TRIAD

centrally located! This fact is a substantial argument for the position of triad based chord systems.

Triads are the only reasonable useful system even if other, alternative systems exist (see later in this

section). The overtones contain a small and a large seventh, a ninth, a sixth, a lowered fifth and

other fifths, thirds and octaves on different levels and grades of "tuning".

Chapter 2, Harmony, Chords


Chords

The chord is a Western European invention. It was invented in the 15th century as a result

of the more and more complicated vocal lines in Church music starting to align eventually

forming simple intervals and ultimately chords. The biggest revolution in music so far;

this was the musical equivalent to the invention of the wheel. Suddenly the composers

were able to build harmonies with more than one voice. The harp players and later pian-

ists could play bass lines and chords to produce a full and rich sound. And the most im-

portant thing; the dynamic use of chords, which allowed the music to build a tension / re-

lease in the music through the functional changes in the chords.

TRIADS

Chords of triads are the fundamentals of modern harmony. In the beginning were two thirds, a large and

a small third, or a small and a large third. Later more thirds arrived. And they ended building upon each

other, layer after layer. Here is the typical example of triad chords with a large and a small third below:

Note: The chords are named after the letter of the primal note

Listen to the Notes

These triads of thirds are the building stones of the chord symbols. Even if you do not always have all

the thirds audible in the chord, these basic 3-, 4-, 5-, 6- and 7-chords form the backbone of modern har-

monies.

A1FIG133.MID



THE CONSTITUTION OF CHORDS

The following rules are the most important part of jazz and rock harmony.

Paragraph 1

A chord is a harmony consisting of at least 3 different notes in a triad.

Paragraph 2

The largest interval in a triad chord is max. #5 min. b5.

Paragraph 3

The smallest interval in a triad chord is max 4 and minimum a small third (minor third).

Paragraph 4

The 6 triad chords meeting the above demands are called the Basic Triads.

Listen to the Notes

Paragraph 5

All triads not meeting the above demands are rudimentary (incomplete) 4-part, 5-part or higher

chords.

Paragraph 6

All chords higher than the 6 basic triads consist of one of the 6 basic triads with one or more added

"colour tones".

Paragraph 7

The system is called Chord Symbols, and the letter of the prime note and the intervals signify the

character and sound of the chord.

A1FIG133.MID



Have you considered cheating by not reading the rest

of the theory CD-ROM? Then just learn the above rules.

THESE RULES ARE THE MOST IMPORTANT RULES IN THE WHOLE BOOK

If you understand the above principles, it is easy to construct every thinkable standard chord. This is

the way to do it. Chords are fun!

TURNS AND ARPEGGIO

Chords can also be played "broken" as an arpeggio, with or without turns. All the following chords have

the same chord symbol "C". The arpeggio figures can of course be played in other positions.

The turns are used to move from one chord to another with as little movements as possible, parallel to

the rules for simple 2-part harmony. Arpeggio is used for ballads or slow numbers, where the chord

should be rich or floating/static.

Determination of Chords

Two chords are identical, when the closest position of their intervals (basic position) is alike and the

position within the octave is the same. Identical, stacked chords do not change the Chord Symbol.



The Closest Position of Intervals determines the Chord Symbol (The position in the scale of the

prime note C' = C'' as chord).

MODAL ASPECTS

The modal aspect is closely connected to functional harmony, as the modal aspects and the sound-

aspects share the ability to give character and colour to the individual chords (see Functional Harmony).

The modal aspect is chiefly a question of major or minor thirds in the basic triad. Modal aspects also

relate to the actual scale of the harmonic functions. This will be more evident later in this chapter. You

can divide the modal aspects of the 6 basic triad chords this way:

Modal Aspects of the 6 basic triad chords

The C(b5) and C+ major chords are among the Major Chords due to the large third in the middle.

On the other hand is Cdim both major and minor (or "neither-nor"), as Cdim readily dissolves in

both C and Cm. Csus is equally ambiguous (“double gender”).

Major Minor Double

C

C(b5)

C+

Cm Cdim

Csus

You should not confuse modal aspects with the sound-aspects. Melodies with frequent major and

minor parallel chords have a tendency, however, to be "coloured". Major with minor prime (C6)

and minor with major prime (Cmaj7) or major 6 and minor 7 (typical jazz colour tones). Only func-

tional chords can possess modal aspects, as they always, according to nature, must behave on the

conditions of the ruling scale system (modal, major or minor). Intervals cannot possess modal as-

pects, as an interval is neutral and only assumes modal character, while 3 or more notes together

form a functional chord.



SOUND-ASPECTS

Opposite to modal aspects, the sound-aspects of intervals and chords go together well.

Sound-aspects within chords

Consonant

This aspect only includes the 6 basic triads

Neutral

4-part Major with sixth (6), flat seventh (7) or ninth (9) Minor with sixth (6), flat seventh (7) or

eleventh (11)

5-part Major with seven + ninth (7+9) or sixth + ninth (6+9) chords, where the added notes are

solely neutral (second forms) to the other notes of the chord.

Dissonant

Mild 4-part dissonance with added sharp seventh (maj7) either in major or minor chords con-

taining minor third + second (for example m9, 6+7, dim(Maj7).

Sharp Major dissonance with eleventh (11) and flat tenth (-10) (major/minor thirds together),

flat ninth (-9) (lowered seconds) flat sixth + fifth relations (more 1/2-notes together)*).

*) Three 1/2-notes together should be avoided, for example C7(add Maj7).



DESCRIPTION OF CHORDS

The most common chords and their character are shortly described in the table below. The examples are

all in C minor or C major for the sake of clarity.

3 Part Chords

C A little fresh, hard sound. Clear profile

Cm Soft sound, but still solid profile

Csus Soft sound, unclear profile

C+ Open sound, but with clear profile of major

C(b5) Major chord, but with unclear profile

Cdim Soft, floating sound, no profile

4 Part Chords

Major C6 Fresh, neutral

C7 Neutral, but a little more "biting"

Cmaj7 Soft and sharp (can be heard as C plus Em)

Minor Cm6 Soft and rough

Cm7 Extremely soft and rather neutral

Cm(maj7) Soft, but with a sharp tint

Cm9 Soft with a "pleasing" dissonance

Sus Csus7 All neutral

Csus(maj7) Extremely sharp dissonance!

+ C+7 All neutral

C+maj7 Very sharp dissonance!

C+9 Neutral

(b5) C(b5)7 Soft and "pleasing" dissonance

C(b5)maj7 Soft, but a little sharper dissonance

(dim) Cdim Always a 4-part



5 Part Chords

Major C6+7 Rough, with a little dissonant sound

C6+maj7 Mildly dissonant and neutral simultaneously

C9 "Neutral" and soft

Cmaj7+9 As above, but a little dissonant

C-9 Neutral, but dissonant

C-10 "Neutral", but sharply dissonant. Broad

C-10(maj7) Soft, but sharp dissonance

Minor Cm6+maj7 As above

Cm6+maj7 As above

Cm7+9 Soft, broad ad "pleasing" dissonance

Cm(maj7)+9 All neutral, broad

Sus Csus7+9 All neutral, broad

Csus-9 Neutral, but with a mild dissonance

+ C+7(+9) All neutral, broad

C+maj7(+9) As above

C+(-9) As above

C+(-10) As above

(b5) C(b5)7+9 Soft and broad

C(b5)maj7+9 Rather dissonant

C(b5)-9 As above

C(b5)-10 As above

(dim) Cdim9 Soft, "pleasing" dissonance

Cdim(maj7) As above



6 Part Chords

Major C11 Partly neutral, partly sharp dissonance

C11(maj7) Sharp dissonance

C11(#4) Neutral, "pleasant" dissonance

Minor Cm11 Soft and neutral

Cm11(maj7) Soft and dissonant

+ C+11 Heavy dissonance

C+11(maj7) Extreme dissonance

(dim) Cdim(maj7+9) Rather dissonant

7 Part Chords

Major C13 Very dissonant, almost bitonal*)

C13(maj7) Extremely dissonant!

Minor Cm13 Partly "pleasant" dissonance

Cm13(maj7) Very dissonant

*) Due to the 6+7 relationship in the chord, often played as a 6+7 chord (fake 13-chord) Bitonal, see Polyharmony

The chords in the above list are the major part of the chords, normally used in the chord symbol system.

Though the theoretical possibilities are unlimited, even the 7-part chords are rare in real life. They are

mostly used in rudimentary form (an ordinary guitar, for example, has only 6 strings). Most chords with

6 notes and less are frequently used, depending on the style and the technical level of the com-

poser/musician. Especially in jazz, a lot of amazing chords with advanced colour notes bloom. Layer

upon layer. Changing from major to dim-variations and minor parallel chords etc. etc. Discover the

chords of jazz! A literally bottomless treasury of harmonic ideas is hidden in the way jazz musicians treat

their innocent victims, the chords of the pop standards.



CHORD TABLE

I have constructed the following table of most common (and uncommon) chords today to present the

previous chord types (in C-major) in a easily understandable form,.

Chord types (example in C-major)



(Chord types continued)




The actual construction of chords is an exciting, but rather extensive subject. Heavy volumes have been

written on guitar and piano chords. Go to a music shop and find yourself one of the good chords "maps"

of the recent years.

Other Chord Symbols

The chord symbols in this book are, unfortunately, far from alone as a "standard" system. Actually

there ought to be international standard for chord symbols, like the standardised note symbols (in

our days). Maybe a regular DIN-norm for chord symbols – a task for a bright standardisation ma-

niac.

Therefore I will show you a selection of competing systems – somewhat against my will! There is

every probability that the bewildered reader will come across these, often illogical and ambiguous

symbols in note sheets and scores. It is not that unusual to see the same composer/note writer use

two or more chord systems in the same note sheet, sometimes in the same song. We must go back

all the way to the baroque period, to find similarly grotesque conditions, where poets spelled the

words at their own pleasure, or according to the letters in the typist's box.



(Other chord symbol systems)

English Names French Names Other Names

C Do C5

Cm Do minor Cmi or C-

Csus Do sus C4 or Csus4

C+ Do aug C(#5) or Caug

C(b5) Do dim Cb5 or C Ø (same type)

Cdim Do dim C o or C Ø

(again, same type!)

Cmaj7 Do maj7 C ma C (triangle) C7m

C(b5)7 Do dim C o (the same symbol for the third time!)

