Pattern Obsession and Music Weaving

User Supported        

(This is a very large page and the links below to the sections do not all work until the page is fully loaded. Scrolling works right away.)

Dr. Dick's Introduction to Pattern Obsession and Music Weaving

Introduction

Nature of Sound

Sine Waves

Pitch

Overtones

Modes

Leading Tones

Pentatonic Scales

Chords

Major Triads

Seventh Chords

Ninth, Eleventh, and Thirteenth Chords

Substitutions

Eleventh and Thirteenth Chord Substitutions

Harmonizing the Minor Scale

Borrowed Chords

Melodic Minor

Inversions

Added Notes

Suspensions

Passing Tones

Chromatic Harmonies

Secondary Dominants

Chains of Secondary Dominants

Secondary Dominants Based on viio

Tritone Substitutions

Misspelled Chords

Interval Based Chords

Quartal Chords

Quintal Chords

The Circle of Fifths

Scales

Circle of Fourths

Minor Scales

Key Signatures

Chord Symbols

Seventh Chords

Minor Sevenths

Major Sevenths

Diminished Seventh

Ninth Chords

Altered Ninths

Eleventh Chords

Thirteenth Chords

Rules for Chord Symbols

Add Chords

Add2

Add4 Chords

6 Chords

Cluster Chords

Atypical Added Notes

Add#2 Chords

Add#6 Chords

Addb2 Clusters

Add#4 Clusters

Addb6 Clusters

No 3rd Chords

No 5th Chords

All the Chords.

Chord Spelling

Inversions

G Bass Inversions

Second Inversion Chords

Third Inversion Chords

Diminished Seventh

Higher Inversions

Bass Passing Tones

Mapping to G

Sorting

Transpositions

Parallel Modes

Harmonic Minor Mode Equivalents

Melodic Minor Mode Ascending Equivalents

Parallel Mode Chords

Symmetrical Patterns

Symmetrical Scales

Chromatic Scale

Whole Tone Scales

Octatonic Scales

Symmetrical Chords

Tone Clusters

Augmented Chords

Diminished Chords

The octatonic scale

Symmetrical Quartal Chords

Higher Interval Chords

Twelve Tone Music

Fretboard Patterns

Stochastic Processes

All Possible Scales

Improvisation

Microtones

Temperament

Alternate Pitch Sets

Timbre

White Noise

Pink Noise

Subtractive Synthesis

Amplitude

Filters

Formants

Compression/Limiting

Expander/Gate

Distortion

Envelopes

Tremolo

Amplitude Modulation

Frequency Modulation

Autotune

Quantizing

Phase

Echo

Delay

Reverberation

Sampling

Rhythm

Polyrhythms

Melody

Texture

Cadences

Form

Groups

Styles

Psychoacoustics

Aesthetics

Evolution

 

Introduction to Pattern Obsession and Music Weaving

An explanation of how musical theory and practice derives from a simple set of natural occurring phenomena.

ABSTRACT

Acoustical phenomena produce simple patterns that build on each other to produce complex musical patterns. The overtone series suggests scales which build into more and more complex chords. Musicians develop notational systems to represent these structures. The mathematics of combinatorics and software allows the presentations of large volumes of musical structures like scales, modes, and chords. These structures eventually evolve into complex mathematical patterns separated from their original context. Evolution of these patterns leads to representations of musical elements such as timbre, harmony, rhythm, melody, and form. Eventually, these patterns break down into music's true purpose: to express ephemeral human emotion and to aid in evolution.

Introduction

This document began as a simple introduction on how all of the complexities of music derive from variations, and how these patterns effect the main part of the Pattern Obsession guitar course. Eventually it grew organically into this quite complex manifesto, as pattern based mathematical functions tend to do.

 

Much of this text may be difficult for people without training in music theory. This is not a traditional theory text with "every good boy does find" or explaining half notes and whole notes. Instead, the text shows the underlying patterns that produce the music and then goes back later and explains the nomenclature as needed. Some theory concepts do not occur at all, as they are interspersed in the guitar method when necessary. The philosophy is to learn the music patterns first, then put the labels on it later.

 

Unfortunately, to write about the increasing complexity if music, use of the jargon is necessary. The section of chord theory is particularly thick, and will lose even a lot of accomplished musicians. So, read through the text, and when your eyes start glazing over because of all the chord symbols or math, skip forward to a new section.

Nature of Sound

Consider a set with all possible musical combinations.

 

First start with the most basic sound possible. Sound occurs when objects vibrate in a medium, usually air, but possibly water, metal or any medium that can vibrate. Despite all the rumbling of ships passing by in Star Wars, no sound propagates in space without air. (The movie Alien got it right – "In space no one can hear you scream.")

 

To produce a sound, first disturb an object in space. For this theoretical example strike a perfectly flat surface that is infinitely rigid, like an impossibly stiff chalkboard suspended in the air in a frictionless manner. Striking the chalkboard causes it to move away from the listener slightly. When the surface moves away from the listener, the air molecules stretch apart slightly, a phenomenon known as rarefaction. Now consider this surface suspended by a perfectly efficient spring that wants the surface to return to its natural position. Striking the surface causes it to move away quickly at first, but as the spring begins to push back, the object slows down and eventually stops moving away.  Once the energy of the initial disturbance dissipates, the surface moves back toward the listener, slowly at first and then gaining speed until it reaches its original position. The object moving back toward the listener eventually nullifies the rarefied air until the air pressure returns to whatever it began with.

 

But Newton proved that energy has to go somewhere, so the energy of the initial strike has produced a momentum of the moving surface. The surface does not stop, but continues toward the listener quickly at first, but eventually slowing down and stopping the same distance from the starting point as the initial movement away from the listener as the spring absorbs the energy of the movement. As the surface moves toward the listener, the air molecules compress in a manner that parallels the movement of the surface.

 

But now the spring absorbs the energy, and so wants to move the surface back to its original position, slowly at first, then increasing speed. Once back in the original position, the surface now has momentum the other direction and wants to repeat the cycle. Nature abhors a vacuum, so the air molecules next to the ones being compressed react by moving into the space with the lower air pressure. Then the compressed molecules that follow push the alternating compressions and rarefactions through the air until they eventually reach the ear drum. The mechanics of the ear translate these vibrations into what the brain perceives as sound.

 

Eventually the friction of the air would slow the object, but for this theoretical example, instead of air, imagine a perfectly consistent medium with no friction. Now, nothing would stop the cyclic movement of the surface moving away from the listener, back to its starting point, toward the listener the same distance, back to its starting point, and the repeating the cycle forever.

Sine Waves

Mathematically, the sine wave, y=sin(x) expressed mathematically, represents the compressions and rarefactions of the medium. Sine waves dominate nature from the waves on a pond, to the propagation of light, to the rolling of hills in geology.

 

The sine wave representing sound begins at the 0 point being the natural pressure of the medium at equilibrium, one standard atmosphere (or 14.7 pounds per square inch, 1,013.25 × 10 3 dynes per square centimeter, 1,013.25 millibars, or 101.325 kilopascals using other measurement systems). The sine wave moving higher represents the air becoming more compressed, quickly at first, then tapering off at 90 degrees (π/2 in radians) returning to the equilibrium point at 180 degrees (π) reaching its most compressed state at 270 degrees (3π/2) and returning to the starting point at 360 degrees (2π). The number of times this cycle repeats in a second is called it frequency, measured in Hertz (Hz).

 

Many sounds wash over us as the brain develops, but certain sets of tones stick out. All sounds can be musical, but music tends to be categorized into sets of sounds. The set of sounds associated with melody and what the Western ear considers music is dominated by timbres with a musical pitch.

Pitch

Again, a set of all possible music would contain many notes we do not consider musical. Between the pitches that Western music considers acceptable notes are an infinite number of notes that sound out of tune to those reared listening to the standard scale. An Asian Indian folk singer might use these pitches, but mostly they are ignored as nonmusical.

 

Western music settles on a group of notes that approximate and subdivide the natural tones produced by a vibrating object. These notes sound most pleasing because they approximate mathematical patterns inherent in vibrating objects.

Overtones

A vibrating string moves back and forth at a certain frequency measured in cycles per second (Hz); a frequency which we perceive as the fundamental pitch of the note. But parts the string also vibrate naturally in other frequencies that mix to produce the timbre, or tone color, of the instrument.

 

A string tuned to A440, standard tuning pitch, vibrates at 440 times per second, but also has a second set of vibrations at double that frequency, 880 Hz, occurring halfway up the string. A guitar player can release this vibration by lightly touching the string half way, at the 12th fret, producing a harmonic. (Think the opening notes of "Roundabout" by Yes). Since the original 440 pitch and the 880 pitch occur so often together, the human mind perceives the 880 frequency as actually the same pitch as 440, just higher.  A note with a doubled frequency is an octave, or the interval (distance between two notes) of a Perfect 8th (P8) musically. (Why certain intervals are perfect and others are major, minor, diminished, or augmented is not important right now. Just observe the labels and their function will fall into place naturally and with further study.)

 

Even though the string is actually producing multiple sine waves at the same time with multiple frequencies, the brain tends to group these frequencies together rather than hearing them separately, just as different frequencies of light mix together to form colors. The string also naturally vibrates in thirds, at the seventh fret harmonic on a guitar. The frequency of this vibration is three times the fundamental, or 1320 Hz. (For a mix of seventh fret and 12th fret harmonics, listen to the opening of "Red Barchetta" by Rush.) This vibration is so common that the mind perceives the distance between the notes as the most consonant interval, the perfect fifth (P5), or sol in solfege. (Solfeggio is do re mi f sol la ti do, listen to "Doe, a Deer" from The Sound of Music.)

 

The P5 interval is so universal that it occurs in many songs, think the opening notes to the Star Wars Theme. A chord based on the fifth scale degree is known as the dominant (V), which signals the return of the tonic (I), or root chord of a key (The chord built on the first note of the scale). This dominant-tonic relationship is ubiquitous in Western music, and the basis for many chord progressions.

 

The next interval in the overtone series is at four times the original frequency. Since four times the frequency is twice the frequency again doubled, the mind perceives this pitch as an octave above the octave at 880, or two octaves above the fundamental. The musical distance between the fifth and the octave above it is known as a perfect fourth (P4), the second most consonant interval. (Think the opening notes of "Here Come the Bride"). The chord built on the fourth degree of the scale is known as the subdominant (IV). Together the I, IV, and V chords are known as the primary chords. The subdominant-dominant-tonic relationship is the basis for cadence (ending a phrase) structures in Western music.  So, see how the structures of western music all derive from a mathematical relationship based on the physics of sound.

 

Continuing up the overtone series, the next two naturally occurring intervals are the major third (M3) and the minor third (m3).  Combinations of major thirds and minor thirds are the basis of the most common chord structures. A note plus a major third plus a minor third above it is known as a major chord, the most common chord. The minor chord is simply the two reversed (root, m3, M3.). Again, chord structure is built on naturally occurring mathematical relationships built of multiples of the fundamental frequency.  Ancient music theorists did not consider the third to be a consonant interval, only fourths and fifths, but the modern ear hears the third as consonant because of its wide use in modern chord structure. Chords that sound good derive from natural mathematical sequences.

