Embed Size (px)
Citation preview
“No Chord Left Behind: A Guitar Navigation Kit”, Ivan Radivojevic
Objective and Method:
• Systematically construct guitar chords.
• Describe chord types based on their constituent intervals and present commonly used playing shapes.
• Examples, references and chord progressions used to provide musical context and to illustrate common uses.
Table of Contents:
1 Introduction
1.1 Prerequisites
1.2 Integer Notation
1.3 Intervals
1.4 Triads
2 Chords
2.1 Major and Minor Chords
2.2 Sixth and Seventh Chords
2.2.1 Chord Types and Naming
2.3 Diminished Chords
2.3.1 Diminished Seventh Chords
2.3.2 Half-Diminished Seventh Chords
2.4 Augmented Chords
2.5 Suspended Chords
2.6 Ninth Chords
2.7 Eleventh and Thirteenth Chords
2.8 Altered Chords
2.9 Open Chords Revisited
3 Advanced Topics
3.1 Chord Aliasing
3.2 Chord Voicing
3.2.1 Drop_2 Voicing
3.2.2 Drop_3 Voicing
3.2.3 Drop_2&4 Voicing
3.2.4 Extensions and Examples
3.3 One-Off Chords
4 Appendix
4.1 Common Scales
4.2 Quartal Harmony
© 2018 Ivan Radivojevic
1.1 Prerequisites
© 2018 Ivan Radivojevic
The presentation in “No Chord Left Behind: A Guitar Navigation Kit” is focused solely on playing guitar chords. We
do not attempt to enumerate and analyze each-and-every chord type and playing shape or to come up with a
“definitive” reference chart. Instead, our goal is a practical toolkit consisting of a balanced mix of theory and
examples that could serve as a valuable complementary source for guitar players eager to expand their knowledge and
understanding of the instrument. For example, a few sections (“Altered Chords”, “Chord Voicing” and “Quartal
Harmony”) open a door to jazz ever so slightly and may expand vocabulary of an otherwise accomplished rock-guitar
performer. Also, even quite skilled, but self-taught players are likely to experience a few “Aha!” moments in sections
covering more advanced topics.
No prior knowledge of music theory is required in order to be able to follow the presentation:
• In Section 1, we provide very basic information on music intervals and structures (e.g., octaves and triads) and
show how they map to guitar fretboard.
• In Section 1, we also introduce the Integer Notation extensively used throughout the presentation.
• While not a prerequisite, for completeness, a rudimentary introduction to musical scales is presented in the
“Common Scales” appendix.
• The ability to read music is not required.
Although we do not start from scratch, as far as any prior guitar playing experience and proficiency level go, the
prerequisites are rather minimal. The Reader can be a beginner, capable of tuning a guitar and strumming a few songs
using a usual starter set of easy-to-play “open” chords: A, Am, C, D, Dm, E, Em and G (highlighted in Fig.1.1.1). We
also assume the Reader is already aware of the concept of “barre” chords (like the F shape also included in
Fig.1.1.1) where the index/first finger is used to cover multiple strings.
In particular, the familiarity with A, Am, E and Em chords shown in Fig.1.1.1(a) is all that is assumed for sections 2.1
through 2.8. Those sections include a discussion of assorted chords types (major, minor, sixth, seventh, diminished,
augmented, suspended, ninth, eleventh, thirteenth and altered) and commonly used playing shapes.
In Section 2.9 (“Open Chords Revisited”), the Reader is expected to be familiar with C, D, Dm and G chords shown in
Fig.1.1.1(b). The Reader proficient in sections 2.1 through 2.8 should be able to absorb Section 2.9 information
easily, but there is quite a bit of it (albeit deceptively packaged in mere three pages).
AA EmEmAmAm EE
GGDmDmCC
FF
(a)
Fig.1.1.1: Prerequisite chords.
(b)
DD
E
B
G
D
A
E
String:
E
B
G
D
A
E
1.1 Prerequisites (Cont.)
© 2018 Ivan Radivojevic
There are two Section 3 chapters covering more advanced topics (“Chord Aliasing” and “Chord Voicing”) and, for
those, we assume the Reader proficient in the whole of Section 2. At that point, the Reader should already understand
chord structures in terms of their constituent intervals and also posses a well-stocked arsenal of common playing
shapes.
• The “Chord Aliasing” section demonstrates that certain chord shapes could be used for playing multiple chord
types—an easy way to increase the number of playing options without having to learn new chord shapes.
• The “Chord Voicing” section presents a formal approach to constructing and playing 4-note chords (including
their inversions) and provides an expansive, rich menu for advanced players. Various “Drop” forms discussed in
the “Chord Voicing” section are used by jazz guitarists in many sophisticated ways that are beyond the scope of
this presentation. Any enthusiastic student, however, will benefit from enhanced fretboard awareness and ability
to locate a playable chord shape at virtually any fret or string position.
In Fig.1.1.1, a sidebar is used to label guitar strings as: E, B, G, D, A and E. This corresponds to the standard tuning
of guitar open strings that we assume throughout the presentation. In the sections following the introduction, to avoid
needless clutter in figures, we omit strings labelling most of the time. In certain instances, we include the sidebar
when showing a full fretboard or a group of chords—e.g., to make the point of playing only a subset of the strings.
When we refer to “high” or “top” strings, those correspond both to high pitches and to being located near the top edge
of a drawn fretboard. Similarly, “low” or “bottom” strings correspond to low pitches and to being located near the
bottom edge of a fretboard drawing. We do not number the strings—instead, we refer to individual strings using their
standard open tuning (e.g., “the D string” and not “the 4th string”). If needed for clarity, we get more specific about
“low-E” and “high-E” strings. No non-standard/alternate tunings (e.g., various “open” tunings) are discussed in this
presentation.
In most figures that follow, we represent chords as dots at particular fretboard positions. When a dot is numbered, the
number identifies the corresponding interval included in the shown chord. Most of the times, we do not discuss
fingering (i.e., which finger to use to press a particular dot). There is no “correct” fingering that works for every
player and all music genres—why, Paco De Lucia and Jimi Hendrix played their chords quite differently and Django
Reinhardt did not even have a full use of all his fingers. Similarly, the presentation is agnostic to what “the proper
place” for the fretting hand’s thumb is and if/when it should be used to play or mute notes on the low-E string.
When referring to chord types, we use interchangeably the numeric form (e.g., 7th chord) and the word form (seventh
chord). Chord types are not capitalized— for example, in Section 2.2, we introduce a minor seventh chord type (not
Minor Seventh). Similarly, for intervals, we use both the numeric form (e.g., minor 7th interval or just minor 7th) as
well as the word form (minor seventh) with no capitalization. Typically, numeric forms are used either for brevity or
to make them stand out in the surroundings.
In a few places, modulo-12 arithmetic is employed. Modulo-12 arithmetic operates on numbers belonging to the range
from 0 to 11. If a 2-input addition results in a number larger than or equal to 12, 12 is subtracted from the number to
produce the final result (i.e., the result is said to “wrap around the number 12”). Thus, for example, “1 + 1” is equal to
2, but so are “3 + 11” or “7 + 7”. And “8 + 4” is 0, not 12.
1.2 Integer Notation
Two tones that are one octave apart differ in pitch as 2:1. A pitch class N corresponds to a set of all notes N whose
pitch is a whole number of octaves apart. Using the Integer Notation, pitch classes are represented in the following
fashion: (a) a “root” note belonging to N is labeled “0”, and (b) all consecutive semi-tones are labeled by increasing
integer numbers. One octave consists of 12 semi-tones, so the Integer Notation uses numbers from 0 to 11. Adjacent
guitar frets are one semi-tone apart. In Fig.1.2.1, Integer Notation is used to represent pitch classes for five different
root notes (E, A, D, G and B) that happen to correspond to the standard tuning of open guitar strings. According to the
definition, the notes corresponding to the top and bottom strings (high-E and low-E) belong to the same pitch class. A
chord is a combination of three or more musical tones played together. A chord rooted in any pitch class can be
represented using the Integer Notation and the same numerical encoding corresponds to a particular chord type
regardless of the pitch—for example, as shown later in this presentation, a major chord’s notation is { 0 , 4 , 7 }.
To make diagrams and examples less busy, we try to avoid using sharp (“#”) and flat (“b”) notes; other than that, we
consider it self-evident that all notes are created equal. Moreover, F# and Gb are played using the same fretboard
positions[1] and we will use the two forms interchangeably; the same applies to: G#/Ab, A#/Bb, C#/Db and D#/Eb.
We can get away with this since music scores will not be used in the presentation. Ignorance is bliss.
In Fig.1.2.2, the following frets are one octave apart: (x0=>x1), (x1=>x2), (y0=>y1) and (y1=>y2). There are two
octaves between x0 and x2; the same is true for y0 and y2. An octave pattern depends on a starting string, but the
patterns repeat in any fret position.
x2
A
B
C
D
E
F
G
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
D
E
F
G
A
B
C
D
E
F
G
A
B
C
0
1
2
3
4
5
6
7
8
9
10
11
D
E
F
G
A
B
C
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
EF
F# / Gb
G
G# / Ab
A
A# / Bb
B
C
C# / Db
D
D# / Eb
EF
F# / Gb
G
G# / Ab
A
A# / Bb
B
C
C# / Db
D
D# / Eb
0
1
2
3
4
5
6
7
8
9
10
11
EF
F# / Gb
G
G# / Ab
A
A# / Bb
B
C
C# / Db
D
D# / Eb
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
G
A
B
C
D
E
F
G
A
B
C
D
E
F
0
1
2
3
4
5
6
7
8
9
10
11
G
A
B
C
D
E
F
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
BC
D
E
F
G
A
BC
D
E
F
G
A
0
1
2
3
4
5
6
7
8
9
10
11
BC
D
E
F
G
A
Fig.1.2.1: Examples of “Integer Notation” for different “root” notes.
Fig.1.2.2: Guitar octave patterns.
© 2018 Ivan Radivojevic
E
B
G
D
A
E
Strings:
E
B
G
D
A
E
x0
y0
y1
x1
x2
y2
y0
x1
x2
x0
y0
x1
y1
y0
y2
x1
x2
______________________________________________________________________________________
[1] See the black dots marked “2” in Fig.1.2.3(a), the same as the dots marked “9” Fig.1.2.3(b).
1.2 Integer Notation (Cont.)
In Fig.1.2.3, Integer Notation is used to map pitch classes to the guitar fretboard. In Fig.1.2.3(a), the root notes belong
to the pitch class of E—all frets are annotated in the top drawing with the root notes (“0”) extracted in the bottom one;
the pitch class of A is depicted in Fig.1.2.3(b). As expected, irrespective of a pitch class and its root note, the Integer
Notations values on the low-E and high-E strings are identical. Similarly, since one octave covers 12 semi-tones, an
open string (white dotes) and the 12th fret on same string map to the same Integer Notation value. All corresponding
frets on adjacent strings are 5 semi-tones away, except for the strings G and B that are four semi-tones apart. For
example, in Fig.1.2.3(a), the fifth fret on the A string is annotated as “10”. The same fret on the D string is then “3”
since (10+5) is equal to 15 and, in modulo-12 arithmetic, 12 has to be subtracted whenever the modulo-12 result is
larger or equal to 12. Also, all shown root note positions (dots marked “0”) are compliant with the octave patterns
described in Fig.1.2.2.
Exercise 1.2.1: Similar to the E and A notes shown in Fig.1.2.3, locate along the fretboard all C, D and G notes.
In Fig.1.2.4(a), a 4-note chord pattern is shown on the four high strings[1]. Next, we simply move each note to the
adjacent lower string as shown in Fig.1.2.4(b). The resulting shape is similar to the starting one as all chord notes
(dots) advance by 5 frets except for the one originating on the B string that moves up by 4 frets (a guitar tuning
quirk). By construction, the two chords in Fig.1.2.4 include the same notes in the same order and should sound the
same. Nevertheless, one of the two shapes is likely to be easier to play as the two shapes are not identical and the fret
width is not uniform along the fretboard. Also, for a particular musical context, we may decide to favor a form that
keeps most of the chords close to each other, thus making the fretting hand’s movements more efficient and economic
when playing chord progressions.
© 2018 Ivan Radivojevic
1
6
11
4
8
1
2
7
0
5
9
2
3
8
1
6
10
3
4
9
2
7
11
4
5
10
3
8
0
5
6
11
4
9
1
6
7
0
5
10
2
7
8
1
6
11
3
8
9
2
7
0
4
9
10
3
8
1
5
10
11
4
9
2
6
11
0
5
10
3
7
0
0
5
10
3
7
0
3fr 5fr 12fr8fr 10frStrings:
E
B
G
D
A
E 8
1
6
11
3
8
9
2
7
0
4
9
10
3
8
1
5
10
11
4
9
2
6
11
0
5
10
3
7
0
1
6
11
4
8
1
2
7
0
5
9
2
3
8
1
6
10
3
4
9
2
7
11
4
5
10
3
8
0
5
6
11
4
9
1
6
7
0
5
10
2
7
7
0
5
10
2
7
3fr 5fr 12fr8fr 10fr
Fig.1.2.3: Pitch class mapping assuming two different root notes: (a) E, and (b) A.
Strings:
E
B
G
D
A
E
0
0
0
0
0
00
3fr 5fr 12fr8fr 10fr
(a) (b)
0
0
0
0
0
0
0
0
3fr 5fr 12fr8fr 10fr
Strings:
E
B
G
D
A
E
4
7
0
3fr 5fr 12fr8fr 10fr
Fig.1.2.4: Moving a chord shape down by one string.
(b)
7
0
4
10
3fr 5fr 12fr8fr 10fr
(a)
10
______________________________________________________________________________________
[1] The shown chord happens to be A7—we will learn more about it and many other chords in the remaining sections of the “No Chord Left
Behind: A Guitar Navigation Kit”.
1.3 Intervals
Integer Notation: Intervals:
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
C
D
E
F
G
A
B
C
D
E
F
G
A
B
0
1
2
3
4
5
6
7
8
9
10
11
C
D
E
F
G
A
B
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Also referred to as “diminished seventh” (d7).
perfect unison
minor second
major second
minor third
major third
perfect fourth
diminished fifth
perfect fifth
augmented fifth
major sixth
minor seventh
major seventh
perfect unison
minor second
major second
minor third
major third
perfect fourth
diminished fifth
perfect fifth
augmented fifth
major sixth
minor seventh
major seventh
Fig.1.3.1: Music intervals and their relationship to Integer Notation (C root note example).
Also referred to as “tritone” or “flat 5” (b5).
Also referred to as “minor sixth” (m6) or “sharp 5” (#5).
The knowledge of music intervals is required to be able to understand chord structures and naming.
• For chord construction purposes, we will use both intervals and Integer Notation. As shown in Fig.1.3.1, there is a
1:1 correspondence between the two.
• For graphical representation of chord shapes, we will mostly use Integer Notation for its compactness (digits only)
and simple interpretation (relative distance in terms of frets).
There are 7 intervals in one octave, so a larger (“compound”) interval from the same pitch class is computed by
adding 7 to the original one (see Fig.1.3.2); there are 12 semi-tones in one octave, so 12 is added in Integer Notation.
In this presentation, a chord is considered a combination of three or more notes played together. More complex
chords are constructed by adding notes to simpler chords and, in the following sections, we will present this process
in a systematic fashion. We will describe chord types based on their constituent intervals as the relationships among
the notes is what defines a particular chord’s type. We will also present and explain commonly used playing shapes.
Examples accompanying more exotic chords will be included and, in certain cases, standard chord progressions will
be employed to provide a musical context for a particular chord type and to illustrate its common uses.
Integer Notation: Intervals:
1 / 8
2 / 9
3 / 10
4 / 11
5 / 12
6 / 13
7 / 14
1 / 8
2 / 9
3 / 10
4 / 11
5 / 12
6 / 13
7 / 14
0 / 12
1 / 13
2 / 14
3 / 15
4 / 16
5 / 17
6 / 18
7 / 19
8 / 20
9 / 21
10 / 22
11 / 23
0 / 12
1 / 13
2 / 14
3 / 15
4 / 16
5 / 17
6 / 18
7 / 19
8 / 20
9 / 21
10 / 22
11 / 23
P1 / P8
m2 / m9
M2 / M9
m3 / m10
M3 / M10
P4 / P11
d5 / d12
P5 / P12
A5 / A12
M6 / M13
m7 / m14
M7 / M14
P1 / P8
m2 / m9
M2 / M9
m3 / m10
M3 / M10
P4 / P11
d5 / d12
P5 / P12
A5 / A12
M6 / M13
m7 / m14
M7 / M14
Fig.1.3.2: Compound intervals.
© 2018 Ivan Radivojevic
0
4
7
0
4
7
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
4
8
0
4
8
0
3
6
0
3
6
Major
{ 0 , 4 , 7 }
Augmented
{ 0 , 4 , 8 }
Minor
{ 0 , 3 , 7 }
Diminished
{ 0 , 3 , 6 }
1.4 Triads
Fig.1.4.3: Examples of triads (cont.).
majormajor
minorminor
• A major triad consists of a “root” note (“0”) and two other higher-pitch notes that are 4 and 7 frets away. Or, in
terms of intervals, a major triad includes P1, M3 and P5—see Fig.1.4.1.
• A minor triad consists of P1, m3 and P5—i.e., the minor third (m3) is included instead of the major third (M3).
• In an augmented triad, the fifth of the corresponding major triad is raised/sharpened (i.e., P5 becomes A5).
• In a diminished triad, the fifth of the corresponding minor triad is lowered/flatted (i.e., P5 becomes d5).
In all triads shown in Fig.1.4.1, adjacent notes are 3 or 4 semi-tones apart—i.e., the notes are “stacked in thirds” (m3
or M3). Basic major, minor, augmented and diminished chords include only notes from the corresponding triads.
Integer
Notation:
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:
Exercise 1.4.1: In Fig.1.4.2, triads are represented as three
dots of the same color. Play the shown triads to get the ear
familiar with the harmonies. The Reader should also
discover and play triads in different positions including using
only two strings like shown in Fig.1.4.3.
NOTE: More ways to play triads, including those with
reordered notes, are presented in Fig.3.1.1 and Fig.3.1.2 in
the “Chord Aliasing” section.
Minor0
4
0
4
7
0
4
7
0
4
7
0
4
7
0
4
7
0
4
7
0
4
7
0
4
7
Minor
0
3
7
0
3
7
0
3
7
0
3
7
0
3
7
0
3
7
0
3
7
Minor
0
3
7
0
3
7
0
3
7
0
3
7
0
4
8
0
4
8
0
4
8
0
4
8
0
4
8
0
4
8
0
4
8
0
4
8augmentedaugmented
diminished 0
3
6
0
3
6
0
3
6
0
3
6
0
3
6
0
3
6
0
3
6
0
3
6
Minor
0
4
0 3
7
7
0
3
7
7
Fig.1.4.1: Structure of triads.
© 2018 Ivan Radivojevic
E
B
G
D
A
E
Strings:
E
B
G
D
A
E
Fig.1.4.2: Examples of triads.