Cmaj7+9 Do maj7+9 Cmaj9

C-9 C(b9)

C-10 C(#9) or C9+

C(b5)-9 C(b5)b9

C(b5)-10 C(b5)#9

C11(#4) C11+

*The French use the Latin note names in their chord symbols:

Translation of the French Note Names

English French

C Do

D Re

E Mi

F Fa

G Sol

A La

B Si



JAZZ CHORD SYMBOLS

This are the jazz chords produced in A-Play with the automatic LilyPond chord creator.

Special Problems in Chord Notation

The logic of the third stacks is indisputable. But reality has its own ways, logic or no logic. 70 years

of musical practice have necessitated a whole bunch of changes or adjustments to chord notation.

Chord symbols are progressive additions of thirds. According to theory, a 9-chord should always

consist of minimum 5 notes (prime, third, fifth, seventh and ninth), but normally only the major 9-

chord is played as a 5-part chord. In all other occurrences (m9, (b5)9, +9 etc.) the seventh is never

included and the chords consequently belongs to 4-part chords.

The dim-chord is originally a 3-part chord (triad), but it has always been played as a 4-part sound.

Anyway, it is classified among the basic triads.



Changes in the Chord Reflected in Notation

You can write down changes within a chord in the following ways:

Alternative bass note (other than prim):

C Major chord with G as Bass Note

C

g

C / G (hand-written)

Added Notes

If one/more particular notes should be added, this is noted (added) in a parenthesis C(add F#).

Accidentals

Used to raise/lower notes:

C (b5) (lowered fifth)

C 11(#4) (Raised fourth)

Shorthand Chord Symbols

Replace # with + (plus) or b with – (minus).

Example: Eb-9 is a better notation than Eb(b9))

( ) is used to distinguish 2 identical letters/signs Example: (Cm (maj7)) and + (plus) is also used as

an addition sign (C6+7)).

Temporary Pause In Third Based Harmony

N.C. = No Chords indicates free tonal passages or unaccompanied/a cappella.

Bitonal Chords

Cm + D7 or cm/D7, 2 different chords sounding at the same time. See "Poly Harmony".

Various Peculiarities

The symbol C5 means a C chord minus the third. This is becoming the popular way of writing

chord symbols for rock played in hollow quarters and fifths.

Ambiguous symbols are unfortunately common in the musical world. If you want to indicate a C13

chord without the eleventh (11), the correct symbol would be C9(add 13) and not C13(-11).

The peculiar practice of playing a 6+7 chord as a fake 13 chord on the guitar was mentioned in the

previous section



The sus4 / sus2 and dim chord symbols originate from the childhood of the chord symbol sys-

tem. Sus stands for "suspension". In the first chord symbols the sus chord was an unresolved major

chord (leading the fourth to a major third), but today you are free to use the sus chord as a stable

chord without resolving it into a major or minor chord. A dominant chord – see "Functional har-

mony". You can find more examples on this type of chord notational problems later in the section

on Functional Harmony.

Chapter 2, Harmony, Chord Boxes (Fret Diagrams)


Chord Boxes (Fret Diagrams)

Chord Boxes – also called fret diagrams – are powerful tools for guitar players. Besides

the chord symbol, the guitarist can see the proposed fingering of the chord. In A-Play, you

can choose between the following predefined A-Play chord boxes, or you can make your

own chord boxes from scratch (see Notes and Chords in A-Play).

MAJOR CHORD BOXES

C

Major

7

Maj7

9

sus4

C#/Db

Major

7

Maj7

9

sus4

D

Major

7



MAJOR CHORD BOXES

Maj7

9

sus4

D#/Eb

Major

7

Maj7

9

sus4

E

Major

7

Maj7

9

sus4

F

Major

7

Maj7



MAJOR CHORD BOXES

9

sus4

F#/Gb

Major

7

Maj7

9

sus4

G

Major

7

Maj7

9

sus4

G#/Ab

Major

7

Maj7

9



MAJOR CHORD BOXES

sus4

A

Major

7

Maj7

9

sus4

A#/Bb

Major

7

Maj7

9

sus4

B

Major

7

Maj7

9



MAJOR CHORD BOXES

sus4

MINOR CHORD BOXES

C

Minor

m7

+

dim

(b5)

C#/Db

Minor

m7

+

dim

(b5)

D

Minor

m7

+

dim



MINOR CHORD BOXES

(b5)

D#/Eb

Minor

m7

+

dim

(b5)

E

Minor

m7

+

dim

(b5)

F

Minor

m7

+

dim

(b5)



MINOR CHORD BOXES

F#/Gb

Minor

m7

+

dim

(b5)

G

Minor

m7

+

dim

(b5)

G#/Ab

Minor

m7

+

dim

(b5)

A

Minor



MINOR CHORD BOXES

m7

+

dim

(b5)

A#/Bb

Minor

m7

+

dim

(b5)

B

Minor

m7

+

dim

(b5)



MOVABLE CHORD BOXES, ADVANCED JAZZ

1

7(#5/b9)

2

7(#5/#9)

3

7(b5/b9)

4

7(b5/#9)

5

maj7(#11)

6

13

7

13

8

13(#11)

9

m13

Chapter 2, Harmony, Other Chord Forms


Other Chord Forms

Third stacks are not the only way to build chords. In our time Bartok, Stravinsky and

many others have experimented with alternative kinds of stacks or "clusters". These chord

systems have not had a large following in rock. Influences can, however, be found in jazz

after the beginning of the 60'ies.

Similar to the experimental rhythm systems and the artificial scales, mentioned earlier,

the alternative chord forms might be an inspiration. They might even help breaking down

the habitual thinking of rock musicians, who are generally more conservative, than they

would like to admit. There are 4 different alternative chord systems. They are common in

a lot of modern music and may be considered a bit of a challenge to any rock or jazz mu-

sician.

CLUSTERS OF 1/1 NOTES

Clusters of 1/1 notes is a modern classical concept, where a piano player takes as many second intervals

as possible, as close as possible. It is noisy but not totally atonal. A favourite system of Bartok's, some-

times found in the late music of Debussy.

Listen to the Notes

CLUSTERS OF 1/2 NOTES

Among the late classical composers like John Cage or Penderecki half note clusters is a popular chord

form (it is easy to produce on a piano, when "the notes" only consist of dynamic indications and ap-

proximate pitch - common in certain types of avant-garde "chance" music!)

A1FIG147.MID



Clusters of 1/2 notes transcends the borders of highly experimental music. It is impossible to hit a lot of

1/2 notes in a nice, structured way, so the modern composers in the 1950-ies invented a so-called “clus-

ter” notation. Here is how the scores from the 50-ies and 60-ies looked like:

Listen to the Notes

Several voluminous books have been published on modern notational symbols. Look for other ways to

write half note clusters in these (see the Bibliography).

ALTERNATIVE CHORDS

Stacks of Quarters

Stacks of Quarters and Fifths are very common in modern jazz, often played by the horn section. It

is a very effective trick, if you aim for a thick, tough sound. That’s the way to go. Here is an exam-

ple in quarters:

Listen to the Notes

Fourth stacks are closely related to sus chords and often appear as "side effects", when you combine

sus chords. Fourth stacks are stimulating and in the spirit of the blues in rock (blues has the fourth as an

important interval).

“Spontaneous” fourth stacks

Listen to the Notes

A1FIG148.MID

A1FIG149.MID

A1FIG150.MID



Stacks of Fifths

Fourths, fifths and theoretically all intervals can be stacked. Fifth and fourth stacks normally occur

together, mostly in music with neutral scales as impressionistic music.

The more fifths, the higher the notes. More than 4 fifths is not advisable, unless you want to get

sued by the musicians’ union:

Listen to the Notes

A1FIG151.MID

Chapter 2, Harmony, Functional Harmony


Relative Harmony

Functional Harmony

Today not the individual notes, but the chords, determine the development of melody.

Chords in the tonal system are interconnected. They are placed on a tension curve with

increases, decreases and resting points. Some chords are stable and definitive. Other

chords "function" as temporary stations on the road to and from the basic chord.

Classical functional harmony deals with chords in one key. But in my book, I have ex-

tended and revised the whole concept of functionality. A musician, trained in older Musi-

cal Theory, will surely be startled over an expression or two. Among the new expres-

sions, I introduce the concept, Transitive Harmony, which stands for more keys in one

melody, a kind of modulation that has become extremely popular in the last 60 years;

more on the subject later in this chapter. The classical functional harmonic principles in

one key have also been heavily extended, and now include blues and modal functions.



BASIC PRINCIPLES OF FUNCTIONAL HARMONY

On every step in a major/minor scale, you have different chords. Beside these traditional functional

chords, both blues scales and modal scales have their own chords. The number of chord functions in one

key has seen a massive increase since the time of Mozart.

A chord in a given key is functional. That implies a given functionality in relation to other chords. The

chord functions in a hierarchical system with the tonic chord (the tonic partly equals the prime) as the

master of the game. The tensions of chords are graduated, which will be described in details later in the

chapter about "Cadences". But first I will portray the constitution of functional harmony.

THE CONSTITUTION OF FUNCTIONAL HARMONY

Paragraph 1

The chord should have an absolute resting point in the tonic chord of the key.

Paragraph 2

Beside the tonic, all other chords must function as part of a cadence to the tonic.

Paragraph 3

A major chord can anytime be replaced by its minor parallel or the other way (except for the double

subdominant and the blues chord functions)



DOMINANT

To understand the harmonic functions you have to understand the relationship between leading notes

and chords. The leading note is a scale step below or above the prime, normally a 1/2 step. In our days,

however, the blues seventh also functions as a leading note and to a certain extent the blues third.

Chords containing a leading note have a "leading" function. The "primary" leading function is called the

DOMINANT.

Leading note Dominant types

DOMINANT (D)

A dominant chord contains the leading note to the

prime of the key, i.e. to the tonic chord.

Maj7 (major) DOMINANT (major)

DIM DOMINANT

7 (minor) MINOR DOMINANT

Blues 7

Maj7 (adjusted) MINOR DOMINANT

(in major keys)

b2 Moorish DOMINANT*)

A "RAGTIME" DOMINANT also plays an important part in modern popular music See "Neapolitan chords"

SUBDOMINANT

Chords on the fourth scale step have a "secondary" leading function. They are called SUBDOMINANT

(sub = "below").

Subdominant types

SUBDOMINANT (SD)

A subdominant chord is a chord on the fourth step of

the key.

