Musical Scales: A Guitar Navigation Kit Ivan Radivojevic...The scales covered in this presentation...

“Musical Scales: A Guitar Navigation Kit”, Ivan Radivojevic

Prerequisites:

• No in-depth command of music theory is required. In practice, however, basic understanding of music intervals

and chord structures is coupled with the process of scale selection and use. Thus, we will assume the Reader

capable of analyzing intervals included in a particular scale and what those mean in terms of chords associated

with the scale. For example, based on 1st, 3rd, 5th and 7th intervals, the Reader should be able to distinguish CM7

from Cm7b5[1].

• The ability to read music scores is not required as they will not be used in the presentation.

Objective and Method:

• Intended as an introduction to the topic of musical scales.

• Deals with the What question by providing descriptions of most common scales.

• The presentation also attempts to addresses the When/Where question of musical contexts in which certain scale

could be used. This is a pretty wide topic, however, and it requires a substantial “ear training” on the part of the

Reader as well. We provide some examples and exercises, but the Reader should make use of near-infinite

amount of information and music available on the Internet.

• For the most part, the How question is barely touched, however—i.e., topics like fingering, picking, practicing

techniques and creative use of scales are beyond the scope of this presentation.

Table of Contents: 1 Notation

2 Major Scale

2.1 Major Scale Modes

3 Minor Scales

3.1 Natural Minor

3.2 Harmonic Minor

3.3 Jazz Melodic Minor

4 Harmonic Major Scale

4.1 Double Harmonic Major Scale

5 Pentatonic Scales

5.1 Minor Pentatonic

5.2 Major Pentatonic

5.3 Dominant Pentatonic

6 Blues Scales

7 Diminished Scale

8 Whole-Tone Scale

9 Augmented Scale

10 Overview

11 Appendix

11.1 Common Major Scale Progressions

11.2 Modulation

11.3 Relative Minor

11.4 I-IV-V Blues Progression

11.5 ii-V-i Progression

11.6 I-vi-ii-V Progression

11.7 Scale Substitution

11.8 3NPS Patterns for Major, Harmonic Minor and Melodic Minor Scales

NOTE:

[1] For example, see “No Chord Left Behind: A Guitar Navigation Kit”, © 2018 Ivan Radivojevic.

© 2018 Ivan Radivojevic

1. Notation


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

CC# / Db

D

D# / Fb

E

F

F# / Gb

G

G# / Ab

A

A# / Bb

B

CC# / Db

D

D# / Fb

E

F

F# / Gb

G

G# / Ab

A

A# / Bb

B

The knowledge of music intervals is required to be able to understand chords and scales.

• For chord/scale analysis, we will use both intervals and Integer Notation. As shown in Fig.1.1, there is a 1:1

correspondence between the two.

• For graphical representation of chord and scales, we will mostly use Integer Notation for its compactness (digits

only) and simple interpretation (relative distance in terms of frets).

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.1.1: Music intervals and their relationship to Integer Notation.

Also referred to as “Tritone” or “flat 5” (b5).

Also referred to as “Minor Sixth” (m6) or “sharp 5” (#5).

x2

Fig.1.2: Guitar octave patterns.

E

B

G

D

A

E

Strings:

E

B

G

D

A

E

x0y0

y1x1

x2y2

y0

x1

x2

x0y0

x1y1

y0

y2

x1

x2

Two tones that are one octave apart differ in pitch as 2:1. In Fig.1.2, 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.

Strings:

E

B

G

D

A

E

0

7

4

5fr 12fr

NOTE: The three

shown patterns are

“barre” chord versions

of “open” A, E and C

chords (left-to-right).

Fig.1.3: C-Major (C) chord in multiple positions.

7

0

4 7

0

0

0

7

7

3fr

0

4

4

7

0

Strings:

E

B

G

D

A

E

3

5fr 12fr

NOTE: The three

shown patterns are

“barre” chord versions

of “open” Am, Em and

Dm chords.

Fig.1.4: C-Minor (Cm) chord in multiple positions.

7

0

3 7

0

0

0

7

7

3fr

3

7

0

1. Notation (Cont.)

Shown in Fig.1.3 and Fig.1.4 are C-Major (C) and C-Minor (Cm) chords in multiple playing positions. Most of the

time, we will use C/Cm chord position at the 8th fret (“8fr”) as the starting point (“canonical position”) of presentations

on different topics. This position is chosen because it corresponds to perhaps most commonly played “barre” chord

forms and could be shifted to any fret position (i.e., pitch). Additionally, this particular form has its root note on both

low-E and high-E strings thus spanning the range of 2 octaves (with one intermediate root on the D string). For easier

orientation, root notes are typically shown as a white dots. We show more that 12 needed frets (i.e., more that one full

octave) to be able to provide a flat view of all chord/scale playing positions and also to avoid discussing boundary

conditions related to using open strings.

For chord instances shown in Fig.1.3 and Fig.1.4, Integer Notation is used to mark individual notes. To summarize:

• Major Triad = { 0 , 4 , 7 } // i.e., in terms of intervals: P1, M3 and P5

• Minor Triad = { 0 , 3 , 7 } // P1, m3 and P5

• Augmented Triad = { 0 , 4 , 8 } // P1, M3 and A5/m6

• Diminished Triad = { 0 , 3 , 6 } // P1, m3 and d5

When describing scales, we use the following notation to indicate the relationship between consecutive notes:

• “H” is used for “Half Step” interval corresponding to one semi-tone (i.e., one fret).

• “W” is used for “Whole Step” interval corresponding to two semi-tones (i.e., two frets).

• “m3” is used for “Minor Third” interval corresponding to three semi-tones (i.e., three frets).

A scale is a set of notes ordered by pitch. For example, the following sequence of notes makes up the C-Major scale:

C – D – E – F – G – A – B – C

Above, we show a full octave of the C-Major scale ending in the high-C note, but there are only 7 notes in the scale

(C through B)—i.e., the C-Major is a heptatonic scale having 7 pitches per octave.

10fr

10fr

8fr

(cannonical postion)

8fr

(cannonical postion)


0

7

1. Notation (Cont.)


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 scale

degree, the tonic being the 1st (I) degree of its scale.

The essential character of the scale can be captured using the steps-based formula indicating intervals between

consecutive notes (i.e., adjacent scale degrees)—for example, in the C-Major scale shown in Fig.1.5, two adjacent

notes are separated by one (“H”) or two (“W”) semi-tones.

The Major scale and many other scales to be discussed in this presentation (e.g., Harmonic Minor, Melodic Minor,

Harmonic Major, Whole Tone, Diminished) have a property that any two scale notes that are two degrees apart form

the interval of a major or minor third (i.e., they are 3 or 4 semi-tones/frets apart). For example, in Fig.1.5, the D and F

notes (i.e., II and IV degree, respectively) are 3 semi-tones (W+H) apart, while G and B (V and VII degree) are 4

semi-tones (W+W) apart; there are no back-to back half steps or any steps larger than two semi-tones.

The Major scale is a heptatonic scale in that it includes 7 different notes per octave. The scales covered in this

presentation fall into the following categories[1]:

• Pentatonic (5 notes): Major, Minor, Dominant.

• Hexatonic (6 notes): Whole Tone, Augmented, Minor Blues, Major Blues.

• Heptatonic (7 notes): Major, Harmonic Minor, Melodic Minor, Harmonic Major, Double Harmonic Major.

• Octatonic (8 notes): Diminished (Half-Whole, Whole-Half).

C – D – E – F – G – A – B – C // C-Major scale notes.

W – W – H – W – W – W – H // Steps between consecutive notes of the C-Major scale.

// (e.g., there is a whole step between F and G notes)

C – D – E – F – G – A – B – C // C-Major scale notes.

W – W – H – W – W – W – H // Steps between consecutive notes of the C-Major scale.

// (e.g., there is a whole step between F and G notes)

Fig.1.5: C-Major scale notes and steps.