0
4
7
0
4
7
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
Major
{ 0 , 4 , 7 }
E
E
F
G
A
B
C
D
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
Minor
{ 0 , 3 , 7 }
Em
E
7fr
A
5fr
“Open”
chords.
“Barre”
chords.
Major-vs-minor
difference.
2.1 Major and Minor Chords
Loosely defined, the term “open chords” refers to simple chords where the fretting hand’s fingers press individual
strings and produce notes together with one or more open (not pressed) strings. In contrast, when playing “barre
chords”, the index/first finger is used to cover multiple strings and no open strings are played, making such chords
portable (i.e., they can be shifted to and played in any fret position). Throughout this presentation, “open” E and A
chord shapes (see Fig. 2.1.2) will be used as two basic patterns to construct more complex chord types. Additional
patterns (e.g., based on the “open” C chord) will be examined in the “Open Chords Revisited” section.
“Barre” E chords look like “open” A chords (and vice versa, see Fig.2.1.2). Any minor/major chord can be played
using the shown “barre” shapes. It is important to be aware where triad notes are as we will build more complex
chords around them.
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:Integer
Notation:
A
Am
Em
7fr
Am
5fr
7
0
4
0
7
0
0
7
0
3
7
0
4
0
7
7
0
7
7
0
7
3
0
7
4
0
7
7
0
7
7
0
7
3
0
7
0
7
0
7
0
0
4
0
7
3
“Open”
chords.
“Barre”
chords.
0
7
Fig.2.1.1: Structure of major and minor chords.
Fig.2.1.2: Examples of major and minor chords.
© 2018 Ivan Radivojevic
2.1 Major and Minor Chords (Cont.)
Most players find the concept of “open” A and “open” E chords convenient and easy to comprehend. From there,
“barre” chords can be viewed as merely shifted (transposed) versions of the corresponding “open” chords. Two Cm
chord examples are shown in Fig.2.1.3 where Cm is played either as Am shifted 3 semi-tones higher or as Em shifted
by 8 semi-tones.
In Fig.2.1.4, we employ the procedure depicted in Fig.1.2.4 to move Am down by one string. Notice that this
effectively transforms an “open” shape into a “barre” shape. This also shows that “open” A and “open” E shapes
merely correspond to playing the same intervals in the same order, but using two different sets of adjacent strings.
Thus, if a guitar player uses solely A and E shapes, the chords will sound similar and predicable.
© 2018 Ivan Radivojevic
Strings:
E
B
G
D
A
E
3
7
0
3fr 5fr 12fr8fr 10fr
Fig.2.1.4 Moving a shape (Am) down by one string.
(b)
7
0
3
3fr 5fr 12fr8fr 10fr
(a)
7
0
7
0
Am
7
0
7
3
0
7
Cm
7
0
7
3
0
7
Em
0
7
0
3
7
0
8fr
0
7
0
3
0
7
3fr
Cm
Fig.2.1.3 “Barre” C chords.
(b)(a)
0
4
7
0
4
7
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
4
7
9
0
4
7
9
Major
{ 0 , 4 , 7 }6
E
0
Minor
{ 0 , 3 , 7 }
A
0
4
7
10
0
4
7
10
7
0
4
7
11
0
4
7
11
M7
0
3
7
9
0
3
7
9
0
3
7
10
0
3
7
10
7
0
3
7
11
0
3
7
11
M76
E6 A6
E7 A7
EM7 AM7
2.2 Sixth and Seventh Chords
NOTE: Only major chords are shown. For minor chord variants, replace “4” (M3) with its corresponding “3” (m3) played on the
same string. The corresponding minor chords: Em, Em6, Em7, EmM7, Am, Am6, Am7 and AmM7.
E
F
G
A
B
C
D
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
Integer
Notation:
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:
7
4
0
7
0
0
0
0
0
0
0
9
0
7
4
4
0
7
10
11
4
0
7
7
0
7
0
7
0
7
10
11
0
7
Sixth and seventh chords are constructed by adding M6 (“9”), m7 (“10”) or M7 (“11”) to a major chord ({ 0 , 4 , 7})
or a minor chord ({ 0 , 3 , 7 })[1]—see Fig. 2.2.1. The Reader should play the shapes shown in Fig.2.2.2 and train the
ear to recognize basic chords types (e.g., major-vs-minor, added M6/m7/M7). The included EM7 shape is a bit tricky
to play—several other, friendlier M7 forms will be discussed in the rest of this and subsequent sections.
Fig.2.2.1: Structure of 6th
and 7th
chords.
Fig.2.2.2: Examples of 6th
and 7th
chords.
© 2018 Ivan Radivojevic
______________________________________________________________________________________
[1] In the “Eleventh and Thirteenth Chords” section, we will describe extended chords where the 6th and the 7th intervals are both included.
7
0
4
9
4
0
7
7
0
4
7
0
4
E7
EM7
In Fig.2.2.3, we start from chords shown in Fig.2.2.2 and present the corresponding shapes where the seventh interval
notes (m7/“10” or M7/“11”) are added one octave lower. The Reader should play all chords shown in Fig.2.2.3 as
both major and minor chord types and observe that two playing options always sound at least slightly different.
Exercise 2.2.1: Using the forms shown in Fig.2.2.3, play the following chords: C7, CM7, Cm7 and CmM7.
• Notice that the highlighted forms are easy to play “barre” and thus to move to other fret positions (3fr and 8fr, for
C chords).
• It is mechanically impossible to play “barre” forms of all shapes that are not highlighted in Fig.2.2.3. Instead, we
can play just four chord notes (that happen to coincide with the black dots) as long as we make sure the remaining
two strings are muted to avoid producing notes that may not belong to the chord. For example, E7 and EM7 have
all chords notes present on the middle four strings; A7 and AM7 have all four chord notes on the high strings. Such
4-note chord playing style is common in jazz; a beginner player may find it a bit tricky to strum or pick such
chords cleanly, however. Similarly, at first, “inverted” chords (forms where a root is not the lowest-pitch/“bass”
note) may seem slightly disorienting.
Exercise 2.2.2: The chord types discussed in Section 2.1 (“Major and Minor Chords”) and Section 2.2 (“Sixth and
Seventh Chords”) are the most common types used in popular music songs[1]. For example, the Beatles classic
“Something” (1969) features the following chord progression:
C - CM7 – C7 – F – D - D7 – G – Am – AmM7 – Am7 – D – ( turnaround: F – Eb – G )
Exercise 2.2.3: In sections 2.3.through 2.8, “open” E and A chord shapes (Fig. 2.1.2) are used as two basic patterns to
illustrate how to construct more complex chords. Additional patterns are examined in Section 2.9 (“Open Chords
Revisited”). We would actually suggest learning a few basic 7th C/D/G chords shown in Fig.2.9.1 before tackling
more complex chord types in the preceding sections (2.6, 2.7 and 2.8, in particular). At that point, the Reader should
repeat Exercise 2.2.2, but, whenever possible, use simpler shapes from Fig.2.9.1; similarly, we suggest playing the
progression transposed to a different key—for example:
C - CM7 – C7 – F – D - D7 – G – Am – AmM7 – Am7 – D – ( turnaround: F – Eb – G )
G - GM7 – G7 – C – A - A7 – D – Em – EmM7 – Em7 – A – ( turnaround: C – Bb – D )
D - DM7 – D7 – G – E - E7 – A – Bm – BmM7 – Bm7 – E – ( turnaround: G – F – A )
A7
AM7
NOTE: Only major chords shown. For minor chord
variants, replace “4” with its corresponding “3”.
4
0
0
0
0
0
7
10
4
0
7
11
10
7
0
7
0
11
Optional since the m7 (“10”) is already
present as open D string one octave lower.
Fig.2.2.3: Examples of 6th
and 7th
chords (cont.).
2.2 Sixth and Seventh Chords (Cont.)
© 2018 Ivan Radivojevic
E7
EM7
4
7
4
11
7
10
0
0
7
0
0
7
10
A7
AM7
7
7
10
0
7
4
7
7
0
7
4
11
______________________________________________________________________________________
[1] Major, minor and 7th
chords, in particular; 6th
chords much less so (these days, in particular).
7
0
4
7
0
4
Once we know what intervals belong to a particular chord type, it is
possible to recognize or construct chords in other, perhaps less common
positions and forms (see the examples below).
Example 2.2.1: A commonly played, diagonal “M7” shape (e.g., AM7 in
Fig.2.2.4) is a slight modification of the related “barre” major chord.
More “M7” chord shapes will be presented in “Open Chords Revisited”
and “Chord Voicing” sections.
(a)
0
0
3
0
7
9
(b)
0
0
7
9
0
3
(d)
0
0
3
9
4fr
7
0
A4fr
7
4
0
7
0
0
Example 2.2.2: In Fig.2.2.5(a-d), we show several ways to construct and play Em6 chords.
• Shape “a” is constructed by adding M6/“9” to the shown Em chord (2fr on the B string).
• We start from the “open” Em6 chord (shape “a”) and move M6 (“9”) one octave lower (from the B string to the A
string) to get the “b” shape. Both shapes “a” and “b” can be played “barre”: as frets get narrower, it gets easier to
stretch fingers than to stack them on top of each other.
• Similar to shape “a”, the “c” shape can be derived from the shown Em, but instead of adding M6 (on the B string),
we lower the D string root (“0”) to M6 (“9”) [1].
• We start from the “c” shape and move the chord notes from the four top/high strings to the middle four strings. to
get the “d” shape[2]. Since all four chord notes ({ 0, 3, 7, 9 }) are present on the middle four strings, shape “d” can
be played in any fret position as long as the low/high-E strings are muted. Notice, however, that the 4-note “d”
shape, when used as Em6, has its root at the highest-pitch note (i.e., the chord is “inverted” with C# being the bass
note)—that would also be true for shapes “a” and “b”, both having all four chord notes (albeit re-ordered) on the
middle four strings.
______________________________________________________________________________________
[1] Shape “c” shows the A string as muted—including the fifth (“7”, as shown, for example, in “a”) would make the shape unplayable. In
cases like this, a player can either finger-pick the chord (and omit the A string) or use a finger pressing some adjacent string to also mute the
A string while strumming the chord. Jazz guitarists are more likely to use this kind of a chord that includes muted strings.
[2] Shape “d” is a very versatile one—we will return to it in later sections (“Half-Diminished Seventh Chords” and “Chord Aliasing”).
11fr
0
9
0
7
3
(c)
Fig.2.2.4: M7 chord example.
Fig.2.2.5: Em6 chord examples.
2.2 Sixth and Seventh Chords (Cont.)
© 2018 Ivan Radivojevic
AM74fr
11
7
4
0
Em
0
0
3
0
7
7
NOTE: Example 2.2.2 demonstrates there are many different ways to play the same chord. As we introduce various
chord types (sections 2.1 through 2.8), we will typically construct only a few derivative shapes based on “open” E and
A chords. A systematic way to arrive at many more playing options will be presented in the “Chord Aliasing” and
“Chord Voicing” sections.
2.2.1 Chord Types and Naming
© 2018 Ivan Radivojevic
______________________________________________________________________________________
[1] In “Appendix: Quartal Harmony”, we also introduce less common “quartal chords” constructed by “stacking fourths”.
In music theory, “tertian” chords are constructed by “stacking thirds”[1].
• Triads (major, minor, diminished and augmented) are the most basic tertian chords including 1st, 3rd and 5th
interval notes.
• Seventh (7th) chords are constructed by adding a 7th interval note (m7 or M7) to a triad.
• Ninth (9th
) chords are constructed by adding a 9th
/2nd
interval note to a seventh chord.
• Eleventh (11th) chords are constructed by adding an 11th/4th interval note to a ninth chord.
• Thirteenth (13th) chords are constructed by adding a 13th/6th interval note to an eleventh chord.
So far, in Section 2, the following 7th
chord types have been discussed:
• Dominant seventh (dom7): a major chord with the minor seventh (m7) interval added (i.e., { 0 , 4 , 7 , 10 }).
• Major seventh (M7): a major chord with the major seventh (M7) interval added (i.e., { 0 , 4 , 7 , 11 }).
• Minor seventh (m7): a minor chord with the minor seventh (m7) interval added (i.e., { 0 , 3 , 7 , 10}).
• Minor major seventh (mM7): a minor chord with the major seventh (M7) interval added (i.e., { 0 , 3 , 7 , 11 }).
Ninth, eleventh and thirteenth chords are also referred to as extended chords. We will study such extended chords in
later sections.
Adding a non-7th (i.e., 2nd/9th, 4th/11th or 6th/13th) interval note to a triad creates an added-tone chord. For example,
adding M9 (“2/14”) to a major triad ({ 0 , 4 , 7 }) creates Aadd9 ({ 0 , 2 , 4 , 7 }) and not A9 ({ 0 , 2 , 4 , 7 , 10 })
since m7 (“10”) is missing from the Aadd9 chord.
Technically, the Sixth chords are added-tone (added-sixth) chords. It is merely a convention (i.e., a naming rule
exception), that, for example, we use G6 (instead of Gadd6/Gadd13) and Gm6 (instead of Gmadd6/Gmadd13).
NOTE: In the Section 2.2 figures, all shown 6th/7th chords include both the perfect fifth (P5/“7”) and added intervals
(m7, M7 or M6). Being the most neutral constituent interval in 6th/7th chords, P5 is sometimes omitted from more
complex chord shapes. When playing in a band, however, guitar players also have an option to drop root notes
(usually supplied by a bass player) before dropping P5. More advanced sections of the presentation include examples
of chords having dropped intervals.
2.3 Diminished Chords
Fig.2.3.1: Structure of diminished triad (dim) chords.
Fig.2.3.2: Examples of diminished chords.
In Fig.2.3.2, portable “dim” chord shapes are derived from
“barre” Am chords. For easier orientation, root notes (“0”) are
shown as white dots.
We start from the 5fr Am “barre” shape and lower the fifths to
get an unplayable shape labelled “Adim (adj4)” in
Fig.2.3.2(b). In that shape, however, all dim chord notes ({ 0 ,
3 , 6 }) are present on any group of four adjacent strings. Two
resulting 4-note dim chords are extracted in Fig.2.3.2(a) and
Fig.2.3.2(c); the pattern on the middle four strings works as
well, but as an inverted form (i.e., its root note A is not the
chord’s lowest-pitch/bass note).
In Fig.2.3.2(d), we start from another “barre” Am chord (at 12/
0fr) and lower the fifths; again, all dim notes can be found on
the four middle/top strings. Of course, the shape shown in
Fig.2.3.2(b) is merely a shifted version of the one shown in
Fig.2.3.2(d)—as shown in Fig.2.1.4, the same relationship
holds for the two Am chords shown in Fig.2.3.2.
In the rest of this section we will also discuss adding intervals
to dim chords to construct more colorful diminished chord
types—in particular:
• In a diminished seventh (dim7) chord, M6/“9” is added to
a diminished triad.
• In a half-diminished seventh (m7b5) chord, m7/“10” is
added to a diminished triad.
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
3
6
0
3
6
Minor
{ 0 , 3 , 7 }
Diminished
{ 0 , 3 , 6 }Integer
Notation:
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:
© 2018 Ivan Radivojevic
Am
12fr
7
0
3
0
7
Cdim
Am
7
0
0
3
0
6
Adim (adj4)
0
7
3
0
5fr
Adim
6
0
3
0
4fr
Adim (adj4)
0
0
4fr
0
0
6
3
4fr
Adim
11fr
(a)
(b)
(c)
(d)
6
6
0
6
3
2.3 Diminished Chords (Cont.)
Using the Integer Notation, a dominant seventh (dom7) chord can be represented as: { 0 , 4 , 7 , 10 }. If we omit the
root of a dom7 chord, the remaining three notes form a diminished triad rooted in the major third (M3/“4”) of the
dom7 chord—i.e., { 4 , 7 , 10 } can be renumbered as { 0 , 3 , 6 }). This property is demonstrated in Fig.2.3.3 for
inverted Adim chords (both with the bass note of C) that map to non-root notes of the underlying F7 shapes. This
topic will be further explored in the “Chord Aliasing” section.
© 2018 Ivan Radivojevic
Fig.2.3.3: dom7 vs. dim chord (examples).
7
4
F7
10
7
7
4
F7
8fr
10
7
1fr
3
0
Adim/C
6
3
3
0
Adim/C
8fr
6
3
1fr
0
0
0
(a) (b)
Adim7
7fr
Cdim7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
0
1
2
3
4
5
6
7
8
9
10
11
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
10fr
Start from the Am6 ({ 0 , 3 , 7 , 9 }) shown below and lower
the fifth/P5 (i.e., move “7” to “6”). The new chord, shown in
Fig.2.3.1.2(b), is Adim7 ({ 0 , 3, 6 , 9 }). Notice that all four
dim7 notes are present on the middle four strings.
0
9
6
3
0
9
6
3
A diminished seventh (dim7) chord repeats as an inversion every 3 frets:
{ 0 , 3 , 6 , 9 } + { 3 , 3 , 3 , 3 } = { 3 , 6 , 9 , 12 } = { 3 , 6 , 9 , 0 }
As shown in Fig.2.3.1.3, Cdim7 includes the same notes are Adim7, so we can also annotate it as Adim7/C (i.e.,
Adim7 inversion with the bass note of C). But the following can also be used: D#dim7/C and F#dim7/C.
• Effectively, there are only three distinct dim7 chords (the other 9 are mere inversions of those three).
Fig.2.3.1.1: Structure of diminished seventh (dim7) chords.
Fig.2.3.1.2: Examples of dim7 chords. Fig.2.3.1.3: Inversion of dim7 chords.
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
3
6
0
3
6
Minor
{ 0 , 3 , 7 }
Diminished
{ 0 , 3 , 6 }
0
3
6
9
0
3
6
9
dim7
{ 0 , 3 , 6 , 9 }Integer
Notation:
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:
Also referred to as
“diminished
seventh” (d7).
© 2018 Ivan Radivojevic
2.3.1 Diminished Seventh Chords
Am6
7
0
0
9
3
0
5fr
Adim7
4fr
4fr
Adim7
(b)
(c)
Adim7
6
0
0
9
3
0
4fr
0
9
3
6
9
3
0
6
(a)
4-note Adim7 pattern on
the low strings extrapolated
from Fig.2.3.1.2(b).
4-note Adim7 pattern on
the high strings
extrapolated from
Fig.2.3.1.2(b). Common
and easy to play.
2.3.1 Diminished Seventh Chords (Cont.)
© 2018 Ivan Radivojevic
3fr
6
5fr
3
0
9
Fig.2.3.1.4: Diminished seventh (dim7) chord and its inversions (Adim7 example)
9
6
3
0
3
0
9
6
12fr8fr 10frStrings:
E
B
G
D
-
-
3fr
6
5fr
3
0
9
6
3
0
9
12fr8fr 10fr
-
B
G
D
A
-
3
6
9 0
3fr
6
5fr
0
0 3
9
12fr8fr 10fr
-
-
G
D
A
E
3
6
9 0
69 3
In Fig.2.3.1.4, we show a diminished chord (Adim7) and its inversions played as 4-note chords on adjacent strings.