SUBDOMINANT (major or minor colours)

NEAPOLITAN SUBDOMINANT

MINOR SUBDOMINANT (minor or major colours)



DOUBLE DOMINANT / SUBDOMINANT

An extra tension level leads to the tonic chord through a secondary dominant to a primary dominant.

This function is called a DOUBLE DOMINANT, the parallel to the DOUBLE SUBDOMINANT. (The

classical terminology does not recognise this function).

Harmonic double functions

Double Dominant / Subdominant

DOUBLE DOMINANT (DD)

DOUBLE SUBDOMINANT (DSD)

A dominant or a subdominant chord has its own

DOUBLE DOMINANT or DOUBLE SUBDOMINANT

chord.

The DOUBLE DOMINANT contains a leading note to

the (primary) dominant. The double dominant (but not

the double subdominant) even has its own dominant, a

TRIPLE DOMINANT.

The DOUBLE SUBDOMINANT is placed as a subdo-

minant function the primary subdominant (on the blues

seventh step, causing the function to divide from the

classical harmony system, even if the chord type is

extremely common in rock music).

MAJOR / MINOR PARALLEL FUNCTIONS

It is of utmost importance for the functional harmony to have a minor parallel to the major chord. Para-

graph 3 in "The constitution of functional harmony", makes the classification of basic functions very

simple. In older functional systems you have a chord for each step in the major key and a similar number

of functions in the minor key (see "Other functional harmony systems").

This leads to a lot of different functions, many of which are merely being each others major / minor

parallels. That is why I have the rule of free interchange between major and minor chords. The curious

result of this, is that chords, seemingly non-compatible as C (major) and F#m, end up being functional

chords within the C major scale (C is the tonic chord, while F#m is triple dominant chord's minor paral-

lel).



BLUES FUNCTIONS

Beside the traditional functions, I have added another new chord function on the blues steps. The chords

are of course on temperated steps, as a real blues chord (half sharp note) cannot be played on the piano.

1 2

Half sharp note in Arab music notation (1) and in LilyPond (2).

Harmonic blues functions

Blues Functions

BLUES 7 Dominant function

BLUES 3 Ambiguous, scale step function)

BLUES 4 Standard Subdominant and blues scale step

function

BLUES b5 Subdominant function

A blues function is a chord placed on a temperated

blues step.

BLUES 7 has dominant characteristics. BLUES 7 is

formally identical to the double subdominant, but with

dominant function.

BLUES 3 is neutral, but "leads" to both tonic and sub-

dominant ("blues 4")

BLUES 4 may under some circumstances function

similarly to BLUES 3, as an expansion of the blues

scale steps in the classic “prime, blues third, fourth and

back again” movements.

BLUES b5 function as a sort of double dominant.



NEAPOLITAN CHORDS

Before I depict the harmonic functions in a table, I will have to explain one special phenomenon a little

closer. An ancient tradition, stemming one must believe from Italy, has created a special function, which

is a favourite in romantic classical music. My great grandfather the Danish composer Niels Wilhelm

Gade (1817-1890) and other composers from his generation used the Neapolitan subdominant over and

over again, as well as the Beatles, especially on the early recordings. The chord was frequently used in

the 50’ies.

The Neapolitan chord has a strange property. It is basically a major subdominant in minor. But it leads

to the tonic on a tension level equal to a dominant. It is partly a dominant chord without containing a

leading note. This has to do with 2 other chords closely related to the Neapolitan subdominant chord,

the Ragtime dominant and the Moorish dominant.

The Neapolitan function family

Neapolitan Chords

NEAPOLITAN SUBDOMINANT VS. RAGTIME

DOMINANT

The note example shows how the common notes are

located in Fm and Ab. Fm is a subdominant (the basic

note is the fourth step in C major), whereas Ab is a

(major) dominant variant due to the basic note (1/2

note over the major fifth), but without the leading note.

NEAPOLITAN SUBDOMINANT VS. MOORISH

DOMINANT

Ab and Fm are also parallel. Db contains the "Moorish"

leading note, 1/2 note above the prime.

NEAPOLITAN SUBDOMINANT VS. RAGTIME

DOMINANT (MAJ7 variant)

Dbmaj7 contains both the Fm and Db chord in one

chord, but functions as a dominant chord due to its

basic note.

Listen to the Notes

A1FIG157.MID



HARMONIC FUNCTIONS IN ONE KEY

Table of Functions

The following examples show all functions within C major (ex.). The functions are divided into the

main groups TONIC, DOMINANT, SUBDOMINANT and DOUBLE FUNCTIONS. The blues

and dim functions are 2 other main groups. An explanation of the character of each function, the in-

fluence of style on the functions, etc. follows later in this section, including the stories behind the

"invented" names as "ragtime" dominant etc. The dim chords and their nature will also be described

in detail.

+ and (b5) chords are functionally identical to major chords. Sus chords have double gender

as dim chords (see also the modal aspect table).



Shorthand Acronyms

T Tonic)

D Dominant

SD Subdominant

“M” below symbol Minor colour

DD double dominant

TABLE OF MODAL ASPECTS

The next table contains a list of the modal relationships of functional chords. Like the intervals and

chords differ in sound-aspects, separate chords and functional chords have different aspects.

Modal Aspects in Functional Harmony

nat = Natural sign

dim = Diminished

Modal as-

pect

Function

MAJOR T D SD DD TD D-Rag D

Moor-

ish

DSD

MINOR T

M

D

M

SD

M

DD

M

TD

M

MODAL D SD

M nat

SD

M nat

SD

Neapolitan

Double

Gender

T

dim

D

dim

SD

dim

BLUES

7

BLUES

3

BLUES

b5

The modal aspect depends on the scale

F7 for example is subdominant in a Dorian C scale ("C minor"), as step 6 in this modal scale

is natural instead of the ordinary Fm (a flat dissolves into A natural) See also "Functions

within pure modal keys"



Modal examples within functional harmony

A few selected examples:

Ex. 1. T SD

M

SD T

Ex. 2. T DD SD T

Ex. 3. T SD

Ex. 4. T

SD

Neapolitan

Comments

Ex. 1 and 2: The difference between subdominant minor and the double dominant is the tonal gen-

der. Consequently, it is a question of a sharper sound in the double dominant (ex. 2). The double

dominant has no leading function in this connection – in spite of its name – as it does not lead to the

primary dominant, but only serves as a modal alteration.

Ex. 2 was found in the Beatles song "8 Days A Week", recorded during a period in which the

Beatles often used modal scales (as did their American heroes, The Miracles).

Ex. 3 and 4: A purely modal difference between SD and SD neap (major to minor)

CHARACTERISTICS OF CHORD FUNCTIONS

TONIC

Both T (major) and T minor are steady resting points.

DOMINANT

D is the classic "second" chord. D rag belongs to ragtime (where the name "ragtime" dominant

comes from, of course), jazz and pop. D moor is much more advanced and often emerges in Arab

("Moorish") music, e.g. Spanish music. D minor and D minor natural are unambiguous classical,

dominant chords.

SUBDOMINANT

SD (major) and SD minor are "third" chords. SD neap has been mentioned earlier. SD minor natural

is very common in rock/blues with Dorian flavour (minor with major sixth).



Double Functions

DD and TD are pure major variants, sharp and "tonal" in the Western sense. DD minor and TD mi-

nor are more "jazzy" and not common in classical music. DSD has a distinct blues character and is

never heard in classical music.

Dim Functions

A dim chord's function can, to the surprise of most people, be found from the placing of the basic

note 1/2 note higher than the basic note in the similar function in major or minor. As the dim chords

are difficult to identify functionally, here is a table to help you out of the headache.

Chord Function

Ex.:

T

dim

sharp prime

C#dim (= A#dim) contains #1 both in major and minor (black notes)

SD

dim

Raised Fourth

F#dim (= D#dim) contains #4 both in major and minor (black notes)

D

dim

Raised Fifth

G#dim (= Fdim) contains #5 both in major and minor (black notes)

Blues Functions

The blues functions are closely associated with blues and rock music in particular styles, e.g. heavy

rock.

Functions within Purely Modal Scales

The modal deviations mentioned in "Modal aspects", become a separate harmonic system, when the

melody strictly follows a modal scale. The modal chord functions are not used that often, but they

can supply you with a welcome change, if the functional harmonies in major/minor get on your

nerves. That happens once in a while, believe it or not!



Functions within modal scales classified on scale steps

The chords marked with red, deviate from the tonal genders of major and minor functions. Note:

Ionian and Aeolian are identical to minor and major with the same tonal genders.

Step Dorian Phrygian Lydian Mixolydian (Locrian)

1 minor minor major major dim(!!)

2 minor major major minor major

3 major major minor dim minor

4 major minor dim major minor

5 minor dim major minor major

6 dim major minor minor major

7 major minor minor major minor

Other Functional Terms

The musical world is hopeless, when it comes to uniform terminology. Only the terms tonic, domi-

nant and subdominant are common. In the following table, I have "translated" my terminology

(based on the traditional names) into 2 other systems.

Chord in

C Major

My suggestion Numbering

System (Jazz)

Classical music

(American variant)

Symbol Name C Major A Minor

C T Tonic I III Tonic

Dm SD

M

Minor sub-

dominant

II IV Supertonic

Em D

M

Minor domi-

nant

III V Median

F SD Subdominant IV VI Subdominant

G D Dominant V VII Dominant

Am T

M

Minor tonic VI I Median

G#dim D

dim

Diminished

dominant

VII II Subtonic



The Number System

A number system seems to have some advantages. It looks deceivingly simple. But to point out a

couple of much unfortunate elements, it is misleading, to put it mildly, to call the tonic parallel mi-

nor chord "VI". It suggests that the chord is one step higher than the dominant. In the real world,

most of the times, you step down to the parallel minor tonic chord. Another problem: The system is

unpractical, as it does not say anything about the tonal gender of the chord (it could be both a major

and a minor context).

The Classical System

Is just as misguiding and silly as the number system; a "supertonic" is not a correspondent function

to the tonic. It is a parallel minor to the subdominant chord. If the tonal gender of the scale is minor,

the term becomes absurd, as you rarely use the chord on the second scale step in minor. Instead it

will be considered a minor double dominant – but certainly not a sort of tonic.

A little example: what does a poor newcomer think a: tonic - supertonic - dominant - tonic is?

Ex. C - Dm - G – C

Has it got something to do with tonic + something-with-tonic + dominant + tonic? Sorry no! The

chords are actually a tonic - subdominant (parallel minor) - dominant – tonic.