 

The next overtone is a minor seventh (m7) above the nearest octave of the fundamental. Chords built on the common triads are the next most commonly used chords, the seventh chord (7), which is a major chord plus m7 interval, and a minor seventh (m7), a minor chord plus a m7 interval ("m7" can designate the interval of the chord, depending on context).

 

The next two overtones are another octave, and then an interval a major second (M2) above that. The major second is the second scale degree, re, and also added to seventh chords to make ninth chords M9 and m9. In the scale, a ninth is essentially the same as the 2nd an octave up since the scale repeats after seven notes.

 

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 1 2

 

The overtones continue to eventually contain all notes, but they become functionally difficult to access and increasingly out of tune on any physical instrument. For some great harmonic work on the guitar, listen to "Top Jimmy" by Van Halen.

 

So, the intervals derived from the overtone series listed so far are

 

P1 P8 P5 P4 M3 m7 M2

(P1 designates a "unison" interval, or the fundamental frequency.)

 

Rearranged in the order from their nearest root note gives

P1 M2 M3 P4 P5 m7 P8

Starting arbitrarily on the note g is the easiest to express these intervals in musical notation. Musically, these intervals can translate to the notes

g a b c d f g

 

Again, why these notes have these labels is less important than knowing their function for now. The could just as easily be labeled with numbers or colors or animal names. Tradition dictates they be labeled with letters, lower case here to avoid confusion later when capital letters stand for something else.

 

Now we have six of the seven notes of a traditional grouping of notes, a scale. All the notes with consecutive letters are the same distance from the note preceding them with the exception of the interval from b to c. The distance for b to c is half the distance of the others, so this interval is a half-step or minor second (m2). The other more common distance is the whole step or major second (M2), which also derived from the overtone series.

 

Also troubling is the interval from d to f. The distance from d to f is three half steps, or minor third (m3), a larger interval than the other scale tones, and why the letter e is missing to leave room to put in another note. Pattern completion demands that interval be filled in. Without knowing from modern scales what note goes in the space, the e could be a half step or a whole step from the d.  This ambiguity of the sixth scale degree can be exploited for variation later, but for now just define the sixth e as a whole step above the d just below it.

 

gabcdefg

 

Which is called the Mixolydian scale. Jazz players use Mixolydian applies to improvise over the dominant chord, so use this scale to improvise over the dominant chord (V) (More explanation on that later).

Modes

Do not be confused that this scale does not sound exactly like the "Doe, a Deer" song learned in elementary school. The modern major scale is not chiseled in stone, but derived from centuries of tradition. To explain how, consider the concept of modes.

 

All scales loop around on themselves naturally, so the scale from above becomes

 

g a b c d e f g a b c d e f g a …

 

Instead of starting on the first note as g, begin with c and work around the scale

cdefgabc

Now this scale sounds like the scale learned in elementary school.

 

To answer why the Mixolydian scale seems misplaced to modern ears, first explore all the modes. Ancient music often used the same combinations of scale relationships that modern music does, but not always with the same starting note.

 

Modes are scales begun on different beginning pitches, designated by the following labels:

 

Ionian Dorian Phrygian Lydian Mixolydian Aeolian Locrean

 

Using the notes from above, the modes would be:

 

Ionian

c

d

e

f

g

a

b

Dorian

d

e

f

g

a

b

c

Phrygian

e

f

g

a

b

c

d

Lydian

f

g

a

b

c

d

e

Mixolydian

g

a

b

c

d

e

f

Aeolian

a

b

c

d

e

f

g

Locrean

b

c

d

e

f

g

a

 

Descriptions of the modes

 

Ionian

Today's major scale

Dorian

Minor with a raised 6th. Great for solos. Listen to "Greensleeves"

Phrygian

Rarely used, Eastern feel

Lydian

Nice raised 4th alternate to major. Listen to Rush "Free Will" intro.

Mixolydian

The most mathematically natural. Solos over dominant V7 chord

Aeolian

Today's minor scale. Compare "What Child is This" to "Greensleeves"

Locrean

Very rarely used

 

Jazz players use these modes for solos that fit the chord progressions.

Leading Tones

 

Dorian Lydian, and Mixolydian scales were very common in ancient music, but Ionian became the standard for the modern ear. The reason Ionian sounds better than the Mixolydian scale that seems to derive from the overtone series probably has to do with the concept of note "gravity."

 

Scales can contain and combinations of whole steps and half steps. When a note in a scale is a half-step away from another note, the "gravity" of the closer note pulls the melody toward that note.

 

For ease of demonstration, most of the following exercises are in the key (a key is a group of common notes) of C,

cdefgab

with no sharps or flats (a flat, b, is an accidental lowers a note in the same way a sharp raises it.) The following chart show the various classifications of the notes of the scale.

 

Note

c

d

e

f

g

a

b

c

Scale degree

1

2

3

4

5

6

7

8

Interval from tonic

P1

M2

M3

P4

P5

m6

M7

P8

Whole or Half Step

W

W

H

W

W

W

H

Solfege

Do

Re

Mi

Fa

Sol

La

Ti

Do

 

Pentatonic Scales

Pentatonic scales form an integral part of rock guitar playing. Five note pentatonic scales are the major or minor scales with two notes left out.

 

For major pentatonic, leave out the 4th and 7th scale degrees from the major scale

 

In C: c d e g a

 

Pentatonic scales are popular because all the notes in the scale sound good over most common musical changes.

Chords

Chords are groups of three or more notes played at the same time. Seeing a complicated chord like Em11b13b9 is intimidated to most musicians because of its complexity. Finding the chord in a reference table and then memorizing is one solution, but does not prepare the player for the next unfamiliar chord.

 

Once the player understands that most chords, even complicated jazz chords like Em11b13b9, derive from the patterns out of scales already known, the process leads to understanding of why these chords sound good and their functionality.

Major Triads

The patterns continue as the major scale stacks into chords. Begin with the standard major scale

 

c

d

e

f

g

a

b

 

Build a three-note chord (triad) by starting on C and skipping every other note.

 

c e g

 

These notes form is the C chord, the first and most common chord in the key of C.

The chord based on the first scale degree is called the Tonic, signified by the Roman numeral I.

 

Build the next chord starting on the fifth scale degree, G. Wrap the scale to supply all the notes

 

c

d

e

f

g

a

b

c

d

e

f

g

a

b

 

Start at g and skip every other note, yielding

 

gbd

 

These notes form the G chord, the second most common chord in C. The chord based on the fifth scale degree is called the dominant (V).

 

Continuing to build chords horizontally not efficient, and does not model chords in the real world since chords on the musical staff build vertically.

 

So, arrange the notes vertically with c at the bottom and the scale going up.

 

c

b

a

g

f

e

d

c

 

Build the next chord by starting on the 4th scale degree, f and moving up, yielding

 

fac

 

These notes form the F chord, the next most common chord in C. The chord based on the fourth scale degree is called the sub-dominant (IV).

 

Together the I, IV, and V chords are known as the primary chords. All the primary chords are major chords. These three chords make up a surprising number of songs.

 

The next chord builds from the second scale degree. Rearrange the column to put the second degree, D, on the bottom, then skip every other note.

c

b

a

g

f

e

d

 

Yielding dfa, the D minor chord. The chord based on the second scale degree is called the super tonic (ii). Note that the Roman numeral representation is in small case for minor chords. The ii chord is a very common substitution for the IV chord in jazz. Instead of playing IV-V-I, a jazz player would substitute ii-V-I. This substitution works because the ii chord and the IV chord share two common notes. In C, ii is dfa and IV is fac.

Since table manipulation is so easy with today's software, for the next chord, use this table that has all the possible modes built vertically.

 

b

c

d

e

f

g

a

a

b

c

d

e

f

g

g

a

b

c

d

e

f

f

g

a

b

c

d

e

e

f

g

a

b

c

d

d

e

f

g

a

b

c

c

d

e

f

g

a

b

 

This table is from the modes section, just transposed into the key of C.

 

Next, find the triad built from the sixth scale degree, a, yielding

ace

the A minor chord. The chord based on the sixth scale degree is called the submediant (vi). Submediant chords can be used as a substitute for the tonic or as a pivot for a key change to the relative minor key.

 

This table is useful, but every other row is not being used, so why not just delete them?

 

b

c

d

e

f

g

a

g

a

b

c

d

e

f

e

f

g

a

b

c

d

c

d

e

f

g

a

b

 

Now all the chords lay out nicely. Use this table to find the chord based on the third scale degree

egb

The chord based on the third scale degree is called the mediant (vi). The mediant chord can act as a substitute for V or as a secondary dominant leading to vi, but is the least common of these chords.

 

The last triad is an unusual tonal color that adds functionality to chord progressions.

bdf

Based on the seventh scale degree is neither major nor minor since two minor triads stack on each other forming a diminished chord. The interval between the root and the fifth of this chord is a diminished fifth (d5). A diminished designation lowers a perfect interval a half step in the same manner a minor designation lowers a major interval.

 

The chord based on the seventh scale degree is known as the leading chord (viio) since the leading tone of B for the root gets sucked into the gravity of the C chord and wants to lead back to the tonic. viio can also be substitute for V or as a pivot chord to many key changes.

 

Root

Chord

Spelling

Roman

Function

Uses

c

C

ceg

I

Tonic

Establishes key

d

Dm

dfa

ii

Supertonic

Substitute for IV

e

Em

egb

iii

Mediant

Substitute for V

f

F

fac

IV

Subdominant

Precedes V

g

G

gbd

V

Dominant

Precedes I

a

Am

ace

vi

Sub Mediant

Substitute for I

b

Bo

bdf

viio

Leading

Substitute for V

 

Seventh Chords

The pattern continues with seventh chords. The techniques from the lesson on building triads grow directly into adding the next chord in the sequence, seventh chords. Seventh chords are simply the major triads with another note put on top. The new note is another third about the last note in the triad.

 

Luckily, the work for completing a chart for building sevenths chords is already complete.

 

b

c

d

e

f

g

a

g

a

b

c

d

e

f

e

f

g

a

b

c

d

c

d

e

f

g

a

b

 

Simply read the columns bottom up, but add the fourth note.

 

So, the seventh chord built on the first scale degree is

cegb

A major chord with a major third added is a major 7th (Maj7), or here CMaj7.

 

Roman numerals, Functions, and uses for seventh chords parallel those for major triads.

 

The seventh chord built on the fifth scale degree is

gbdf

A major chord with a major third added is a 7th chord (7), or here G7.

 

The seventh chord built on the second scale degree is

dfac

A minor chord with a minor third added is a minor 7th chord (m7), or here Dm7.

 

The seventh chord built on the seventh scale degree is

bdfa

A diminished chord with a major third added is a half diminished 7th chord (m7b5), or here Bmj7b5.  The label Bo7 would seem to fit the pattern here, but that designation refers to a fully diminished seventh chord, which only occurs in minor keys naturally (explained fully later).

 

Full explanation of why chord symbols might have a flat or sharp designation will need to wait until after the explanation of key changes. Feel free to jump ahead to that section if not knowing what the chord symbols means bothers you, but for now, a better strategy for understanding is to just absorb the chords and their functions, so that the understanding of the nomenclature will evolve naturally.