• The highlighted boxes correspond to Adim7 chords constructed in Fig.2.3.1.2.
• Notice the repetitive pattern every three frets.
• Based on the insight from Fig.2.3.1.3, in addition to Adim7, the same pattern also fits Cdim7, D#dim7 and
F#dim7.
Exercise 2.3.1.1: A neat trick is to transition through multiple inversions of a dim7 chord while moving in the same
pitch direction.
• If overused, this can get a bit too schmaltzy, however…
6
9
9
0
6
3
0
9
3
6
0
3
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
3
6
0
3
6
Minor
{ 0 , 3 , 7 }
Diminished
{ 0 , 3 , 6 }
0
3
6
10
0
3
6
10
m7b5
{ 0 , 3 , 6 , 10 }
NOTE: “Half-diminished seventh”
typically referred to as “minor
seventh flat five” (“m7b5”).
2.3.2 Half-Diminished Seventh Chords
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:Integer
Notation:
Fig.2.3.2.1: Structure of half-diminished seventh (m7b5) chords.
© 2018 Ivan Radivojevic
Start from the Am7 ({ 0 , 3 , 7 , 10 }) shown below and lower
the fifth/P5 (i.e., move “7” to “6”). The new chord is Am7b5 ({
0 , 3, 6 , 10 }) shown in Fig.2.3.2.2(b). Notice that all four
m7b5 notes are present on the middle four strings.
Fig.2.3.2.2: Examples of m7b5 chords.
Am7
7
0
0
3
0
5fr
Am7b5
5fr
Am7b5
(b)
(c)
Am7b5
6
0
0
3
0
5fr
0
3
6
5fr
10
3
0
6
(a)
4-note Am7b5 pattern on the
low strings extrapolated from
Fig.2.3.2.2(b).
4-note Am7b5 pattern on the
high strings extrapolated from
Fig.2.3.2.2(b). Common and
easy to play.
10 10
10
Fig.2.3.2.3: Examples of m7b5 chords (cont.)
For reference, we also show an extended pattern over all six
strings. Notice a 0-6-0-6 “tritone” pattern on the four low
strings.
Am7b5
5fr
0
6
0
3
10
6
Am7
12fr
7
0
7
3
10
7
We can also start from a “barre” Am7 chord (12/0fr) and
lower the fifth/P5 (“7”) on the D string to get a Am7b5 on
the middle four strings. This non-inverted form (root/ “0”
as the bass note) is easy to play and very common. Notice
that this pattern can also be derived by moving all chord
notes from Fig.2.3.2.2(a) down by one string.
As expected, m7b5 shapes (Fig.2.3.2.2) are very similar to dim7 shapes (Fig.2.3.1.2) as the two chord types differ in
only one note (M6/“9” vs. m7/“10”).
See also “Chord Aliasing” and “Chord Voicing” sections for more ways to construct and play half-diminished
seventh chords.
Cdim
0
3
10
6
Am7b5
12fr
2.3.2 Half-Diminished Seventh Chords (Cont.)
Example 2.3.2.1: The Beatles’ 1967 double A-sided single (“Penny Lane” and “Strawberry Fields Forever”) is a great
example of their melody-making mastery and it includes several effective uses of diminished chords:
• m7b5: “… people that come and…” (“Penny Lane”, 1967).
• dim7: “meanwhile” in “… and meanwhile back...” (“Penny Lane”, 1967).
• dim7: “… nothing is real…” (“Strawberry Fields Forever”, 1967).
Example 2.3.2.2: The opening chord of Sting’s “Moon over Bourbon Street” (1985) is F#m7b5.
Example 2.3.2.3: We can also remember the m7b5 chord type as the seventh chord from the following progression
approximating the seven modes of the C major scale[1]:
CM7 — Dm7 — Em7 — FM7 — G7 — Am7 — Bm7b5 — CM7
Example 2.3.2.4: The m7b5 chord type is very common in jazz—e.g., in the ii-V-i progression discussed in the
Section 2.8 (“Altered Chords”).
______________________________________________________________________________________
[1] See “Appendix: Common Scales”.
© 2018 Ivan Radivojevic
2.4 Augmented Chords
0
4
7
0
4
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
4
8
0
4
8
Major
{ 0 , 4 , 7 }
Augmented
{ 0 , 4 , 8 }
Common ways to play.
Start from an A chord
({ 0 , 4 , 7 }) and move
“7” (P5, lightly shaded)
to “8” (A5).
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
0
3
8
0
3
8
???
{ 0 , 3 , 8 }
NOTE: Why is { 0 , 3 , 8 } not
considered a triad?
Technically, a triad should have its
notes “stacked in thirds” (i.e., separated
by 3 or 4 semi-tones, not 5 as shown
here).
Assume that { 0 , 3 , 8 } corresponds to
Emadd#5 chord consisting of { E , G ,
C }. The chords is an inversion of the C
chord { C, E , G }—i.e., { 0 , 3 , 8 } is
an inversion of a major triad.
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Integer
Notation:Intervals:
8
4
0
8
0
4
Augmented Triad shown
spread across all 6 strings.
Notice that all three triad
notes ({ 0 , 4, 8 }) are
present on any three
adjacent strings.
Fig.2.4.1: Structure of augmented (aug) chords.
Fig.2.4.2: Examples of augmented (aug) chords. Fig.2.4.3: Inversion of augmented (aug) chords.
5fr
A+
A+
5fr
0
8
4
0
8
4
0
8
7
7
0
© 2018 Ivan Radivojevic
5fr
7
An augmented/+ (aug) chord repeats as an inversion every 4 frets:
{ 0 , 4 , 8 } + { 4 , 4 , 4 } = { 4 , 8 , 12 } = { 4 , 8 , 0 }
As shown in Fig.2.4.3, C#+ includes the same notes are A+, so we can also annotate it as A+/C# (i.e., A+ inversion
with the bass note of C#); F+/C# can also be used.
• Effectively, there are only four distinct aug chords (the other 8 are mere inversion of those four).
5frA+
0
8
4
0
0
C#+
0
8
4
0
0
9fr
2.4 Augmented Chords (Cont.)
© 2018 Ivan Radivojevic
3fr 5fr
0
8
8
4
4
0
8
12fr8fr 10frStrings:
E
B
G
D
-
-
4
3fr 5fr
0
8
4
4
0
8
12fr8fr 10fr
-
B
G
D
A
-
4 0
In Fig.2.4.4, we show an augmented chord (A+) and its inversions played as 4-note chords on adjacent strings.
• The highlighted boxes correspond to A+ chords constructed in Fig.2.4.2.
• Notice the repetitive pattern every four frets.
• Based on the insight from Fig.2.4.3, in addition to A+, the same pattern also fits C#+ and F+.
Exercise 2.4.1: Similar to dim7 chords, a neat trick is to transition through multiple inversions of an aug chord
while moving in the same pitch direction.
• And again, if overused…
Example 2.4.1:
• A few uses made famous by the Beatles: the bridge-ending chord of “… and keep you satisfied…” in “From Me to
You” (1963) and the opening chord of “Oh! Darling” (1969).
• “You Are the Sunshine of My Life” (Stevie Wonder, 1973): the latter of the two opening chords is augmented.
• A raised fifth interval (a.k.a. A5 or “#5” or “b13”) can be simply added to some existing major/minor chord: e.g.,
“James Bond” theme/sequence (1962): Em, Emadd#5, Em6, Emadd#5.
NOTE: An augmented seventh (aug7) chord has the minor 7th interval (m7/“10”) added to an augmented triad ({ 0 ,
4 , 8 }). We will discuss this and related chord types in the “Altered Chords” section (e.g., see Fig.2.8.3).
0
8
4
0
4
8
8
0
Fig.2.4.4: Augmented (aug) chord and its inversions (A+ example)
3fr 5fr
0
8 4
8
12fr8fr 10fr
-
-
G
D
A
E
4 0
08
4
8
0
4
0
4
7
0
4
7
0
3
7
0
3
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
5
7
0
5
7
0
2
7
0
2
7
Major
{ 0 , 4 , 7 }
sus4
{ 0 , 5 , 7 }
Minor
{ 0 , 3 , 7 }
sus2
{ 0 , 2 , 7 }
E Asus2
AmEsus4
A
Asus4
2.5 Suspended Chords
E
F
G
A
B
C
D
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
Integer
Notation:
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:
“Behind Blue Eyes”
(The Who, 1971)
opening chord.
Suspended (sus) chords construction is illustrated in Fig.2.5.1:
• In a sus4 chord, the third of the corresponding major triad is raised/sharpened (i.e., M3 becomes P4).
• In a sus2 chord, the third of the corresponding minor triad is lowered/flatted (i.e., m3 becomes M2).
Thus, sus chords are neither of major nor minor quality since the third (M3 or m3) is omitted—see Fig.2.5.1 and
examples in Fig.2.5.2. Notice that a sus chord notes are not “stacked in thirds” as they have adjacent notes that are
2 or 4 semi-tones apart.
0
0
7
0
0
7
0
7
2
7
0
7
7
7
0
0
7
3
7
7
0
7
7
0
0
7
4
0
7
5
0
7
4
0
7
5
Fig.2.5.1: Structure of suspended chords.
Fig.2.5.2: Examples of suspended chords.
© 2018 Ivan Radivojevic
2.5 Suspended Chords
Asus2sus4
0
4
0
7
5
2
AM7sus2
11
7
2
0
7
Fig.2.5.3: Examples of sus chord variants.
© 2018 Ivan Radivojevic
In Fig.2.5.3, we show several examples of sus chord variants. More information on the chords’ construction and
naming is provided below.
• AM7sus2: AM7 is a major triad with M7 added (i.e., { 0 , 4 , 7 , 11 }); similarly, AmM7 is { 0 , 3 , 7 , 11 }. As M2
is used instead of M3 (or m3), the shown shape is neither a major nor minor chord, but a sus2 chord. Play
AM7sus2 and compare it to related chords AmM7, AM7 and AM7sus4.
• Asus2sus4: M3 is dropped from the A major chord and both M2 and P4 are included instead. This composite
sus chord is used in “Box of Rain” (Grateful Dead, 1970) opening.
• Aadd2/Aadd9: This is not a sus chord, but an added-tone chord as the 2nd/9th interval is merely added to the
major triad. Play also the corresponding Amadd2/Amadd9 shape by moving the M3 note to m3.
Exercise 2.5.1: The shapes in Fig.2.5.4 are incremental modifications of basic C7 “barre” shapes. Verify that all
shown chords correspond to C7sus4. Play the shown shapes—they all include the same four interval notes (P1, P4,
P5 and M7), but may sound slightly different due to note re-ordering. Playing the lightly-shaded notes is optional—in
Fig.2.5.4(a), for example, either interval played on the D string is already included among the rest of the chord’s
notes. The compact shape shown in Fig.2.5.4(b) is a multi-purpose chord quite common in jazz[1]; the shape is moved
down to the four middle strings in Fig.2.5.4(e).
Aadd2/Aadd9
7
0
2
7
4
Fig.2.5.4: C7sus4 chord (examples).
3fr 3fr 8fr
(b)(a) (c)
______________________________________________________________________________________
[1] Further discussed in Example 4.2.3 in the “Quartal Harmony” appendix.
8fr
(d)
8fr
(e)
0
4
7
0
4
7
0
3
7
0
3
7
0
14
4
7
0
14
4
7
Major
{ 0 , 4 , 7 }add9
E
Minor
{ 0 , 3 , 7 }
0
4
7
10
0
4
7
10
7
0
14
4
7
10
0
14
4
7
10
0
14
3
7
0
14
3
7
0
3
7
10
0
3
7
10
7
0
14
3
7
10
0
14
3
7
10
9add9
Eadd9
E7
E9
Eadd9
2.6 Ninth Chords
Example 2.6.1: With a bit of practice, the two shown add9
chords (i.e., no m7) can also be played “barre” to great
effect. Emadd9 was used as the opening chord of “The
Continuing Story of Bungalow Bill” (The Beatles, 1968) and
“Welcome to the Machine” (Pink Floyd, 1975). Emadd9
NOTE: Only major chords are shown. For minor chord
variants, replace “4” with its corresponding “3”.
Intervals:
P1 / P8
m2 / m9
M2 / M9
m3 / m10
M3 / M10
P4 / P11
d5 / d12
P5 / P12
A5 / A12
M6 / M13
m7 / m14
M7 / M14
P1 / P8
m2 / m9
M2 / M9
m3 / m10
M3 / M10
P4 / P11
d5 / d12
P5 / P12
A5 / A12
M6 / M13
m7 / m14
M7 / M14
Integer
Notation:
0 / 12
1 / 13
2 / 14
3 / 15
4 / 16
5 / 17
6 / 18
7 / 19
8 / 20
9 / 21
10 / 22
11 / 23
0 / 12
1 / 13
2 / 14
3 / 15
4 / 16
5 / 17
6 / 18
7 / 19
8 / 20
9 / 21
10 / 22
11 / 23
E
F
G
A
B
C
D
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
4
0
7
0
0
7
7
0
0
0
0
0
7
0
0
7
0
3
7
14
7
14
4
4
0
7
4
0
7
4
0
7
14
10
14
10
E90
4
7
14
E9
4
0
14
10
10
7
E9 is constructed by adding M2/M9 to E7.
A 7th chord includes 1st, 3rd, 5th and 7th intervals (i.e., its notes are “stacked in thirds”). Similarly, a 9th chord is
constructed by adding the 9th interval to a 7th chord (see Fig.2.6.1)—e.g., C7 + M9 = C9.
NOTE: Notes labeled as “12” and higher do not have to be played in the higher octave—any note from the same
pitch class can be used. Forming a chord in such a fashion does not change its essential properties. In the introductory
examples below, a newly added note is the highest pitch one and we use “14” (instead of “2”) mostly for emphasis.
Fig.2.6.1: Structure of 9th
chords.
Fig.2.6.2: Construction and examples of 9th
chords.
© 2018 Ivan Radivojevic
99
This E9 sounds great, but, as shown, it is not
playable—to play its “barre” variants, a
human would need an extra finger or two.
In such cases, it is possible to mute (avoid
playing) some strings or to move individual
notes to a different octave (e.g., m7/“10”) and
perhaps also omit P5 (“7”)—see the
highlighted portable shapes.
2.6 Ninth Chords (Cont.)
E
7fr
E7
7fr In Fig.2.6.3, we start from an E7 played “barre” at 7fr and move “4”
(M3) down by an octave (from the B string to the D string); what is left
beneath is “2” (or, depending where one counts from, “14”). The
resulting chord is E9 (E7 plus M2/M9) shown in Fig.2.6.3(a). This E9
form is very common in blues and jazz. The shape can be shifted to any
key and is a must-have for every guitar player. It is somewhat tricky to
play cleanly: e.g., use the thumb for the low-E string or mute/skip it
altogether—more playing options are discussed in Fig.2.6.5.
Example 2.6.2: David Bowie’s classic “Stay” (1975) has its verse
consisting solely of the 9th chords: G9 - A9 - C9 - F9 (i.e., the shape
shown in Fig.2.6.3(a) played in four different fret positions).
The corresponding minor-type variant (Em9) is shown in Fig.2.6.3(b).
The shape is commonly played using middle four strings (although, for
extra color, it can also include lightly-shaded P5/“7” on either E string).
The shown Em9 shape and its derivatives (e.g., see Em7 shapes
discussed in Fig.2.6.4) are very common and useful.
In Fig.2.6.3(c), we show another way to arrive to the same E9 shape.
We start from E9 constructed in Fig.2.6.2, and move each note to the
next lower string. As discussed previously (Fig.1.2.4), the resulting
shape is similar to the starting one as all chord notes (dots) advance by
5 frets except for the one originating on the B string that moves up by 4
frets. By construction, the two E9 chords in Fig.2.6.3(c) include the
same notes in the same order and sound the same. In the “Chord
Aliasing” and “Chord Voicing” sections, we will present more ways to
construct and play 9th chords.
7
7
0
7
10
7
0
4
0
7
4
7
Em9
5fr
10
14
0
3
E9
6fr7
10
14
0
7
4
Fig.2.6.3: Construction and examples
of 9th
chords (cont.).
© 2018 Ivan Radivojevic
7
7
E9
4
0
14
10
E9
6fr
10
14
0
4
(a)
(b)
(c)
6fr7
10
14
0
4
no P5
6fr
10
14
0
4
no P1
6fr7
10
14
4
no P1
6fr
10
14
4
no M3
6fr7
10
14
0
7
full
Fig.2.6.5: E9 playing options.
(a) Em7
5fr
3
10
15
0
(b) Em7
10
0
3
0
5fr7
Fig.2.6.4: Minor 7th
chords revisted.
In Fig.2.6.4, we digress for a moment to derive two commonly used minor-seventh forms starting from the Em9 shape
shown in Fig.2.6.3(b). In Fig.2.6.4(a), we move the Em9's “14” (M2) to “15” (“3”/m3) and transform Em9 to the
shown Em7 chord. In Fig.2.6.4(b), we move “14” (M2) to “0” (root) to get another common “m7” form; for extra
color, we can put back “7” (P5, lightly shaded) as the highest note and have all chord notes on the four high strings.
NOTE: Certain 9th chords get tricky to play as full chords including all the constituent intervals (e.g., E9 consists of
P1, M3, P5, m7 and M9). As mentioned previously, being the most neutral constituent interval, P5 is sometimes
omitted from more complex chord shapes. Also, when playing in a band, guitar players also have an option to drop
root notes (usually supplied by a bass player). In Fig.2.6.5, we illustrate several playing options for a 9th chord (E9, in
this example). Different shapes may work better in certain contexts: e.g., when hearing multi-note chords, our ears
tend to latch to two extreme pitches: the lowest one for bass notes and the highest one for melody. (Note: The “no
M3” option is E7sus2. Playing the four low strings notes reduces the chord to E7.)
2.6 Ninth Chords (Cont.)
E7#9
6fr
E7b9
6fr
In Fig.2.6.6, several 9th chord variants are constructed by performing
minor, incremental modifications of E9 shapes discussed earlier in
this section. (For reference, two highlighted 6-note E9 chords are also
included in the figure.)
In Fig.2.6.6(a), the 9th interval is either raised (E7#9) or lowered
(E7b9). Another E7#9 shape is shown in Fig.2.6.6(b). We will return
to 7#9 and 7b9 chords in the “Altered Chords” section.
Example 2.6.3: E7#9 shown in Fig.2.6.6(a) is also known as the
“Hendrix chord” (“Purple Haze”, “Foxy Lady”, 1967). “Taxman”
(The Beatles, 1966) uses the same chord, but two frets/semi-tones
lower (D7#9).
Example 2.6.4: E7b9 shown in Fig.2.6.6(a) is used as a bridge chord
in “I Want You (She’s So Heavy)” (The Beatles, 1969).