Ex. C - Dm - G - C = T - SD minor - D - T

My Suggestion

Both the number system and its classical counterpart are incomprehensible, illogical and inexact.

And they do not reveal anything about the functional chords in between, as the SD minor and D mi-

nor in a major scale or the tonal gender of the chords.

But behold! If you combine minor and major in one functional system, you are suddenly able to

analyse any tonal case without constantly changing system. Most melodies change between major

and minor chords all the time, often replacing the functions with the minor or major parallels.



A Special Problem in Functional Harmony

There has been much theoretical disagreement over one innocent chord. If we use good, old C ma-

jor again:

Many jazz theorists want to class this chord type as a dim variant. They call if Co7 (half diminished

seventh chord). Take the ragtime dominant for example, lower the major third and you get a minor

chord. But at the same time you modulate to another key! Ebm6 with c in the bass does not belong

to C major at all, but to C minor! The German theorist Joe Viera (see Bibliography) calls the chord

Cm7/b5, which is better, but unnecessary, as the chord still remain an Ebm6 in disguise! By the

way: I do not like the lowered minor chord (e.g. Cm(b5)) as the chord normally is identical to a ru-

dimentary dim chord symbol.

Chapter 2, Harmony, Harmonic Cadences


Harmonic Cadences

The whole functional system strives for tension and release between the chords in one

key; to reach the stable tonic. You can say that all other chords than T or T minor are

part of a "cadence", i.e. a movement in the direction of the tonic chord (or an ending). The

chords are placed on a tension curve in a hierarchical system of tension levels.

TENSION LEVELS OF CHORD FUNCTIONS

Note: The blues tension levels are extremely complicated!

The harmonic cadences can be divided in 2 main categories, the neutral standard cadence and the

cadence ostinato or "vamp", which will be described in the next section.

STANDARD CADENCES

1 A true standard cadence contains minimum 3 and maximum 6 members

2 Any chord can be replaced by its parallel minor/major chord (except for the double subdominant

and the blues functions)

3 A standard cadence starts and ends in the tonic chord



(Standard Cadences continued)

DOMINANT Rows

Simple T D T

Double dominant T DD D T

Triple dominant T TD DD D T

SUBDOMINANTS Rows

Simple T SD T

Double Subdominant T DSD SD T

Compound Rows

Simple 4-member Cadence

Dominant type T SD D T

Subdominant type T D SD T

Simple 5-member Cadence

Dominant type T D SD D T

Subdominant type T SD D SD T

DOUBLE DOMINANT and SUBDOMINANT

Dominant type T D DD D T

T SD DD D T

SUBDOMINANT type T D DD SD T

T DD SD T

T D DSD SD T

Mixed DD/DSD type T DSD DD D T

T DD D DSD SD T

T DSD SD DD D T



(Standard Cadences continued)

Blues Rows

Simple blues cadences

Dominant type T Blues 7 T

T Blues 3 Blues 7 T

Subdominant type T Blues 3 T

Mixed blues and Standard Cadences

Dominant type T D Blues 7 T

Subdominant type T Blues 7 D T

CADENCE OSTINATOS

A cadence ostinato is a repeated pattern of chords in the form of cadences. Standard cadences are in

themselves a sort of cadence ostinatos, if they are repeated as "fill" in a passage, where the main melody

pauses. Such an "empty" middle piece was called a "vamp" in the early days of jazz.

A cadence ostinato is usually constructed in a way that is characteristic for its style. Such "style cadence

ostinatos" belong to Form and style, and in the last chapter of this book, Form and style I include a sec-

tion with some typical examples. Most melodies are built around a few cadences. They can be long, with

lots of chords, but if you analyse them thoroughly, you often discover that it is actually a standard ca-

dence with minor parallels, inserted dim chords, turns of the chord, rudimentary chords etc. Therefore it

is wise to get accustomed to new "strange" elements of the cadence, instead of starring blindly at minor

parallel chords etc.

"Simple 5-member Cadence of the Subdominant Type"

Cm Eb Edim Fm7 Adim Abm9 G Bb9 Fm7 Ab9 Abm Eb6+9

T M

T

T dim

SD M

SD dim

SD neapol.

D M nat

D

SD M

SD

SD neapol.

T

TONIC SUBDOMINANT DOMINANT SUBDOMINANT TONIC

Actually a long row of standard cadence elements!



OTHER CADENCES

You may finish a melody in countless ways. The classical cadence is only one of them. Below you will

find a row of nowadays alternatives. There are, however, a couple of good reasons to have the "har-

monic cadence" in mind, as this cadence type is the key to understanding transitive harmony. "Function

shifts" which are the fundamentals of Transitive harmony, are based on harmonic cadences; more on this

subject in the next section.

Fade

Far from all melodies, especially on records, finish with a harmonic cadence. It is a typical trait in

certain periods of rock history, to have most of the numbers "fading" rather than ending with a

"normal" cadence (see "General, cadences". (Note example in the Note Writing chapter under "End-

ings").

"Fading" means damping the sound gradually until it has suddenly all disappeared. It is a hard art to

die smoothly, and technically it belongs to the work field of a producer/sound technician. It is possi-

ble to fade on stage, and it can be an excellent effect, if e.g. one or more instruments stay on the

original level, and the others die away. Provided it is done simultaneously and precise.

Rhythmical Cadence

A rhythmical cadence is rhythms and not harmonies ending a melody. If the rhythmical structure

(see "The inner structure of Rhythm" + "Form and style") prepares for a natural ending by the

rhythm group, a "rhythmical" cadence can sometimes be more effective than a harmonic one. Occa-

sionally it can even come "cross" a "normal" cadence.

In spite of lacking a harmonic ending, the cadence feels satisfactorily concluded.

Listen to the Notes.

A1FIG169.MID



Rhythmical Cadences

Lowering the tempo, the phrasing (natural demarcation by the performing musician) and dynamic

dying away (ritardando) can create a rhythmical cadence.

1 Rhythm periods with an inherent ending.

2 Rhythmical phrasing - often across the group of bars.

3 Decrescendo (dying out dynamically).

4 Lowering the tempo.

Rhythmical cadences are common in music, where the tonality is floating - or absent. When the key is

gone, a rhythmical cadence is often necessary to end the melody (in much free-form jazz; for example,

you lower the tempo, rattle a bit with the cymbals, and the melody is over.)

Linear Cadence

In unison passages the intervals fifth to prime or the general leading notes maj7, blues 7 and b2 a

natural substitute for a harmonic cadence. Sometimes the harmonies can be implied in the voice,

which later in turn is repeated with harmonies and the usual harmonic cadence. It can be an exciting

game, to guess the chords behind a sophisticated voice (see All Aspects of ROCK AND JAZZ,

Volume 2, The Electric Bass, Harmonies to voices). And then get a surprise, when the harmonies

eventually reveal themselves! Many jazz versions of well-known melodies are based on an advanced

voicing over some equally advanced harmonic variations of the original harmonies.

1 Use of leading note (maj7, blues 7 or b2)

2 Use of fifth or fourth to prime.

3 Coloured passing notes maybe combined with a rhythmical cadence.

Listen to the Notes

Frankly speaking, the linear cadence is a relic from our polyphonic past without chords. It is fairly sel-

dom to hear linear cadences and music without chords at all today. Only sporadic appearances of this

old cadence type are heard in modern music – mostly as unaccompanied song passages or solos.

A1FIG171.MID

Chapter 2, Harmony, Advanced Jazz Chords


Advanced Jazz Chords

The basic Chord form is the Triad. It consists of three notes played at the same time. Ex-

tended chords are triads with one or more added “colour” notes.

REHEARSING THE CHORDS

When you rehearse the chords on the piano, you must learn the typical sound of the chord (Sound As-

pect) as well as its “mechanics”, i.e. the typical colour notes and interval structure of each chord. This

knowledge is essential for being able to recognize the chords by ear and to construct a powerful, yet

clear arrangement of all kinds of chord, even the heavily extended ones.

ROCK AND JAZZ TERMINOLOGY

The use of Chord and Functional Harmony terminology differs greatly between rock and jazz. In books

written by jazz players, Roman numerals are used for Chord functions (American tradition). The rock

version of the function symbols is added after the numeral. (D(m) = Dominant SD(m) = Subdominant

DD = Double Dominant m = Parallel Minor). The green colour is also used for different chord symbols

in rock.

FUNCTIONAL HARMONY / DIATONIC TRIADS

In the All Aspects of ROCK & JAZZ 1 / Music Theory, you will find a comprehensive chapter of Har-

mony, including the complicated theory on Functional Harmony, i.e. the functional relationship between

chords in a scale. In the next two figures, you can find examples of a major and a minor scale.

Diatonic Triads in D Major

American Rock

System System

I major T (Tonic)

II minor SDm (Subdominant parallel minor)

III minor Dm (Dominant parallel minor)

IV major SD (subdominant)

V major D (dominant)

VI minor Tm (Tonic parallel minor)

VII diminished -



Diatonic Triads in D Minor

American Rock

System System

I minor Tm (Tonic parallel minor)

II diminished -

III major T (Tonic)

IV minor SDm (Subdominant parallel minor)

V minor Dm (Dominant parallel minor)

VI major Sd (Subdominant)

VII major D (Dominant)



SEVENTH CHORDS (4 PARTS)

Seventh Chords in D Major

Seventh Chord Types Major 7, minor 7, dominant 7 and minor 7 (b5) (m(b5)7).

Function Seventh Chord Names Imaj7 (T maj7), IImi7 (SDm 7), IIImi7 (Dm 7), IVmaj7 (SD

maj7), V7 (D 7), VImi7 (Tm 7), VIImi7(b5).

Jazz The ten seventh chord main types

Major 7 (maj7) Root, major third, perfect fifth, major seventh.

Minor 7 (m7) Root, minor third, perfect fifth, minor seventh.

Dominant 7 (7) Root, major third, perfect fifth, minor seventh.

Diminished 7 (dim) Root, minor third, diminished fifth, diminished seventh.

Minor/major 7 (m(maj7)) Root, minor third, perfect fifth, major seventh.

Major 7 (#5) (+(maj7)) Root, major third, augmented fifth, major seventh.

Major 7 (b5) ((b5)maj7) Root, major third, diminished fifth, major seventh.

Dominant 7 (#5) (+7) Root, major third, augmented fifth, minor seventh.