______________________________________________________________________________________

[1] We also show one nonatonic (9-tone) blues scale, but it merely combines two hexatonic blues scales (see “Blues Scales” section) .

2. Major Scale

Strings:

E

B

G

D

A

E

Fig.2.2: C-Major scale (canonical position).W-W-H-W-W-W-H

4

9

2

11

5

11

4

7

0

2

0

5

7

9

Fig.2.1 defines the C-Major scale using the Integer Notation,

intervals and the formula based on steps within the scale.

The shaded boxes corresponds to the notes included in the scale

(C, D, E, F, G, A, B) and the intervals w.r.t. the root/tonic (C).

Fig.2.2 shows somewhat more than 2 octaves of the C-Major

scale around the C chord’s canonical position.

Using the recipe from Fig.2.1, it is possible to extend the

pattern in Fig.2.2 to cover the whole guitar neck (fretboard)

with the C-Major scale-related dots. Simply by placing

appropriately shifted { 0, 2, 4, 5, 7, 9, 11 } pattern on individual

strings, we come up with Fig.2.3 showing positions of all notes

belonging to the C-Major Scale. The whole scale can be seen

unrolled on the A string between two roots at 3fr and 15fr,

respectively, and also on the B string (1fr to 13fr).

We will return to Fig.2.3 throughout the presentation. For the

time being, the Reader can ignore 5 overlapping segments (S1,

S2, S3, S5 and S6) marked in the drawing.

The Major scale has multiple modes and what we have

discussed so far is only the Ionian Mode corresponding to the

first (I) degree of the scale. Different modes and degrees are

discussed in Section 2.1 (“Major Scale Modes”).

2

011

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

1

2

3

4

5

6

7

Fig.2.1: C-Major scale.

Steps:

W

W

H

W

W

W

H

5fr 12fr8fr

(canonical position)3fr 10fr

Strings:

E

B

G

D

A

E

Fig.2.3: C-Major scale (full).W-W-H-W-W-W-H

5fr 12fr3fr 10fr

5

0

5

9

4

11

7

2

5

0

7

11

9

4

0

7

2

9

5

11

2

9

4

11

0

7

5

0

4

11

2

9

5

0

7

2

4

11

7

2

9

4

5

0

5

9

4

11

7

2

5

0

7

S5

S3 S6

S1 S3

S2

8fr

(canonical position)15fr


2. Major Scale (Cont.)

Strings:

E

B

G

D

A

E

5fr 12fr8fr

Fig.2.4: C-Major scale (misc. positions).

3fr

W-W-H-W-W-W-H

4

2

11

0

5 117

0 59 4

7

0 2

7

9

10fr

S6 S3

In Fig.2.4, we excerpt two Major scale sub-patterns, each covering one octave and including all notes from the scale.

The shown “S6” pattern can be played sequentially “root-to-root” (i.e., from one “0” to the next “0” and back). But

one can also experiment within the scale’s boundary—for example, try something like the following pattern starting

from the G string:

0G – 4 – 7 – 5 – 9 – 0

E – 7 – 11 – 2 – 0

G

Or perhaps try playing the other (“S3”) pattern starting from the high-E string to observe how it weaves its way

towards the root note on the B string:

4 – 5 – 7E – 4 – 5 – 2 – 4 – 0 – 2 – 11 – 0 – 9 – 11 – 7

G – 9 – 11 – 0

The patterns in Fig.2.4 (also in Fig.2.2) span four frets and could be played “in-place” (i.e., without moving the left/

fretting hand) by keeping/using individual fingers always in the same fret position. Generally speaking, this is

considered an efficient playing practice (to the extent possible), but it is not typical of all playing styles and music

genres. Also, getting locked in one playing position tends to start sounding predictable and it is important to practice

moving horizontally (left and right) between different positions.

In the remainder of this presentation, we will provide descriptions of most common scales and we will also address

the question of musical contexts in which certain scale could be used. The ability to read music scores is not required

as they will not be used in the presentation.

In this presentation, we do not intend to discuss topics like fingering and picking and we will not attempt to cover

various scale practicing techniques (such as “playing in thirds”, “playing in triads”, etc.). We will also stop using

numbered playing sequences like those associated with Fig.2.4 examples and we consider the topic of creative use of

scales to be beyond the scope of this presentation.


2.1 Major Scale Modes

C D E F G A B CW W H W W W HIonian modeI

C D E F G A B CW H W W W H WDorian modeII

C D E F G A B CH W W W H W WPhrygian modeIII

C D E F G A B CW W W H W W HLydian modeIV

C D E F G A B CW W H W W H WMixolydian modeV

C D E F G A B CW H W W H W WAeolian modeVI

C D E F G A B CH W W H W W WLocrian modeVII

P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7 P8P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7 P8Intervals: P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7 P8Intervals:

0 1 2 3 4 5 6 7 8 9 10 11 0Integer Notation: 0 1 2 3 4 5 6 7 8 9 10 11 0Integer Notation:

Major Scale Mode:

Fig.2.1.1: Major scale modes transposed to the common tonic (C).

The Major scale has 7 different modes described in Fig. 2.1.1. The Ionian mode is the first (I) degree mode of the

Major scale and was discussed in the previous section. Its constituent notes are C, D, E, F, G, A and B, and are shown

as shaded boxes. The Ionian mode formula is: W—W—H—W—W—W—H.

All other higher degree modes of the Major scale can be generated by rotating the Major scale’s formula. For the

second (II) degree mode (Dorian), the formula is rotated counter-clockwise by one position; for the third (III)

degree mode, the rotation is by 2 (i.e., the degree value minus one), and so on. The resulting modes (all having the

common tonic C) are shown in the table in Fig.2.1.1.

Another way to interpret the above is to observe that the second (II) degree mode is the same as playing the C-Major

scale from its second note (D)—that new scale would be the D-Dorian scale. Similarly, the third (III) degree mode

is the same as playing the Major scale from its third note (E)—that new scale would be the E-Phrygian scale. The rest

of this analysis is illustrated in Fig.2.1.2. Notice that the 7 scales in Fig.2.1.2 differ only in their “root”—otherwise,

they all include identical notes (C, D, E, F, G, A and B).

Degree:

Formula:

C D E F G A B CW W H W W W HIonian modeC

D E F G A B C DW H W W W H WDorian modeD

E F G A B C D EH W W W H W WPhrygian modeE

F G A B C D E FW W W H W W HLydian modeF

G A B C D E F GW W H W W H WMixolydian modeG

A B C D E F G AW H W W H W WAeolian modeA

B C D E F G A BH W W H W W WLocrian modeB



Major Scale Mode:

Fig.2.1.2: Major scale modes in the key of C.

Root:

Formula:


2.1 Major Scale Modes (Cont.)

Using the Integer Notation, the Major scale sequence can be represented as: { 0 , 2 , 4 , 5 , 7 , 9 , 11 }. For example,

the C-Major scale includes the following notes: { C , D , E , F , G , A , B }. Using the information from Fig.2.1.2, we

can analyze the C-Major scale modes.

C-Major scale includes the following triads:

• Major Triads: C (notes: C, E, G), F (notes: F, A, C) and G (notes: G, B, D).

• Minor Triads: Dm (notes: D, F, A), Em (notes: E, G, B), and Am (notes: A, C, E).

• Diminished Triads: Bdim (notes: B, D and F).

Ionian, Lydian and Mixolydian modes are related to the major triads listed above. Dorian, Phrygian and Aeolian

modes are related to the minor triads above. Locrian mode is related to the diminished triad.

By assuming each scale note a root and identifying the 3rd

/5th

interval notes within the corresponding mode (see

Fig.2.1.2), 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.2.1.2) 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).

Exercise 2.1.1: Play the above C-Major chord progressions (also shown in Fig. 2.1.3) in both directions.

Exercise 2.1.2: For each mode, the Reader should play the corresponding chord from the table in Fig.2.1.3 before

playing the scale itself. Initially, the Reader could use simpler, triad-based chords before switching to more specific

seventh chords.