 

 

Root

Chord

Spelling

C

CMaj7

cegb

D

Dm7

dfac

E

Em7

egbd

F

F7

face

G

G7

gbdf

A

Am7

aceg

B

Bm7b5

bdfa

 

Ninth, Eleventh, and Thirteenth Chords

While ninth, eleventh, and thirteenth chords seem daunting, they are simply formed by adding more rows to the process already developed.

 

First, extend the chart to finish all possible notes in thirds

 

a

b

c

d

e

f

g

f

g

a

b

c

d

e

d

e

f

g

a

b

c

b

c

d

e

f

g

a

g

a

b

c

d

e

f

e

f

g

a

b

c

d

c

d

e

f

g

a

b

 

To find the ninth chord on the first scale degree (CMaj9), read up the first 5 rows

cegbd

To find the eleventh chord on the first scale degree (CMaj11), read up the first 6 rows

cegbdf

To find the thirteenth chord on the first scale degree (CMaj13), read all rows

cegbdfa

 

Root

9th Chord

Spelling

11th Chord

Spelling

13th Chord

Spelling

c

CMaj9

cegbd

CMaj11

cegbdf

CM13

cegbdfa

d

Dm9

dface

Dm11

dfaceg

Dm13

dfacegb

e

Em7b9

egbdf

Em11b9

egbdfa

Em11b13b9

egbdfac

f

FMaj9

faceg

FMaj9#11

facegb

FMaj13#11

facegbd

g

G9

gbdfa

G11

gbdfac

G13

gbdface

a

Am9

acegb

Am11

acegbd

Am13

acegbdf

b

Bm7b9b5

bdfac

Bm11b9b5

bdface

Bm11b13b9b5

bdfaceg

 

(Full explanation of the chord symbols comes later.)

 

Substitutions

Parsing the chord names is quite intimidation. But being able to break down Em11b13b9 is not as important as recognizing that this is a diatonic chord in the key of C. When reading music in the key of C, the appearance of this chord symbol should trigger that this is a 13th chord based on the third scale degree. So, if the chord is unknown, just play an Em7, and the function is the same.

 

Careful reading of the patterns provides a more sophisticated way playing chords that function the same as the higher note chords. Playing a full thirteenth chord is impossible on the guitar because the six strings cannot play seven notes. So, the payer must choose notes to leave out.

 

The first note to leave out when making a substitution is the root note because that note is played by the bass payer anyway. In fact, leaving out the root on the lower pitched strings is a great jazz technique even on chords that are fully playable so as not to interfere with the bass player.

 

Consider the CMaj9 chord, cegbd. Removing the root note c yields

egbd

This is an Em7 chord, which is much more playable. Now look at the chart for seventh chords from above.

 

Root

Chord

Spelling

C

CMaj7

cegb

D

Dm7

dfac

E

Em7

egbd

F

FMaj7

face

G

G7

gbdf

A

Am7

aceg

B

Bm7b5

bdfa

 

The Em7 chord is the third row of this chart. Compare the seventh chart with the ninth chart, but move the Em7 chord to the first row, and all other chords up two rows, moving the first two rows to the bottom.

 

Root

9th Chord

Spelling

7th Chord

Substitution

C

CMaj9

cegbd

Em7

egbd

D

Dm9

dface

F7

face

E

Em7b9

egbdf

G7

gbdf

F

FM9

faceg

Am7

aceg

G

G9

gbdfa

Bm7b5

bdfa

A

Am9

acegb

CMaj7

cegb

B

Bm7b9b5

bdfac

Dm7

dfac

 

So, the table of seventh chords already mastered can substitute for the more complicated ninth chords without any loss of function, and actually sound better in jazz. Just be careful not to play guitar voicings with heavy emphasis on the lower pitched strings. An Em7 chord played with an open low E string will sound wrong because the low E will interfere with the bass player and also sound like the root of a chord. Simply mute the lover strings when doing substitutions.

Eleventh and Thirteenth Chord Substitutions

Since an eleventh chord is simply a ninth chord with another note on top, five-note ninth-chord substitutions for eleventh chords follow directly from the previous chart. Just use one of the prebuilt 9th chords based on the third scale degree.

 

11th Chord

Spelling

9th Chord Substitution

CMaj11

cegbdf

Em7b9

egbdf

Dm11

dfaceg

FMaj9

faceg

Em11b9

egbdfa

G9

gbdfa

FM9#11

facegb

Am9

acegb

G11

gbdfac

Bm7b9b5

bdfac

Am11

acegbd

CMaj9

cegbd

Bm11b9b5

bdface

Dm9

dface

 

But, if the player is using substitutions for higher order chords because of lack of knowledge of how to play these chords, memorizing the difficult ninth chords may not be an option. The simplicity of the four-note substitution for the ninth chord is quite appealing since one would assume anyone attempting an eleventh chord already has a grasp of seventh chords.

 

A quick and dirty substitution for an eleventh chord might be to just eliminate the first two notes of the chord, building a seventh chord base on the fifth of the original chord.

 

11th Chord

Spelling

7th Chord Substitution

CMaj11

cegbdf

G7

gbdf

Dm11

dfaceg

Am7

aceg

Em11b9

egbdfa

Bm7b5

bdfa

FMaj9#11

facegb

CMaj7

cegb

G11

gbdfac

Dm7

dfac

Am11

acegbd

Em7

egbd

Bm11b9b5

bdface

F7

face

 

However, this substitution, while simple, is hardly satisfying musically. With ninth chords, leaving out the root note is acceptable since the bass player supplies that note, or in solo work, the brain subconsciously imagines the note from the context of the progression. The third of the chord is actually a very important note because the third provides the information on whether the cord is major or minor.

 

A better substitution would be to leave out the root and the fifth of the chord. Since the fifth is the same for major and minor chords, the fifth is not essential for identifying the chord function.

 

Take the remaining notes and build a suspension based on the third above, as before. For example, the eleventh chord built on I in C is cegbdf. Leaving out the c gives egbdf. Also leaving out the fifth leaves ebdf. This could be an E chord with a suspended lowered second. For the 13th chord, replace the f with a sus4.

 

11th

sus substitution

13th

sus substitution

I

Maj11

iii

7susb2

I

Maj13

iii

7sus4

ii

m11

IV

Maj7sus2

ii

m13

IV

Maj7sus#4

iii

m11b9

V

7sus2

iii

m11b9b13

V

7sus4

IV

Maj9#11

vi

7sus2

IV

Maj13#11

vi

7sus4

V

Maj7

vii

7b5susb2

V

13

vii

7b5sus4

vi

m11

I

Maj7sus2

vi

m11b13

I

Maj7sus4

vii

m11b5b9

ii

7sus2*

vii

m11b5b9b13

ii

7sus4*

 

*These substitutions are not optimal for diminished-based chords because they leave out the important b5. Learning the full chord may be necessary for advanced players.

 

The forms above are not the best for thirteenth chords because they leave out the seventh of the chord, which is an important note. A better substitution would include both the suspended fourth and the second.

 

13th

sus add substitution

I

Maj13

iii

7sus4addb2

ii

m13

IV

Maj7sus#4add2

iii

m11b9b13

V

7sus4add2

IV

Maj13#11

vi

7sus4add2

V

13

vii

7b5sus4addb2

vi

m11b13

I

Maj7sus4add2

vii

m11b5b9b13

ii

7sus4add2*

 

*Not optimal

 

 

Understanding the patterns can lead to other substitutions also.

 

Taking the Am11 chord acegbd and eliminating the root and fifth yields

cgbd

More than one chord contains these four notes. Rearranging the notes to

gbcd

Has the notation Gadd4, since the c is the fourth scale degree in the G scale.

Another notation with already learned patterns would be

G/C

The slash indicates a G chord with a c in the bass, although in this case the c need not be played as the lowest note.

 

 

11th Chord

Spelling

Add 4 Sub.

/Chord

Spelling

CMaj11

cegbdf

Boadd4

B/E

ebdf

Dm11

dfaceg

Cadd4

C/F

fceg

Em11b9

egbdfa

Dmaddb4

D/G

gdfa

FMaj9#11

facegb

Emadd4

E/A

aegb

G11

gbdfac

Fadd#4

F/B

bfac

Am11

acegbd

Gadd4

G/C

cgbd

Bm11b9b5

bdface

Amadd4

A/D

dace

 

Thirteenth chords are by their very nature complex, and the substitutions are also complex.

 

Six-note substitutions eliminating the bass are fairly rudimentary; just build an eleventh chord based on the third.

 

13th Chord

Spelling

11th Chord

Substitution

CMaj13

cegbdfa

Em11b9

egbdfa

Dm13

dfacegb

FMaj9#11

facegb

Em11b13b9

egbdfac

G11

gbdfac

FMaj13#11

facegbd

Am11

acegbd

G13

gbdface

Bm11b9b5

bdface

Am13

acegbdf

CMaj11

cegbdf

Bm11b13b9b5

bdfaceg

Dm11

dfaceg

 

 

 

An alternate   five-note substitution is to change the add4 chords to sevenths with the same added 4th.

 

13th Chord

Spelling

Add 4 Sub.

/ Chord

Spelling

CMaj13

cegbdfa

Bm7b5add4

Bm7b5/E

ebdfa

Dm13

dfacegb

CMaj7add4

CMaj7/F

fcegb

Em11b13b9

egbdfac

Dm7add4

Dm7/G

gdfac

FMaj13#11

facegbd

Em7add4

Em7/A

aegbd

G13

gbdface

FMaj7add#4

FMaj7/B

bface

Am13

acegbdf

G7add4

G7/C

cgbdf

Bm11b13b9b5

bdfaceg

Am7add4

AMaj7/D

daceg

 

The quick and dirty method for four note substitutions builds seventh chords based on the seventh of the scale, but a better method is to eliminate the seventh, and build chords based on the 9th with an added third,

 

Taking the CM13 chord cegbdfa and eliminating the root, fifth, and seventh yields

edfa

Rearranged to

defa

is a D minor add 2 (Dmadd2) since e is the second scale degree in D.

A slash notation alternative is Dm/E

 

13th Chord

Spelling

Add 2 Sub.

/ Chord

Spelling

CMaj13

cegbdfa

Dmadd2

DMaj7/E

edfa

Dm13

dfacegb

Emadd2

EMaj7/F

fegb

Em11b13b9

egbdfac

Fadd2

FMaj7/G

gfac

FMaj13#11

facegbd

Gadd2

G7/A

agbd

G13

gbdface

Amadd2

AMaj7/B

bace

Am13

acegbdf

Boadd2

Bo/C

cbdf

Bm11b13b9b5

bdfaceg

Cadd2

CMaj7/D

dceg

 

An experienced jazz player might argue that eliminating the seventh of the chord is not acceptable because the difference between the major seventh and minor seventh is so important to the color of the chords. So, the five-note substitution for is more appropriate for the thirteenth chord. The player could eliminate either the ninth or eleventh (in addition to the root and fifth) and retain the seventh. However, chords based on these substitutions are more difficult to parse than the five note substitutions, so why use them?

 

Three note substitutions might have an application as substitutes for seventh chords.