Example 2.6.5: “Don’t Take Me Alive” (Steely Dan, 1976) opens
with a 6-note “barre” G7#9 arpeggio (like the E7#9 shown in
Fig.2.6.6(b), but moved to the 3rd fret).
Example 2.6.6: In Fig.2.6.6(b), we also show E7#9 with M3 lowered
to m3. The resulting “minor Hendrix chord” is Em7 (i.e., not
Em7#9). For a dark, heavy rendition, listen to the opening chord of
Robin Trower’s “Bridge of Sighs” (1974). Notice that the four high
notes map to the Em7 shown in Fig.2.6.4(a).
Several “jazzier” 9th chords (including examples of moving 9th chords
along the fretboard) are shown in Fig.2.6.7.
• Both EM9 and a Bossa Nova-sounding E6/9 (a.k.a. E6add9) are
colorful chords sometimes also used as EM7 substitutes in jazz
progressions. (NOTE: We show all 6 notes Fig.2.6.7(a) and
Fig.2.6.7(b), but see Fig.2.6.5 for 9th chord playing options and
simplifications.)
• Notice that the two E6/9 shapes in Fig.2.6.7(b) are very similar.
(Corollary: E6/9 and A6/9 chords differ in only one note.)
• The rootless m6/9 shape shown in Fig.2.6.7(c), has multiple
functions in jazz and we will return to it in later sections—e.g.,
see Fig.2.8.6 (“Altered Chords” section), Fig.3.1.8 (“Chord
Aliasing” section) and Fig.4.2.2(d) (“Quartal Harmony”
appendix).
0
0
0
0
10
15
0
4
10
13
0
4
Fig.2.6.6: Examples of 9th
chord variants.
© 2018 Ivan Radivojevic
E7#90
4
0
7
10
15
E6/9
5fr
9
14
0
4
7
EM9
6fr
11
14
0
4
(b)
(a)
E9
6fr7
10
14
0
7
4
(a)
EM9
10fr
14
7
4
11
0
Em70
3
0
7
10
15
(b)
7
14
9
4
10fr
E9
0
4
0
7
14
10
Fig.2.6.7: More 9th
chord variants.
7
7 0
Em6/9
5fr
9
14
0
3
7
(c)
7
14
9
3
Em6/9
(no P1)
10fr
0
0
7
E6/9
2.6 Ninth Chords (Cont.)
Db6/9
3fr
9
14
0
4
Eb9
5fr
10
14
0
4
Ebm9
4fr
10
0
D9
4fr
10
14
0
4
Db6/9
3fr
9
14
0
4
D6/9
4fr
14
0
3
14
Example 2.6.7: A famous Bossa Nova progression from “The Girl from Ipanema” (1962) is based on three 9th chord
variants previously introduced in Fig.2.6.3 and Fig.2.6.7. As shown in Fig.2.6.8, the progression can be played using
middle four strings; it is easy to play since the chord shapes are similar and compact.
Exercise 2.6.1: Play “The Girl from Ipanema” progression as shown in Fig.2.6.8, but experiment with different
options discussed in Fig.2.6.5.
Fig.2.6.8: Chord progression based on 9th
chords.
Eb9
4fr
10
14
0
4
Ebm11
4fr
10
0
14
Fig.2.6.9: Chord progression based on 9th
chords (cont.).
D9b5
4fr
10
0
14
...... 3
5 6
4 ...
4
9
Eb9
6fr
10
14
0
4
Dm9
5fr
10
0
14
Fig.2.6.10: Turnaround based on “Tritone Substitution”.
3
77
7 7
Em9
7fr
10
0
14
3
7
7
Db9
4fr
10
14
0
4
7
7
Example 2.6.9: Many popular music standards include a turnaround based on the iii-VI-ii-V-I chord structure
(e.g., Em7-A7-Dm7-G7 resolving in CM7). By doing the “Tritone Substitution” (replacing a dom7 chord like A7
with a same-type chord rooted six semitones away—e.g., Eb7), we can produce a jazzier, chromatically descending
version like the one shown in Fig.2.6.10. All intervals are shown, but a player can pick a subset of notes as depicted
in Fig.2.6.5. See also Fig.3.1.8 (“Chord Aliasing” section) for more related info.
© 2018 Ivan Radivojevic
NOTE: After Tritone Substitution, M3 and m7
notes from a starting dom7 chord are preserved in
the new chord, but the notes’ roles as intervals are
reversed.
{ 0 , 4 , 7 , 10 } + { 6 , 6 , 6 , 6 } =
{ 6 , 10 , 13 , 16 } = { 6 , 10 , 1 , 4 }
Example 2.6.8: In Fig.2.6.9, we refer to the chord progression shown in Fig.2.6.8 to illustrate effects of adding
intervals to 9th chords (to the third and the fourth chord of the original progression, in this example). The Reader
should return to this example after becoming familiar with the next two sections (“Eleventh and Thirteenth Chords”
and “Altered Chords”). For the time being, just observe how extra notes add color to the existing chords. Also, notice
that certain sequences of complex chords can be played with little change in fingering. All three chords in Fig.2.6.9
include three identical notes characteristic of 9th chords (root, m7 and M9) and it is possible to play the three shapes
by merely changing the position of the left hand’s index finger (to cover notes labeled “3” through “6”).
2.7 Eleventh and Thirteenth Chords
0
4
7
0
4
7
0
3
7
0
3
7
Major
{ 0 , 4 , 7 }
Minor
{ 0 , 3 , 7 }
0
4
7
10
0
4
7
10
7
0
14
4
7
10
0
14
4
7
10
9 11
0
14
4
17
7
10
0
14
4
17
7
10
0
14
4
17
7
21
10
0
14
4
17
7
21
10
13
0
3
7
10
0
3
7
10
7
0
14
3
7
10
0
14
3
7
10
9 11
0
14
3
17
7
10
0
14
3
17
7
10
0
14
3
17
7
21
10
0
14
3
17
7
21
10
13
A 7th chord includes 1st, 3rd, 5th and 7th intervals (i.e., its notes are “stacked in thirds”). Extended (9th, 11th and 13th)
chords are built by incrementally adding an interval to the corresponding simpler type. The 9th chords are constructed
by adding the 9th interval to 7th chords. Similarly, the 11th chords are built by adding the 11th interval to 9th chords; in
the 13th chords, the 11th interval is added to 9th chords. See Fig.2.7.1 and Fig.2.7.2.
E
E7
E9
E11
E13 E13 E13
E
F
G
A
B
C
D
E
F
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
E13 chord is constructed by adding M13/M6 (“9”) to
E11. By definition, however, a 13th chord consists of 7
notes, so some have to be dropped when played on a 6-
string guitar. A few options are shown here—the most
commonly played form adds only m7 and M6 to the
underlying triad.
EM11
Intervals:
NOTE: Only major chords shown. For minor chord
variants, replace “4” with its corresponding “3".
Integer
Notation:
0 / 12
1 / 13
2 / 14
3 / 15
4 / 16
5 / 17
6 / 18
7 / 19
8 / 20
9 / 21
10 / 22
11 / 23
0 / 12
1 / 13
2 / 14
3 / 15
4 / 16
5 / 17
6 / 18
7 / 19
8 / 20
9 / 21
10 / 22
11 / 23
P1/P8
m2/m9
M2/M9
m3/m10
M3/M10
P4/P11
d5/d12
P5/P12
A5/A12
M6/M13
m7/m14
M7/M14
P1/P8
m2/m9
M2/M9
m3/m10
M3/M10
P4/P11
d5/d12
P5/P12
A5/A12
M6/M13
m7/m14
M7/M14
0
0
7
4
7
10
0
0
7
0
7
10
0
5
7
10
0
5
7
0
5
10
0
10
0
0
10
0
7
4
14
7
4
14
4
14
11
4
14
4
9
14
4
9
7
4
9
7
Add m7 to E.
Add M9 to E7.
Add P11 to E9. Add P11 to EM9.
EM7
0
7
0
7
4Add M7 to E.11
EM9
0
7
0
7
4Add M9 to EM7.11
14
Fig.2.7.1: Structure of 11th
and 13th
chords.
Fig.2.7.2: Construction of 11th
and 13th
chords.
© 2018 Ivan Radivojevic
E9 E9sus4
Example 2.7.5: Starting from a known E9 shape,
we construct two chords that frequently get
misclassified as E11.
• E7add11: E11 without the ninth interval.
• E9sus4: E11 without the third interval. E7add11
7fr
SUMMARY: Extended chords are built by incrementally adding an extra interval to the corresponding simpler
type—e.g.: C7 => C9 => C11 => C13. Notes labeled as “12” and higher do not have to be played in the higher
octave. Forming a chord in such a fashion doesn’t change its essential properties.
Example 2.7.1:
E7 = E + m7 = (P1 + M3 + P5) + m7
E9 = E7 + M9 = (P1 + M3 + P5 + m7) + M9
E11 = E9 + P11 = (P1 + M3 + P5 + m7 + M9) + P11
7fr
7
10
14
0
7
4
7fr
7
10
14
0
7
5
10
0
4
0
5
Em9
14
0
10
5fr
3
Em11
5
7
10
0
14
5
7
10
0
14
4 3
E11 Em11
14
0
10
5fr
3
17
Example 2.7.2: Below, we derive Em11 from E11 by moving M3 (“4”) to m3 (“3”). We also derive Em11 from
Em9 by adding P11 (“17”/“5”). Notice that the second form (right) has its notes all “in order” (P1, m3, m7, M9,
P11) contributing to the shape’s distinctive sound and making it very effective either strummed or played
arpeggio-style.
P1
m7m3P5
M9
P11P1
m7m3P5
M9
P11x
m3m7M9
P11
P1x
m3m7M9
P11
P1
Em13
0
5
10
3
9
7fr
Em13
0
7
10
3
97fr
Em
0
7
0
3
7
7frExample 2.7.3: We show two “m13” chords based on
the open-Am shape. As mentioned previously, not all
seven notes can be included in such chords; at
minimum, the highest (13th) interval is added to a
minor seventh chord. As always, for the corresponding
major 13th chord, m3 (“3”) is raised to M3 (“4”).
E13
7fr
10
14
0
4
E9
7fr7
10
14
0
4
E13
7fr
10
0
4
9 9
4Example 2.7.4: Starting from a known E9 shape,
we show E13 chords variants often heard in funk/
disco.
E11P1
m7M3P5
M9
P11P1
m7M3P5
M9
P11 5
7
10
0
14
4
2.7 Eleventh and Thirteenth Chords (Cont.)
© 2018 Ivan Radivojevic
2.8 Altered Chords
0
4
7
0
4
7
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
0
4
6
0
4
6
Major Triad
{ 0 , 4 , 7 } { 0 , 4 , 6 }
0
4
6
10
0
4
6
10
dom7b5
{ 0 , 4 , 6 , 10 }Integer
Notation:
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
Intervals:
NOTE: Typically referred to as
“dominant seventh flat five”
(dom7b5).
8fr
We have already discussed diminished, half-diminished and augmented chords that include certain forms of the
altered (raised or lowered) fifth interval. In this section, we present several other chords types including altered
intervals. For example, a class of altered dominant chords starts from a dominant seventh chord (dom7) and alters
(raises or lowers) 2nd/9th and/or 5th intervals. We will provide examples of altered dominant chords in the context of
common jazz and popular music progressions.
8fr
Dominant seventh flat five (dom7b5) chords are introduced
in Fig.2.8.1. We observe that dom7b5 chords repeat as
inversions every 6 frets:
{ 0 , 4 , 6 , 10 } + { 6 , 6 , 6 , 6 } = { 6 , 10 , 12, 16 } =
{ 6 , 10 , 0 , 4 }
In Fig.2.8.2, we demonstrate the above result by showing
common easy-to-play C7b5 forms on four adjacent strings.
An augmented seventh (aug7) chord has the minor 7th
interval added to an augmented triad. In Fig.2.8.3, augmented
seventh C7#5 chords are derived from “barre” C7 forms (at
3fr and 8fr) by raising the fifth (i.e., move “7” to “8”). The
shown non-inverted form (C7#5) is usually played as a 4-
note chord (the middle four strings or the top three strings
plus the A string root). See also Example 3.2.4.1 (“Chord
Voicing: Extensions and Examples” section) for more ways
to construct and play aug7 chords.
0
8
4
10
0
7
4
10
0
7
0
8fr
NOTE: Technically, { 0 , 4 , 6 } is not
considered a triad since its intervals
are not “stacked in thirds”: M3 and d5
are only 2 semi-tones apart.
Fig.2.8.1: Structure of altered chords (dom7b5 example).
Fig.2.8.3: Examples of augmented seventh chords.
© 2018 Ivan Radivojevic
3fr
2fr
6
8fr
4
0
10
0
10
6
4
2fr 8fr
0
10
6
4
6
4
0
10
2fr 8fr
6
0
4
10
0
6
10
4
C7#5/BbC7C7#5C7
Fig.2.8.2: Dominant seventh flat five chord (C7b5).
3fr
4
10
7
7
0
3fr
4
10
8
8
0
8fr
C7#5/G#
3fr
4
0
8
10
Strings:
-
-
G
D
A
E
-
B
G
D
A
-
E
B
G
D
-
-
2.8 Altered Chords (Cont.)
Example 2.8.1: The chords shown in Fig.2.8.4(a) can be
classified as Altered Dominant chords. We start from a
dominant seventh chord (e.g., C7) and alter (raise or lower)
the 2nd/9th interval. In Fig.2.8.4(b), the 5th is altered as well. In
Fig.2.8.4(c), we also show two commonly played shapes
derived from a C “barre” chord at 8fr. We do not show all
possible alterations, but those in Fig.2.8.4 are easy to play and
effective as dominant chords returning to the minor key.
Exercise 2.8.1: Play altered C chords shown in Fig.2.8.4
followed by Fm. Do the same with C7b5 shapes from
Fig.2.8.2 and C7#5 from Fig.2.8.3.
Exercise 2.8.2: In this exercise, we explore different ways to
play the ii-V-i progression[1]
.
• In Fig.2.8.5(a), we show a common ii-V-i form:
Em7b5—A7—Dm7.
• Frequently, however, the progression employs an altered
chord as the V chord. Playing a basic A7 certainly works
fine, but an altered chord could be a more colorful choice
that creates extra tension resolved by returning to the i
chord—e.g., Em7b5—A7#5b9—Dm6 sequence shown in
Fig.2.8.5(b).
• Play both “(a)” and “(b)” and observe the differences.
• Another chord selection is shown in Fig.2.8.5(c), with
A7b5/Eb as the V and DmM7 as the i. (Since a dom7b5
chord repeats as an inversion every 6 semitones, A7b5/
Eb and Eb7b5 include the same notes.) Notice how the
mM7 chord type leaves such descending sequence
(Em7b5—Eb7b5—DmM7) in somewhat of a tense and
suspended state.
• The more notes get included in a chord, the less likely it is
there will be many playable options for the chord. In the
“Chords Voicing” section, we will describe ways to
reduce more complex chords to easy-to-play 4-note forms
(including chord inversions). In Fig.2.8.6, we show an
instance of ii-V-i employing 4-note rootless chords.
Notice that the altered V chord (A7b9), with its root
dropped, has a dim7 shape (see Fig.2.3.1.4) and differs
from the ii chord in only one note. The shown Dm6/9
was introduced in Fig.2.6.7.
A7#5b9(V)
8
13
0
4
10
5fr
Em7b5(ii)
6fr
Dm6(i)
9fr
0
9
0
7
3
© 2018 Ivan Radivojevic
6fr
4
10
6
0
A7b5/Eb(V)
5fr
11
3
0
7
DmM7(i)
Fig.2.8.5: ii-V-i progression (examples).
Em7b5(ii)
6fr
Dm7(i)
5fr5fr
7
0
0
4
10
7
A7(V)
7
0
7
3
10
7(a)
(b)
(c)
C7#9
2fr
10
15
0
4
C7b9
10
0
2fr
C7#5#9
2fr
10
0
4
20
15
C7b5b9
2fr
10
0
13
4
(a)
(b)
(c)
Fig.2.8.4: Altered dominant chords (examples).
Fig.2.8.6: ii-V-i with rootless chords.
Em7b5(ii)
6fr
18
13
4
______________________________________________________________________________________
[1] Uppercase Roman numerals indicate major chords; lowercase Roman
numerals are used for minor-type chords. The ii-V-i progression
includes chords of the same type as the second, the fifth and the first chord
of the Harmonic Minor scale—e.g., in the key of C, we could play:
Dm7b5—G7—CmM7 (see “Appendix: Common Scales”). The progression
in Fig.2.8.5(c) is of the described type. The two other, more commonly
played forms shown in Fig.2.8.5(a) and Fig.2.8.5(b) replace the mM7 i
chord with m7/m6-type chords.
6fr
A7b9 (no P1)
8fr
Em7b5
6fr
0
6
10
3
7
1
4
10
9
14
3
7
Dm6/9 (no P1)
0
6
10
3
0
6
10
3
0
6
10
3
C7#9
7fr
C7#5b9
0
10
13
8
4
7fr
0
0
7
15
10
4
2.8 Altered Chords (Cont.)
A7#5b9(VI)
8
13
0
4
10
5fr
CM7(I)
711
4
0
7
73fr
G13b9(V)
9
13
0
4
10
3fr
C#dim7(vi)
6
3
0
6
3fr
9
C9
2fr7
10
14
0
4
C9b5
2fr
10
14
0
4
6
C9b5
7fr
0
10
14
4
6
Example 2.8.3: There are many altered chords and more ways to
play them, so we will let the Reader discover them as needed and
if interested. We highlight just one more chord type present in
many standards of the old. In Fig.2.8.9, we show a form derived
from a 9th
chord by lowering the fifth (C9b5) and also move the
shape from the top to the bottom strings.
Exercise 2.8.4: Watch Ginger Rogers and Fred Astaire dance to “Cheek to Cheek” (“Top Hat” movie, 1935). This
classic song is based on the I-vi-ii-V progression—see if you can incorporate some of the ideas suggested
earlier. Also, look for Bb9b5 chord (hint: the opening verse has two instances of the chord).
Dm11(ii)
14
0
10
3fr
3
17
© 2018 Ivan Radivojevic
______________________________________________________________________________________
[1] Voice leading is an advanced topic related to transitions between chords. In classical music, there are rather strict rules favoring relatively
small, incremental differences between successive chords. The same principles are applicable to many jazz forms, although perhaps not
enforced as strictly—e.g., moving all voices of the chord in the same direction and by the same amount can sound jazzy in certain cases
(while it would typically be avoided in classical music as too predictable). Only briefly, voice leading considerations are re-visited in the
“Chord Aliasing” section (Exercise 3.1.3 and Exercise 3.1.5) and the “Chord Voicing” section (Exercise 3.2.4.3 and Exercise 3.2.4.4).
Advanced students are advised to study the topic elsewhere in a systematic fashion and greater depth.