• First, for the I degree mode, play the corresponding chord (C or CM7) and then play the C-Major scale (Fig.2.3)

from the mode’s root node (“0”).

• Then, for the II degree mode, play Dm (or Dm7) chord and then the scale starting from “2” (this mode’s root D).

• And so on… We suggest starting this exercise in the “canonical” (8fr) position (to get used to the sound of a

particular scale) and gradually moving to the outside (to become proficient in playing over the whole fretboard).

Exercise 2.1.3: Show that the G-Major scale consists of: { G, A, B, C, D, E, F# }. Notice there is only a single-note

difference w.r.t. C-Major scale (F# vs. F). Construct the table of G-Major triad/seventh chords (similar to Fig.2.1.3).

Notice that the chord types corresponding to the same note may differ (e.g., D vs. Dm or GM7 vs. G7).

Mode:

Ionian

Triad Chord:

C

Locrian Bdim

Lydian F

Aeolian Am

Degree:

I

VII

IV

VI

Dorian Dm

Phrygian Em

II

III

Mixolyidan GV

Seventh Chord:

CM7

Bm7b5

FM7

Am7

Dm7

Em7

G7

Fig.2.1.3: Chords associated with the C-Major scale modes.


The analysis from Fig.2.1.2 has profound implications illustrated in Fig.2.1.4. We reprint Fig.2.3 here, since we will

rely on it for our further discussion.

Strings:

E

B

G

D

A

E

Fig.2.3 (reprint): C-Major scale (full). W-W-H-W-W-W-H

5fr 12fr8fr


5

0

5

9

4

11

7

2

5

0

7

11

9

4

0

7

2

9

5

11

2

9

4

11

0

7

5

0

4

11

2

9

5

0

7

2

4

11

7

2

9

4

5

0

5

9

4

11

7

2

5

0

7

S5

S3 S6

S1 S3

S2

Strings:

E

B

G

D

A

E

Fig.2.1.4: C-Major scale modes in their canonical positions.

5fr 12fr8fr3fr 10fr

2

9

4

0

7

10

5

0

4

2

9

5

0

7

2

10

11

2

9

4

11

0

7

5

0

4

11

2

9

5

0

7

2

0

7

3

10

5

0

5

8

1

5

0

7

7

10

1

8

3

Strings:

E

B

G

D

A

E

5fr 12fr8fr3fr 10fr

0

7

3

10

5

0

8

2

5

0

7

2

3

10

0

7

3

10

5

0

2

9

5

0

7

2

3

10

3

2

9

8

3

Strings:

E

B

G

D

A

E

5fr 12fr8fr3fr 10fr

0

3

10

5

0

1

8

6

1

5

0

3

10

6

1

8

3

11

6

2

9

4

11

0

7

0

4

11

6

2

9

0

7

2

G

Mixolydian

C

Ionian

E

Phrygian

A

Aeolian

D

Dorian

B

Locrian

F

Lydian

In Fig.2.3, we show all notes from the C-Major scale (Ionian mode at 8fr) super-imposed on a guitar fretboard. By

construction, the shown pattern actually includes all 7 modes having 7 different roots as described in Fig.2.1.2 and

shown in Fig.2.1.4. For clarity, we use multiple backgrounds to avoid overlapping patterns. For each pattern (i.e., a

scale), we use Integer Notation with “0” at each scale’s root. Thus, for example, the D-Dorian scale (its root D being

two semi-tones away from C), can be re-annotated by reducing by two the corresponding number from Fig.2.3.

2



Fig.2.1.5: Five patterns to play the Major scale in any key and any mode.

Fig.2.1.5 is a generalization of Fig.2.1.4 showing 5 overlapping segments containing patterns that can be used to

play the Major scale in any key and any mode. We choose to name individual patterns based on the C-Major scale

mode they represent when played in corresponding canonical positions:

• S1 (I degree, Ionian mode, but also covers the VII degree Locrian mode as shown in Fig.2.1.4 and Fig.2.1.5)

• S2 (II degree, Dorian mode)

• S3 (III degree, Phrygian mode, but also covers the IV degree Lydian mode as shown in Fig.2.1.4 and Fig.2.1.5)

• S5 (V degree, Mixolydian mode)

• S6 (VI degree, Aeolian mode)

Using S1 as a reference (fret “X”), all other segments have their root notes (white dots) in the expected positions:

• S2 is at 2 semi-tones higher (or, using “modulo-12” arithmetic[1], 10 semi-tones lower) position.

• S3 is at 4 semi-tones higher (8 semi-tones lower) position.



In the original example, S1 (C root) was at position (fret) 8, S2 (D) at 10, S3 (E) at 12, S4 (G) at 3, and S6 (A) at 5.

We observe the following:

• The order of segments is always the same—clockwise: S1, S2, S3, S5, S6.

• The segments can be shifted to any position on the fretboard to accommodate any key.

• Any segment spans at least 2 octaves and thus includes all 7 modes that are distinguished merely by their

corresponding starting points within the segment.

• All patterns include no more than 3 notes per string and no more than one “whole step” (W) per string.

Strings:

E

B

G

D

A

E

Strings:

E

B

G

D

A

E

S5(Mix.)

S1(Ion./Loc.)

S3(Phr./Lyd.)

S6(Aeo.)

S2(Dor.)

(X+4)

mod12X

(X+7)

mod12

0

2

2

0

0

Fret:

(X+2)

mod12

(X+9)

mod12Fret:



______________________________________________________________________________________

[1] Modulo-12 arithmetic operates on numbers belonging to the range from 0 to 11. (NOTE: There are 12 simit-tones in one octave.) 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.

We can interpret the patterns from Fig.2.1.5 in the following fashion. In order to play a particular mode-specific scale,

we can go to the corresponding root note/fret on the low-E string and start playing the segment corresponding to the

desired mode. All other four segments are laid out in the consistent, orderly fashion: i.e., S1=>S2=>S3=>S5=>S6

(perhaps folded back at the 12 fret to reflect the repetitive per-octave nature of our tonal system) as seen in Fig.2.1.5.

Example 2.1.1: The A-Dorian mode has the S2 pattern rooted at the 5 th fret (“5fr”) since that is where “A” note is

found on the low-E string. Using the S2 formula from Fig.2.1.5, (X+2) is, thus, 5. The X being 3 then, we can

substitute it in formulae for other segments resulting in the following root positions: S3 (7fr), S5 (10fr), S6 (12fr or, if

folded, 0), S1 (15fr or, if folded, fr3).

Of course, this kind of a calculation is not something a player thinks of in real-time. Given enough practice, players

should be able to move to and between multiple segments smoothly. Also, as illustrated in the following example

(Fig.2.1.6 and Fig.2.1.7), being aware of underlying chords helps the player’s orientation (e.g., where the root notes

are)—this could make it easier to start playing any mode from inside of any position and segment.

Example 2.1.2: Certain major chord shapes can be found in S5, S1 and S3 patterns in Fig.2.1.4 and we can also find

minor chords under S6 and S2. Assuming the C-Major scale, we show C and Dm shapes in Fig.2.1.6. As shown, the

patterns belong to the same instance of the Major scale, so the scale can be used be used to play over both chords.

Exercise 2.1.4: We can extend the example 2.1.2 by noticing that the G chord can also be found in several patterns as

shown in Fig.2.1.6. Thus, we can try to use the same scale (C-Major) to improvise over a standard jazz progression

like Dm7-G7-CM7 (a.k.a., ii-V-I progression in Major key). The Reader should verify that the full chords (i.e.,

including their corresponding m7 or M7 notes) are all covered by the scale.

Fig.2.1.6: C, Dm and G chords in multiple positions.

Strings:

E

B

G

D

A

E

Strings:

E

B

G

D

A

E

S5 S1 S3

S6 S2

12fr5fr

C chord in

multiple

positions.

Dm chord in

multiple

positions.


Strings:

E

B

G

D

A

E

S5 S1 S3S2

8fr3fr 10fr

“Open” G chord (as

commonly played at

3fr).