 

Chord

Substitution

CMaj7

Em

Dm7

F

Em7

G

F7

Am

G7

Bo

Am7

C

Bm7b5

Dm

 

But are not satisfying for higher-level chords. A good use for these three note patterns is learning to parse eleventh chords

 

Consider the G11 chord gbdfac

Conceptualizing six notes is difficult, but the brain works well with two groups of three

gbd and fac

Since gbd is simply the G chord and fac is an F chord, the eleventh chord is just a G chord mixed with an F chord. So, to make an eleventh chord, take the root chord and add the triad based on the note one down the scale.

 

11th Chord

Spelling

Chord 1

Chord 2

CMaj11

cegbdf

C

Bo

Dm11

dfacegb

Dm

C

Em11b9

egbdfac

Em

Dm

FMaj9#11

facegbd

F

Em

G11

gbdface

G

F

Am11

acegbdf

Am

G

Bm11b9b5

bdfaceg

Bo

Am

 

Thirteenth chords come from adding a seventh to the second column.

 

13th Chord

Spelling

Chord 1

Chord 2

CMaj13

cegbdfa

C

BMaj7b5

Dm13

dfacegb

Dm

CMaj7

Em11b13b9

egbdfac

Em

DMaj7

FMaj13#11

facegbd

F

EMaj7

G13

gbdface

G

FMaj7

Am13

acegbdf

Am

G7

Bm11b13b9b5

bdfaceg

Bo

AMaj7

 

 

This process takes the quick and dirty method to a new level. Using these stacked chords is approachable in theory for even students with limited chord grasp. Am11 is difficult to understand, but seeing an A minor chord, going a step down to G and playing a G chord is easy to understand. Pattern recognition turns difficult chord into what they really are: clusters of simple chords.

 

The Learning Chords section of the guitar course has some more practical methods of using substitutions.

Harmonizing the Minor Scale

 

Consider again the ancient modes, this time centered on the C scale as Ionian (major).

 

Ionian

c

d

e

f

g

a

b

Dorian

d

e

f

g

a

b

c

Phrygian

e

f

g

a

b

c

d

Lydian

f

g

a

b

c

d

e

Mixolydian

g

a

b

c

d

e

f

Aeolian

a

b

c

d

e

f

g

Locrean

b

c

d

e

f

g

a

 

In some ancient cultures, Dorian was the preferred scale, but tradition dictates that the major mode dominates modern music. The second most prevalent mode in today's music uses the same notes as the Aeolian mode. Modern theorists refer to this scale minor, or the minor mode, or natural minor to separate this naturally occurring scale from variations of the minor scale.

 

The minor key with no flats or sharps is A minor

a

b

c

d

e

f

g

 

And for minor pentatonic scale, leave out the 2nd and 6th degrees from the minor scale.

 

In Am: a c d e g

 

The minor pentatonic scale is the most important scale for blues and rock music. Despite its simplicity, adapted with bends and other tricks, it forms the basis of a surprising number of rock and blues solos.

 

Even though the harmonizations previously discussed use C major as a home key, using A minor as a first chord makes more sense than C minor, because the C minor scale would have flatted notes in it.

 

So, Am becomes the tonic key, with the A minor chord spelled ace designated by the lower case Roman numeral (i). Natural minor chords need not be recalculated because they are simply the major diatonic chords rearranged and with the Roman numeral analysis adjusted to match the new pattern of majors and minors.

 

Root

Chord

Spelling

Roman

a

Am

ace

i

b

Bo

bdf

iio

c

C

ceg

III

d

Dm

dfa

iv

e

Em

egb

v

f

F

fac

VI

g

G

gbd

VII

 

The seventh chords follow the same rearranged pattern with another not a third above

 

Root

Chord

Spelling

a

AMaj7

aceg

b

Bmb5

bdfa

c

CMaj7

cegb

d

Dm7

dfac

e

Em7

egbd

f

F7

face

g

G7

gbdf

 

And continue to the higher note chords.

 

Root

9th Chord

Spelling

11th Chord

Spelling

13th Chord

Spelling

a

Am9

acegb

Am11

acegbd

Am13

acegbdf

b

Bmb9b5

bdfac

Bm11b9b5

bdface

Bm11b13b9b5

bdfaceg

c

CMaj9

cegbd

CMaj11

cegbdf

CMaj13

cegbdfa

d

Dm9

dface

Dm11

dfaceg

Dm13

dfacegb

e

Em7b9

egbdf

Em11b9

egbdfa

Em11b13b9

egbdfac

f

FMaj9

faceg

FMaj9#11

facegb

FMaj13#11

facegbd

g

G9

gbdfa

G11

gbdfac

G13

gbdface

 

Borrowed Chords

Returning to the G Mixolydian, scale

 

gabcdef

 

Because of note gravity, melodies that contain a f tend to sound more pleasing when followed by the e rather than moving up the scale to the next g.

So, a common substitution in Gregorian Chant was to substitute a note a half step higher than f, f#, with the # being called an accidental. The f# sounds better when moving from the seventh scale degree to the octave.

 

gabcdef#

 

This substitution is so pleasing to the ear that the pattern with the raised seventh, major scale, became ubiquitous.

In a G major scale, the f# is called a leading tone, because it leads back to the tonic, g.

 

Leading tones often infect other scales, such as the harmonic minor. Leading tones are also essential for secondary dominants, chromatic harmonies, and tritone substitutions. (Explanation of these terms come later.)

 

In the major scale, leading tone seventh degree pulls the root of the chord because of proximity and strong gravity of the tonic. This leading tone relationship is the reason the dominant seventh chord (V7) moves so nicely to the tonic I. In C, the b note in the gbd chord is pulled up c note and the f note is pulled down to e note leading to the tonic chord ceg. This dominant-tonic relationship (V-I) is essential to Western music.

 

In the minor more, the chord based on the fifth scale degree is minor, so the dominant-tonic relationship is weak. To reestablish the relationship, minor keys often borrow the dominant chord from the major key. So, in A minor the (v) chord egb becomes eg#b (V). A dominant chord substitute to signal an approaching chord a fourth above is called a secondary dominant.

 

The g# also works as a substitute in the chord based on the seventh scale degree. The gbd (VII) chord becomes g#bd (viio). This substitution reestablishes the leading tone relationship from major keys.

 

The substituting in the third triad containing g establishes a new chord. The (III) chord ceg becomes ceg# (III+). This is the first naturally occurring augmented chord, indicated in Roman numeral analysis with a + sign and chord chards as C+. Augmented chords are stacks of two major thirds, with the interval from the root to the fifth scale degree notated an augmented fifth (A5). An augmented interval raises a perfect interval a half step.

 

Root

Chord

Spelling

Roman

a

Am

ace

i

b

Bo

bdf

iio

c

C+

ceg#

III+

d

Dm

dfa

iv

e

E

egb

V

f

F

fac

VI

g

G#o

g#bd

Viio

 

The g# also infects the other possible chords. To find harmonizations, first consider a minor scale with the g replaced by g#

a

b

c

d

e

f

g#

and harmonize this new scale in the same manner as the major scale harmonized previously.

 

To find the seventh chords, return to the stacked version of the triads, but with the note a moved to the bottom as the root and all the instances of g replaced by g#.

 

g#

a

b

c

d

e

f

e

f

g#

a

b

c

d

c

d

e

f

g#

a

b

a

b

c

d

e

f

g#

Observe the chords changed by the g#.

The chord based on e is a pattern from the major mode, eg#bd, or E7.

The other changes yield new chords.

The chord based on the root note a is a minor chord with a major seventh, notated as Am(Maj7).

 

The chord based on the third note c is an augmented chord with a major seventh, notated as CMaj7#5 (not C+7).

 

The chord based on the seventh degree is a g# diminished seventh chord, notated as g#o7. This chord is fully diminished, unlike the half-diminished chord from the major scale.  A fully diminished chord has four notes all a minor third from each other. The seventh is an interval of a diminished seventh (d7) from the root. Diminished intervals lower perfect or minor intervals a half step.

 

Fully diminished chords are quite useful because they are symmetrical stacks of minor thirds, so the same diminished exists with different spellings in multiple keys.

 

The fully diminished scale is the first naturally occurring instance of a flatted note. A flat accidental lowers a tone a half step in the same manner a sharp raises it.

 

Only three diminished chords exist, g#bdf, acebgb and a#c#eg, with all other diminished chords being different spellings of these three chords.

 

So, the chart of seventh chord harmonizations is

 

Root

Chord

Spelling

a

Am(Maj7)

aceg#

b

Bm7b5

bdfa

c

CMaj7#5

ceg#b

d

Dm7

dfac

e

E7

eg#bd

f

FMaj7

face

g

G#o7

g#bdf

Continue up the chart of notes.

 

f

g#

a

b

c

d

e

d

e

f

g#

a

b

c

b

c

d

e

f

g#

a

g#

a

b

c

d

e

f

e

f

g#

a

b

c

d

c

d

e

f

g#

a

b

a

b

c

d

e

f

g#

 

to produce ninth, eleventh, and thirteenth chords

 

 

Root

9th Chord

Spelling

11th

Spelling

13th

Spelling

a

Am(Maj9)

aceg#b

Am(Maj11)

aceg#bd

Am(Maj11)b13

aceg#bdf

b

Bm7b9b5

bdfac

Bm11b9b5

bdface

Bm11b13b9b5

bdfaceg#

c

CMaj9#5

ceg#b

CMaj11#5

ceg#bd

CMaj13#5

ceg#bdfa

d

Dm9

dface

Dm9#11

dfaceg

Dm13#11

dfaceg#b

e

E7b9

eg#bdf

E11b9

eg#bdfa

E11b13b9

eg#bdfac

f

FMaj7#9

faceg#

FMaj7#9#11

faceg#b

FMaj13#9#11

faceg#bd

g#

G#m7b9b5

g#bdfa

G#m11b9b5

g#bdfac

G#m13b9b5

g#bdface

 

These chord symbols are extremely difficult to parse, but become less important after realizing that these chords are just the simpler chords stacked on each other,

Melodic Minor

Raising the seventh scale degree in minor keys works well for chords, but leads to some challenges for melodies and solos based on these chords. The scale based on a minor pattern with a raised seventh is the harmonic minor scale, as from previous lessons

 

a

b

c

d

e

f

g#

 

This is a strange sounding scale because of the distance from the f to the g# being three half steps. A three half-step interval is a minor third in most circumstances, but here f to g is not a third, but a second, so f to g# is an augmented second (A2). Augmented seconds are difficult to read and notate, and produce an eastern sounding feel which, although nice in certain situations, does not fit into the usual alternation of whole- and half-steps from other scales.

 

To alleviate the problem, the ascending melodic minor scale raises the sixth scale degree to

a

b

c

d

e

f#

g#

 

This pleasant-sounding scale has the minor character of the lowered third together with the functionality of the major scale. The raised sixth is also reminiscent of the Dorian mode.

 

However, the raised sixth and seventh lose some of the character of the minor mode. To restore the minor flavor, the melodic minor mode returns the sixth and seventh to their natural state when descending.