[2] Uppercase Roman numerals indicate major chords; lowercase Roman numerals are used for minor-type chords. The I-vi-ii-V
progression includes chords of the same type as the first, the sixth, the second and the fifth chord of the Major scale—e.g., in the key of C, we
could play: CM7—Am7—Dm7—G7 (see “Appendix: Common Scales”). As shown in Exercise 2.8.3, the progression’s vi chord is sometimes
played as major (i.e., “VI” instead of “vi”).
A
5fr
7
0
0
4
0
7
A13b9
9
13
0
4
10
5fr
A13b9 (no P1)
10fr
10
13
4
9
Fig.2.8.7: Altered dominant chords (examples).
Exercise 2.8.3: One of numerous ways to play the I-vi-ii-V
progression[2] (e.g., CM7—Am7—Dm7—G7) is:
CM7—A7#5b9—Dm11—G13b9
• Play the progression as shown in Fig.2.8.8.
• Try C#dim7 as the vi chord—notice a chromatic C—C#—D
bass line and similarities between the chord shapes.
• Similar to Fig.2.8.6, verify that the shown C#dim7 can be
re-annotated as a rootless A7b9.
Fig.2.8.8: I-vi-ii-V progression (example).
Example 2.8.2: Another common altered dominant chord adds a flatted 9th interval to a 13th chord (having both M6
and m7 present)—see A13b9 chord and its shrunk, rootless version (no P1/“0”) in Fig.2.8.7.
NOTE: Exercise 2.8.2 illustrates two contrasting approaches to playing chords progressions. The progression in
Fig.2.8.5(b) sounds dramatic, but the three chords are all over the fretboard including using different subsets of
strings to play individual chords’ notes. The progressions in Fig.2.8.5(c) and Fig.2.8.6 keep successive chords in a
closer proximity: they are played using the same subset of strings and tend to include one or more common notes
played in the same position. As such, the latter approach leads to more economic fingering and smooth, connected
transitions between chords[1].
Fig.2.8.9: Altered chords (examples).
2.8 Altered Chords (Cont.)
© 2018 Ivan Radivojevic
Fig.2.8.10: Circle-of-fifths progression (example).
2fr
0
2
4
7
9
11
2fr
0
9
2
4
6
Am7add11
3
0
10
3fr
3
10
2
0
10
3fr5
5
D9sus4 GM13 C(6/9)b5
5fr
0
10
2
3
5
5fr
0
10
1
4
7
F#m7b5
3
0
10
1fr
0
10
1fr6
6
B7b9b5 Em11 E7b9
1
4
Exercise 2.8.5: Consider an instance of the “circle-of-fifths” progression consisting of the following chords[1]:
Am7 — D7 — GM7 — CM7 — F#m7b5 — B7 — Em7 [ — E7 (optional, add to return to Am7) ]
As an exercise, in Fig.2.8.10, we show a jazzier version of the progression using certain more complex chord types
discussed in earlier sections (e.g., 9th, 11th, 13th, altered). The Reader should verify the chords are properly labelled
(based on the included intervals) and play them as shown, but also experiment with other ways to play the
progression. For the sake of this example, the chosen chords are all played in a similar fashion[2] and some of them
are very colorful as they include 5 and even 6 different intervals. In a later section on “Chord Voicing”, we will
present a systematic way to construct 4-note chords that are almost as colorful, but typically easier to play and to
move around the fretboard.
______________________________________________________________________________________
[1] See also Exercise 4.1.2.1 (“Appendix: Common Scales”).
[2] In particular, notice the pairs of adjacent chords have similar shapes and share two or more common notes: [Am7add11, D9sus4],
[GM13, C(6/9)b5], [F#m7b5, B7b9b5] and [Em11, E7b9].
2.9 Open Chords Revisited
C CM7 C7
D DM7 D7
Dm DmM7 Dm7
In addition to “open” E and A chords studied so far, the “open” chords shown in Fig.2.9.1 are also commonly used:
• Fig.2.9.1(a): “Open” C shapes.
• Fig.2.9.1(b): “Open” D shapes.
• Fig.2.9.1(c): “Open” G shapes
• Fig.2.9.1(d): “Open” B shapes.
Assuming the Reader is already familiar with C, D, Dm and G chords (highlighted in Fig.2.9.1), all other shown chords
can be constructed using the rules described in earlier sections. The knowledge of B7 is not essential. The Reader
should be able to recognize the shown “B-shapes” from earlier examples and we will also see that B7 itself is just a
boundary case of a C-shape discussed in Fig.2.9.3(b).
Dm7b5
D+
C6 C+
D6
Dm6
Cadd9 C9
4
0
0
4
0
7
4
7
4
11
7
4 4 4
4
7
4
7
4
0
4
0
0
10
4
0
0
9
4
0
0
8
4
14
0
10
4
0
14
0
7
0
7
0
7
9
0
7
0
0
9
0
7
0
7
0
7
0
7
4
11
7
4
10
7
4
7
4
0
8
10
6
3
7
3
10
7
3
11
7
3
0
7
CM9
7
0
CM9Cadd9add#11
18
0
4
14
Fig.2.9.1: Examples of “open” C, D, G and B chords (continues next page).
© 2018 Ivan Radivojevic
7
7
4
14
0
11
C Cm Cm CmM7 Csus4
4
0
0
7
11
7 7
7
3
0
3
7
0
3
0
0
5
0
0
57
37 7
11
2
44
7
(a)
(b)
Dsus2 Dsus4 D7sus4 DM7b5D7#5
0
7
0
7
0
7
0
7
4
0 0
5
0
7
5
10
7
10
8
4
11
6
2
3
2.9 Open Chords Revisited (Cont.)
G GM7 G7
B7
Exercise 2.9.1: In Fig.2.1.4, we showed that “open” A and “open” E shapes merely correspond to playing the same
intervals in the same order, but using two different sets of adjacent strings. Repeat the exercise by moving the “open”
C shape down by one string to get the G-chord shape. Also, compare the ordering of constituent intervals in A and C
chords.
In practice, “open” chords are not only typically easier to play, but it is also possible to play quite a bit of music using
them. For example, the C major scale[1] includes the chords listed below—notice that all 5 basic “open” shapes (C, D,
E, G and A) are included.
C — Dm — Em — F — G — Am — Bdim
G+
B11 Bm7 Bm11
0
4
0
7
4
0
7
4
0
7
0
0
0
4
11
0
4
10
0
4
0
0
4
8
50
3 3
5
4
7
0
10
4
14
0
10
7
0
10
14
0
10
B7add11#9
4
0
10
155
G6
4
0
7
9
0
4
© 2018 Ivan Radivojevic
Gsus2
2
7
0
0
7
G6sus4
0
9
0
0
5
G9
4
7
10
0
2
Gadd9
2
4
0
0
4
G7
10
0
0
0
4
4
7
Gm7
7
Gsus4
0
5
0
0
7
Gm
0
7
G
7
0
0
0
4
G+
8
0
0
0
4
4
7
(c)
(d)
Fig.2.9.1: Examples of “open” C, D, G and B chords (continued from previous page).
7
0
0
3
7
0
3
3
7
2
______________________________________________________________________________________
[1] See “Appendix: Common Scales”.
“Open” C-chord shape can be played as a “barre”
chord—see Fig.2.9.2. Very common and very
useful!
G7
8fr
“Open” C-chord shapes can be moved to any fret position—
e.g., the “G” chords shown in Fig.2.9.3(a). Those portable
shapes use the middle four strings with the low/high E strings
muted. In certain common chord, open strings can be included
to add extra color (e.g., D9, Fig.2.9.3(b)) or for emphasis (E7,
the same figure).
Notice that the shown and very common E7 includes only
three intervals: P1, M3 and m7 (i.e., P5 is omitted). In
Fig.2.9.3(b), we also show an unplayable shape labelled “E7
(top4/bot4)”. This chord includes all four notes and it is
possible to play more colorful, full (albeit inverted) E7 chords
on the top four strings (E7/G#) or bottom four strings (E7/
B). Notice that the “open” B7 shape (Fig.2.9.1) is merely a
boundary case of this “top4/bot4” shape. See also the
“Chord Voicing” section for more ways to play dominant-
seventh chords.
G6
8fr
G+
8fr
Similarly, the “open” Dm shape can be moved
along the fretboard (see Fig.2.9.5).
D9
3fr
E7
5fr
4
0
0
10
4
0
0
9
4
0
0
8
4
0
0
10
2
0
4
0
0
10
0
0
FM75fr
4
0
4
7
11
F5fr
0
4
0
4
7
Fm5fr
3
0
7
0
F3fr
0
4
7
F5fr
0
4
0
4
7
0
We transform the “open” C to
the “open” D major shape by
moving the root note (“0”)
from the A string to D (no
change on G/B/E strings)—see
Fig.2.9.4. Thus, we can
employ known “open” D
shapes like the shown F7 and
FM7 chords.
F73fr
10
4
7
0
7
Fm3fr
0
3
7
0
Dm1fr
0
3
7
2.9 Open Chords Revisited (Cont.)
FM73fr
0
4
11
7
Fig.2.9.2: Portable shapes based on “open” C chord.
Fig.2.9.4: Portable shapes based on “open” D chord.
Fig.2.9.5: Portable shapes based on “open” D chord (cont.).
C5fr
4
0
0
Fig.2.9.6: Portable G shape.
4
7
A portable shape based on the “open” G is shown in
Fig.2.9.6. Notice how the shape connects two common
“barre” chord forms of the same major chord. 5fr
7
0
4
7
40
7
7 0
0
4
0
7
C C
© 2018 Ivan Radivojevic
Fig.2.9.3: Examples of chords based on “open” C chord.
E7 (top4/bot4)
5fr
4
0
0
7
10
7
(a)
(b)
In the remainder of this section, we will explore making shapes from Fig.2.9.1 portable.
Fm73fr
10
3
7
0
3.1 Chord Aliasing
A chord is a combination of three or more notes[1] played together. Chord types are described based on their
constituent intervals as the relationships among the notes is what defines a particular chord’s type. Reordering of a
chord’s notes does not change its type, but such different variants of the same chord can have a very distinct sound.
This adds variety to playing and can also lead to more economic fingering when playing chord progressions.
We will refer to two chords including the same notes as aliases. In the following example (“Triad Inversions”), we
discuss major and minor triads having their notes reordered in a particular fashion; chords including more than three
notes will be discussed after that. We will also present several cases where a reduced form of some complex chord
maps to a simpler, common chord type: e.g., dropping the root note of a 5-note Am9 results in a 4-note CM7 chord.
Example 3.1.1: Triad Inversions. A triad consist of the 1st, 3rd and 5th intervals. A major triad includes P1, M3 and
P5 ({ 0 , 4 , 7} in the Integer Notation), while a minor triad consists of P1, m3 and P5 (i.e., { 0 , 3 , 7 }). A triad in its
“root” position has its intervals ordered as “1-3-5”, meaning the root as the lowest pitch (“bass”) note, the 5th as the
highest, and the 3rd in between. The first inversion of a triad rotates the notes by shifting the third to the bass position
and has the notes ordered as 3-5-1. The second inversion does another shift/rotation to stack intervals as 5-1-3;
performing another inversion would result in the original 1-3-5 triad.
In Fig.3.1.1(a), the A major triad patterns are shown as alternating black and shaded dots. Each set of dots of the same
color includes only the triad notes ({ 0 , 4 , 7 }) and spans all 6 strings vertically. The Reader should observe that the
patterns outline the basic chords shapes (those based on “open” A, G, E, D and C chords). Any three notes on three
adjacent strings form triads in different inversions—for example, going from the low-E to the high-E string, the
leftmost set of black dots moves across the following overlapping triplets: { 0 , 4 , 7 }, { 4 , 7 , 0 }, {7 , 0 , 4 } and
back to { 0 , 4 , 7 }. The same thing happens on each set of same-colored dots. Moreover, we can pick any three
adjacent strings and the same pattern occurs as we move from left to right—e.g., on the three high strings, the first set
of black dotes is { 0 , 4 , 7 }, followed by shaded { 4 , 7 , 0 }, moving to { 7 , 0 , 4 } (black dots) and so on.
By moving M3 dots (“4”) to m3 dots (“3”), in Fig.3.1.1(b), we get similar patterns corresponding to A minor triads.
© 2018 Ivan Radivojevic
2fr 5fr 7fr 12fr
Strings:
E
B
G
D
A
E
0
4
0
7
0
0 4
7
4
0
0
7
4
7
7
7
4
4
E
B
G
D
A
E
0
3
0
7
0
0 3
7
3
0
0
7
3
7
7
7
3
3
7
0
4
7
7
0
3
7
3
A-shape G-shape E-shapeD-shape
C-shape
A-shape
Fig.3.1.1: Triad patterns for: (a) A major, and (b) A minor.
(a)
(b)
______________________________________________________________________________________
[1] More precisely, we are talking about “pitch classes” (see the “Integer Notation” section of the introduction). For example, when we say
that the C chord includes notes C, E and G, we are really referring to the tree pitch classes.
E
B
G
D
A
E
E
B
G
D
A
E
E
B
G
D
A
E
E
B
G
D
A
E
E
B
G
D
A
E
E
B
G
D
A
E
3.1 Chord Aliasing
Exercise 3.1.1: Play groups of triad notes shown in Fig.3.1.1 in both vertical and horizontal directions. Also, repeat
the exercise in several different keys (e.g., E and C)—this is a great way to improve fretboard awareness.
Exercise 3.1.2: Based on the patterns from Fig.3.1.1, explore playing major/minor chords by using groups of four
notes on four adjacent strings. It is OK to mix black and shaded dots as long as all three triad notes get included.
In Fig.3.1.2, we show triadic patterns for major, minor, diminished and augmented D-chords. The patterns for D and
Dm are merely shifted versions of those shown in Fig.3.1.1.
• The Daug pattern can be derived from the D pattern by moving “7” in Fig.3.1.2(b) to “8” in Fig.3.1.2(a).
• Similarly, the Ddim pattern can be derived from the Dm pattern by moving “7” in Fig.3.1.2(c) to “6” in
Fig.3.1.2(d).
© 2018 Ivan Radivojevic
0
4
0
7
0
04
7
4
0
0
7
4
7
7
7
4
4
0
3
0
7
0
03
7
3
0
0
7
3
7
7
7
3
3
Fig.3.1.2: Triad patterns for: (a) Daug, (b) D, (c) Dm, and (d) Ddim.
(b)
(c)
0
3
0
6
0
03
6
3
0
0
6
3
6
6
6
3
3
(d)
2fr 5fr 7fr 12fr10fr2fr 5fr 7fr 12fr10fr
Strings:
E
B
G
D
A
E
Strings:
E
B
G
D
A
E
0
4
0
8
0
04
8
4
0
0
8
4
8
8
8
4
4
(a)
2fr 5fr 7fr 12fr10fr2fr 5fr 7fr 12fr10fr
2fr 5fr 7fr 12fr10fr2fr 5fr 7fr 12fr10fr
3.1 Chord Aliasing (Cont.)
EF
G
A
B
C
D
EF
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
EF
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
F
G
0
1
2
3
4
5
6
7
8
9
10
11
Example 3.1.2: Esus4 and Asus2 include the same notes and are inversions of each other. More formally, Asus2
is the first inversion of Esus4; Esus4 is the second inversion of Asus2.
Example 3.1.3: G6 is the first inversion of Em7. Similarly, Em7 is the third inversion of G6. We also show the two
chords with re-numbered notes.
Property 3.1.1: As demonstrated in earlier sections:
• A diminished seventh (dim7) chord ({ 0 , 3 , 6 , 9 } in Integer Notation) repeats as an inversion every 3 frets—
see Section 2.3.1.
• An augmented/+ chord ({ 0 , 4 , 8 }) repeats as an inversion every 4 frets—see Section 2.4.
• A dominant seventh flat five” (dom7b5) chord ({ 0 , 4 , 6 , 10 }) repeats as an inversion every 6 frets—see
Section 2.8.
EF
G
A
B
C
D
EF
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
G
A
B
C
D
E
F
G
A
B
C
D
E
F
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
Esus4 Asus2
Example 3.1.2:
0
7
0
7
0
5
7
2
7
0
7
0
There are many other examples where ambiguities arise between different chords, either because they are mutual
inversions or because some notes may get omitted (e.g., when playing in a band with a bass player).
Em7 G60
0
7
0
10
7
4
9
0
4
0
3
G6/E Em7/G9
9
4
9
7
10
7
0
3
7
3
0
Esus4 Asus2 Em7 G6
© 2018 Ivan Radivojevic
Example 3.1.3:
For chords constructed by “stacking thirds”, we can observe the following:
• A 4-note 7th chord includes its root and a triad rooted in the starting chord’s 3rd interval.
Example 3.1.4: We illustrate the preceding observation using the following examples. To distinguish them from
chords, all root notes are italicized. Together with the Integer Notation-based numbering of individual notes, we also
identify the corresponding root note (P1).
• Em7b5 = { 0 , 3 , 6 , 10 }(P1=E) = E + { 3 , 6 , 10 }(P1=E) = E + { 0 , 3 , 7 }(P1=G ) = E + Gm
• Em7 = { 0 , 3 , 7 , 10 }(P1=E) = E + { 3 , 7 , 10 }(P1=E) = E + { 0 , 4 , 7 }(P1=G ) = E + G
• EmM7 = { 0 , 3 , 7 , 11 }(P1=E) = E + { 3 , 7 , 11 }(P1=E) = E + { 0 , 4 , 8 }(P1=G ) = E + G+
• EM7 = { 0 , 4 , 7 , 11 }(P1=E) = E + { 4 , 7 , 11 }(P1=E) = E + { 0 , 3 , 7 }(P1=G#) = E + G#m
• E7 = { 0 , 4 , 7 , 10 }(P1=E) = E + { 4 , 7 , 10 }(P1=E) = E + { 0 , 3 , 6 }(P1=G#) = E + G#dim
3.1 Chord Aliasing (Cont.)
Property 3.1.2: Assume a note X and a note Y that is four semitones higher than X; also, a note Z that is three
semitones higher than the note Y. The following properties hold:
• Ym7 = Z6 // See Example 3.1.3.
• Ym7b5 = Zm6 // See Example 3.1.6.
• X9 = X + Ym7b5 // i.e., a rootless X9 includes the same four notes as Ym7b5—see Example 3.1.6
• Ym9 = Y + ZM7 // i.e., a rootless Ym9 includes the same four notes as ZM7—see Example 3.1.7.
• XM9 = X + Ym7 // i.e., a rootless XM9 includes the same four notes as Ym7—see Example 3.1.8.
© 2018 Ivan Radivojevic
Similarly, for chords constructed by “stacking thirds”, we can observe the following:
• A 5-note 9th chord includes its root and a 4-note seventh chord rooted in the starting chord’s 3rd interval.
Example 3.1.5: We illustrate the preceding observation using the following examples.