NOTE: It is always possible to pick a scale for each individual chord in a progression. Frequently, however, a piece

of music is written in such a way that it uses only notes from one scale (e.g., a song “in the key of C” would use the

notes from the C-Major scale) and the same scale can be used to play over all chords of the progression.

The above statement applies to all examples presented so far in this section and the Reader should confirm that they

are also compatible with Fig.2.1.3 (“Chords associated with the C-Major scale modes”). More generally, from

Fig.2.1.3, we can conclude that a chord progression having more than one Dominant Seventh chord cannot be played

over using the same Major scale; in the key of C, for example, G7 is the only such chord—the other two major chords

from the scale (CM7 and FM7) include M7 (not m7). Also, one Major scale can cover up to 3 major chords, but not

more than that. For more examples, please see “Appendix: Common Major Scale Progressions”.

So far, only the C-Major scale has been used in all playing examples. The Reader should use the pattern from Fig.2.3

appropriately shifted/rotated to play in other keys—e.g., the A-Major scale ({ A, B, C#, D, E, F#, G# }) corresponds

to the Fig.2.3 pattern rotated counter-clockwise by 3 frets.

Exercise 2.1.6: The following chord sequence comes from the Pink Floyd song “Time” (1973). Verify that all chords

are from the A-Major scale and play over them using the same scale. Repeat the exercise after transposing the

progression to the key of C-Major.

DM7 — AM7 — DM7 — AM7 — DM7 — C#m7 — Bm7 — E


Exercise 2.1.5: As stated before, each segment in Fig.2.1.5 contains all 7 modes, so we should expect to find multiple

chords (of both major or minor type) per segment pattern. Find another Dm shape under S3. Locate Am under S6 and

S3 patterns and identify the corresponding root notes.

As expected, in Fig.2.1.6, in the same “S” pattern, the root position (white dot) depends on the chord played (e.g., C

and G, in the case of S5 pattern). Thus, although the same pattern can be used to play over multiple chords, the

emphasis may shift during the chord progression.

Scale Selection Tips:

Figuring out a chord’s root/pitch and its major-vs-minor type is relatively easy. But how to decide which mode to

use? Of course, the Reader should practice (play and sing along) and also listen to examples (e.g., try Internet search),

but a few quick tips for beginners follow... (See also: “Appendix: Common Major Scale Progressions”.)

Modes of the Major type are likely to be Ionian or Mixolydian; the only difference between them is one tone: m7

(Minor Seventh or “10” in Integer Notation) is present in the Mixolydian scale and M7 (“11”) in the Ionian. Thus, the

Ionian natural home is with M7 chords and the Mixolydian can be used with Dominant Seventh chords (e.g., blues).

And, if the first chord of a progression sounds very bright and cheerful, perhaps try the Lydian mode.

Minor type modes are likely to be Dorian or Aeolian; the only difference between them is one tone: M6 (“9”) is

present in the Dorian scale and A5 (“8”) in the Aeolian, so perhaps play both and look for better fit (i.e., playing a

wrong note is likely to sound dissonant.) And, in a less likely case, if the melody sounds vaguely “Spanish” or

perhaps very dark, try Phrygian mode.

Locrian mode is associated with the half-diminished chords (e.g., Bm7b5) and is likely to be used only in transitions

(i.e., to play over individual chord instances, but not whole chord progressions).


3. Minor Scales

Natural C-Minor scale

(Aeolian Mode)

C D E F G A B CW W H W W W HIonianI

C D E F G A B CW H W W H W WAeolian (Natural Minor)VI



Mode:

Fig.3.1: Minor scales transposed to the common tonic (C).

Degree:

Formula:

C D E F G A B CH * H W H W WPhrygian DominantV

C D E F G A B CW H W W W W HJazz Melodic MinorI

NOTE:

[*] “Minor Third” (m3).

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

Jazz 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

C D E F G A B CW H W W W H WDorianII

As discussed earlier, the Major scale has 7 modes and three of those modes are of the minor type: Dorian, Phrygian

and Aeolian. In Fig.3.1, we show all three of those minor modes. The VI degree (Aeolian mode) of the Major scale is

also referred to as the Natural Minor scale (and even just the Minor scale for short).

Harmonic Minor scale is derived from the Aeolian mode (Natural Minor) by raising m7 to M7. (Notice that there is

no Major scale’s minor mode that includes M7.) Among the Harmonic Minor’s 7 modes, one is very distinctive and

frequently used (Phrygian Dominant) and is included in Fig.3.1 as well. The Phrygian Dominant includes M3 (i.e.,

not m3), so it is really a major scale; in fact, the Third interval is the only difference from the Phrygian mode of the

Major scale. We will show all Harmonic Minor modes and analyze the scale’s harmonic context in a later section.

Jazz Melodic Minor is similar to the Major scale’s Ionian mode, but it includes m3 instead of M3. Also, this minor

scale is similar to Dorian (but with M7 instead of m7) and there is only one note difference between the Jazz Melodic

Minor and the Harmonic Minor (M6 instead of m6). The natural fit of the Jazz Melodic scale are “minor-major

chords” (e.g., CmM7). Jazz Melodic Minor can also be played in 7 modes and they will be presented in a later section.

Fig.3.2 shows the previously mentioned minor scales in their canonical positions.

Exercise 3.1: Play the scales from Fig.3.2 and listen to the differences. When playing scales from-low-to-high, 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 (“8” moves to “9”).

Fig.3.2: Comparison of Minor scales (canonical position).

C D E F G A B CW H W W H * HHarmonic MinorI

C D E F G A B CH W W W H W WPhrygianIII


3. Minor Scales (Cont.)

(a) Natural C-Minor scale (full). W-H-W-W-H-W-W

(b) Harmonic C-Minor scale (full) W-H-W-W-H-m3-H

5fr 12fr8fr


5

0

8

3

5

11

7

2

5

0

7

8

3

11

8

0

7

2

5

8

3

11

2

11

0

7

3

5

0

8

11

2

5

0

7

2

3

8

3

11

7

2

5

0

8

3

5

11

7

2

5

0

7

8

3

11

8

15fr

S3

S2 S5

S6 S2

S1

(c) Jazz Melodic C-Minor scale (full). W-H-W-W-W-W-H

5fr 12fr8fr


5

0

3

5

9

11

7

2

5

0

7

3

11

9

0

7

2

9

5

3

11

2

9

11

0

7

3

5

0

11

2

9

5

0

7

2

3

3

11

7

2

9

5

0

3

5

9

11

7

2

5

0

7

3

11

15fr

Fig.3.3: Comparison of Minor scales (full).

S3

S2 S5

S6 S2

S1

5fr 12fr8fr


5

0

8

3

10

5

7

2

10

5

0

7

8

3

8

0

7

2

10

5

8

3

10

2

0

7

3

10

5

0

8

2

5

0

7

2

3

10

8

3

7

2

5

0

8

3

10

5

7

2

10

5

0

7

8

3

8

15fr

S3

S2 S5

S6 S2

S1

In Fig.3.3(b), we show a full fretboard worth of the Harmonic C-Minor scale. The basic playing segments (S1-S6) are

in their expected locations and individual patterns need only incremental adjustments compared to the Natural Minor

shown in Fig.3.3(a). This is because one note (the shaded “11”) moved in the Harmonic Minor compared to the

Natural Minor (i.e., as discussed earlier, m7 became M7). Fig.3.3(c) also includes the Jazz Melodic Minor. Again, its

pattern is an incremental change from the Harmonic Minor—the Sixth interval got raised thus eliminating that wide

“m3” step of the Harmonic Minor.

In Fig.3.3, three common scales are mapped to overlapping playing patterns (S1-S6). Another approach to playing

those scales is based on the “three-notes-per-string” (3NPS) patterns (see “Appendix: 3NPS Patterns...”). The Reader

should be aware, however, that getting locked in a particular playing position tends to sound predictable, so it is

imperative to develop more a global view and awareness of the guitar fretboard—we discuss this in Fig.3.4.