 

a

g

f

e

d

c

b

 

A harmonization of the descending melodic scale is the same as the natural melodic scale, but the addition of the raised 6th (f#) adds some new wrinkles to harmonizing the ascending scale. Returning to the note stacking chart with f replaced by f# yields

 

f#

g#

a

b

c

d

e

d

e

f#

g#

a

b

c

b

c

d

e

f#

g#

a

g#

a

b

c

d

e

f#

e

f#

g#

a

b

c

d

c

d

e

f#

g#

a

b

a

b

c

d

e

f#

g#

 

Three triads affected are bdf# becoming Bm, df#a becoming D and f#ac becoming F#o

 

Root

Chord

Spelling

a

Am

ace

b

Bm

bdf#

c

C+

ceg#

d

D

df#a

e

E

egb

f#

F#o

f#ac

g#

G#o

g#bd

 

Continuing with seventh chords and up

 

Root

7th Chord

Spelling

 

a

Am(Maj7)

aceg#

 

b

Bm7

bdf#a

 

c

CMaj7#5

ceg#b

 

d

D7

df#ac

 

e

E7

eg#bd

 

f#

F#m7b5

f#ace

 

g#

G#m7b5

g#bdf#

 

 

 

 

 

 

9th Chord

11th

13th

a

Am(Maj9)

aceg#b

Am(Maj11)

aceg#bd

Am(Maj13)

aceg#bdf#

b

Bm7b9

bdf#ac

Bm11b9

bdf#ace

Bm13b9

bdf#aceg#

c

CMaj9#5

ceg#b

CMaj9#11#5

ceg#bd

CMaj13#11#5

ceg#bdf#a

d

D9

df#ace

D9#11

df#aceg

D13#11

df#aceg#b

e

E9

eg#bdf#

E11

eg#bdf#a

E11b13

eg#bdf#ac

f#

F#m9b5

f#aceg#

F#m11b5

f#aceg#b

F#m11b13b5

f#aceg#bd

g#

G#m7b57b9

g#bdf#a

G#m11b9b5

g#bdf#ac

G#m11b13b9b5

g#bdf#ace

 

Most of these chords are actually easier to parse than the harmonic version, although admittedly G#m11b13b9b5 is intimidating. But remember, these are just stacks of chords, so knowing all the nomenclature is not necessary.

 

All the note in the melodic minor scale reordered would be

abcdeff#gg#

Typically chords mixing the ascending and descending versions of the scale do not occur. But if they did, new charts would not be necessary.

abcdefg# is the harmonic minor, so use those charts.

abcdeff#gg is the Dorian mode, so use the chords from the major chart starting in the second row (or the 4th row here). Or, take the melodic ascending chart and lower all the g# notes to g.

 

Comparison chart

 

Natural

 

Harmonic

 

Melodic Ascend

 

Am

ace

Am

ace

Am

ace

Bo

bdf

Bo

bdf

Bm

bdf#

C

ceg

C+

ceg#

C+

ceg#

Dm

dfa

Dm

dfa

D

df#a

Em

egb

E

egb

E

egb

F

fac

F

fac

F#o

f#ac

G

gbd

G#o

g#bd

G#o

g#bd

Am7

aceg

Am(Maj7)

aceg#

Am(Maj7)

aceg#

Bm7b5

bdfa

Bm7b5

bdfa

Bm7

bdf#a

CMaj7

cegb

CMaj7#5

ceg#b

CMaj7#5

ceg#b

Dm7

dfac

Dm7

dfac

D7

df#ac

Em7

egbd

E7

eg#bd

E7

eg#bd

F7

face

FMaj7

face

F#Maj7b5

f#ace

G7

gbdf

G#o7

g#bdf

G#Maj7b5

g#bdf#

Am9

acegb

Am(Maj9)

aceg#b

Am(Maj9)

aceg#b

Bm7b9b5

bdfac

Bm7b9b5

bdfac

Bm7b9

bdf#ac

CMaj9

cegbd

CMaj9#5

ceg#b

CMaj9#5

ceg#b

Dm9

dface

Dm9

dface

D9

df#ace

Em7b9

egbdf

E7b9

eg#bdf

E9

eg#bdf#

FMaj9

faceg

FMaj7#9

faceg#

F#m9b5

f#aceg#

G9

gbdfa

G#o7b9*

g#bdfa

G#m7b57b9

g#bdf#a

Am11

acegbd

Am(Maj11)

aceg#bd

Am(Maj11)

aceg#bd

Bm11b9b5

bdface

Bm11b9b5

bdface

Bm11b9

bdf#ace

CMaj11

cegbdf

CMaj11#5

ceg#bd

CMaj9#11#5

ceg#bd

Dm11

dfaceg

Dm9#11

dfaceg

D9#11

df#aceg

Em11b9

egbdfa

E11b9

eg#bdfa

E11

eg#bdf#a

FMaj9#11

facegb

FMaj7#9#11

faceg#b

F#m11b5

f#aceg#b

G11

gbdfac

G#o11b9*

g#bdfac

G#m11b9b5

g#bdf#ac

Am13

acegbdf

Am(Maj11)b13

aceg#bdf

Am(Maj13)

aceg#bdf#

Bm11b13b9b5

bdfaceg

Bm11b13b9b5

bdfaceg#

Bm13b9

bdf#aceg#

CMaj13

cegbdfa

CMaj13#5

ceg#bdfa

CMaj13#11#5

ceg#bdf#a

Dm13

dfacegb

Dm13#11

dfaceg#b

D13#11

df#aceg#b

Em11b13b9

egbdfac

E11b13b9

eg#bdfac

E11b13

eg#bdf#ac

FMaj13#11

facegbd

FMaj13#9#11

faceg#bd

F#m11b13b5

f#aceg#bd

G13

gbdface

G#o11b13b9*

g#bdface

G#m11b13b9b5

g#bdf#ace

 

*9th, 11th, and 13th chords built on fully diminished chords are rare, so chord symbols representing these chords may vary.

 

Substitutions for these chords function just as in the major chords

For ninth chords, remove the root and play the seventh chord based on the third scale degree.

For eleventh chords, remove the root and play the ninth chord based on the third scale degree, or play the triad based on the seventh scale degree and add the third scale degree.

For thirteenth chords, remove the root and play the eleventh chord based on the third scale degree, or play the seventh chord based on the seventh scale degree and add the third scale degree.

Inversions

Often chords do not have the root in the bass note. The technical term for playing a chord note other than the root as the lowest note is an inversion.

 

A slash indicates and inversion, with the bass note after the slash.

 

Chord

Spelling

1st inv.

Spelling

2nd inv.

Spelling

C

ceg

C/E

egc

C/G

gce

Dm

dfa

Dm/F

fad

Dm/A

adf

Em

egb

Em/G

gbe

Em/B

beg

F

fac

F/A

acf

F/C

cfa

G

gbd

G/B

bdg

G/D

dgb

Am

ace

Am/C

cea

Am/E

eac

Bo

bdf

Bo/D

dfb

Bo/F

fbd

Notes other than the bass note can be in any order.

 

Chords with more notes in the first and second inversions follow the patterns / the triads

G7/B, G7/D

Seventh chords could have an additional third inversion with the seventh in the bass.

G7/F

Ninth chords could have another additional fourth inversion /ninth in the bass.

G9/F, G9/A

Eleventh chords could have another additional fifth inversion /eleventh in the bass.

G11/F, G11/A, G11/C

Thirteenth chords could have an additional sixth inversion /thirteenth in the bass.

G13/F, G11/A, G11/C, G13/E

Added Notes

All the chords in the chords studied so far have had some kind of harmonic function; they are important to the chord structure. Sometimes notes can be added to a harmony for other reasons.

 

The substitutions section showed how an added 4 (add4) can substitute a ninth chord and an added second (add2) can substitute an eleventh chord. Possible diatonic add 2 chords are

 

major

Minor

Harmonic

Melodic

Cadd2

Amadd2

Amadd2

Amadd2

Dmadd2

Boaddb2

Boaddb2

Bmaddb2

Emaddb2

Cadd2

C+add2

C+add2

Fadd2

Dmadd2

Dmadd2

Dadd2

Gadd2

Emaddb2

Eaddb2

Eaddb2

Amaddb2

Fadd2

Fadd2

F#oadd2

Boadd2

Gadd2

G#oaddb2

G#oaddb2

 

Note the b2 on half step intervals starting on e, b, and g#.

Add2 intervals on seventh chords do not make sense since an added 2nd to a seventh chord just makes a ninth chord. Since ninth, eleventh, and thirteenth notes already have the note, adding a second here also does not apply.

 

Possible add4 chords include

 

major

Minor

Harmonic

Melodic

Cadd4

Amadd4

Amadd4

Amadd4

Dmadd4

Boadd4

Boadd4

Bmadd4

Emadd4

Cadd4

C+add4

C+add#4

Fadd#4

Dmadd4

Dmadd#4

Dadd4

Gadd4

Emadd4

Eadd4

Eadd4

Amadd4

Fadd#4

Fadd#4

F#oadd4

Boadd4

Gadd4

G#oadd4

G#oaddb4

CMaj7add4

Am7add4

Am(Maj7)add4

Am(Maj7)add4

Dmadd4

Bm7b5add4

Bm7b5add4

Bm7add4

Em7add4

CMaj7add4

CMaj7#5add4

CMaj7#5add#4

F7add#4

Dm7add4

Dm7add#4

D7add4

G7add4

Em7add4

E7add4

E7add4

Am7add4

F7add#4

FMaj7add#4

F#Maj7b5add4

Bm7b5add4

G7add4

G#o7add4

G#m7b5addb4

 

Add4 chords on ninths would be elevenths, and elevenths and thirteenths already have the fourth scale degree.

 

The other scale degree not yet discussed is the sixth scale degree.

 

Adding a sixth to a chord conjures up the feeling of a thirteenth chord because scale degrees 6 and 13 are just the same scale degree in a different octave.  The designation (6) indicates an added sixth (not add6). A C6 chord is cega. Notice that cega is just aceg, the A minor seventh chord rearranged. Some chords have more than one possible name.

 

A 6th can be added to higher note chords also, such as C67 C69 or any of the possibilities from the complicated chord charts (other than 13th, which already have the 6th). Add2 and add4 notes also appear in other chords not containing seconds and fourths.

 

major

Minor

Harmonic

Melodic

C6

Amaddb6

Amb6

Am6

Dm6

Bob6

Bo6

Bm6

Emb6

C6

C6#5

C6#5

F6

Dm6

Dm6

D6

G6

Emaddb6

Eb6

Eb6

Amb6

F6

F6

F#ob6

Boaddb6

G6

G#oaddb6

G#ob6

CMaj67

Am7addb6

Am(Maj7)addb6

Am(Maj7)6

Dm67

Bm7b5addb6

Bm67b5

Bm67

EMaj7b6

CMaj67

CMaj7#56

CM67#5

F67

Dm67

Dm67

D67

G76

EMaj7b6

E7b6

E7b6

AMaj7addb6

F67

FMaj76

F#m7b5addb6

BMaj7b5addb6

G67

G#o7b6

G#m7b5addb6

CM69

Am9addb6

Am(Maj9)b6

Am(Maj69)

Dm69

BMaj7b9b5b6

Bm9b5b6

Bm9b6

EMaj7b9addb6

CM69

C(Maj9)6#5

C(Maj9)6#5

FM69

Dm69

Dm69

D69

G69

EMaj7b9b6

E7b9b6

E9b6

Am9b6

FM69

F(Maj9)b7

F#m9b5addb6

Bm7b9b5addb6

G69

G#o7b9addb6

G#Maj7b9b5addb6

 

Added notes on other scale degrees are just inversions, add3 would be first inversion, add5 would be second inversion, and add7 would be third inversion, so those add chords use the slash notation from the inversions section. A special case might be adding a note to a chord that did not have it, such as Boadd3, spelled bded#, but this would be rare indeed. Add notes can also be raised Fadd#4 or lowered Gaddb2.