Dominant 7 (b5) ((b5)7) Root, major third, diminished fifth, minor seventh.

Minor 7 (b5) (dim) (or half diminished chord) root, minor third, diminished fifth, minor

seventh.

The Ten Seventh Chords

NOTE the second line of chords follows the rock tradition



SIXTH CHORDS (4 / 5 PARTS)

The sixth chord is the most common coloured chord, beside the seventh chords. It was also the first

extended chord in the 1800-ies, in the beginning regarded as a sharply dissonant chord. The sixth note is

the same in both the major and minor versions of the chord despite the fact the minor scale sixth should

be half a note lower than the major sixth. This chord, also called a Naples Chord, has a very long tradi-

tion in classical music. It was extremely popular in early jazz and even Beatles has used it a lot on their

early records.

Sixth Chords

SUS CHORDS

Suspended chords (sus) are neutral, working well in either major or minor. Traditionally, it is used for

cadences, resolving into a major chord (the suspended note, usually a fourth down to a major third). In

modern rock music, the suspended chords are often used as a background chords, sometimes mixed with

eleventh chords. This way, the gender of the scales is blurred, making way for both blues, modal and

major scales. Typical examples of suspended chords can be found in the music of Nirvana. Normally the

suspended chords are simply called sus, but in jazz there are two types of suspension, sus4 and sus2.

The two types can actually be seen as two different chords depending on the context either having the

root in the bottom or at the top (fifth note).



CHORDS WITH ADDED NOTES

If you want to add a specific colour to a chord, for example a ninth, without the normal seventh, you

write (add 9). You could of course also use (add #11) or (add 13), but for historical reasons, the (add 9)

chord is by far the most common “added chord”. You may choose to add dissonant colours, too, for

example C(add G#) or E(add F). See also the comments under Minor 9 chords.

(add 9) Chord

EXTENDED CHORDS

Extended chords are very common in all modern music, rock, jazz, pop, soul etc. Before 1970, extended

chords were mostly played by advanced jazz musicians, but the fusion of rock and jazz in 1970’ies

meant a liberation for the somehow stagnated use of chords in rock and soul, and nowadays you will

find event the most complex extended chords in many songs on the radio or on MTV. A couple of ex-

planations are needed to understand the construction of extended chords. An extended chord is a triad

with one or more extra colour notes. As the triad chord uses the 1st, 3

rd and 5

th note in the scale, the “ex-

tended” notes uses higher numbers, for example 9th instead of the 2

nd interval, in order to provide a logi-

cal, transparent construction of the extensions. In real life, though, you can place the 9th and all other

colour notes where you want, using 2nd

/ 9th depending on the circumstances. The extended high scale

steps are named:

9th Major (9), minor (b9) ((-9))or augmented (#9) ((-10)).

11th Perfect (11) or augmented (#11).

13th Major (13) or minor (b13).



NINTH CHORDS (5 PARTS)

The major ninth chords are the first step into the Jazz sound, but it is also widely used in pop.

Major Ninth Chords with Major Seven


Minor Ninth Chords

NOTE In the rock tradition, the m9 chord does not have a minor seventh. It is traditionally

played as a minor chord with a ninth added. The m9 chord understood as the 7 and 9 is wri t-

ten m7+9 in rock.

Ninth Chords with Minor Seven

NOTE the second line of chords follows the rock tradition.



DOUBLE-ALTERED CHORDS

Jazz Double-altered chords are dominant chords with altered fifth and ninth. These strongly coloured

dominant chords are typical for modern jazz.

Double Altered Chord (m9(5) (m(b5)7+9))


ELEVENTH CHORDS (6 PARTS)

Eleventh Chords are typical for jazz and normally not used in standard rock (except for the famous A11

chord that starts “A Hard day’s Night” with the Beatles).

Eleventh Chords


The eleventh chords and higher are so complex that they tend to be “muddy” and dissonant. To lighten

up the sound, the musicians traditionally leave out one or two notes, focussing on the chord’s peculiar

sound, in this case the eleventh note (or Fourth note) colliding sharply with the major third with the mild

minor seventh to cool down the dissonance.



THIRTEENTH CHORDS (7 PARTS)

The thirteenth chords are usually played as a reduced chord. There is a long tradition for playing a 6+7

chord instead of the thirteenth chord, thus making the chord easy to play on the guitar.

Thirteenth Chords

STACKED CHORDS

JAZZ Chords build on triads are not the only chords in the world. In the experimental music of the last

century (especially the new classical music and advanced jazz), the composers used some new types of

chords, based on fourth and fifth, the so-called Stacked Chords. Even more advanced chords, e.g.

the polychords, are very common in modern jazz and classical music. Stacked Chords are used in-

tensely in the jazz brass section, especially in combinations of saxophones and trumpets / cornets.

TIP The bass to a stacked chord can be any of the notes in the chord, as the stacked chord itself is neu-

tral.

POLYCHORDS

JAZZ Polychords are one, two or more triads stacked upon each other. For obvious reasons, this is much

easier for a piano player than for a guitar player to use these chords.

Bm

C or

Bm/C

Some typical jazz polychords:

C / D

Em / Am

Cm7 / Bb

C7 / D

C7 / F#

C7 / A

Chapter 2, Harmony, A Transition


A Transition

The burning question is: must you end a piece of music at all? Rock and jazz have a ten-

dency to continue without any limits or closed, finite forms. A repeated rhythmic or har-

monic motif. A cadence ostinato again and again as seen in the dance. An inciting rhythm

conceived in the eternal repeats. Is there in fact any sense in stopping?

I clearly remember my parents' records; The feeling of wounded pride, pervading over

many of the 30’ies' swing records, when the band has to end. Listen to the saxophonist

Lester Young and his orchestra break off the last notes. Abruptly, staccato and insulted.

"It is really a shame, we have to stop here – oh, just 2-3 recordings more!" (It must have

been pretty frustrating with the short playing time on the old 78'is opposite to the 74 min-

utes of a CD).

This interesting point is discussed later in the chapter on "Style".

Chapter 2, Harmony, Transitive Harmony (Modulation)


Transitive Harmony (Modulation)

The principles of functional harmony and the harmonic cadence types are the foundation

of harmonising in all tonal music in one key. But what about music in 2 or more keys?

Such as about 40% of all modern melodies, no matter the style. If you have 2 keys, and

you intend to use them in the same melody, you must first find out, how to be make them

"pass" from one key to the other. The Latin verb "Transeo" means "pass (to)". In the lin-

guistic sciences, transitive means a verb that can connect itself with another verb (ex-

plained very superficially). Therefore I have chosen the term TRANSITIVE for harmo-

nies with 2 or more keys.

I have been much in doubt, whether I should limit "transitive" to 3 or more keys. Many

otherwise functional melodies move in "non-functional" steps on 1/2 or 1/1 note. And you

could, with some right, claim that it was only a simple transposing (change in key) and

not a coherent inner feature in the music. On the other hand; many "genuine" transitive

melodies also have this kind of non-functional modulations. And where do you draw the

line? Until better ideas pop up, I suggest that you simply name all melodies with more

than 1 key "transitive". Be it more or less.

Classical music frequently modulates. But it was not before Wagner, that the modulations began spread-

ing to the smaller melodic/harmonic levels. Mozart modulated from one large section to another, care-

fully planned over many previous bars. These modulations of course partly follow the transitive rules

and functional shifts. But the modulations never become genuinely integrated elements of the inner har-

monic structure of the melody, before Wagner wrote Tristan and Isolde (1865). Today the "transitive"

tendency is so established that almost all new classical music is 100% transitive, both harmonically and

melodic. In rock there is about 40-70% transitive songs, depending on the style. Jazz is more reluctant,

as heavily transitive harmonies make fluent improvisations difficult. But transitive harmony was the heart

of the 1970-ies' "symphonic" rock style, for a time replacing the "composition" music of the last centu-

ries. Here the chords reigned supreme, creating the melody moving from one key to another in one long

chain.

The whole concept of transitive harmony was born of the musical curiosity of a century, using chords

without any veneration for prohibited intervals or sinister attention to some "unbreakable" principles

(created in their time by violating some still older rules!). But even the seemingly untameable freedom

has its rules. There are actually a whole lot of rules. But they can be summed up in a few "dogmas".



POSSIBLE MODULATIONS BETWEEN 2 KEYS

Function Shift

1 A function in key I shifts to a new function, belonging to key II.

2 This function shift can be prepared through a change of key before the change of chord, but this

is not an absolute necessity.

Non-Functional Steps

All modulations 1/2 - 1 - 1.1/2 (minor third) note up or down and b5 (lowered fifth) up or down are

non-functional, as function shifts are unnecessary in so short, closely related steps*).

Major to Minor

Major to minor and vice versa is to be counted as a non-functional step (e.g. C to C minor equal to

C to Eb, equal to 1.1/2 note step, according to point 2 non-functional step).

*) Note the surprising coincidence between a tonic (b5) chord and tonic (b5) on the key on step b5 above the prime (e.g. C(b5) - F#(b5), C major to F# major – they are almost identical.

THE TRANSITIVE PRINCIPLES

A key modulates to another key in 2 separate ways. I distinguish in transitive harmony between function

shift and non-functional steps. Precisely as the 2 aspects, sound and modal have 2 different meanings in

chords and intervals, a transitive function differs a little from a standard harmonic function. Non-

functional changes simply mean that the melody jumps 1/2 note, 1 or 1.1/2 notes (a minor third) or a

lowered fifth (b5), without the use of the very important transitive tool, the function shift.

Function Shift

The most common transitive principle is to let a function in key I "shift" to a new function in key II.

There are a finite number of possibilities to change functions between 2 keys. The following table

has been constructed on a strict "mathematical" basis, and it is the table is most difficult of all the

tables in the whole book. I have therefore left out all function shifts implying a "hidden" non-

functional step.



FUNCTION SHIFTS (TRANSITIVE HARMONY)

The example is in C major as usual. The keys are all in major. In this connection, (b5), +, sus and dim

chords count as "major".