NOTE: Inside of one

octave of the Major scale,

there are 3 full columns

(fret positions 1, 3 and 8

as shown here) and one

empty (fret position 2).

NOTE: Unlike the Major

scale, the Harmonic

Minor has neither full nor

empty columns. It also

includes wider (m3) steps.

NOTE: The Melodic

Minor has one full

column (10fr) and no

empty ones. All steps are

H or W (i.e., no m3).


3. Minor Scales (Cont.)

11

11

11

11

11

11

11

11

9

9

9

9

9

9

9

Fig.3.4: Comparison of common scales.

5fr 12fr8fr3fr 10fr

10

10

10

10

10

10

10

10

0

15fr


5fr 12fr8fr3fr 10fr

8

8

8

8

8

8

8

8

8

15fr

5fr 12fr8fr3fr 10fr

3

3

3

3

3

3

3

3

15fr

4

4

4

4

4

4

4

Harmonic C-Minor

Natural C-Minor

(a)

Melodic C-Minor

Harmonic C-Minor

(b)

C-Major

Melodic C-Minor

(c)

The differences between the three common scales discussed in Fig.3.3 are very small. In Fig.3.4, all such single-note

differences are shown as numbered black dots. (For reference, the root notes are kept as white dots; all other notes are

shown as shaded and are not numbered.)

It takes some time and practice, but it is extremely rewarding to be able to locate notes and intervals on the guitar

fretboard. For example, when switching between two scales, it should be easier to think in terms of moving one note

slightly, than to keep track of all patterns (“S1-S6” or “3NPS”) for all scales and navigate between those.

As shown in Fig.2.1.1 and Fig.3.1, the Natural Minor scale is the VI degree (Aeolian) mode of the corresponding

Major scale. The Natural Minor is frequently referred to as the Minor scale for short and, using the Integer Notation,

its sequence can be represented as:

{ 0 , 2 , 3 , 5 , 7 , 8 , 10 }

Thus, in the key of C, the Natural Minor scale consist of:

{ C , D , D# , F , G , G# , A# }.

We remind the Reader that the Natural C-Minor scale (shown in Fig.3.3(a)) is the VI degree mode of D#-Major scale

that consists of:

{ D# , F , G , G# , A# , C , D }.

The Natural C-Minor scale includes the following triads:

• Major Triads: D# (notes: D#, G, A#), G# (notes: G#, C, D#) and A# (notes: A#, D, F).

• Minor Triads: Fm (notes: F, G#, C), Gm (notes: G, A#, D), and Cm (notes: C, D#, G).

• Diminished Triads: Ddim (notes D, F, G#).

We can associate the following Seventh chords sequence with the Natural C-Minor scale shown in Fig.3.3(a):

Cm7 — Dm7b5 — D#M7 — Fm7 — Gm7 — G#M7 — A#7 — Cm7

Exercise 3.1.1: Use Am-Aeolian scale (i.e., Natural Minor from the C-Major scale) to play along the Am-G-F-Em

chord progression. Notice the Major Triads for F (notes: F, A, C) and G (notes: G, B, D) and Minor Triads for Am (A,

C, E) and Em (notes: E, G, B) are all included in the C-Major scale (notes: C, D, E, F, G, A, B).

Using only the Natural Minor for a Spanish-sounding Am-G-F-E progression does not work, however. The reason is

that the E-Major Triad (notes: E, G#, B) includes one note (G#) not present in the C-Major scale. So, after using the

Am-Aeolian scale for the first three chords (Am, G, F), we switch to the Harmonic A-Minor for the final E chord.

This is a common use of the Harmonic Minor scale: playing over the V chord in a minor key progression. (More on

this below.)

Notice that, in the Minor scale, the fifth chord is minor (i.e., “v” and not “V”). In the A-Minor scale, the

corresponding chord would be Em7—thus, in the earlier Am-G-F-E example, we had to introduce the Harmonic

Minor for the major V chord in a minor progression.

Exercise 3.1.2: A popular music standard “Autumn Leaves” (orig. 1945) is based on the following chord progression:

Am7 — D7 — GM7 — CM7 — F#m7b5 — B7 — Em7

Except for B7, the rest of 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 Minor can be employed instead.

3.1 Natural Minor Scale




Mode:

Fig.3.2.1: Harmonic Minor modes transposed to the common tonic (C).

Degree:

Formula:


NOTE: [*] “Minor Third” (m3).


C D E F G A B C* H W H W W HLydian #2VI

3.2 Harmonic Minor Scale

C D E F G A B CH W W H * H WLocrian #6II

C D E F G A B CW W H * H W HIonian #5III

C D E F G A B CW H * H W H WDorian #4IV

C D E F G A B CH W H W W H *SuperlocrianVII

Comment:

Minor M7 chord—not found in the Major scale.

Triad Chord:

Cm

Bdim

Fm

Also includes #9 (i.e., m3).G#

Degree:

I

VII

IV

VI

Ddim

Augmented.D#+

II

III

a.k.a. Altered Phrygian, Spanish, Gipsy, Freygish...GV

Seventh Chord:

CmM7

Bdim7

Fm7

G#M7

Dm7b5

D#M7#5

G7

Fig.3.2.2: Chords associated with the Harmonic C-Minor scale modes.

The Harmonic Minor modes are shown in Fig.3.2.1. Using the Integer Notation, the Harmonic Minor sequence can

be represented as: { 0 , 2 , 3 , 5 , 7 , 8 , 11 }. In the key of C, the Harmonic Minor includes: { C, D, D#, F, G, G#, B }.

The Harmonic C-Minor scale includes the following triads:

• Major Triads: G (notes: G, B, D) and G# (notes: G#, C, D#).

• Minor Triads: Cm (notes: C, D#, G), Fm (notes: F, G#, C).

• Diminished triads: Ddim (notes: D, F,G#) and Bdim# (notes: B, D, F).

• Augmented Triads: D# (notes: D#, G, B).

The chords associated with the Harmonic Minor scale are shown in Fig.3.2.2. There are only two Major Triads in the

Harmonic Minor scale and they are a semi-tone apart. There are also only two Minor Triads (with the I degree mode

being a minor-major CmM7). Notice that the Harmonic Minor introduces two chords types—the minor-major and the

augmented—not present in the Major Scale.

Example 3.2.1: The famous guitar introduction to Janis Joplin’s version of “Summertime” (1968) is in the Harmonic

G-Minor.

Exercise 3.2.1: Earlier, we showed that it is possible to play the ii-V-I progression (e.g., Dm7-G7-CM7) using

the C-Major scale. We can also use the Harmonic C-Minor for the V chord (G7 in this example), while still playing

the C-Major over I-ii chords. This works since the G7 (notes: G, B, D, F) is covered by the Harmonic C-Minor and

the inclusion of D# and G# notes (not from the C-Major scale) has an effect of adding tension to the V chord to be

resolved by going to the I chord. (This is the same as playing G7#5b9 instead of G7 in the progression.)

Exercise 3.2.2: Incorporate the Harmonic Minor into a Tango-like sequence Cm-Fm6-G7-Cm.


In Fig.3.2.3(a), we excerpt the modified S3 pattern from Fig.3.3(b). The shown V degree Phrygian Dominant mode

of the Harmonic Minor scale is one of the most distinctive guitar scales. We re-number it to reflect its canonical

position (3fr) and show some additional ways to play it. In Fig.3.2.3(a), we can observe that the G-Phrygian

Dominant scale can be completely covered with G ({0, 4, 7}) and G# ({1, 5, 8}) chords with the m7 (“10”) interval

added (i.e., the scale is completely covered by G7 and G# chords). The “3-notes-per-string” pattern (the one on the

left side of Fig.3.2.3(b)) becomes more attractive as frets get narrower in the higher-pitch positions and, due to its

regular structure, allows for easier picking and faster playing. (See also “Appendix: 3NPS Patterns”.) The other

pattern shown in Fig.3.2.3(b) is a special (but common) case of playing the Phrygian Dominant scale in the key of

E—there, we could use open strings to produce a lot of notes and phrases with minimal finger stretching.