• Em9 = { 0 , 3 , 7 , 10 , 14 }(P1=E) = E + { 3 , 7 , 10 , 14 }(P1=E) = E + { 0 , 4 , 7 , 11 }(P1=G ) = E + GM7
• EmM9 = { 0 , 3 , 7 , 11 , 14 }(P1=E) = E + { 3 , 7 , 11 , 14 }(P1=E) = E + { 0 , 4 , 8 , 11 }(P1=G ) = E + GM7#5
• EM9 = { 0 , 4 , 7 , 11 , 14 }(P1=E) = E + { 4 , 7 , 11 , 14 }(P1=E) = E + { 0 , 3 , 7 , 10 }(P1=G#) = E + G#m7
• E9 = { 0 , 4 , 7 , 10 , 14 }(P1=E) = E + { 4 , 7 , 10 , 14 }(P1=E) = E + { 0 , 3 , 6 , 10 }(P1=G#) = E + G#m7b5
Next, we formalize earlier observations and provide additional examples.
C9
7fr
Em7b5
Em7b5
7fr
Example 3.1.6: Shown in Fig.3.1.3(a) are C9 and Em7b5 chords played in “2fr” position. If low-E/A strings are
muted, the chords consist of identical notes. This is also true for the shown Gm6 and the altered F#7#5b9 chord.
Notice that Em7b5 and Gm6 chords are mutual inversions consisting of the same notes. Similarly, in Fig.3.1.3(b), we
show C9 chord moved to “7fr” position—the full chord is unplayable, but with low/high E strings muted, the rest of
the chord (no root) is identical to a commonly used Em7b5 chord shape; as expected, a rootless F#7#5b9 as well as
an inverted Gm6 can also be found in the same position on the middle four strings. In Fig.3.1.3(c), we start from a C9
“barre” shape (8fr) and analyze the pattern on the four high strings to identify other previously mentioned chords. For
easier comparison, all Integer Notation-based numbering is normalized to the basic (0 .. 11) range.
2fr
C9
2fr7
10
2
0
7
4
3
6
10
0
0
2
7
4
0
10
10
3
0
6
F#7#5b9
2fr
0
10
F#7#5b9 (no P1)
7fr
8
1
10
4
Gm6
2fr
0
9
Gm6/E
7fr
7
0
9
3
1
8
4
0
7
3
C9
8fr
Em7b5/Bb
2
4
7
F#7#5b9 (no P1) Gm6
8fr10
0
8fr8
10
8fr7
9
0
0
10
7
6
3
4
1
3
0
(a)
(b)
(c)
Fig.3.1.3: Chord aliasing (examples).
3.1 Chord Aliasing (Cont.)
Exercise 3.1.3: A chord sequence Em7b5—A7#5b9—Dm6 is one way to play the ii-V-i progression (see the
“Altered Chords” section). Notice that, based on the analysis from Example 3.1.6, the same shape could be played
throughout.
• Play the progression using the four middle strings as shown in Fig.3.1.4.
• Move the chameleon shape to the four low strings (the shown A7b5 option) and try it as the V chord. And, while
we’re at it, try also the shown rootless A7b9.
© 2018 Ivan Radivojevic
A7b5 (V)
5fr
10
4
0
6
Em7b5(ii)
7fr
10
3
0
6
A7#5b9 (no P1)
(V)
10fr
8
1
10
4
Dm6/B(i)
14fr
7
0
9
3
Fig.3.1.4: Playing ii-V-i progression using a common shape.
A7b9 (no P1)
(V)
5fr
7
1
10
4
NOTE: The sequence from Fig.3.1.4 is a contrived one: there is no reason to insist on moving the same shape up and
down the fretboard. In addition to being inefficient, such playing style is less likely to be melodically interesting.
3fr2
10
7
3
Em9
3
10
7
2
7
3
10
2
00 0
2fr
Em9 Em9 Em9
7fr 10fr
7
2
3
10
0
Fig.3.1.5: m9 chords played using M7 shapes (examples).
Example 3.1.7: A rootless m9 chord type maps to the M7 type rooted three semitones higher (i.e., the m3 note of the
original chord is the new root). In Fig.3.1.5 we show several instances of Em9 chord played using GM7 shapes. We
pick four notes (all four different intervals) from M7 shapes previously discussed in sections 2.1 to 2.8.
• Play the shapes shown in Fig.3.1.5 and observe differences due to reordering of constituent intervals.
• For this example’s sake, we included the open low-E string that could be played as a sustained bass note to
resolve potential ambiguities about the intended context.
Example 3.1.8: A rootless M9 chord type maps to the m7 type rooted four semitones higher (i.e., the M3 note of the
original chord is the new root). The leftmost shape in Fig.3.1.6 is an EM9 obviously very similar to a “barre” G#m7 at
4fr, but other 5-note EM9 shapes are not as easy to play. However, since we know that a rootless EM9 maps to G#m7,
we can simply use any “minor-seventh” shape we already know—e.g., see Fig.3.1.6.
• For this example’s sake, we included the open low-E string that could be played as a sustained bass note to
resolve potential ambiguities about the intended context.
4fr
0
4
7
11
2
Fig.3.1.6: M9 chords played using m7 shapes (examples).
10
2
3
75fr
Em9 0
3
7
10
212fr
Em9 0
6fr
2
7
11
4
2
7
4
9fr11
12fr4fr2
7
4
11
4
11
0
7
2
0 0 0
EM9
11fr
4
7
2
11
0
EM9EM9EM9EM9EM9
3.1 Chord Aliasing (Cont.)
© 2018 Ivan Radivojevic
Fig.3.1.8: Turnaround based on rootless 9th
chords.
3fr 5fr
10
7
3
2
Em9
Eb9
Dm9
Db9
C6/9
B7#9
E7sus4/B
7fr
10
7
4
2
10
7
3
2
10
7
4
2
9
7
4
2
10
7
4
3
5
0
10
5fr 7fr 10fr
2
3
10
7
Em9
2
4
10
7
Eb9
2
3
10
7
Dm9
2
4
10
7
Db9
2
4
9
7
C6/9
3
4
10
8
B7#5#9
10
0
5
2
E9sus4
12fr
Db6/9
8fr
2
7
4
9
Eb9
10fr
2
7
4
10
Ebm9
9fr
2
3
D9
9fr
2
7
4
10
Db6/9
8fr
2
7
4
9
D6/9
9fr
7
10
7
9
2
4
Fig.3.1.7: Chord progression based on rootless 9th
chords.
Exercise 3.1.4: We revisit “The Girl from Ipanema” progression from Example 2.6.7. Play the progression using the
rootless chords from Fig.3.1.7. Notice that the shown Ebm9 (no P1) aliases to F#M7; similarly, the rootless Eb9
looks like Gm7b5. Explore adding root notes (i.e., “0”) on the high-E string.
(b)(a)
Exercise 3.1.5: A popular music standard
“Autumn Leaves” (orig. 1945) includes the
following turnaround:
Em7—Eb7—Dm7—Db7—CM7—B7—Em7
Play the above progression using the chord
types shown in Fig.3.1.8(a) and Fig.3.1.8(b).
In both cases, except for the final chord, all
chords are played as inverted and rootless
and using the same set of four strings.
Confirm that the shown rootless altered
chord B7#5#9 aliases to several other
chords types:
• Rootless Cm6/9 (e.g., see it used in the
ii-V-i instance in Fig.2.8.6), and
• EbM7add#11 (a.k.a. Lydian chord—see
the “Quartal Harmony” appendix for
more on this chord type).
7
3.2 Chord Voicing
Integer Notation: Intervals:
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
EF
G
A
B
C
D
EF
G
A
B
C
D
0
1
2
3
4
5
6
7
8
9
10
11
EF
G
A
B
C
D
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
P1
m2
M2
m3
M3
P4
d5
P5
A5
M6
m7
M7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
perfect unison
minor second
major second
minor third
major third
perfect fourth
diminished fifth
perfect fifth
augmented fifth
major sixth
minor seventh
major seventh
perfect unison
minor second
major second
minor third
major third
perfect fourth
diminished fifth
perfect fifth
augmented fifth
major sixth
minor seventh
major seventh
11fr
11
7
4
0
Shown in Fig.3.2.1 are two instances of a dominant seventh G7 chord. Both shapes include the same intervals: P1,
M3, P5 and m7 (or, using the Integer Notation: { 0 , 4 , 7 , 10 }). The intervals are not ordered in the same fashion in
the two chords, however, and they sound quite different. Notice that both chords have all four chord notes present on
the top four strings.
Chord voicing is a more formal, advanced topic related to the ordering of pitches within a chord. This topic is
important because the same chord having different ordering of constituent intervals (and perhaps also played in
different fretboard positions) may sound very different and may also make chord progressions easier to play.
By its definition, a 7th chord includes 1st, 3rd, 5th and 7th intervals. A chord in its closed root position has the root note
as the lowest pitch (“bass”) and its intervals are stacked as 1-3-5-7 with all notes residing within a single octave.
For example, a major seventh (“M7”) chord type includes P1, M3, P5 and M7 (or, using the Integer Notation: { 0 , 4 ,
7 , 11 }). In Fig.3.2.2(a), the shaded entries describe the chord using both Integer Notation and intervals.
In Fig.3.2.2(b), we show an EM7 chord form played on the four high strings and having its notes ordered as described
previously (i.e., stacked as 1-3-5-7). As usual when drawing chords, Integer Notation is used to label individual notes.
Playing other seventh chords could get tricky, however, when the root position 1-3-5-7 voicing is applied to the four
top strings (in particular in some other position where a fret spacing gets wider)—e.g., see the Em7 shape also shown
in Fig.3.2.2(b).
EM7
(1-3-5-7)
Fig.3.2.2: (a) EM7 represented using Integer Notation and intervals, (b) EM7 and Em7 in “closed root position”.
© 2018 Ivan Radivojevic
Fig.3.2.1: Interval ordering in two G7 chord shapes.
(b)(a)
0
7
G7
10
4
0
10
4
0
G7
10
4
0
Strings:
E
B
G
D
A
E
4
G7
3fr
7
4
10
0
7
0
10fr
7
3
0
Em7
(1-3-5-7)
10
3.2.1 Drop_2 Voicing
2fr
10
3
7
0
10
3
0
5fr7
Em7/B
(5-1-3-7)
7fr 12fr10
3
0
7
0
7
3
10
1-3-5-7
1st inversion
2nd inversion
3rd
inversion
root
3-5-7-1
5-7-1-3
7-1-3-5
5-1-3-7
7-3-5-1
1-5-7-3
3-7-1-5
Intervals: Drop_2:Voicing:
Em7/D
(7-3-5-1)
Em7
(1-5-7-3)
Em7/G
(3-7-1-5)
Fig.3.2.1.1: Construction of Drop_2 chords.
Fig.3.2.1.2: Em7 Drop_2 forms using the top four strings (high-E to D).
Strings:
E
B
G
D
-
-
© 2018 Ivan Radivojevic
______________________________________________________________________________________
[1] Statistically, in Drop_2 forms, two consecutive notes are 5 semitones apart. This is how most guitar strings are tuned (the exception being
a 4-semitone transition between the B/G strings), thus increasing the probability that the four fingers of the fretting hand are tightly clustered
on the fretboard.
[2] As pointed out previously, being the most neutral of the constituent intervals, the P5 interval is sometimes omitted when playing 7th
chords. This can make it easier to play certain chords shapes, but the full chord (i.e., P5 included) still has a richer sound.
Instead of being stacked as 1-3-5-7, the four chords notes could be rotated to produce three chord inversions: 3-5-7-1,
5-7-1-3 and 7-1-3-5—see the “Intervals” column, in Fig. 3.2.1.1. “Drop 2” voicing (referred to as Drop_2 in this
presentation) starts from a chord in its closed root position (or from its three inversions) and moves the second
highest-pitch note an octave lower to the bass position—see the “Drop_2” column in Fig.3.2.1.1. As a result of this
transformation, a Drop_2 chord’s range is always larger than one octave. The chord’s root note (P1/”0") could be
located on any of the four strings.
The following properties make Drop_2 chords are extremely useful:
• Most of Drop_2 chords are easy to play on four adjacent strings without an excessive finger stretching[1].
• Drop_2 chords are expressive and colorful in that their compact form includes all four chord notes[2].
Example 3.2.1.1: In Fig.3.2.1.2, black dots labeled ({ 0 , 3 , 7 , 10 }) correspond to Em7 Drop_2 forms using the top
four strings (high-E to D). By now, the Reader should be familiar with all four Em7 variants shown in Fig.3.2.1.2. We
also show a few (lightly shaded) notes that would be included in the playing shapes extending beyond the top four
strings.
It is also possible to derive playable Drop_2 shapes on the middle four strings (B to A) or the low ones (G to low-E).
This topic will be addressed next (Fig.3.2.1.3).
3.2.1 Drop_2 Voicing (Cont.)
7fr
4
0
7
10
C
4
0
0
4
7
7
D
4
0
7
0
7
12/0fr
7
0
4
10
E
7
0
4
0
7
0
4
0
7
7
0
7
A
12/0fr
10
7
4
0
7fr
4
10
7
0
E7/G#(3-7-1-5)
4fr
0
10
4
7
2fr
10
7
0
4
4fr
0
7
4
10
12/0fr
0
7
4
10
5fr
4
10
7
0
2fr
7
4
0
10
E7/B(5-1-3-7)
E7/D(7-3-5-1)
E7(1-5-7-3)
10
0
4
7
9fr
9fr
0
7
4
10
Strings:
E
B
G
D
A
E
Strings:
E
B
G
D
-
-
-
B
G
D
A
-
-
-
G
D
A
E
In the Fig.3.2.1.3, we show all Drop_2 forms of the E7 chord and its three inversions (see Fig.3.2.1.1). We also show
basic “open” chords D, C, A and E, as the Drop_2 shapes played on the top four strings (high-E to D) are closely
related. Next, without changing how individual intervals are ordered, we move each of those shapes by one string to
play them on the lower four strings. At each step, the chord notes (dots) advance by 5 frets except for those
originating on the B string that move up by 4 frets. For easier orientation, the root notes are highlighted as white dots.
Exercise 3.2.1.1: In Fig.3.2.1.3, show that forms having the root (“0”) on the G string could be inferred from the
“open” G chord.
Exercise 3.2.1.2: Play all E7 forms shown in Fig.3.2.1.3. Do it both horizontally (i.e., play four different inversions
using the same four adjacent strings) and vertically (i.e., play the same inversion using three different groups of four
strings).
Exercise 3.2.1.3: Explore shapes for other chord types (e.g., EM7, Em7, Em7b5) by moving chord notes around. (For
a related exercise, see also Fig.3.2.2.3 later in this section.)
Fig.3.2.1.3: E7 Drop_2 chord forms.
© 2018 Ivan Radivojevic
3.2.2 Drop_3 Voicing
In the rest of this section, we will explore relationship between Drop_2 and Drop_3 forms.
In Fig.3.2.1.3, all 12 Drop_2 forms of one chord type (dominant seventh) are shown. In Fig.3.2.2.3, the same Drop_2
or Drop_3 voicing is used for several common chord types: CM7, C7, Cm7, Cm7b5 and Cdim7. Not all variants are
shown, but those selected are common and easy to play. (The Reader is encouraged to investigate other options.)
Drop_2 shapes on the four low strings are somewhat less useful (they may sound dark and collide with the bass
player), so we omitted them from this example. We included dim7 chords, but only to demonstrate how little they
change in different Drop forms; the other four types are the four seventh chord types from the Major scale[1].
The non-inverted forms on the high four strings are based on “open-D”—see Fig.3.2.2.3(a); on the middle four
strings, such shape is “open-A”—see Fig.3.2.2.3(f). Not shown in the figure, “open-E” is such shape on the four low
strings.
1-3-5-7
1st inversion
2nd inversion
3rd inversion
root
3-5-7-1
5-7-1-3
7-1-3-5
3-1-5-7
5-3-7-1
7-5-1-3
1-7-3-5
Intervals: Drop_3:Voicing:
Fig.3.2.2.1: Construction of Drop_3 chords.
Fig.3.2.2.2: Examples of Drop_3 chords.
© 2018 Ivan Radivojevic
“Drop 3” voicing (referred to as Drop_3 in this presentation) starts
from a chord in its closed root position (or from its three
inversions) and moves the third highest-pitch note an octave lower
to the bass position (see the “Drop_3” column in Fig.3.2.2.1).
Notice that all 8 Drop_2 and Drop_3 voicings are unique.
Drop_3 chords have the bass note separated from the rest of the
chord notes providing jazz guitarists a clear boundary between the
bass and the melody line. In Fig.3.2.2.2, we present several
examples of Drop_3 chords (all of them having intervals stacked as
1-7-3-5):
• In Fig.3.2.2.2(a), the A string is skipped over.
• The D string is not played in the chords shown in
Fig.3.2.2.2(b).
11fr
4
11
4
7
0
3
9
6
0
3
10
-
B
G
D
-
E
7
0
7
10
0
7
0
3
10 (a)
Em6 Em7b5Em7EM7 E7
11fr 11fr 11fr 11fr
6fr
4
11
4
7
0
3
9
6
0
3
10
E
B
G
-
A
-
7
0
7
10
0
7
0
3
10(b)
Em6 Em7b5Em7EM7 E7
6fr 6fr 6fr 6fr
______________________________________________________________________________________
[1] See “Appendix: Common Scales”.
9fr
11
7
0
4
2fr
4
11
7
2fr
4
7
2fr
3
10
6
0
2fr
3
7
-
B
G
D
A
-
9fr
10
7
0
49fr
10
7
0
39fr
10
6
0
3
4fr
4
0
7
11
2fr
3
6
0
9fr
9
6
0
3
4fr
4
0
7
104fr
3
0
7
104fr
3
0
6
104fr
3
0
6
9
7fr
4
11
7fr
4
7fr 7fr
6
0
3
10
7fr
6
0
3
9
2fr
4
11
2fr
4
2fr
3
10
6
0
2fr
3
E
B
G
-
A
-
2fr
3
0
0
7
0
7
10
0
0
10
0
7
0
10
10
6
9
9
E
B
G
D
-
-
E
B
G
D
-
-
E
B
G
D
-
-
7fr
4
11
7fr
4
7fr 7fr
6
0
3
10
7fr
6
0
3
9
-
B
G
D
-
E
0
7
7
0
7
10
0
7
0
3
10
7
0
3
10
CM7 C7 Cm7 Cm7b5 Cdim7CM7 C7 Cm7 Cm7b5 Cdim7
(a)
(c)
(d)
(e)
(f)
(g)
Fig.3.2.2.3: Examples of Drop_2 and Drop_3 forms: (a) Drop_2 1-5-7-3, (b) Drop_2 5-1-3-7, (c) Drop_2 3-7-1-5,
(d) Drop_2 7-3-5-1, (e) Drop_3 1-7-3-5, (f) Drop_2 1-5-7-3, and (g) Drop_3 1-7-3-5.
0
7
10
© 2018 Ivan Radivojevic
3.2.2 Drop_3 Voicing (Cont.)
1fr 1fr
4
10
0
71fr 1fr 1fr
E
B
G
D
-
-
(b)4
11
0
7
3
10
0
7
3
10
0
6
3
9
0
6
Drop chords are an absolute must-have for jazz guitarists as they use a lot of chords while accompanying other
instruments (“comping”) or playing melodies using chords. Any enthusiastic student, however, should benefit from
enhanced fretboard awareness and ability to locate a playable chord shape at virtually any fret or string position.