 

Multiple add not can appear on one chord. Triads could have two added notes

add2 and add4, Cadd2add4

add2 and add6,  Cadd2add6

add4 and add6, Cadd4add6

or even all three Cadd2add4add6

Seventh chords could have an add4 and an add6, CMaj7add2add6.

Any other combination would be one of the higher order chords. One reason to use multiple add chords would be to leave out a note from a complicated chord. Cadd2add4add6 is just CMaj13 without the seventh degree.

Suspensions

Sometimes an added note replaces a chord tone rather than adds to the chord.

 

The most common of these suspensions replaces the third of the chord with a fourth. Replace the third of the C chord ceg with an f produces cfg, a Csus4 (or just Csus) chord. The gravity of the third e below the fourth f tends to drag the suspension down, so The suspended usually precedes the tonic chord or some other chord with an e. The classic suspension progression is G7-Csus-C, with the f in the G7 hanging into the Csus chord, thus delaying the resolution to the C chord in a pleasing matter. Suspended notes and be added to other chords also, such as C7sus4.

 

Suspensions follow the patterns of the add chords, with a few exceptions. The biggest difference is that since the suspension replaces the third scale degree, major and minor chords have the same suspension. Csus4 and Cmsus4 would be the same chord, so do not use Cmsus. The other difference is that chords with a diminished or augmented reference need to be rewritten, since the diminished implies a lowered third and augmented implies a raised third.

 

major

Minor

Harmonic

Melodic

Csus4

Asus4

Asus4

Asus4

Dsus4

Bosus4

Bosus4

Bsus4

Esus4

Csus4

C#5sus4

C#5sus#4

Fsus#4

Dsus4

Dsus#4

Dsus4

Gsus4

Esus4

Esus4

Esus4

Asus4

Fsus#4

Fsus#4

F#osus4

Bb5sus4

Gsus4

G#b5sus4

G#susb4b5

CMaj7sus4

A7sus4

AMaj7)us4

AMaj7sus4

D7sus4

B7b5sus4

B7b5sus4

B7sus4

E7sus4

CMaj7sus4

CMaj7#5sus4

CMaj7#5sus#4

F7sus#4

D7sus4

D7sus#4

D7sus4

G7sus4

E7sus4

E7sus4

E7sus4

A7sus4

F7sus#4

FMaj7sus#4

F#7b5sus4

B7b5sus4

G7sus4

G#b5sus4d7

G#7b5susb4

 

 

The next most common suspension is the 2nd degree. A Csus2 (cdg) chord is similar to a Cadd2 chord, but the suspended note replaces the third. The second technically resolves upwards to the third, but in practice can move downward to the root by using Csus2 as a substitute for the more harmonically accurate Cadd2-C progression. Dsus4-D-Dsus2 is a common pattern on guitar because of its ease of play and usefulness for transitioning to the G and C chords.

 

major

Minor

Harmonic

Melodic

Csus2

Asus2

Asus2

Asus2

Dsus2

Bosusb2

Bosusb2

Bsusb2

Esusb2

Csus2

C#5sus2

C#5sus2

Fsus2

Dsus2

Dsus2

Dsus2

Gsus2

Esusb2

Esusb2

Esusb2

Asusb2

Fsus2

Fsus2

F#b5sus2

Bb5sus2

Gsus2

G#b5susb2

G#b5susb2

 

A variation of the suspended 2nd that moves downward is called an appoggiatura. In a true appoggiatura would replace the root rather than the third, for example a four part harmony cegd  moving to cegc. Chord notation does a poor job representing this, but Cadd9-C often approximates it.

 

A similar classical technique is to replace the upper root with the seventh cegb to cegc. The seventh resolves upward. In chord notation CMaj7-C can approximate this.

 

Another commonly used suspension is on the sixth scale degree. In Csus6 (cea), the 6th scale degree replaces the fifth and resolves down to the fifth. The 6 of the sus6 chord could move upward to the seventh as a substitute for a passing chord Csus6-CMaj7-C, but this is not a true suspension, just using the Csus as a substitute for C6.

 

major

Minor

Harmonic

Melodic

Csus6

Amsusb6

Amsusb6

Amsus6

Dmsus6

Bmsusb6

Bmsus6

Bmsus6

Emsusb6

Csus6

C+sus6

C+sus6

Fsus6

Dmsus6

Dmsus6

Dsus6

Gsus6

Emsusb6

Esusb6

Esusb6

Amsusb6

Fsus6

Fsus6

F#msusb6

Bmsusb6

Gsus6

G#msusb6

G#msusb6

CMaj7sus6

Am7susb6

Am(Maj7)susb6

Am(Maj7)sus6

Dm7sus6

Bm7b5susb6

Bm7b5sus6

Bm7sus6

Em7susb6

CMaj7sus6

CMaj7#5sus6

CMaj7#5sus6

F7sus6

Dm7sus6

Dm7sus6

D7sus6

G7sus6

Em7susb6

E7susb6

E7susb6

AMaj7susb6

F7sus6

FMaj7sus6

F#Maj7b5susb6

BMaj7b5susb6

G7sus6

G#msusb6d7

G#Maj7b5susb6

CM9sus6

Am9susb6

Am(Maj9)susb6

Am(Maj9)sus6

Dm9sus6

BMaj7b9b5susb6

BMaj7b9b5sus6

BMaj7b9sus6

EMaj7b9susb6

CM9sus6

CMaj9#5sus6

CM9#5sus6

FM9sus6

Dm9sus6

Dm9sus6

D9sus6

G9sus6

EMaj7b9susb6

E7b9susb6

E9susb6

Am9susb6

FM9sus6

FMaj7#9sus6

F#m9b5susb6

BMaj7b9b5susb6

G9sus6

G#msusb6b7b9

G#Maj7b9b5susb6

 

Suspended chords have fewer combinations than add chords. Since sus2 and sus4 both replace the third, these would not appear together.

 

Either of these chords could appear with a sus6,

Csus4sus6

Csus2sus6

leading to a nice double resolution to C.

 

Consider the resolution CMaj7sus4sus6 to C. Try borrowing a trick from renaissance polyphonic music by resolving each of the suspensions separately

CMaj7sus4sus6- CMaj7sus- Csus4-C.

Passing Tones

Sometimes notes add to a chord to facilitate movement from one chord to another. A common guitar pattern when moving from G to C is

G-G/A-G/B-C

Analysis of the a in the G/A chord could lead to the (improper) conclusion that G/A is a Gsus2 chord, and music books often do notate the chord this way. The true function of this walking bass lick is to pass from the G to the C, hitting all the scale notes in between. Passing tones may appear notated as suspensions.

 

Passing tones are usually the 2nd,4th, and 6th scale degrees moving between chord tones. In C, C/D, C/F, and C/A move between the chord inversions, but have no true functional harmony otherwise.

 

C, C/D, C/E. C/F, C/G, C/A, CMaj7/B, C

 

Listen to "Friend of the Devil" by the Grateful Dead for some nice passing tone work.

Chromatic Harmonies

Chromatic notes may also function as passing tones, but may also have a harmonic function known as chromatic harmony.

 

Consider the transition from F to C. The notes move from fac to ceg. Rearrange the notes on the C chord into first inversion to egc. Written here vertically:

c

c

a

g

f

e

This inversion highlights the natural gravity of the f to the e in a pleasing manner.

Now add an F minor (fabe) chord between the two chords.

c

c

c

a

ab

g

f

f

e

The transition from Fm to C now has an additional gravitational pull between the ab and the G leading to a pleasing result. The Fm chord here would be an example of a chromatic harmony.

 

Any two chords with notes a step apart are candidates for chromatic harmonies. The most fruitful of these are ii-I, IV-V. Vi-V, since the chord roots are a step apart.

 

Consider the ii-I progression, dfa-ceg. The root, and fifth all have space for a chromatic note placed between them, with possible results being

 

a

a

g

a

ab

g

a

ab

g

f

f

e

f

f

e

f

f

e

d

db

c

d

d

c

d

db

c

ii

bii+

I

ii

iio

I

ii

bII

I

Dm

Db+

C

Dm

Do

C

Dm

D

C

 

Rearranging the ii chord to first inversion reveals more combinations

a

ab

g

d

d#

e

f

f

c

 

So, new chords fad# and fabd# come out of the patterns. These chords would be difficult to analyze. Adding the seventh note c to the ii chord helps, yielding facd#. Since d# is enharmonic to Eb, the result is a misspelled F7 chord, which will suffice.

 

c

c

c

c

c

c

a

a

g

a

ab

g

a

ab

g

d

d#

e

d

d

e

d

d#

e

f

f

c

f

f

c

f

f

c

Dm7/F

F7

C

Dm7/F

DMaj7b5

C

Dm7/F

Fm7

C

 

Rearranging ii into third inversion yields another set of combinations.

c

c

f

f#

g

d

d#

e

a

a

c

 

c

c

c

c

c

c

f

f#

g

f

f

g

f

f#

g

d

d

e

d

d#

e

d

d#

e

a

a

c

a

a

c

a

a

c

Dm/A

D7

C

Dm/A

F7/A

C

Dm/A

A#o7

C

 

The A#o7 is probably better written as F#o7/A since its function seems to be a secondary dominant of g. The series d-d#-e might interfere with the 4-3 (f-e) resolution. It could go into another octave leaving the f-e as a doubled note.

 

d

d#

e

c

c

g

f

f

e

a

a

c

Dm7/A

F7/A

C

 

Allowing for multiple octaves also allows combinations among the three groups. Now the d-d#-E pattern could with the d-db-c pattern in a different octave.

 

d

d#

e

a

a

g

f

f

e

d

db

c

Dm

Dbadd2

C

 

For the purposes of analysis, consider the D# an Eb to yield Dbadd2.

 

So, any combination of the chromatic harmonies is possible. As an alternate to doing all those combinations, make a list of all the chromatic lines

 

a

ab

g

d

db

c

d

d#

e

f

f#

g

 

Now isolate the altered notes

 

ab

db

d#

f#

 

Insert the altered noted into the chords one by one

c

c

c

c

a

a

a

ab

f

f

f#

f

db

d#

d

d

DbMaj7#5

F7

D7

Dm7b5

 

Or in pairs, substituting enharmonics when necessary to aid analysis.