Exercise 3.2.3: Play the G-Phrygian Dominant scale (from the Harmonic C-Minor) in S2 position (a slightly modified

Dorian pattern shown in Fig.3.2.3(c)). We highlight two action-packed 4-by-3 boxes (each being a full octave of

friendly fingering) that are relatively easy to switch between. The whole region can also be traversed in a shredding-

friendly “3-notes-per-string” fashion. But, as the side detail shows, we can also identify a compact 2x4 box containing

all seven scale notes and play a melody there using only two fingers.

Exercise 3.2.4: Use the Phrygian Dominant scale to play over the flamenco-like progression E-FM7add#11

(basically, the “open” E chord followed by the same chord shape shifted one fret/semi-tone higher.)

The Phrygian Dominant scale is also referred to as Altered Phrygian, Spanish, Gipsy and Freygish, to name but a few

aliases.

3fr

85

4

7

0

1

0

5

7

8

1

Fig.3.2.3(a): G-Phrygian Dominant (canonical position).

10

0

4

1

10

85

4

1

0

5

7

8

1

4

4

10

0

1

10

7

3fr

S2

Fig.3.2.3(c): G-Phrygian Dominant (“Dorian” position).

12fr

4

1

15fr

S3

S3

H-m3-H-W-H-W-W

0

5

Fig.3.2.3(b): 3-notes-per-string pattern and open string pattern.

85

4

1

0

5

7

8

1

4

4

10

0

1

10

0fr

0

7

10 0 1

8

4

4

7

0

10

8

5

1

10

5

0

7

10

4

7

0

10

8

5

1

12fr

(detail)

3.2 Harmonic Minor Scale (Cont.)


3.3 Jazz Melodic Minor Scale



Mode:

Fig.3.3.1: Jazz Melodic Minor modes in the key of C.

Degree:

Formula:

C D D# F G A B CW H W W W W HJazz Melodic MinorI

F G A B C D D# FW W W H W H WLydian DominantIV

A B C D D# F G AW H W H W W WLocrian #2VI

B C D D# F G A BH W H W W W WSuperlocrianVII

Mode:

Melodic Minor

Chord:

CmM7

Superlocrian, Altered (Dominant), Diminished Whole-tone B7alt

Lydian Dominant, Lydian b7, Mixolydian #4, Overtone F7

Locrian #2, Half-Diminished, Aeolocrian Am7b5

Degree:

I

VII

IV

VI

Function:

i chord in minor progression. Also, used with Cm6.

Dominant V returning to i. Altered: b2, b3, b5, b6.

Dominant chord not resolving in i.

ii chord in minor progression.

In Fig.3.3.1, we describe the 7 modes of the Jazz Melodic Minor scale. Using the Integer Notation, the Jazz Melodic

Minor sequence can be represented as: { 0 , 2 , 3 , 5 , 7 , 9 , 11 }. For example, in the key of C, the Melodic Minor

includes: { C, D, D#, F, G, A, B }. Obviously, it differs from the Ionian scale in only one tone (D# instead of E)

reflecting the flatted Third interval (i.e., switching the mode from major to minor).

The Jazz Melodic C-Minor scale includes the following triads:

• Major Triads: F (notes: F, A, C) and G (notes: G, B, D).

• Minor Triads: Cm (notes: C, D#, G) and Dm (notes: D, F, A).

• Diminished Triads: Adim (notes: A, C, D#).

• Augmented Triads: D#aug (notes: D#, G, B).

Technically, we could associate with the B note both the Diminished Triad (notes: B, D, F) and the Augmented Triad

(notes: B, D#, G), but this is because this scale is associated with altered dominant chords. As commonly used in

jazz, they are Dominant Seventh chords (e.g., C7) with the Fifth and Second/Ninth interval altered (either raised or

flatted or both). For example, C7#5 would be a common altered chord—similarly, C7#5#9 (a.k.a. C7alt) that also

includes the raised Ninth (meaning that minor-signaling m3 is also present adding even more tension to the chord).

Noticed that in the “altered dominant” mode/scale, every interval other than M3, is flatted.

Based on its harmonic content, the scale is rarely used to play over multiple chords—typically, it is instanced for each

individual chord in the progression. In Fig. 3.3.1, we include multiple descriptive aliases used for the individual

modes and also provide some additional info on most commonly used modes (I, IV, VI and VII) in the “function”

column.

Dorian b9, Phrygian #6 Dm7

Lydian Augmented, Lydian #5 D#M7#5

II

III

Mixolyidan b13, Aeolian Dominant, Melodic Major, Hindu G7V

D D# F A B C DH W W W W H WDorian b9II

D# F G A B C D D#W W W W H W HLydian AugmentedIII

G A B C D D# F GW W H W H W WMixolydian b13V

G


3.3 Jazz Melodic Minor Scale (Cont.)

Strings:

E

B

G

D

A

E

Fig.3.3.2: Jazz Melodic C-Minor scale sub-patterns. W-H-W-W-W-W-H

5fr 12fr8fr


5

0

3

5

9

7

5

7

9

7

9

5

3

11

9

0

7

5

2

9

5

7

3

11

7

9

5

0

9

11

7

2

5

0

7

3

11

15fr

2011

11 0 2 3

3

5

2011

32011

32

One interesting property of the scale is shown in Fig.3.3.2 . We see that there are two alternating patterns: “Half-

Diminished” (H-W-H) and Whole Tone (W-W-W-W). (The VII degree of the scale is sometimes also called

“Diminished Whole-Tone” for this reason; we will discuss Diminished and Whole-Tone scales in later sections.)

Because the Sixth interval of the Harmonic Minor got raised, there are no wide “m3” steps present in the Melodic

Minor. Still, playing the Melodic Minor in this fashion is a bit more involved than playing the Major scale: no matter

how re-arranged, some patterns include two consecutive “W” steps per string (e.g., 3-5-7 or 7-9-11) or even playing

four notes (e.g., 11-0-2-3) per string. (NOTE: But see also “Appendix: 3NPS Patterns (Melodic Minor Scale)”.)

The Jazz Melodic Minor scale is likely to sound unfamiliar to those who listen mostly to rock music. The scale is very

common in jazz and its natural home are minor-major chords (e.g., CmM7) associated with the I degree mode of the

scale. The scale works well over jazz progressions like ii-V-i, but the usage rules are somewhat involved and a

different scale is played over individual chords (see the “Function” column in Fig.3.3.1 ,“Appendix: ii-V-i

Progression” and “Appendix: I-vi-ii-V Progression”). Instead, in Fig.3.3.3 and Fig.3.3.4, we suggest two ways

for the Reader to get introduced to the scale. We transpose the scale to E-Minor as there is a simple way to finger-

pick EmM7 using three open strings (G, low/high E) along with the 4th fret on the B string (i.e., Eb note).

In Fig.3.3.3, we show the Jazz Melodic E-Minor scale in all positions. We emphasize the underlying Em chords

(Minor Triads, shown as black dots) and also highlight two additional intervals that contribute to the scale’s very

distinct flavor (M7 and M6, shown as shaded dots). The Reader should play over the EmM7 chord using the shown

interval information. The Reader can also try playing over other simple chords like Em6 (the same as the previously

described EmM7, but, on the B string, play the second fret instead of the fourth).