FUNCTION SHIFT

Chord Key I Original

Function

New

Function Key II Distance to

new key in

scale steps

C C (major) T D F 4

SD G 5

D rag E major3

D M nat Ab major3

G D T G 5

DD F 4

DD M nat Ab #5

blues 3 E major3

F SD T F 4

D moor E major3

TD Ab #5

DSD G 5

Fm SD neap T minor Ab #5

Ab D rag T Ab #5

D moor G 5

blues 3 F 4

Db D moor SD Ab #5

D rag F 4

TD E major3

TD M nat G 5



FUNCTION SHIFT


Function

New


new key in

scale steps

D DD D G 5

TD F 4

DSD E major3

TD M nat Ab #5

A C (major) TD SD E major3

D moor Ab #5

DD G 5

Bb DSD SD F 4

D Ab #5

SD M nat Ab #5

Blues 3 G 5

E D M nat T E major3

D rag Ab #5

TD G 5

B DD M nat D E major3

D M nat G 5

blues 3 Ab #5

F# TD M nat D moor F 4

DD E major3

DSD Ab #5

DD M nat G 5

Am T minor SD neap E major3

D minor F 4

SD minor G 5

DD minor Bb #7

Em D minor T minor G 5

SD minor D 2

DD minor F 4

TD minor Bb #7

Dm SD minor SD neap Bb #7

T minor F 4



FUNCTION SHIFT


Function

New


new key in

scale steps

D minor Bb #7

TD minor Ab #5

Bm DD minor SD neap F# b5

D minor G 5

SD minor A 6

TD minor F 4

F#m TD minor SD neap E major3

T minor A 6

SD minor E major3

DD minor G 5

Eb Blues 3 D Ab #5

D rag G 5

DSD F 4

D M nat B maj7

Gm*) DSD minor SD neap D 2

T minor Bb #7

SD minor F 4

DD minor Ab #5

TD minor Db b2

*) Rather unusual!

Due to their particular scale/tonal character (minor), the functions marked with blue also include modu-

lations to minor scales. The parallel major (Key II) otherwise belongs to non-functional steps.

NON-FUNCTIONAL STEPS

Lower or raise

1/2 note

1 note

1.1/2 note (the minor 3 step)

b5 (lowered fifth or tritonus)



In all 4 cases you can jump from:

Major to major

Minor to minor

Major to minor

Minor to major

Guidelines Function Shift

The middle part of the table is the general part. The examples in C major are only there to visualise

the principles. The table is extremely useful as a tool, when you want to know, where precisely a

melody chord progression modulates from one key to another. You do like this:

Find the First Key

and follow the chords until you know, without doubt, that you have entered a new, stable key.

Compare Intervals in Key I and Key Ii

for example C major to G major = 1 - 5 on the C major scale and find the "number" of key II's. This

number is found a few columns to the right of the table ("Step in new key"). If the number is b2, 2,

minor 3, b5, 6, natural 7 or maj7 it is a non-functional step, you are looking for.

Find the Function Shifts

When you have found the number, then find the function shifts to the right of the 2 functions below

the "FUNCTION SHIFT" top line (there are 15 different possible function shifts by the numbers 1 =

key I / 5 = key II).

Search both Forwards and Backwards in the Melody

Now comes the hard part! You can search both forwards and backwards in the melody. Sometimes,

somehow, you will– hopefully – find one of the possible function shifts. And if the melody unambi-

guously changes key there (which melodies unfortunately seldom do in an unambiguous way!), is it

here, you must change key on your instrument!

The method is helpful, when analysing very difficult transitive modulations. Apart from that, the

table can serve as an inspiration, if you compose and you want to try to work with more than one

key.

The table is somewhat crowded, and as I mentioned in "Scales, Transitive use" the melody line can un-

der some circumstances proceed as if nothing has happened, even if the key changes in the chords for

short while. Anyway, you need years of experience, before you can really understand the travel of the

melody through one key to another (which by the way reminds me a whole lot of the ways of love!).



Blues Chords

There is a problem I call the "blues schism” (schism: contradiction). The blues chords are functional

in one key. But many musicians believe that e.g. C major changes to Eb major, when a functional

blues 3 (= Eb) appears. The solution is simple.

As any blues musician knows, you cannot play "real" blues notes (microtones) on a piano or as

chords without using tricks with the tone bender. All blues chords are therefore temperated to the

Western system with 12 equal 1/2-note scale steps. This can give a classically trained listener the er-

roneous impression that the melody is in minor. This is wrong. Fundamental blues harmony is al-

ways in major chords. Whereas the transitional forms between blues and other tonalities are innu-

merable. Before the true nature of blues became known, white musicians always used minor, espe-

cially minor third, second and prime, which is a primitive approximation to the blues third, when

they wanted to imitate the blues. Listen to dance music from the 20'ies, to hear for yourself.

Gershwin, however, understood what it was all about in "Porgy & Bess" – or in "Rhapsody in

blue".

"The Ravel Step" – "# Minor 3"

This very powerful harmonic "trick" was repeatedly used by the French composer Ravel. It is an

extremely effective way of transposing. The receipt is just as the headline suggests.

1 Take a minor chord.

2 Imagine the minor third (only imagine) being raised 1/2 note to the major third.

3 Place a new minor chord/key on the imaginary major third ("# minor3") - and modulate.

Example: Cm to Em or Am to C#m)

Ravel uses the "# minor 3" step in for example "Daphne and Cloe" with an almost non-functional

effect.

EPILOGUE TO TRANSITIVE HARMONY

Transitive tendencies come and go following the changing of the styles and their degree of ethos or pa-

thos (see Form and style). For 5-6 years, advanced music with complex rhythms and heavily transitive

harmonies is common. Then suddenly cold storms blow from the right, and chords beside the tonic,

dominant and subdominant (in major, thank you!) become the only legal chords. And the rhythms stag-

ger uncomfortably in 2/2, adjusted 4/4 or (once a year) a waltz.

Transitive harmony is a progressive style trait. So are changing odd rhythms. But it is important to

stress that transitive traits can exist, even in works from “traditional” composers/styles (see Form and

style, General introduction). But the transitive tendency has been overwhelmingly strong in the last cen-

tury, and there is absolute no sign of the unambiguous harmonies taking total power again in the fore-

seeable future. Transitive harmony has come to stay.

Chapter 2, Harmony, Orchestration Tutor


Orchestration Tutor

This is what used to be nightmare number one for a rock musician, a score. Although the

jazz musicians learned to read notes literally a hundred years ago, rock musicians has ne-

glected note reading since the birth of Rock’n’roll in 1950-ies until the middle of the

1990-ies (only 45 years), when the modern music schools gave note writing a renais-

sance; it became hip to read notes. Now I will try to take the last step into music produc-

tion – the arrangement of rock / jazz music with classical instruments. In the new century,

most bands use classical instruments in the studio, at least strings and brass instruments,

not necessarily played on physical instruments, but most often with MIDI and sampled

sounds. This chapter leads you into the wonderful world of the classical symphony or-

chestra.

This orchestration tutor is a basic introduction to arranging for a symphony orchestra. As

the symphony orchestra contains almost all the jazz instruments except for drums, it will

be fairly easy to change the score layout to a big band score. The tutor covers the layout

of a symphony score, an introduction to each of the instruments in the orchestra including

range, technical details, the dos and don’ts and finally examples of good orchestration

practises.



THE SYMPHONY ORCHESTRA SCORE

A score is a computer or paper sheet with a number of instruments in a certain order. The normal order

of a symphony orchestra is as follows:

1 Woodwinds

Flute

Piccolo

Obo

English horn

Clarinet

Bass clarinet

Bassoon

Contrabassoon

2 Brass

French Horn

Trumpet

Trombone

Tuba

3 Percussion

Timpani

Cymbals etc.

4 Keyboards

Harp

Piano

5 Strings

Violin

Viola

Cello

Double Bass

6 Vocals

Solo

Choir Example: Large score



A Very Simple Score Layout

TIP Please note that the tuba and violin voices collide with each other in the sample score. A

typical problem when writing scores with high and low instruments. How to avoid the colli-

sion? Use a temporary bass clef with high 8va to lift the tuba. Then return to the standard

bass clef.



THE INSTRUMENTS OF THE SYMPHONY ORCHESTRA

Each instrument is described in details concerning transposition, range, techniques and special needs of

the instrument. All illustrations of tonal ranges are from the Wikipedia public domain collection.

Table of Contents of Instruments

Woodwinds

Transverse Flute

Piccolo Flute

Oboe

English Horn

Clarinet

Bass Clarinet

Saxophone

Bassoon

Brass

French Horn

Trombone

Trumpet

Tuba

Percussion

Drums and Percussion

Keyboards

Harp

Piano

Sting

Violin

Viola

Cello

Double Bass



Woodwinds

Transverse Flute

The transverse flute and the cello are the warm and romantic voices of the orchestra. The flute is

often used to add a streak of light to the strings or the light woodwinds. A deep flute solo also has a

mysterious meditative sound.

Transpose The common transverse flute is not transposed, whereas the less common flute vari-

ants often are.

Range

MIDI Sample

Technical Description The flute is very hard to hear when the notes are lover than the G over

the middle C, so dampen the other instruments until the flute goes higher up again. Don’t use the

highest notes, as they might be out of tune. If the strings play very loud, avoid topping with the

flute.

Speciality A powerful solo instrument, and great together with the oboe and the clarinet.

NFLUTE.mid



Piccolo Flute

The small piccolo flute with its metallic sound is a distant cousin to the earliest flutes cut out of

bone with holes. Contrary to the romantic transverse flute, the piccolo flute is used to give the

woodwinds a dramatic, almost warlike sound.

Transpose Sounds 1 octave higher than written.

Range

MIDI Sample

Oboe

The oboe is a lyrical instrument. The light voice of the oboe renders an extra dimension to the

woodwinds. The oboe is excellent for solos. It is a born twin to the clarinet. Oboe and clarinet in

pairs are typical for classical music.

Transpose Sounds as written.

Range

MIDI Sample

Technical Description Not as often out of tune as the clarinet is.

Speciality Solo and together with the clarinet.

NPICCO.mid

NOBOE.mid



English Horn

The English horn is close to the oboe, but sounds darker; a bit like the viola compared to the violin.

Transpose Sounds 5 notes lower than written.

Range

MIDI Sample

Nehorn.mid



Clarinet

Like the flute, the clarinet is a descendant of the earliest instrument maybe 30,000 years ago. The

Indo-Europeans invading Greece 3,000 BC played on early clarinets. The sound of the clarinet is

strongly nasal and it has a tendency to go out of tune. In the core of the woodwinds are the oboe,

the clarinet and the bassoon.

Transpose There are several clarinet models. The following are the most common clarinets:

A clarinet (soprano) sounds 3 notes lower than written.

Bb clarinet (soprano) sounds 3 notes higher than written.