 

eb

c

c

c

c

c

c#

c

a

ab

a

a

ab

a

ab

f#

f

f

f#

f

f

f#

db

db

db

d#

d#

d#

d

F#add#4

Fmb6/Db

F(b6)/Db

D#o7

Fmb7/D#

F#5b7

D7b5

 

 

Groups of three or four

 

eb

c

c

c

c#

ab

ab

ab

ab

f#

f

f#

f

db

db

d#

d#

DbMaj7sus4

Db9

D#add4d7(no 5th)

D#7add4(no 5th)

eb

c

c#

ab

ab

f#

f

db

d#

Db11(no 3rd)

D#sus2

 

These last sets of notes seem to defy analysis. If anyone can come up with better chord symbols, please let me know. The chords notated here may not be the best versions of the groups of notes, depending on context. This is just a quick way to come up with all the possible chromatic harmonies. Adding more octaves could produce other chords, such as leaving d as the root and putting the db as an altered ninth, but these changes would just be variations of the chords here:

 

DbMaj7#5

F7

D7

DMaj7b5

F#add#4

Fmb6/Db

F(b6)/Db

D#o7

Fmb7/D#

F#5b7

D7b5

DbMaj7sus4

Db9

D#add4d7(no 5th)

D#7add4(no 5th)

Db11(no 3rd)

D#sus2

 

Moving from IV7-V7 yields three obvious chromatics

 

e

f

c

c#

d

a

a#

b

f

f#

g

 

With possible combinations

 

e

f

e

f

e

f

c

c

d

c

c

d

c

c#

d

a

a

b

a

a#

b

a

a

b

f

f#

g

f

f

g

f

f

g

FMaj7

F#o

G7

FMaj7

Fsus4

G7

FMaj7

F+

G7

e

f

e

f

e

f

e

f

c

c

d

c

c#

d

c

c#

d

c

c#

d

a

a#

b

a

a

b

a

a#

b

a

a#

b

f

f#

g

f

f#

g

f

f

g

f

f#

g

FMaj7

F#4b5

G7

FMaj7

F#m

G7

FMaj7

F#5sus4

G7

FMaj7

F#

G7

 

These combinations work without the seventh also. The e to f is a nice chromatic, so it adds to the process here.

 

Instead of working through all the inversions separately, use the techniques from the last section as shortcuts. First examine the chord tones of the final chord, where the chromatic harmony resolves, in this case, gbd. (Chromatic alterations could lead to other tones such as the seventh, ninth, eleventh, and thirteenth, but the strongest resolutions occur in order on the root, the fifth, and then the third.)

 

So, taking the notes g, b, and d, move out a whole step in either direction,

 

a-g-f

c#-b-a

e-d-c

 

Then look for notes in the first chord that are the same or enharmonic equivalents. Common notes include a, f, a again, e, d, and c. So, the possible places are

a-g

f-g

a-b

e-d

c-d

The note c# does not appear because it is not a chord tone. It might occur in a string of chromatics like d-c#-c-a, but again, save that for later.

 

Take the relationships and insert a chromatic note. If the direction of the line is downward, us a flat, and if it is upward use a sharp or the appropriate enharmonic equivalent.

 

a-ab-g

f-f#-g

a-a#-b

e-eb-d

c-c#-d

 

Make a table that replaces the notes of the original chord with the substitutions, doubling if necessary.

 

eb

c#

a# or ab

f#

 

Now begin substituting the altered tones for the original tones, first one by one.

 

e

e

e

e

eb

c

c

c

c#

c

a

ab

a#

a

a

f#

f

f

f

f

F#m7b5

Fm(Maj7)

FMaj7sus4

FMaj7#5

F7

 

Then add in pairs, using enharmonic when necessary.

 

e

e

e

eb

c

c

c#

c

ab

a#

a

a

f#

f#

f#

f#

Ab7#5/F#

F#7b5sus4

F#Maj7

F#o

bb

e

e

eb

c#

c

c

ab

ab

ab

f

f

f

Fm(Maj7)#5

Fm(Maj7)add4

FMaj7

g#

e

e

eb

eb

c#

c

c

c#

a#

a#

a#

a

f

f

f

f

FMaj7#5sus4

FMaj#9sus4

F7sus4

F7#5

 

Then groups of three or more

 

bb

e

e

eb

c

c#

c

ab

ab

ab

f#

f#

f#

AbMaj9#5/Gb

Ab7#5/Gb

Ab7/Gb

g#

e

e

eb

c

c#

c

a#

a#

a#

f#

f#

f#

F#m9b5

F#7

F#Maj7b5

bb

g#

e

eb

e

eb

c#

c#

c#

c#

ab

ab

a#

a#

f

f

f

f

Fm(Maj7)b5add4

Fm7#5

FMaj7#9#5sus4

F7#5sus4

bb

g#

eb

eb

eb

eb

c#

c#

c#

c#

a

a

a#

ab

f

f

f#

f#

F7#5add4

F7#9#5

bb

g#

bb

g#

eb

eb

eb

eb

c#

c#

c#

c#

a

a

ab

a#

f#

f#

f

f#

F#m7add4

F#m7#9

Fm7b9#5

F9sus4

 

 

Summary of IV-V Chromatic Harmonies

 

F#Maj7b5

Fm(Maj7)

FMaj7sus

FMaj7#5

Ab7#5/F#

F#7b5sus4

F#Maj7

F#o

Fm(Maj7)#5

Fm(Maj7)add4

FMaj7

F7

FMaj7#5sus4

FMaj#9sus4

F7sus4

F7#5

AbMaj9#5/Gb

Ab7#5/Gb

Ab7/Gb

F7add4#5

F#m9b5

F#7

F#Maj7b5

F7#9#5

Fm(Maj7)b5add4

FMaj7#5

FMaj7#5sus4#9

F7#5sus4

F#m7add4

F#m7#9

FMaj7b9#5

F9sus4

 

 

Note that an of the chromatic harmonies work in both directions.

IVMaj7

IVsus4

V7

Reversed to V7-IVsus4-IVMaj7 has the same notes, but the a# would be the enharmonic Bb to promote voice leading. In traditional notation, sharp accidentals look better moving up a-a#-b and flats moving down b-bb-a.

Adding seconds, fourths, or sixths to these chords (when those degrees are not in the original chords) produces more complex chords with the same function. Defining those as ninth, eleventh, and thirteenth chords is difficult for many because of the manipulations necessary to force harmonic notation to its limits.

 

The chromatic harmonies based on other intervals have fewer chromatic harmonies, but still plenty. Consider V-I, the most important cadence.

 

Following the procedure, the possible places for chromatic harmonies leading to the tonic are

 

f-g-a

d-e-f#

bb-c-d

 

so, the appropriate intervals to check are

 

f-g

f#

a-g

ab

d-e

d#

f#-e

f

 

Looking at the notes to be replaced, gbd, the only appropriate replacement is changing the d to d#.

 

f

f

e

d

d#

e

b

b

g

g

g

c

V7

V7#5

I

 

The note f is already in the seventh chord, so does not need replacement.

Replacing the f with f# to lead to g actually weakens the cadence, as it removes the 4-3 resolution. The notes ab and c# would be ninths and elevenths, which would be interesting, if not as strong a chromatic harmony as those based on the triad.

 

a

ab

g

f

f#

g

d

d#

e

b

b

c

g

g

c

V9

VMaj7b9#5

I

 

This contains all the alterations. This chord contains a wealth of chromatics, and is easier to grasp than many of the awkward chords based on ii-I or IV-V.

 

Each chromatic taken one at a time yields

 

a

a

ab

f

f#

f

d#

d

d

b

b

b

g

g

g

V9#5

VMaj9

Vb9

 

More than one

 

a

ab

ab

ab

f#

f

f#

f#

d#

d#

d

d#

b

b

b

b

g

g

g

g

VMaj9#5

V9#5

VMaj7b9

VMaj7b9#5

 

And a few strange cords with f and f# (gb) in different octaves.

 

a

a

ab

ab

f#

f#

f#

f#

f

f

f

f

d

d#

d

d#

b

b

b

b

g

g

g

g

VMaj9Add#6*

VMaj9#5Add#6

VMaj7b9Add#6

VMaj7b9#5Add#6

 

*A chord with both a minor seventh and a major seventh at the same time is difficult to analyze. The #6 is the minor seventh enharmonically, so Maj7add#6 is a chord with a major and a minor seventh at the same time. These chords would be rare, practically non-existent in actual music, but an interesting theory thought experiment.

 

With the exception of the last grouping, these chords are easier to grasp than previous examples, and additions of elevenths and thirteenths not as difficult.

 

GMaj7b9#5

G9#5

GMaj9

Gb9

GMaj9Add#6

GMaj9#5Add#6

GMaj7b9Add#6

GMaj7b9#5Add#6

GMaj11b9#5

G11#5

GMaj11

G11b9

GMaj11Add#6

GMaj11#5Add#6

GMaj11b9Add#6

GMaj11b9#5Add#6

GMaj13b9#5

G13#5

GMaj13

G13b9

GMaj13Add#6

GMaj13#5Add#6

GMaj13b9Add#6

GMaj13b9#5Add#6

 

Any chord change has possible chromatic harmonies.  IV-I changes are similar to ii-I, so those serve as a good substitution since IV and ii contain overlapping notes. V-vi overlaps V-I for the same reason. Minor keys parallel the structure of major keys somewhat, with the obvious differences in thirds, and the addition of many more possibilities with raise sixths and sevenths. An exhaustive list of all the possibilities, such as the ones supplied here for the chosen intervals, would need to come in a separate document.

 

Two more sophisticated uses of chromatic harmonies secondary dominants and tritone substitution.

Secondary Dominants

The section on the harmonic minor scale showed how a manipulation of the (v) chord to (V) produced a more satisfying chord resolution to the tonic. This manipulation was simply a chromatic substitution of the third scale degree of the chord. The notes egb because eg#b.

 

A dominant-style chord substituting for another chord to highlight the chord after it is called a secondary dominant. Dominant style chords include major triads, in addition to seventh (7), ninth (9), eleventh (11), and thirteenth (13) chords. Other chords with a major third as the first interval can also serve the same function.

 

Consider the common IV-V-I cadence in the key of C.

 

c

d

g

a

b

e

f

g

c

Now, add a secondary dominant D major triad (even though he key suggests A minor) d f# a but spell it in first inversion f# to highlight the chromatic harmony.

 

c

d

d

g

a

a

b

e

f

f#

g

c

 

Notice how the gravity of the g in the bottom line pulls the f# up.

The lines are even cleaner when using a seventh chord.

a

c

d

d

g

a

c

b

e

f

f#

g

c

 

Completing the four note chords with a V7 and rearranging provides lots of nice voice leading.

 

 

f

a

f

e

c

d

d

g

a

c

b

c

f

f#

g

low c

 

Now all four lines have a nice clean flow, and any of them could be a melody. Performing this exact pattern of a guitar would be difficult, so when recognizing chromatic harmonies, try to choose voicings that keep the lines together when possible.

 

Roman numeral notation would read

 

IV

II7

V7

I

 

The II7 notation for the secondary dominant is accurate, but does not really reflect the true function of the chord. The function of the D7 is to highlight the chord that comes after it, the G chord (V). D is the dominant chord in the key of G, so D is the V of G. Since G is the V of C, D is the V of [the V of C] (VofV). Substituting V7ofV for II7 yields.