Fig.3.3.3: Jazz Melodic E-Minor scale (full).W-H-W-W-W-W-H

5fr 12fr7fr3fr 10fr

5

0

3

5

9

11

7

2

5

0

7

3

11

9

0

7

2

9

5

3

11

2

9

11

0

7

3

5

0

11

2

9

5

0

7

2

3

3

0

7

3

7

0

11

2

9

5

0

7

2

3

3

11

7

2

9

// Black dots:

Minor Triad = {0, 3, 7}

// Shaded dots:

Major Sixth = {9}

Major Seventh = {11}

E

B

G

D

A

E

Exercise 3.3.1: With its 7 modes (Fig.3.3.1), the Jazz Melodic Minor is a rich scale providing a variety of flavors to

be explored by the Reader. We suggest to first play the corresponding I degree mode chord (CmM7 from the “Chord”

column) and then play the C-Minor scale (Fig.3.2.2) from the mode’s root node (“0”). Then, for the II degree mode,

the Reader should play Dm7 chord and then the scale starting from “2”, and so on—e.g., for the IV degree mode, play

F7 (or just F) starting from “5”. We suggest starting this exercise in the “canonical” (8fr) position (to get used to the

sound) and gradually moving to the outside (to become proficient in playing over the whole fretboard). The Reader

can also do this exercise in the key of E, by transposing the chords accordingly and using the scale from Fig.3.3.3.


3.3 Jazz Melodic Minor Scale (Cont.)

5fr 12fr7fr3fr 10fr

5

0

3

9

7

5

3

11

9

0

7

11

2

9

0

3

11

9

5

0

30

7

3

11

2

5

0

3

11

7

2

(a) Jazz Melodic E-Minor scale (thirds/sixths). W-H-W-W-W-W-H

Thirds (m3 or M3):

- D/G strings (0/3, 2/5, 3/7...)

Sixths (m6 or M6):

- G/high-E strings (3/0, 5/2…)

E

B

G

D

A

E

B7 C#m7b5 D#(7alt) EmM7A7Fm7EmM7 GM7#5

In Fig.3.3.4(a), we show positions of the Melodic Minor scale’s “thirds” (notes separated by m3 or M3) as alternating

pairs of black and shaded dots on strings D and G. The Reader should go over the full scale (e.g., going from lower to

higher pitches and back) by playing the corresponding pairs together:

(0-3) (2-5) (3-7) (5-9) (7-11) (9-0) (11-2) (0-3)

Exercise 3.3.2: This being Em, try playing the described thirds pattern on D-G strings together with open B and high-

E. (Perhaps finger-pick using the D string for bass notes?)

Exercise 3.3.3: Discover the shapes corresponding to the thirds on G-B strings and play the same pairs of notes as

before.

Exercise 3.3.4: In Fig.3.3.4(b), we show the thirds of the Natural E-Minor scale (that is the VI degree mode of the G-

Major scale). Observe (and play and listen to) the differences w.r.t. the Jazz Melodic E-Minor.

If we move the notes from the D string one octave higher (to high-E), the pairs on G and high-E strings correspond to

m6 or M6 interval. (E.g., D-G “(0-3)” m3 interval, becomes “(3-0)” M6 interval on G-E strings.) In Fig.3.3.4, we

also show the Sixth intervals as alternating pairs of black and shaded dots on strings G and low-E. The Reader should

also train the ear to recognize those.

5fr 12fr7fr3fr 10fr

5

0

3

8

7

5

3

10

8

0

7

10

2

8

0

3

10

9

5

0

30

7

3

11

2

5

0

3

11

7

2

(b) Natural E-Minor scale (thirds/sixths). W-W-H-W-W-W-H

Thirds (m3 or M3):

- D/G strings (0/3, 2/5, 3/7...)

Sixths (m6 or M6):

- G/high-E strings (3/0, 5/2…)

E

B

G

D

A

E

Bm7 CM7 D7Am7F#m7b5Em7 GM7

3

Fig.3.3.4: Interval comparison between Melodic/Natural Minor scales.

Em7


4. Harmonic Major Scales

C D E F G A B CW W H W W W HIonian (Major Scale)I

C D E F G A B CW H W W H W WAeolian (Natural Minor)VI



Mode:

Fig.4.1: Harmonic Major scales.

Degree:

Formula:

NOTE:



C D E F G A B CW W H W H * WHarmonic MajorI

As discussed earlier and re-iterated in Fig.4.1, the Harmonic Minor scale can be derived from the Aeolian mode

(Natural Minor) of the Major scale by raising m7 to M7. The Harmonic Major scale is the same as the Harmonic

Minor, but with m3 raised to M3. Alternatively, the Harmonic Major is the Ionian Mode with flatted M6. The three

scales’ canonical positions are shown in Fig.4.2; the full fretboard is shown in Fig.4.3. Compared to other scales

discussed so far, the Harmonic Major is rarely used in popular music and we will not analyze all seven of the scale’s

modes. The Harmonic Major scale is more common in jazz.

Exercise 4.1: Play the three scales from Fig.4.2 and observe the differences.

Exercise 4.2: Play the Harmonic C-Major over CM7-FmM13 progression. (FmM13 is also shown in Fig.4.3. Note:

CM7 and FmM7 are seventh chords corresponding to the I and IV degree modes of the Harmonic C-Major scale.) Try

also playing the Melodic F-Minor over the second chord of the progression.

8fr

8

2

5

4

7

0

2

0

5

7

8

2

0

11

11

11

Fig.4.2: Harmonic C-Major scale (canonical position).

8fr

8

2

5

3

7

0

2

0

5

7

8

2

0 3

3

11

11

11

4

8fr

9

2

5

4

7

2

0

5

7

9

2

0

11

11

11

4

Ionian C-Major Harmonic C-Major Harmonic C-Minor

C D E F G A B CH * H W H * HDouble Harmonic MajorI

W-W-H-W-H-m3-W

0

C D E F G A B CW H * H H * HHungarian MinorIV

E

B

G

D

A

E

Fig.4.3: Harmonic C-Major scale (full).

5fr 12fr8fr


5

0

8

5

4

11

7

5

0

7

8

11

8

4

0

7

5

8

11

4

11

0

7

5

0

8

4

11

5

0

7 8

4

11

7

4

5

0

8

5

4

11

7

5

0

7

8

11

8

15fr

W-W-H-W-H-m3-W

2

2

2

22

2

2


7

3

0

FmM13

11

9

1fr


4.1 Double Harmonic Major Scale

8fr

85

4

7

0

0

5

7

8

1

0

11

11

11

4

1

1

For those who were wondering how diagonal a scale pattern could get, we also discuss a beautiful Double Harmonic

Major (a.k.a., Byzantine, Arabic, Gipsy Major) scale in Fig.4.1.1. It is the same as the Phrygian Dominant scale, but

with M7 instead of m7—because of this modification, the Double Harmonic Major scale includes two wide m3 steps.

Fig.4.1.1: Double Harmonic C-Major scale (canonical position). H-m3-H-W-H-m3-H

Trivia 4.1.1: The famous opening of

“The Pink Panther Theme” (H. Mancini,

1963) employs all 7 notes from the

Double Harmonic B-Major scale.

Notice two “m3” steps.

Notice how this shape tightly

hugs underlying oh-so-sad chords

(e.g., Fm-C#-C or Fm-G7-C).

Strings:

E

B

G

D

A

E

Fig.4.1.2: Double Harmonic C-Major (full).H-m3-H-W-H-m3-H

5fr 12fr8fr


5

0

8

5

1

4

11

7

5

0

7

8

11

1

8

4

0

7

5

1

8

11

4

11

0

7

5

0

1

8

4

11

1

5

0

7

1

8

4

11

7

4

5

0

8

5

1

4

11

7

5

0

7

8

11

1

8

15fr

Strings:

E

B

G

D

A

E

Fig.4.1.3: Hungarian a.k.a. Double Harmonic C-Minor. W-H-m3-H-H-m3-H

12fr8fr 10fr

3

0

8

11

6

2

0

7

2

3

6

8

3

11

7

2

0

6

From the definition in Fig.4.1 and the full fretboard pattern shown in Fig.4.1.2, we can see that the Double Harmonic

C-Major scale can be completely covered with C ({0, 4, 7}) and C# ({1, 5, 8}) chords with the M7 (“11”) interval

added (i.e., the scale is completely covered by CM7 and C# chords). This is similar to the corresponding C-Phrygian

Dominant scale covered by C7 and C# chords. In Fig.4.1.2, we highlight two 3-by-3 boxes, each packing all 7 notes

(shaded dots clustered around the root note) of the Double Harmonic Major scale—within each box, very effective

phrasing and Oriental/Flamenco-sounding licks could be played using only 3 fingers. The Double Harmonic Major is

common to music forms ranging from the Central European Gipsy music to jazz (e.g., Miles Davis’s “Nardis” uses

both the Double Harmonic Major and Phrygian Dominant scales).