Eb clarinet (alto) sounds 3 notes higher than written.

G clarinet (soprano) sounds 5 notes lower than written.

Range

MIDI Sample

Technical Description The foundation of the woodwinds is the clarinets and oboes in pairs with

the French horn and the bassoon as the bass line. If you do have a bass clarinet (see next page), use

it in pairs with the bassoon.

NCLARIN.mid



Bass Clarinet

The very versatile bass clarinet has a unique sound with 4 octaves like the bassoon.

Transpose: Sounds 1 octave deeper than written,

Range

MIDI Sample

NBCLARIN.mid



Bassoon

The large bassoon has a light nasal voice in spite of its size. The instrument has a sorrowful tone

that penetrates the orchestra in a subtle way.

Transpose: Sounds as written.

Range Bassoon

MIDI Sample

Specialty Solo and deep bases; blends well with French horn and trombone.

../Graphics%20and%20MIDI%20files%20etc/MIDI/NFAGOT.mid



Saxophone

The saxophone – or sax – is one of the most popular instruments in the world competing with the

guitar. It is used in classical music, but are much more prominent in big bands and jazz groups. The

sax family has many members, but the tenor, alto and soprano are the most common variants.

Tenor Alto Soprano

Transpose

Bb Tenor sax: Sounds 2 notes lower than written.

Eb alto: Sounds 9 notes lower than written.

Eb Soprano: Sounds 2 notes lower than written.

Eb Baritone: Sounds 9 notes lower than written.

Range

The four saxophone members are written individually according to the above explanation.

MIDI Sample

Technical Description Use the three sax types in trios to enforce the sound and dynamics.

Don’t place the soprano sax too deep.

Nsax.mid



Brass

French Horn

The French horn replaced the ancient nature horn in the early 1800-ies. The nature horn was “out of

tune”, i.e. not temperated and the French horn were able to play in all keys. But the feeling of the

deep forests is still there with the dark, hollow tone. Opposite the rest of the woodwind group, you

can use French horn to play in fifths and quarters a little under or over the middle C.


Range

MIDI Sample

Technical Description Try to keep the French horn in a limited area between the E under the

middle C and A over the middle C; just sounds better. French horn and trombone in tight pairs are

very effective.

NFHORN.mid



Trumpet

You cannot mention a trumpet without hearing Louis “dipper mouth” Armstrong and Dizzy Gilles-

pie in your head. The trumpet is the king of jazz and Mexican music.

Transpose There are several trumpet models. The following are the most common ones:

An A trumpet sounds 3 notes lower than written.

The Bb trumpet sounds 2 notes lower than written.

The D trumpet sounds as written.

Range

MIDI Sample

Technical Description A loud and beautiful instrument, when played well. If the trumpet player

is bad, use a sax and a trombone instead. Trios with trumpet, sax and trombone are typical for jazz.

Speciality trumpet muffled with a hand gives a very special effect.

NTRUMPET.mid



Trombone

The trombone is a strange instrument where the tones are produced by pulling the tuning slide for-

wards and backwards. It is the most flexible brass instrument, capable of astounding glissandos and

blues notes. In the classical orchestra, it is an effective bass instrument.


Range

MIDI Sample

Technical Description Remember to use the trombone glissandos!

NTROMB.mid



Tuba

The tuba is much more than “umpa umpa” and lederhosen. The tuba is very important in a sym-

phony orchestra laying a firm bass under the rest of the instruments. It also enforces the general

tone of the orchestra. The tuba can be used as a solo instrument.

Transpose. Sounds as written.

Range

MIDI Sample

ntuba.mid



Percussion

The percussion group of a symphony orchestra normally consists of two musicians, a timpani per-

cussionist and a jack-of-all-trades for the cymbals, the tubular bells and the other exciting hardware

in the special effects department. The timpani are tuned and used almost as a melodic instrument.

A 4-piece timpani setup

Range Depends on the type and number of timpani.

MIDI Sample

Technical Description Read volume 4 in the All Aspects of ROCK & JAZZ series, Drums,

where you can find most of the percussion instruments and have to play them.

../Graphics%20and%20MIDI%20files%20etc/MIDI/NTIMPAN.mid



Other

Harp

The harp is not always a part of a “standard” orchestra. The instrument has a loud and clear tone,

but it needs to be placed in a fitting musical surrounding. Use it as a solo accompanying instrument

or to add its colourful sound to light woodwinds or low strings.


Range

MIDI Sample

../Graphics%20and%20MIDI%20files%20etc/MIDI/NHARPE.mid



Piano

The piano concert is a classical form, but beware – it’s really hard to fight the arrogant grand piano.

If you use the piano all the time, the other musicians will not be heard and the arrangement will be

chaotic. Use it only for shorter sections.

Transpose Sounds as written

Range 7-8 octaves.



Strings

Violin

The violin is the queen of the stringed instruments. If you only want to use one classical instrument,

then choose the violin. Rock music with strings gives you the opportunity to create a dynamic car-

pet of static or fast moving strings. Jazz music, too, gains from having strings behind the brass in-

struments and the piano.


Range

The strange square, empty note is an overtone. See chapter Scales.

MIDI Sample

nviolin.mid



Viola

The viola is like the violin, but lower with a nasal, broad tone. It is notated in the C-clef.


Range


MIDI Sample

nviola.mid



Cello

The romantic cello is an all-round bass instrument; effective in solos adding a solid bass line to-

gether with the double bass.


Range


MIDI Sample

ncello.mid



Double Bass

The double bass is the mother of the bass guitar (the author’s main instrument). In the bass team-

work of an orchestra, the double bass, cello, tuba and trombone play an important role for the dy-

namics of the music and the sound.

Transpose Sounds 1 octave lower than written.

Range

The strange square, empty note is an overtone. See chapter Note Writing and Scales.

MIDI Sample

../Graphics%20and%20MIDI%20files%20etc/MIDI/NBASS.mid



GOOD ORCHESTRATION PRACTICES

Learning to arrange for the Symphonic Orchestra is not an easy task. Unlike rock and jazz music

with a steady rhythm on the drums and bass, the classical orchestra is driven by a wealth of individual

voices creating the pulse, sound and dynamics. The orchestra works fine with a rock or jazz group

in the front. But the arrangement must be able to work without the drums, saxophones and guitars. The

learning period is often 20 years or more. You can start here, but this is only a fragment of the musical

history behind the symphony orchestra. Go to the bibliography in the chapter Style and checkout the

best book ever written about orchestration by the Russian composer and music teacher Rimsky Kor-

sakov.

Number of Duplicate Instruments

The density (solidity / power) of the orchestra is created through combining small or large groups of

musicians playing the same notes. The following examples are the result of 700 hundred years of

musical practices.

Woodwinds

Double woodwind: 2 flutes, 2 oboes, 2 clarinets, 2 bassoons

Triple woodwind: 2 flutes and 1 piccolo flute, 2 oboes and 1 English horn, 2 clarinets and 1 bass

clarinet, 2 bassoons and 1 contrabassoon.

Brass

4 horns, 3 trumpets, 3 trombones and 1 tuba

Percussion

2-4 timpani

Strings

16 First Violins, 14 Second Violins, 12 Violas, 10 Cellos and 8 Double Basses.



Strings and Woodwinds

Strings and woodwinds are the basis for a classical orchestra. The brass section, piano, harp, per-

cussion are nice to have, whereas strings and woodwinds define and move the orchestra. Without

these two groups, there would not be a symphony orchestra.

Here is an example where a rock band is accompanied by strings and woodwinds. Please note the

exchange between the two groups and the thinning / intensifying of the groups. Listen to the midi

file. “Den første sne” Music and text by H.W. Gade © 1973/2007.

Bar 101-108 The bassoon appears with dark strings

ork_01.mid

ork_01.mid

ork_01.mid



Bar 109-116 The strings take over building up a climax in bar 114’s high chord stack



Bar 117-124 A massive tension is build just before the chorus, where the string are muted



Bar 125-132 The chorus is near the end and the strings begin to move



Bar 133-140 The bassoon reappears



Bar 141-148 A classic moving pair of flutes and oboes to lift the dynamic



Bar 149-156 Trills fuel the score with electric energy. The strings play in staccato.



Bar 157-164 High flutes and oboes and long notes on the bassoon. The strings stops.



String Chord Texture

A violinist can play 2 strings at a time, but this is mostly for solo purposes. So normally the strings

are divided into single string parts, which form the harmonies of the music. Here are some short ex-

amples of harmonizing with strings.

Building an E-minor chord The bass plays the primal note. The cello plays the bass line of the

verse and the strings play a widespread chord with G + G + E (an octave is forbidden in classical

music, but who cares).

Moving Chords The bass and cello plays the same note, which they often do. The high chord has

now become closer and it starts moving in syncopated rhythms. Last bar the chord is divided by

large distances.



Arpeggio Strings

The strings are certainly not limited to chords. The chords can – as on piano and harp – be divided

into arpeggios. Listen to the midi file. “Morungen Lieder” Music by H.W. Gade © 1989/2002.

Text by Heinrich von Morungen about 1200.

Woodwinds and Brass

By combining the tough brass instruments with the soft woodwinds, you create the depths and

warmth of the symphony orchestra. Here is an example to show how static notes and movable

melodies and bass line create the full effect of the orchestra.

Bar 89-92 The brass and woodwinds play the same figure. Then the oboe breaks loose.

ork_02.mid



Bar 93-100 Now it becomes complicated. The flute, oboe and clarinet form a trio with polyphone

voices in the clarinet. The bassoon now plays very deep notes, which the bassoon is very good at.



Bar 101-108. The flute pauses and the oboe and clarinet moves in pairs. The French horn and the

bassoons are active in the bass. In the last bar the bassoon moves to a very high position.



Bar 109-116 The flute and the clarinet play a dynamic melody (the pause in each bar creates a

nervous energy). In the last bars, the brass group sets in and attacks.



Bar 117-120 The woodwinds and the brass end in a common chord. The flute ends the passage

with a small solo.



Fat and Thin Textures

By increasing the number of notes and by adding bass lines, strings and woodwinds, you create a

fat texture, i.e. a solid wall of sound like Phil Spector did in the 1960-ies pop songs.

First the woodwinds and the brass:



Then the strings, harp and choir arrive:



By removing most of the bass, reducing the strings and refraining from using more than a few

woodwinds and brass instruments, you create a thin texture, which is needed in soft parts of a

choir work or during spoken dialogues in a musical.