Although the sheer number of different forms looks intimidating, somewhat surprisingly, the things are not all that
complicated. Basically, for any chord type, all that is needed are four Drop_2 inversions on the high four strings (i.e.,
the first row of Drop_2 forms shown in Fig.3.2.1.3)—as described previously, the rest of the Drop_2 forms merely
move the notes to other, lower strings. Moreover, as we will show next, Drop_3 forms can be derived from Drop_2
forms.
© 2018 Ivan Radivojevic
3.2.2 Drop_3 Voicing (Cont.)
In Fig.3.2.2.4, we extract a few shapes from Fig.3.2.2.3 to point out that certain Drop_2 and Drop_3 forms are parts
of a common “barre” chord. More important, Drop_3 forms can be derived from Drop_2 forms in the following
fashion:
• For Drop_2 chords on the four high strings, move the highest-pitch note from the high-E string to the low-E string
(i.e., drop it by two octaves) to get the corresponding Drop_3 chord—see Fig.3.2.2.4(a).
• For Drop_2 chords on the middle four strings, move the D string note to the high-E string (i.e., raise it by one
octave) to get the corresponding Drop_3 chord—see Fig.3.2.2.4(b).
Example 3.2.2.1: So far, all shown Drop_3 chords have been 1-7-3-5 voicings (see Fig.3.2.2.2, Fig.3.2.2.3 and
Fig.3.2.2.4). Two inverted Drop_3 forms are shown in Fig.3.2.2.5.
• In Fig.3.2.2.5(a), we derive a Drop_3 form by moving the high-E string note (“4”) to the low-E string.
• In Fig.3.2.2.5(b), a Drop_3 shape is derived by moving the D string note up by one octave.
Fig.3.2.2.5: Drop_2 vs. Drop_3 (examples).
E7(Drop_2 7-3-5-1)
4fr
0
4
10
7
4fr
0
10
4
7
E7(Drop_3 7-5-1-3)
(a) (b)
D => high-E
2fr
10
7
0
42fr
10
7
0
4
high-E => low-E
E7(Drop_2 1-5-7-3)
E7(Drop_3 3-1-5-7)
2fr
3
7
7fr
2fr
3
0
7
0
10
10
7fr
7
0
3
10
7
0
3
10
2fr
3
0
7
10
7fr
7
0
3
10
7
0
7
7
Drop_2
Barre
Drop_3
Fig.3.2.2.4: Examples of Drop_2 and Drop_3 forms (Cm7).
(a) (b)
high-E => low-E D => high-E
© 2018 Ivan Radivojevic
3.2.3 Drop_2&4 Voicing
1-3-5-7
1st inversion
2nd inversion
3rd inversion
root
3-5-7-1
5-7-1-3
7-1-3-5
1-5-3-7
3-7-5-1
5-1-7-3
7-3-1-5
Intervals: Drop_2&4:Voicing:
Fig.3.2.3.1: Construction of Drop_2&4 chords.
E7
7
4
5-1-3-7
10
1-5-7-3
7
4
7-5-1-3
7
4
0
1-7-3-5
4
1-5-3-7
7
4
10
5-1-7-3
4
10
7
0
10
0
10
10
7
10
0
0
7
10
0
7
4
0
7fr
E7
7
4
7
0
10
7
7fr
Drop_2
Barre
Drop_3
Drop_2&4
Drop_2
Drop_2&4
Fig.3.2.3.2: Drop chords construction example (E7).
Fig.3.2.3.3: Drop_2&4 examples (Em7).
For completeness, we will also provide a brief
introduction to “Drop 2 and 4” voicing (referred
to as Drop_2&4 in this presentation). We start
from a chord in its closed root position (or from its
three inversions) and move the second and the
fourth highest-pitch notes an octave lower to the
bass positions. This produces four new note
orderings (see Fig.3.2.3.1) distinct from Drop_2
and Drop_3 voicings.
Drop_2&4 chords consist of two groups of two
notes with an unused string in between (see
examples in Fig.3.2.3.2 and Fig.3.2.3.3)—as such,
they are not easy to strum cleanly using a pick and
finger-picking would be a more typical playing
style. The constituent notes are spread out wide,
producing a rich and interesting sound, especially
when sustained.
Drop_2&4 shapes could be derived from Drop_2
chords by moving the second lowest-pitch note
one octave lower. In Fig.3.2.3.2, we show a
simple case where all Drop shapes map to
common, easy-to-play “barre” chords; a few less
conventional shapes are derived in Fig.3.2.3.3.
Exercise 3.2.3.1. Play the 5-1-7-3 Em7/B shown
in Fig.3.2.3.3, but include also open G and low-E
strings. The shape can be played as a six-note
“barre” (a voicing sometimes confused for
Em7#9)—see also Fig.2.6.6(b) in the “Ninth
Chords” section.
2fr
10
3
7
0
10
3
0
5fr7
Em7/B
(5-1-3-7)
7fr 12fr10
3
0
7
0
7
3
10
Em7/D
(7-3-5-1)
Em7
(1-5-7-3)
Em7/G
(3-7-1-5)
2fr
10
3
7
0
10
3
0
5fr7
Em7
(1-5-3-7)
7fr 12fr10
3
7
0
7
3
10
Em7/G
(3-7-5-1)
Em7/B
(5-1-7-3)
Em7/D
(7-3-1-5)
0
3.2.4 Extensions and Examples
© 2018 Ivan Radivojevic
Fig.3.2.4.1: Derivative Drop_2 chords (examples).
E7(Drop_2 7-3-5-1)
4fr
0
4
10
7
(b)(a)
E7#5
4fr
0
4
10
8
1fr
4
10
7
0
E7(Drop_2 5-1-3-7)
1fr
4
10
8
0
E7#5
Drop forms make it easy to look for playable shapes for less common chord types and, in this section, we will show
several examples how this could be accomplished by moving and replacing chord notes in Drop_2 forms. We will
also show several examples of chord progressions using Drop chords.
Example 3.2.4.1: Augmented seventh (aug7, { 0 , 4 , 8 , 10 }) Drop_2 shapes can be derived from the
corresponding dominant seventh (dom7, { 0 , 4 , 7 , 10 }) Drop_2 shapes. In Fig.3.2.4.1, we demonstrate this using
two cases from Fig.3.2.1.3. As we did throughout Section 2, we start from a known chord shape and wiggle one note
(move “7” to “8”)—the difference is that now we have a much larger set of starting options and they have a common
4-note format. Notice that aug7 chords shown in Fig.2.8.3 (“Altered Chords” section) happen to be Drop_2
compatible as well.
Example 3.2.4.2: In Fig.3.2.4.2, we start from a C7 Drop_2 shape and transform it to several related chord types.
• In Fig.3.2.4.2(a), a suspended C7sus4 shape is derived by raising the C7's M3 to P4.
• In Fig.3.2.4.2(b), the original chord’s color notes are preserved, but the root is replaced to get a C7b9 shape.
Notice that the transformation is incremental and localized to moving a single note (P1/root) to its adjacent
interval (m2). Additionally, this rootless C7b9 aliases to a dim7 shape, so we know all C7b9 forms including
inversions (see Fig.2.3.1.4)—any dim7 shape that includes a C# note (m2) can be played as C7b9.
• In Fig.3.2.4.2(c), C7b9 is converted to C13b9 (see Example 2.8.2,“Altered Chords” section) by moving P5 to
M6.
As demonstrated in Example 3.2,4.2, for more complex chords where additional intervals (i.e., more than four notes)
are needed, we can re-use compact and familiar Drop forms by judiciously replacing certain notes. In particular, we
can extend Drop_2 chords by using the following transformations:
• the 9th/2nd replacing the root note (P1), and
• the 13th/6th replacing the 5th interval note (P5).
Exercise 3.2.4.1: Extend Em7 Drop_2 forms from Fig.3.2.1.2 to Em9 by including M2 instead of the root.
P5 => A5 P5 => A5
7fr
4
7fr
4
0
7
1
7
10
C7(Drop2 7-3-5-1)
10
C7b9(no P1)
Fig.3.2.4.2: Derivative Drop_2 chords (examples).
7fr
4
1
10
C13b9(no P1, no P5)
9P1 => m2P5 => M6
7fr
C7sus4
5
0
7
10
P4 <= M3
(b)(a) (c)
3.2.4 Extensions and Examples (Cont.)
© 2018 Ivan Radivojevic
Example 3.2.4.3: In Fig.3.2.2.3, in Cm7 column, we can move “10” to “9” (i.e., play M6 instead of m7) to produce
various forms of Cm6.
• Dominant 9th chords: Based on Example 3.1.6 (“Chord Aliasing” section), we know that constructing all Cm6
4-note Drop shapes is the same as producing all Am7b5 shapes; moreover, all rootless F9 (no P1) and all
B7#5b9 (no P1, no P5) would also map to that same set of shapes. We illustrate some of this in Fig.3.2.4.3 using
Drop_2 patterns corresponding to: Cm6 (white root note), Am7b5 (shaded root note) and rootless F9. We show
the missing F notes as dashed/crossed (not played) dots to make it easier to relate F9 chord shapes to previously
discussed F7 Drop_2 shapes. (Note: A rootless 9th Drop form can be produced by moving the corresponding 7th
chord’s P1 to M2.)
• Minor 9th chords: Similarly, based on Example 3.1.7 in the same section, we know that we can use 4-note CM7
Drop shapes for 4-note Am9 (no P1). Re-visit also Exercise 3.2.4.1—there, as expected, rootless Em9 forms
should correspond to GM7 Drop_2 forms.
• Major 9th chords: See Example 3.1.8 in the same section.
Exercise 3.2.4.2: We pick one Drop_2 form from Fig.3.2.4.3 and show it in several fretboard positions in Fig.3.2.3.4.
Some of the shown voicings are very effective (e.g., M7/m9 and m6), but tend to get overlooked by guitar players.
• In Fig.3.2.4.4(a), the same ordering of intervals (3-7-1-5) and the same fingering are used for three different chord
types (CM7, Cm7b5 and Cm7) using three different sets of adjacent strings.
• In Fig.3.2.4.4(b), the shapes from Fig.3.2.4.4(a) are renumbered to illustrate several aliasing cases discussed
previously (see Property 3.1.2,“Chord Aliasing” section).
3fr 6fr
8fr2fr
12/0fr10fr
10fr5fr
Strings:
E
B
G
D
-
-
-
B
G
D
A
-
Fig.3.2.4.3: Cm6, Am7b5 and F9 Drop_2 forms.
: C
: A
: F (no P1, not played)
Fig.3.2.4.4: Chord voicing and chord aliasing (example).
0
4
7
11 0
3
6
10
Cm7b5Cm7b5 Cm7Cm7CM7CM7
3
7
10
2 9
0
3
7
Ebm6Ebm6 Eb6Eb6Am9
(no P1)
Am9
(no P1)
5fr 10fr
7
10
0
3
4
7
0
9
Strings:
E
B
G
D
A
E
E
B
G
D
A
E
(a)
(b)
5fr 10fr
3.2.4 Extensions and Examples (Cont.)
© 2018 Ivan Radivojevic
0
3
6
10
Cm7b5/EbCm7b5/Eb
5fr
7
10
1
4
F7b9
(no P1)
F7b9
(no P1)
5fr
Bbm6/FBbm6/F
5fr
9
7
3
0
Exercise 3.2.4.3: Inverted Drop_2 forms can be used to play colorful tight chord progressions with smooth
transitions. For example, see two instances of the ii-V-i progression in Fig.3.2.4.5.
Fig.3.2.4.5: ii-V-i progression in two inversions.
3
6
0
Cm7b5/F#Cm7b5/F#
8fr
10
10
1
7
8fr
4
F7b9
(no P1)
F7b9
(no P1)
3
8fr
0
Bbm6/GBbm6/G
9
7
Fig.3.2.4.6: ii-V-I progression.
Exercise 3.2.4.4: In its most basic form, the ii-V-I progression includes three seventh chords from the Major
scale—e.g., Dm7-G7-CM7. (Notice that the I chord is of a major type.) Two compact variants are shown in
Fig.3.2.4.6. In Fig.3.2.4.6(a), adjacent chords have multiple common notes. Similar to its function in the ii-V-i
progression, a passing dim7 shape (G7b9 alias) can be used to connect ii and I. In Fig.3.2.4.6(b), the altered V
chord is an example of the tritone substitution (i.e., a rootless C#9) creating a smooth descending transition between
the surrounding ii and I chords.
3
10
Dm7/FDm7/F
2fr
7
10
CM9
(no P1)
CM9
(no P1)
2fr 2fr7
11
2
4
0
7
4
1
G7b9
(no P1)
G7b9
(no P1)
3
10
2fr
8
10
C6/9
(no P1)
C6/9
(no P1)
2fr 2fr7
9
2
4
2
7
4
Dm9
(no P1)
Dm9
(no P1)
1
G7#5b9
(no P1)
G7#5b9
(no P1)
(a) (b)
Em7
5fr
3
10
3
0
Finally, we want to point out that, for all their qualities, Drop forms
are not some “magic chords” that make obsolete everything presented
in the preceding sections.
In Fig.3.2.4.7(a) , we show a common Em7 chord shape discussed
earlier (see Fig.2.6.4). This minor-seventh chord includes only three
intervals (i.e., P5 is omitted), but exhibits a very unique voicing.
Notice that no Drop form shown in either Fig.3.2.1.1, Fig.3.2.2.1 or
Fig.3.2.3.1 has P1 and m3/M3 as two lowest pitch notes.
Similarly, in Fig.3.2.4.7(b) we revisit Em6 introduced in
Fig.2.2.5(b)—as shown, it is not a Drop form, but a distinct playable
closed-form 3rd inversion of Em6. (Also: 1-3-5-7 form of C#m7b5.) Fig.3.2.4.7: Em7 (a) and Em6 (b) revisited.
7
9
0
3
(a)
(b)
Em6
3.3 One-Off Chords
It is important to understand chord structures and to be able to construct chords in a systematic fashion. Typically,
this leads to chord shapes that are reusable and portable. Moreover, deriving a new chord type tends to involve only
relatively small, incremental modifications to some existing variant. Obviously, the construction of Drop chords fits
the bill.
There is nothing wrong, however, about also using “one-off” chords customized to a particular key (e.g., by including
notes playable on open strings). As shown in this section, this can make playing easier and result in unique, colorful
voicings.
We hope that this final section will not leave the Reader agonizing: “Oh, what now?! Random stuff?”. Instead, we
should rejoice at guitar being a fun instrument offering so many avenues to experiment and to be creative.
Example 3.3.1:
• Two Em6 chords shown below have the same easy-to-play shape at different fretboard positions (4fr and 10fr).
• A pleasant Am9 can be played with minimal effort as shown below.
• We also show two chords (C and Emadd9/B) where the same simple shape includes open strings interleaved
with notes played far along the fretboard—such chords sound unusual and interesting (especially when played
arpeggio-style) as the pitch of successive strings bounces higher and lower several times.
Example 3.3.2: Shown below are Am9, Em7 and Dm13 chords employing the identical “minor seventh” triplet
pattern ({ 0 , 3 , 10 }). The Reader should explore other fretboard positions (e.g., C#m7, F#7add11, Bm7add11)[1]
.
© 2018 Ivan Radivojevic
Em6
0
0
7
9
3
3
10fr
3
optional
Am9
7
0
2
10
3
4fr
Emadd9/B
0
7
2
3
C
4
0
7
7
7fr8fr
Am9
7
2
0
10
10fr
3
Em7
0
7
0
10
5fr
3
Dm13
2
9
0
10
3fr
3
Example 3.3.3:
• “Entangled” (Genesis, 1976) features a memorable Bm9 chord that the main melody is built upon.
• F#7add11 and Aadd9 both come from “Rooster” (Alice in Chains, 1992)—there, the common open strings
provide a connection between two major chords that famously open the song and keep returning as they
accompany the storytelling.
Bm9
0
0
2
7fr10
3
F#7add11
5
7
2fr10
0
0
4
Aadd9
2
7
5fr7
0
0
4
F#m7add11
5
7
2fr10
0
10
3
Exercise 3.3.1: Play all chords from
Example 3.3.2 using the shown
“minor seventh” shape with reordered
intervals and P5 included[2]
.
______________________________________________________________________________________
[1] As a high-school math teacher used to tell his students (this author among them): “A trick that worked twice becomes a method.”
[2] The colorful F#m7add11 from Exercise 3.3.1 includes the same intervals as the all-string “barre” at 2fr—i.e., a shifted version of the
chord corresponding to the standard tuning of guitar open strings. Notice the difference made by reordering of the notes. See also a famous
“So What” chord of Example 4.2.1.
0
0
7
3
9
9
4fr
3
optional
Em6
3.3 One-Off Chords (Cont.)
5 7
10
0
4
2
5
9
0 2
10
7
4
7
4
0
7
9
10
Example 3.3.4: Go to YouTubeTM
and watch/hear Steve Howe use some of the above midway through his classic “Clap” (orig.
Yes, 1971).
Exercise 3.3.4: Repeat Exercise 3.3.2, but play Am7 instead of A7 (i.e., move each “4” to its adjacent “3”).
© 2018 Ivan Radivojevic
5fr 12fr7fr3fr 10fr5fr 12fr7fr3fr 10fr
Exercise 3.3.3: In the figure below, treat the corresponding pairs of black (or shaded) dots on strings B and D as
chords when combined with the three opens strings (high-E, G, A). Notice that, in the key of A, the three open strings
correspond to P1, P5 and m7 intervals forming a neutral seventh chord (A7omit3) that comes “for free”. Show that
the following chord progression is produced as we move from left to right:
A7 – A7sus4add6 – A7omit3 – A7add6omit3 – A7sus2 – A7 – A9sus4 – A7
Trivia 3.3.1: Not only does the shown C#9add#9 have a fancy name, but it also
includes three adjacent intervals (M2, m3 and M3). It is likely to be the only such
chord in the whole of “No Chord Left Behind: A Guitar Navigation Kit”
presentation. Thank you for attending!
Ivan Radivojevic, Oct. 2019.
10
2
3
0
4
4fr
C#9add#9
Exercise 3.3.2: Play Example 3.3.3 chords in different positions and contexts.
• The “Entangled” Bm9 shape also works for G9 (at 3fr, see Fig.2.9.1). The two chords even sound OK when
played back-to-back.
• The “Rooster” shape played at 1fr becomes FM7add#11; such chord is sometimes heard in Flamenco-style E-F
progressions.
4.1 Appendix: Common Scales
© 2018 Ivan Radivojevic
While not a prerequisite for learning chords, for completeness, a rudimentary introduction to musical scales is
presented in this section. We discuss three most common scales: the Major scale, the Harmonic Minor scale and the
Melodic Minor scale. For those primarily interested in rock music, knowing the Major scale and the Harmonic Minor
scale might suffice; being a staple of jazz, the Melodic Minor scale is included as well. Those interested in music
harmony and soloing are advised to study this topic elsewhere in a systematic fashion and greater depth.