 

IV

V7ofV

V7

I

 

If VofV is acceptable, then what about secondary dominants of other notes? Perhaps to highlight an upcoming A minor (vi) chord, for a key change to the relative minor, a player would insert a secondary dominant just before it. To find the root of the proper secondary dominant, take the root note of the chord (in this case a) and move down a perfect fourth to e to form an E7 chord. The E7 chord could be notated as III7, but a better notation is Vofvi. Any chord can have a secondary dominant.

 

In C

A Minor

Harmonic

Melodic

(VofI)

G

(Vofi)

E

E

E

Vofii

A

Vofiio

F#

F#

F#

Vofiii

B

VofIII

G

G

G

VofIV

C

Vofiv

A

A

A

VofV

D

Vofv

B

B

B

Vofvi

E

VofVI

C

C

C#

Vofviio

F#

VofVII

D

D#

D#

 

Any seventh (7) chord and its higher order permutations can be  secondary dominant, so chords like V13ofIV are possible.

Chains of Secondary Dominants

Consider the cadence

D7

G7

C

V7ofV

V7

I

If any chord can have a secondary dominant associate with it, then what about a secondary dominant for D7? Following the procedure, take d down a fourth to a then build a dominant A7, for example. A7 is certainly VI7 in the key of C, but that notation does not promote understanding. Follow this logic:

D7 is V7ofV

A7 is V of [D7] (Brackets added for clarity.]

So, A7 is V7of[VofV] or V7ofVofV. (Put the "7" on the first item only.)

 

Putting several secondary dominants together is called a chain of secondary dominants. The next in the chain is V7of{Vof[VofV]}, an E7 chord. Chaining secondary dominants is a great technique for folk music. Listen to "Her Majesty" by The Beatles for some great uses of secondary dominants and chromatic harmonies.

 

The full chain of secondary dominants would be

 

C7F7Bb7Eb7Ab7(Db7 or C#7)F#7B7E7A7D7G7C

 

Playing chords in series is a great exercise for learning the seventh chords, and is the basis for the chord weaving section of the guitar method.

Secondary Dominants Based on viio

Any chord with a dominant function can be a secondary dominant. The most common is the viio chord. A viio chord highlights the chord a half step above the root. So, viioofF is an Eo chord followed by and F chord.

 

In C

A Minor

Harmonic

Melodic

(viioofI)

Bo

(viioofi)

G#o

G#o

G#o

viioofii

C#o

viioofiio

A#o

A#o

A#o

viioofiii

D#o

viioofIII

Bo

Bo

Bo

viioofIV

Eo

viioofiv

C#o

C#o

C#o

viioofV

F#o

viioofv

D#o

D#o

D#o

viioofvi

G#o

viioofVI

Eo

Eo

E#o

viioofviio

A#o

viioofVII

F#o

Fxo

Fxo

 

Half diminished seventh chords function the same way, as well as ninth, eleventh, and thirteenth chords based in the diminished triad. The viio7 chord can be extremely powerful as a pivot to a new key. Since viio7 is just a series of minor thirds, any note in the chord can be a secondary dominant leading to the chord just above it.

Tritone Substitutions

Jazz players use another type of chromatic harmony to pass from one chord to another. The tritone substitution uses a tritone (d5), three whole steps, as a passing tone between two chords.

Consider the very common ii-V-I jazz pattern in C.

 

f

a

d

g

f

b

e

d

g

c

Dm

G7

C

ii

V7

I

 

One issue with this pattern is the big jump in the bass line d-g-c.  So, instead of the g in the second chord, substitute the note that lies between the d in the first chord and the c in the third chord, db.

 

f

a

g

g

f

b

e

d

db

c

Dm

G7b5/Db

C

ii

V7b5

I

 

The tritone here is from g, the expected root, to db, a tritone(d5) from g.

 

Now rearrange the last chord accentuation the 4-3 resolution.

 

g

g

a

b

c

f

f

e

d

db

c

Dm

G7b5/Db

C

ii

V7b5

I

 

Tritone substitutions and other jazz tricks are an art form. Refer to a jazz text for more examples.

 

Chromatic harmonies may occur any place where a scale has a major second. The patterns 2-b2-1 (above), 2-#2-3, 4-#4-5, 6-b6-5, 6-b7-7-1 all lead to chord tones, so they make good chromatic harmonies. The ii-V7-I jazz pattern with these chromatic harmonies.

 

2-#2-3

Dm

G+7

C

d-d#-c

4-#4-5

Dm

GMaj7

C

f-f#-g

6-b6-5

Dm

G7b9

C

a-ab-g

6-b7-7-1

Dm

G7#9-G7

C

a-a#-b-c

Misspelled Chords

Chromatic harmonization shows how notating an accidental as a flat suggests that the next note might be the pitch just below and notating with a sharp may signal an ascending line. The seventh degree of the F7 chord, spelled facEb, suggests the note should resolve downward to d, and that resolution is commonplace. But what if the same group of notes were spelled the enharmonic equivalent, facd#? Now the d# wants to resolve upward to an e.

 

Consider in the key of C an Ab7 chord. Written in the standard way, AbcEbGb, the chord seems like a VofDb secondary dominant, which would resolve to Db. But written AbcEbf#, now the f# suggest resolution to g, with eb moving down to d and ab down to g.

 

f#

g

eb

d

c

b

ab

g

Ger#6

V

 

Traditionally written with a I chord in second inversion delaying the resolutions.

 

f#

g

g

eb

eb

d

c

c

b

ab

g

g

Ab

Cm/G

G

 

This is German sixth chord is the first of a number of altered chords widely used in classical music, the others being the French sixth

 

f#

g

d

d

c

b

ab

g

Fr#6

V

 

Italian Sixth

 

f#

g

c

d

c

b

ab

g

It#6

V

 

And English (or Swiss, or Alsatian, or double German)

 

f#

g

g

D#

e

d

c

c

b

ab

g

g

En#6

C/G

V

 

 

 

This group, known as augmented sixth chords because of the distance between ab an g#, usually precedes a V cord, but could theoretically resolve to other chords with notes a half step below the bass. Blues players use a chord based on b6 just before a dominant often.

 

A Neapolitan chord functions in a similar manner. N6 chords are major chords in first inversion built on the flat second scale degree. In C, the chord resolves down to I

 

db

c

a

g

f

e

Db/F

C/E

 

Traditionally delayed by the addition of a V chord.

e

db

b

c

a

g

g

f

d

c

Db/F

G/D

C

 

The most famous misspelled chord is the Tristan chord b-d#-f-g#., from the opera Tristan und Isolda by Richard Wagner. Use of this chord signaled the move away from classical functional harmonies into more structurally built chords, and new tonalities based on chromaticism.

Interval Based Chords

So, far most of the chords listed are stacks of thirds on top of each other because that relationship follows from the physics of sound. But chords built on other intervals also have their place.

Quartal Chords

Chords based on fourths are called quartal chords.

Take the columns of notes from the original note stack, but extend to three octaves.

 

b

c

d

e

f

g

a

a

b

c

d

e

f

g

g

a

b

c

d

e

f

f

g

a

b

c

d

e

e

f

g

a

b

c

d

d

e

f

g

a

b

c

c

d

e

f

g

a

b

b

c

d

e

f

g

a

a

b

c

d

e

f

g

g

a

b

c

d

e

f

f

g

a

b

c

d

e

e

f

g

a

b

c

d

d

e

f

g

a

b

c

c

d

e

f

g

a

b

b

c

d

e

f

g

a

a

b

c

d

e

f

g

g

a

b

c

d

e

f

f

g

a

b

c

d

e

e

f

g

a

b

c

d

d

e

f

g

a

b

c

c

d

e

f

g

a

b

 

 and choose every fourth note instead of every third, from c to f.

g

a

b

c

d

e

f

d

e

f

g

a

b

c

a

b

c

d

e

f

g

e

f

g

a

b

c

d

b

c

d

e

f

g

a

f

g

a

b

c

d

e

c

d

e

f

g

a

b

 

Any stacks of three or more notes make up a quartal chord.

 

Traditional analysis breaks down for quartal chords. Traditional analysis of quartal chords is possible but does not truly represent their function. For example, a suspender fourth would not usually resole down to a third as in traditional harmony. Here are some traditional forms forced onto the quartal chords:

 

13th

CMaj13

Dm13

Em11b13b9

FMaj13#11

G13

Am11b13

Bm11b13b9b5

11th

C11sus6

Dm11sus6

Em11b9susb6

FMaj9#11sus6

G11sus6

Am11susb6

Bm11b9susb6

5 note

CMaj7sus6add4

DMaj7sus6add4

EMaj7susb6ad4

FMaj7sus6add#4

G7sus6add4

AMaj7sus6badd4

BMaj7susb6ad4

7th

CMaj7add4(no5th)

DMaj7add4(no5)

EMaj7add4(no5)

FMaj7add#4(no5th)

G7add4(no5th)

AMaj7add4(no5)

BMaj7add4(no5)

triads

CMaj7sus4(no5th)

D7sus4(no5th)

E7sus4(no5th)

FMaj7sus#4(no 5th)

G7sus4(no5th)

A7sus4(no5th)

B7sus4(no5th)

 

Notice that no true ninth exists and the chords built on the seventh scale degree lack any diminished quality until the thirteenth chord.

 

Listen to music by Debussy or the theme to the original Star Trek for uses of quartal chords.

 

Quartal chords based on other scales also exist. Many jazz players like to solo in fourths, so these patterns are useful even if not used in chords.

 

Quartal chords of the harmonic minor lead to some interesting substitutions, particularly on the seventh scale degree.

 

AmMaj11b13

Bm13b9b5

CMaj13#5

Dm13#11

E11b13b9

Fm6(Maj7)add#4

G#b5add#2add#6addb9

AmMaj11susb6

Bm11b9sus6

C11#5sus6

Dm9#11sus6

E11b9susb6

FMaj7#9#11sus6

G#add#2add#6addb9

AmMaj7susb6add4

Bm67add4

CMaj7#5sus6add4

DMaj7sus6add#4

E7susb6add4

FMaj7sus6add#4

G#add#2add#6

AmMaj7add4(no5th)

BMaj7add4(no5)

CMaj7add4(no5th)

DMaj7add#4(no5)

E7add4(no5th)

FMaj7add#4(no5th)

G#msusb7

AMaj7sus4(no5th)

B7sus4(no5th)

CMaj7sus4(no5th)

D7sus#4(no5th)

E7sus4(no5th)

FMaj7sus#4(no 5th)

G#o7(no5th)

 

On g# chords of 3 or more notes, the c is effectively the third, with the m3 treated as #2.

Quartal chords on melodic minor ascending

Am(Maj13)

Bm13b9

CMaj13#11#5

D13#11

E11b13b9

F#m6(Maj7)#11

G#7b13b9b5add#2

Am(Maj11)sus6

Bm11b9sus6

C9#11#5sus6

D9#11sus6

E11b9susb6

F#Maj7#9#11sus6

G#7b9add#2susb6

Am(Maj7)sus6add4

Bm67add4

CMaj7#5sus6add#4

D7sus6add#4

E7susb6add4

F#Maj7sus6add#4