Tutti

The tutti parts of a score is the most challenging parts to write, and it takes years to master. And

even then, it is very, very difficult to keep track of all the instruments playing individual voices, ap-

pearing and disappearing. The example is from the finale of Morungen Lieder. Listen to the midi

file.

Bar 1-4 Everyone’s busy except for the brass group.

ork_03.mid

ork_03.mid

ork_03.mid



Bar 5-8 Still busy.



Bar 9-12 Activity everywhere. Please note how the harp induces energy into the music.



Bar 13-16 The woodwinds are phased out and the harp stops.



Bar 17-20 Oboe and clarinets play trills and the strings play in tremolo and solo voices.



Bar 21-24 The tutti part ends, and a very quiet passage follows.



A “Floating” Score without a pulse

Modern scores often contain very complex rhythms and ways of distributing and moving the notes

of the chords. The following example is from my 1970-ies band Nekropolis. Listen to the midi file.

“Tordenvejr” text and music by H.W. Gade © 1974/2005. Note the lack of pulse in the music.

Bar 1-4 The cello starts the theme. The French Horn starts moving.

ork_04.mid



Bar 5-8 The other instruments set in.



Bar 9-12 The woodwinds begin to play faster and faster.



Bar 13-16 The orchestra stops with a musical vision of a wet summer morning. The band starts.

Chapter 2, Harmony, Other Harmonic Systems


Other Harmonic Systems

I would like to end the Harmony chapter the way I ended the Rhythm and Scale chapters,

with some interesting examples of different kinds of music. And with this section, I also

end the music theoretical material proper. The next chapter deals with music, seen in rela-

tion to style and society.

PARALLELISM

This common form of alternative harmonies consists of non-functional chord movements, either in major

or minor, but never mixed. Some people claim that blues 3 and blues 7 chord functions are parallel chord

movement. The argument seemingly holds, as blues chords moves in parallel. But blues 3 and blues 7 are

fully functional, in spite of the apparent non-functional, parallel steps. You can play comfortably in blues

scales over a major scale with blues functional chords! The 2 chords have over the years attained a cer-

tain cadence character (e.g. blues 3 – blues 7 – T). So blues 3 and blues 7 have become approved as

functional by the majority of rock and blues musicians.

Nonetheless, true non-functional parallel movements are not that uncommon in rock.

Parallelism non-functional, parallel chord movements

Example: Minor parallel chords on scale steps in C minor

Main rules

1 Chords without function within the key.

2 Only major chords or only minor chords.

3 The chords move on standard scale steps, chromatic steps, whole note steps or mixed forms. Listen

to the Notes.

Many newcomers feel tempted to use parallel chord movements. That gets rid of all the uncomfortable

harmonic functions. But then you have to change from chord to chord or transpose heavily within the

"scale". And that is actually more uncomfortable! The principle is outworn in classical music, and it has

had its day in rock music. The harmonic possibilities were not that exciting.

A1FIG175.MID

A1FIG175.MID

A1FIG175.MID



POLYHARMONY / BITONALITY

There are lots of possibilities in polyharmony, also called bitonality. Polyharmony is the use of

chords with different basic notes, played simultaneously. As you almost never use more than 2 different

chords at one time, the second name for the principle is bitonality (double tonality). There are no fixed

rules for how and when. The only rule, you might follow, is a sort of tension curve, where the chords

relate to one another as intervals in more or less dissonance. Note! This rule also applies to bitonal 2-

part melodies!

Polyharmony (bitonal chord relations)

MAJOR CHORDS

Sharp Dissonance Mild Dissonance Neutral

C + Db (b2)

C + E (major3)

C + G# (#5)

C + B (maj7)

C + F# (#4)

= C11(#4)

C + D (2)

C + Eb (minor3)

C + F (4)

C + G (5)

C + A (6)

C + Bb (7)

= D11

= C-10

= Fmaj7+9

= Cmaj7+9

= A-10

= C11

MINOR CHORDS


Cm + Dbm (b2)

Cm + Em (major3)

Cm + Gbm (b5)

Cm + G#m (#5)

Cm + Am (6)

Cm + Bbm (7)

Cm + Bm (maj7)

Cm + Dm (2)

Cm + Ebm (minor3)

Cm + Fm (4)

Cm + Gm (5)

= Fm7+9

= Cm7+9

MINOR + MAJOR CHORDS


Cm + Db (b2)

Cm + E (major 3)

Cm + Gb (b5)

Cm + A (6)

Cm + B (maj7)

Cm + D (2)

Cm + Eb (min3)

Cm + F (4)

Cm + G (5)

Cm + Ab (#5)

Cm + Bb (7)

Cm7

F9

Cm(maj7)+9

Abmaj7

Cm11



(Polyharmony (bitonal chord relations) continued)

MAJOR + MINOR CHORDS


C + Dbm (b2)

C + Ebm (minor 3)

C + Fm (4)

C + G#m (#5)

C + Gbm (b5)

C + Bbm (7)

C + Bm (maj7)

C + Dm (2)

C + Em (maj3)

(C6+9+11)

Cmaj7

C + Gm (5)

C + Am (5)

C9

C6 or Am7

The table shows some different degrees of dissonance between major and minor basic triads. Other triad

forms as for example (b5) or + chords can also be used, so the possibilities are almost unlimited.

An example of bitonality by the author himself; a harmonic principle I have used on an increasing num-

ber of occasions, for example in my operas "The Burning Lands" from 1993 and “Frozen Positions”

from 1995. The example below is from my 1970-ies production.

Bitonality - example

("Death" Nis Petersen/H.W. Gade copyright © 1979)

Listen to the Notes

A1FIG177.MID



CHORD ROWS

A sort of endless cadence row comes to life, if you let chords continue perpetually on a single interval,

e.g. fourth or fifth. This is a typical jazz phenomenon. In a short while any chord row will use every

chromatic note in the temperated system!

Fourth Rows

The fourth chord row moves upwards in fourths, but ends in the dominant chord (fifth)

C F Bb Eb Ab Db Gb B E A D G

T4 4 4 4 4 4 4 4 4 4 4 D

Fifth Rows

The fifth chord row move downwards in fifths, but ends in the subdominant chord (fourth)

C G D A E B Gb Db Ab Eb Bb F

T5 5 5 5 5 5 5 5 5 5 5 SD

Note: the basic notes in fourth and fifth rows are themselves a fourth, respectively a fifth stack (see Other chord forms)

In this clever way, you can dissolve any functional tendency in apparently functional movements. Chord

rows form a superb basis for improvisation (C - G = C major, D - A = D major etc.). And for the same

reason chord rows are more common in jazz than transitive harmonies, described in the previous sec-

tions.

NON-FUNCTIONAL HARMONY / COLOUR CHORDS

Even if both parallelism, polyharmony and chord rows are non-functional, we still have not reached the

outer boundaries of harmony: the colour chord, a chord whose whole existence is purely vertical, pure

sound. The functional chords live a double life. They "function" in horizontal movements to and from a

tonal centre. And they "sound" vertically as sound "colours", dissonant or consonant. But a chord can

easily stand alone, only being, only sounding in itself. You have probably heard the lonely chord of the

foghorn over the dark sea, or the diffuse sound of many human or animal voices, whose chaotic relative

movements become static sound. This way the notes can create a sound structure that does not need

anything but its own existence.

According to their very nature, all chords can of course be isolated sound colours - alone! But often

one or more chords can be put in functional circumstances, where they achieve a non-functional signifi-

cance as pure sound.



(Non-functional Colour Chords Continued)

Definition: Pure "vertical" sound, without function, sometimes surrounded by functional chords

Excerpt from the rock opera "GOLGOTHA", 2nd Act, 11th picture (Copyright © H.W. Gade 1974)

Listen to the Notes

Especially Debussy and Ravel, but also Messiaen and others use colour chords as effective sound layers

without melodic function.

And with this, the victory of pure chord over melody, I end my chapter on harmony.

A1FIG179.MID

Chapter 2, Harmony, Index Harmony


Index Harmony

Use the Index! By looking up in the index, you can find much more than you were looking for! Follow

the strange leads and weird words. Learn by accidence. Be curious!

A

Arpeggio, 12

B

Bach, J.S., 4, 9

Bartok, Bela, 25

Beatles, The, 31, 35

Bitonality, general, 54, 55

Blues, general, 29, 31, 42,

49, 50, 52

C

Cadence, general, 42, 43, 44

Cadence, rhythmical, 43, 44

Cadence, standard, 40, 42

can, 58

Chord symbols, 23

Chord, Neapolitan, 31

Chord, rows, 56

D

Debussy, Claude, 25, 26, 57

Decrescendo, 44

Dominant, 24, 29, 30, 31, 34,

37, 41, 42

E

Endings, 43

Enharmonic notes, 6

F

Fade, 43

Fifth (5), 6, 26, 56

Function shift, transitive, 43

Functional harmony, general,

6, 24

G

Gade, Niels W., 31

I

Intervals, general, 4

L

Leading note, 29

M

Melody, doubling, 8

Melody, phrasing, 44

Meter, bars, general, 44, 46

MIDI, general, 31

Minor, 13, 14, 30, 34, 37, 51,

53

Modal, aspects, 13, 32, 34,

36

Modulation, 46

Musical, 4, 27

N

N.C. / No Chord, 24

Natural sign, 34

Notes, hand-written, 23

Notes, tonal gender, 7, 35,

37, 38

O

Octave shift, 8va, 15va, 9

P

Parallelism, 8, 53

Polyharmony, 17, 54, 55

R

Ragtime, description, 32

Rhythm, inner structure, 43

S

Scale, Aeolian (minor), 37

Scale, artificial, 25

Scale, Ionian, 37

Scale, Locrian, 37

Scale, Lydian, 37

Scale, Mixolydian, 37

Scale, Phrygian, 37

Scale, whole note, 7, 8, 25,

53

Second (2), 6, 25

Sharp (#), 14, 17, 54, 55

Stravinsky, 25

Subdominant, 29, 30, 31, 34,

37, 41, 42

Subdominant, double, 41

Chapter 2, Harmony, Index Harmony


T

Third (3), 6, 7

Third stack (triad), 9, 10, 11,

13, 23, 55

Tonic (chord), 34, 37

Transitive harmony, general,

33, 43, 46, 52

Triads, basic 3-part chords,

9, 10

W

Wagner, Richard, 7, 46

Harmony - NORDISC Music

Documents

Transcript of Harmony - NORDISC Music