4.1.1 Major Scale
Using the Integer Notation, the Major scale is represented as the following sequence:
{ 0 , 2 , 4 , 5 , 7 , 9 , 11 }
Thus, for example, the C major scale consists of the following notes:
{ C , D , E , F , G , A , B }
The first note of a scale is referred to as a tonic. A position of a note within a particular scale is referred to as a scale
degree, the tonic being the first (I) degree of its scale. A scale’s mode corresponds to the scale played from a
particular note/degree. All modes of a particular scale include the same notes.
We describe the C major scale and its seven modes in Fig.4.1.1. The I degree (Ionian) mode is also referred to as the
Major scale itself. The VI degree (Aeolian) mode of the Major scale is frequently referred to as the Natural Minor or
the Minor scale and its Integer Notation formula is: { 0 , 2 , 3 , 5 , 7 , 8 , 10 }.
By assuming each scale note a root and identifying the 3rd/5th interval notes within the corresponding mode (see
Fig.4.1.1), we associate the following triad chords with the C major scale modes:
C — Dm — Em — F — G — Am — Bdim
Similarly, we associate the following seventh chords with the C major scale by including the 7th interval (m7 or M7):
CM7 — Dm7 — Em7 — FM7 — G7 — Am7 — Bm7b5
Basically, each Major scale mode (a horizontal line in Fig.4.1.1) can be viewed as a 7-note chord. In the above chord
progressions, we reduce each mode to a 3-note or a 4-note chord by “stacking thirds” (i.e., picking every other scale
note starting with its root). Notice that the Major scale includes only one dominant seventh (dom7) chord (e.g., G7 in
the C major) and no minor major seventh (mM7) chords; also, there is no augmented triad (aug) in the Major scale.
Using the generic Integer Notation-based formula, we can the construct a Major scale in any key—e.g., D major scale
includes { D , E , F# , G , A , B , C# } and its chords could be transposed accordingly.
C D E F G A BIonian (Major scale)I
D E F G A B CDorianII
E F G A B C DPhrygianIII
F G A B C D ELydianIV
G A B C D E FMixolydian modeV
A B C D E F GAeolian (Natural Minor, Minor scale)VI
B C D E F G ALocrianVII
Mode:
Fig.4.1.1: C major scale and its modes.
Degree:
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 110 1 2 3 4 5 6 7 8 9 10 11
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 11
4.1 Appendix: Common Scales (Cont.)
© 2018 Ivan Radivojevic
Example 4.1.1.1: All chords shown below are from the C major scale and the scale can be used to play over the
whole progression:
CM7 — Am7 — Dm7 — G7
The progression can be classified as the I-vi-ii-V indicating it consist of chords of the same type as the first, the
sixth, the second and the fifth chord of the Major scale. Uppercase Roman numerals indicate major chords; minor
chords are shown as lowercase Roman numerals.
Similar progressions are frequently employed in popular music—e.g.: C—Am-F-G or C-G-Am-F. (Think of
standards like “Stand by Me”, “Let it Be” and “No Woman No Cry”.)
4.1.2 Harmonic Minor Scale
Using the Integer Notation, the Harmonic Minor scale is represented as the following sequence:
{ 0 , 2 , 3 , 5 , 7 , 8 , 11 }
Thus, for example, the Harmonic C minor scale consists of the following notes:
{ C , D , D# , F , G , G# , B }
The following chords are associated with the Harmonic C minor scale modes (see Fig.4.1.2):
CmM7 — Dm7b5 — D#M7#5 — Fm7 — G7 — G#M7 — Bdim7
In the Harmonic Minor formula, there is only a single-note difference (M7/“11” instead of m7/“10”) w.r.t. to the
Minor scale formula (see Section 4.1.1). The Harmonic Minor includes two chord types not found in the Major scale:
minor major seventh (mM7) and augmented (aug). Notice that, in Fig.4.1.1, all adjacent notes are one or two semi-
tones apart; the Harmonic Minor (Fig.4.1.2) introduces one wider gap (three semi-tones).
In rock music, the Phrygian Dominant mode is frequently used for Flamenco/Oriental-sounding licks and shredding.
Also, the famous introduction to Janis Joplin’s version of “Summertime” (1968) is in the Harmonic G minor.
Example 4.1.2.1: The C major scale cannot be used over the whole progression shown below.
Am — G — F — E7
The problem is the E7 chord that does not belong to the C major scale: in particular, its M3 interval is G#, a note not
found in the scale. Over the first three chords, we can still play the C major scale (i.e., the scale’s VI degree Natural
A minor mode). For the final chord, we can switch to the Harmonic A minor scale that includes E7 as the V chord.
This kind of a progression (in a minor key with a dominant V chord returning to i) is common across music forms.
Harmonic MinorI
Locrian #6II
Ionian #5III
Dorian #4IV
Phrygian DominantV
Lydian #2VI
SuperlocrianVII
Mode:
Fig.4.1.2: Harmonic C minor scale and its modes.
Degree:
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 110 1 2 3 4 5 6 7 8 9 10 11
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 11
G G# B C D D# F
C D D# F G G# B
G# B C D D# F G
D D# F G G# B C
D# F G G# B C D
F G G# B C D D#
B C D D# F G G#
4.1 Appendix: Common Scales (Cont.)
© 2018 Ivan Radivojevic
Exercise 4.1.2.1: A popular music standard “Autumn Leaves” (orig. 1945) is based on the following chord
progression:
Am7 — D7 — GM7 — CM7 — F#m7b5 — B7 — Em7
Show that, except for B7, the progression consists of G major (Natural E minor) scale chords and can be played over
using the same scale. B7 is a dominant V chord w.r.t. Em7 and is outside of the G major scale (Bm7 belongs there), so
the Harmonic E minor can be employed instead.
4.1.3. Melodic Minor Scale
Using the Integer Notation, the Melodic Minor scale is represented as the following sequence:
{ 0 , 2 , 3 , 5 , 7 , 9 , 11 }
Thus, for example, the Melodic C minor scale consists of the following notes:
{ C , D , D# , F , G , A , B }
The following chords can be associated with the Melodic C minor scale modes (see Fig.4.1.3):
CmM7 — Dm7 — D#M7#5 — F7 — G7 — Am7b5 — Balt
There is only a single-note difference (m3/“3” instead of M3/“4”) w.r.t. to the Major scale formula—i.e., the Melodic
Minor is a minor-type version of the Ionian Mode (Fig.4.1.1). The modification produces the minor major seventh
(mM7) chord type not present in the Major scale.
The VII degree mode of the Melodic Minor scale includes both alterations of the 2nd/9th interval (b9, #9) and the 5th
interval (b5, #5). The seventh chord associated with this mode covers a number of altered dominant chords discussed
in the “Altered Chords” section and is thus annotated “alt” for short.
Example 4.1.3.1: In a simple case, a piece of music is written in a particular key (e.g., C major) meaning it uses only
notes from one scale that can be used to play over the whole chord progression (e.g., see Example 4.1.1.1). On the
other extreme, for harmonic and/or esthetic reasons, a different scale is sometimes played over each individual chord.
For example, the ii-V-i progression shown in Fig.2.8.5(b) of Exercise 2.8.2 can be played over using a different
Melodic Minor scale for each chord: G minor (Em7b5), Bb minor (A7#5b9) and D minor (Dm6), respectively.
Below, we outline why the proposed arrangement can work:
• i chord: All notes ({ 0 , 3 , 7 , 9 }) belong to the I degree mode of a Melodic Minor.
• ii chord: All notes ({ 0 , 3 , 6 , 10 }) belong to the VI degree mode of a Melodic Minor.
• V chord: All notes ({ 0 , 1 , 4 , 8 , 10 }) belong to the VII degree mode of a Melodic Minor.
Melodic MinorI
Dorian b9II
Lydian AugmentedIII
Lydian DominantIV
Mixolydian b13V
Locrian #2 (Half-Diminished)VI
Superlocrian (Altered Dominant)VII
Mode:
Fig.4.1.3: Melodic C minor scale and its modes.
Degree:
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 110 1 2 3 4 5 6 7 8 9 10 11
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 11
C D D# F G A B
F G A B C D D#
A B C D D# F G
B C D D# F G A
D D# F A B C
D# F G A B C D
G A B C D D# F
G
4.1 Appendix: Common Scales (Cont.)
© 2018 Ivan Radivojevic
Natural C minor scale(Aeolian Mode of Eb major scale)
8fr
8
2
5
3
7
0
2
0
5
7
8
2
0 3
3
Harmonic C minor scale
11
11
11
8fr
2
5
3
7
0
2
0
5
7
9
2
0 3
3
Melodic C minor scale
11
11
11
9
8
2
5
3
7
0
2
0
5
7
8
2
0 3
3
10
10
8fr
Fig.4.1.4.1: Comparison of Minor scales (comparison).
2
5
3
7
0
2
0
5
7
9
2
0 3
3
Melodic C minor scale
11
11
11
9
Fig.4.1.4.2: Major and Melodic Minor scales (comparison).
2
5
4
7
0
2
0
5
7
9
2
0
4
C major scale
11
11
11
9
8fr 8fr
4.1.4 Comparison of Scales
For comparison, in the Fig.4.1.4.1 and Fig.4.1.4.2, all scales are shown in the same position: having two root notes at
8fr on both E strings with another root in between (D string, 10fr).
Exercise 4.1.4.1: Play the scales from Fig.4.1.4.1 and listen to the differences. The Harmonic Minor sounds more
dramatic than the Natural Minor—this is accomplished by raising m7 to M7 (i.e., by moving “10” to “11” and, thus,
closer to the high-root note). This opens a 3-semitone gap (“8” to “11”), however. The Melodic Minor does re-
balancing of intervals between “7” and “11” by raising m6 to M6 (i.e., “8” moves to “9”). Notice how much
difference a single note makes.
Exercise 4.1.4.2: Play the scales from Fig.4.1.4.2. Again, notice how much difference a single note (M3 vs. m3)
makes.
Exercise 4.1.4.3: The C major scale shown in Fig.4.1.4.2 includes more than two octaves worth of the scale’s notes
and, in Fig.4.1.4.3, we identify all scale’s seventh chords, each one having all four of its notes on adjacent strings. For
each chord, we show its root as a white dot while preserving the original Integer Notation from the C major scale. The
Reader should find two missing chord types—minor major seventh (mM7) and augmented (aug)—in the other two
scales (Harmonic and Melodic Minor).
Fig.4.1.4.3: C major scale chords.
0
CM7
8fr
5
FM7
8fr
7
G7
8fr
Am7
9
8fr
Bm7b5
11
9fr
2
Dm7
10fr
4
Em7
8fr
2fr
11
7
0
4
7fr
4
11
7
7fr
4
7
7fr
3
10
6
0
7fr
3
7
-
B
G
D
A
-
2fr
10
7
0
42fr
10
7
0
32fr
10
6
0
3
00
10
0
10
E
B
G
D
-
-
(a)
(c)
Fig.4.2.2: Comparison of Drop_2 and Quartal chord shapes.
In Fig.4.2.2, we show Drop_2 non-
inverted voicings for all four Major scale
chord types (E7, Em7, EM7 and Em7b5)
using the high strings (“a”) or the middle
strings (“c”).
In Fig.4.2.2(b) and Fig.4.2.2(d), we
present four basic “quartal” chord types
exhibiting very similar and easy-to-play
shapes[2].
© 2018 Ivan Radivojevic
4.2 Appendix: Quartal Harmony
EM7E7 Em7 Em7b5
EM7E7 Em7 Em7b5
7fr
4
11
5
7fr
4
5
7fr
4
11
6
0
7fr
3
5
-
B
G
D
A
-
00
10
0
10
EM7add11E7add11 Em7add11 EM7add#11
2fr
11
5
0
42fr
10
5
0
42fr
10
5
0
32fr
11
6
0
4E
B
G
D
-
-
(b)
EM7add11E7add11 Em7add11 EM7add#11
(d)
______________________________________________________________________________________
[1] See “Appendix: Common Scales”.
[2] In case of E7 and Em7, “7” is merely moved to “5”. EM7 shape morphs into two quartal shapes by moving “7” to either “5” or “6”.
C D E F G A BIonian (Major scale)I
D E F G A B CDorianII
F G A B C DPhrygianIII
F G A B C D ELydianIV
G A B C D E FMixolydian modeV
A B C D E F GAeolian (Natural Minor, Minor scale)VI
C D E F G ALocrianVII
Mode:
Fig.4.2.1: Quartal chords construction using the C major scale.
Degree:
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 110 1 2 3 4 5 6 7 8 9 10 11
Intervals:
Integer Notation:
P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7
0 1 2 3 4 5 6 7 8 9 10 11
E
It is possible to construct chords by “stacking fourths” instead of “stacking thirds”. That is, instead of incrementally
adding every other interval (1st, 3rd, 5th, 7th, 9th, 11th, 13th), we can keep adding every third interval (1st, 4th, 7th, 10th/3rd,
13th/6th, 16th/2nd, 19th/5th). Such “quartal chords” sound ambiguous and suspended and are common in jazz.
In Fig.4.2.1, the C major scale[1] is used to construct 4-note quartal chords. For each mode, we start with its root note,
skip over two scale notes, include the following note and so on. By analyzing the highlighted 1st, 3rd, 4th and 7th
interval notes included for each mode, we get the following progression:
CM7add11 — Dm7add11 — Em7add11 — FM7add#11 — G7add11 — Am7add11 — Bm7add11
B
7fr
3
5
0
10
7
Em7add11(a.k.a. “So What” chord)
Example 4.2.1: By adding P5/“7” to
Em7add11 in Fig.4.2.2(d), we get a
famous “So What” chord voicing (Miles
Davis, “Kind of Blue”, 1959). The chord
also maps to the standard tuning of open
guitar strings. See also Exercise 3.3.1.
© 2018 Ivan Radivojevic
4.2 Appendix: Quartal Harmony (Cont.)
Exercise 4.2.1: Using the chords shown in Fig.4.2.2, play the chord progressions described below and shown in
Fig.4.2.3. For easier orientation, chords are depicted as alternating black, shaded or white dots. All chords employ
only notes from the same (D major) scale.
(a) Using the shapes from Fig.4.2.2(a), play the E-Dorian scale (II degree mode of the D major scale) chord
progression shown in Fig.4.2.3(a):
Em7 — F#m7 — GM7 — A7 — Bm7 — C#m7b5 — DM7
Play the sequence starting from different chords (DM7 being the most natural starting point for the D major scale).
(b) Using the shapes from Fig.4.2.2(b), play the progression listed below and shown in Fig.4.2.3(b).
Em7add11 — F#m7add11 — GM7add#11 — A7add11 — Bm7add11 — C#m7add11 — DM7add11
Add also the open low-E bass note or try playing all listed quartal chords over a sustained Em7 background. Notice
that the chords float ambiguously and have an interesting, unresolved sound.
(c) Same as (a) above, but use the shapes from Fig.4.2.2(c) and Fig.4.2.3(c).
(d) Same as (b) above, but use the shapes from Fig.4.2.2(d) and Fig.4.2.3(d).
Exercise 4.2.2: Show that combining the corresponding 4-note forms shown in Fig.4.2.3(b) and Fig.4.2.3(d) is the
same as adding an extra interval (m6 or M6) from Fig.4.2.1 to produce extended 5-note quartal chords. For example,
if we add another note to CM7add11, we get CM13[1].
Exercise 4.2.3: As demonstrated in Example 3.1.2, Asus2 is the first inversion of Esus4, and Esus4 is the second
inversion of Asus2. Show that the remaining inversion corresponds to a quartal chord B7sus4 ({ 0 , 5, 10 }, P5
omitted).
3fr 5fr 12fr8fr 10fr
Bm7add11
Em7add11
3fr 5fr 12fr8fr 10fr
Bm7
Em7(b)(a)
3fr 5fr 12fr8fr 10fr3fr 5fr 12fr8fr 10fr
(d)(c)
Fig.4.2.3: D major scale chords (“a” and “c”) and quartal chords (“b” and “d”).
______________________________________________________________________________________
[1] As discussed in the “Eleventh and Thirteenth Chords” section, it is not mandatory to include all 7 intervals in a 13th chord.
© 2018 Ivan Radivojevic
4.2 Appendix: Quartal Harmony (Cont.)
Example 4.2.2: As shown in Fig.4.2.4, quartal chords alias to numerous chord types and variants.
• As an illustration, in Fig.4.2.4(a), we re-annotate the chords from Fig.4.2.3(d) assuming all of them are rooted in
E (instead of using the A string bass notes).
• In Fig.4.2.4(b), we demonstrate that the most common quartal shape (m7add11) also aliases to rootless “6/9”
chords—see C6/9 and in Fig.4.2.4(b).
• Notice that another quartal shape aliases to the minor variant of the same chord type—see Em6/9 in Fig.4.2.4(a);
if we add 1 to each note of the shown Em6/9, we also get { 4 , 10 , 3 , 8 } corresponding to a rootless altered
Eb7#5#9 as shown in Fig.4.2.4(c).
Example 4.2.3: Examples of Drop_2 inverted forms of 4-note quartal chords are shown in Fig.4.2.5.
• In Fig.4.2.5(a), we show Em7add11 Drop_2 forms. Compare the forms to Em7 Drop_2 inversions. The forms
also alias to several chord types as discussed in Example 4.2.2.
• In Fig.4.2.5(b), we show EM7add#11 Drop_2 forms. Compare the forms to EM7 Drop_2 inversions. The forms
also alias to several chord types as discussed in Example 4.2.2.
• Move the shapes to the middle four strings—most of them get a bit trickier to play there.
0
0
3
5
0
10
10
0
7
5
0
2
9
7
5
7
2
0
Em7add11E7sus4
(Bm7add11)
Esus2sus4
(F#m7add11)
E6sus2
(C#m7add11)
Fig.4.2.4: Many faces of quartal chords.
0
0
9
5
2
3
10
9
7
9
3
2
Em13
(DM7add11)
Em13
(A7add11)
Em6/9
(GM7add#11)
10
3
7
9
4
2
C6/9 (no P1)
7fr
7fr 7fr12fr 12fr
(a)
(c)
8
10
4
3
Eb7#5#9 (no P1)
12fr
2fr
10
3
5
0
10
3
0
5fr5
(5-1-3-7)
7fr 12fr10
3
0
5
0
5
3
10
(7-3-5-1)(1-5-7-3) (3-7-1-5)
Fig.4.2.5: Examples of Drop_2 forms: (a) Em7add11, and (b) EM7add#11.
Strings:
E
B
G
D
-
-
(a)
2fr
11
4
6
0 4
0
5fr6
(5-1-3-7)
8fr 12fr11
4
0
6
0
6
4
11
(7-3-5-1)(1-5-7-3) (3-7-1-5)
Strings:
E
B
G
D
-
-
(b)11
(b)