The most commonly used mode of the Double Harmonic Major scale is its IV degree Hungarian Minor. As shown

in Fig.4.1, the Hungarian Minor differs from the Harmonic Minor in just one note, so it is frequently referred to as the

Double Harmonic Minor. In Fig.4.1.3, we show a “3-notes-per-string” shredding-friendly playing pattern (shaded

numbered dots) that allows for fluid playing covering extended stretches of the fretboard. In contrast, moving

between the two highlighted boxes shown in Fig.4.1.2 is relatively cumbersome.


5.1 Minor Pentatonic Scale

Strings:

E

B

G

D

A

E

5fr 12fr8fr

(canonical position)

Fig.5.1.2: C-Minor Pentatonic scale (canonical position)

3fr

m3-W-W-m3-W

30

5

10

3

7

0

0

5

7

3

10

Fig.5.1.3: C-Minor Pentatonic scale (full) m3-W-W-m3-W

C D E F G A B CW H W W W H WDorian

C D E F G A B CW H W W H W WNatural Minor (Aeolian)

C D E F G A B Cm3 W W WMinor Pentatonic



Scale:

Fig.5.1.1: Minor Pentatonic scale

Formula:

m3

C D E F G A B CH W W W H W WPhrygian

In Fig.5.1.1, we define the Minor Pentatonic scale and show its relationship to several Major scale modes. The

Minor Pentatonic scale has only 5 notes including two “m3” intervals that span three semi-tones as also shown in the

Fig.5.1.2. We see that the Minor Pentatonic is fully covered by all three Major scale modes of “minor” quality. In

addition to the root note, the Minor Pentatonic scale also includes the other two notes constituting the Minor Triad ({

0 , 3 , 7 }). Included also is the Minor Seventh (“10”) making this scale applicable to all Major scale’s minor modes

(since none of them has M7).

In Fig.5.1.3, we show all Minor Pentatonic scale positions.

Exercise 5.1.1: In Fig.5.1.3, fill in the missing dots corresponding to Dorian, Phrygian or Aeolian modes of the Major

scale in the canonical position.

Strings:

E

B

G

D

A

E

5fr 12fr8fr

(cannonical position)3fr 10fr

5

0

3

5

7

10

5

0

7

3

0

7

10

5

3

10

0

7

3

10

5

0

5

0

7

3

10

3

7

5

0

3

10

5

7

5

0

7

3

15fr

10

10


5.2 Major Pentatonic Scale

C D E F G A B CW W H W W W HMajor (Ionian)

C D E F G A B CW W H W W H WMixolydian

C D E F G A B Cm3W W WMajor Pentatonic



Scale:

Fig.5.2.1: Major Pentatonic scale

Formula:

m3

Strings:

E

B

G

D

A

E

5fr 12fr8fr

Fig.5.2.2: C-Major Pentatonic scale (canonical position).

3fr

W-W-m3-W-m3

20

4

9

2

7

0

0

4

7

2

9

Strings:

E

B

G

D

A

E

Fig.5.2.3: C-Major Pentatonic scale (full).

5fr 12fr8fr3fr 10fr

0

9

4

7

2

0

7

9

4

0

7

2

9

2

9

4

0

7

0

4

2

9

0

7

2

4

7

2

9

4

0

9

4

7

2

0

7

15fr

In Fig.5.2.1, we define the Major Pentatonic scale and show its relationship to several Major scale modes. The

Major Pentatonic scale has only 5 notes including two “m3” steps that span three semi-tones as also shown in the

Fig.5.2.2. We see that the Major Pentatonic is fully covered by all three Major scale modes of “major” quality. Unlike

the Minor Pentatonic, to make the scale mode-neutral, no Seventh interval (m7 or M7) is included.

Viewed as a 5-note chord, the Minor Pentatonic is an inversion of the Major Pentatonic (starting with its M6):

{ 0 , 2 , 4 , 7 , 9 } + { 3 , 3 , 3 , 3 , 3 } = { 3 , 5 , 7, 10 , 12 } = { 3 , 5 , 7, 10 , 0 }

This property is exhibited in Fig.5.2.3 by the back-to-back patterns rooted at 5fr and 8fr.

Similarly, the Major Pentatonic scale is an inversion of the Minor Pentatonic scale (starting with its m3):

{ 0 , 3 , 5 , 7, 10 } + { 9 , 9 , 9 , 9 , 9 } = { 9 , 12 , 14 , 16 , 19 } = { 9 , 0 , 2 , 4 , 7 }

This property is exhibited in Fig.5.1.3 by the back-to-back patterns rooted at 8fr and 11fr.

Notice that the full fretboard patterns of Fig.5.1.3 (Minor Pentatonic) and Fig.5.2.3 (Major Pentatonic) are identical

(albeit shifted). We explore this further in the following section and Fig.5.2.4.

C D E F G A B CW W W H W W HLydian mode

W-W-m3-W-m3


5.2 Major Pentatonic Scale (Cont.)

C D E F G A B CW W W



Chord type:

Fig.5.2.4: Major Pentatonic scale modes in the key of C.

Formula:

I

Degree:

D E F G A B C DW * *II

E F G A B C D E* W WIII

G A B C D E F GW * WIV

A B C D E F G A* W *V

*

W

*

W

W

*

W

W

*

W

NOTE:


Major, no m7/M7.

Suspended, m7 included.

Minor, m7 included.

Suspended, no m7/M7.

Minor, m7 included.

The two Pentatonic scales discussed so far (Minor and Major) abstract out the Major scale’s “mode” information:

once the pitch/tonic is known, the playing pattern is mode-independent. The Major Pentatonic scale is applicable to

all major modes of the Major scale: Ionian, Lydian, and Mixolydian. The Minor Pentatonic scale is applicable to

Dorian, Phrygian and Aeolian modes of the Major scale: Locrian mode does not work because it does not include the

Perfect Fifth (“7”); thus, we have to be careful when playing over “Half-Diminished” chords (e.g., Cm7b5).

As previously discussed, if treated as chords, the Minor/Major Pentatonic scales are mutual inversions and they use

the same 5 playing patterns (appropriately shifted). As shown in Fig.5.2.4, similar to the Major scale, we can formally

define one Major Pentatonic scale. The scale’s I degree mode is the Major Pentatonic as discussed so far; the

Minor Pentatonic is the V degree mode of the Major Pentatonic scale as defined in Fig.5.2.4. For each mode, we

summarize the corresponding chord type based on:

- Third interval: major, minor or suspended (if neither m3 nor M3 is included)

- Seventh interval: either not present or m7.

While somewhat sparse in terms of notes, the Pentatonic scale provides a great scaffolding for improvisation and has

been widely used by rock guitarist. Also, when harmonies/modes/etc get complicated and taxing (e.g., in jazz), the

Pentatonic can serve as both a safe haven and a resting place.

See also: “Appendix: Relative Minor” and “Appendix: Pentatonic Superimposition”.

Exercise 5.2.2: Play the IV degree mode of the Major Pentatonic. It is also known as Ritusen scale or Yo scale and is

common in several Asian cultures. Both the Third and the Seventh interval are missing from the scale giving it a very

distinctive, neutral sound.

Exercise 5.2.3: Show that neither Major nor Minor Pentatonic (I and V degree of the Major Pentatonic scale) can be

played over any mode of the Harmonic Minor scale (Fig.3.2.1 and Fig.3.2.2).

Exercise 5.2.4: Show that the Minor Pentatonic (V degree of the Major Pentatonic scale) can be played over the Jazz

Melodic Minor scale (II degree Dorian b9, Fig.3.2.1); the Major Pentatonic (I degree of the Major Pentatonic scale)

can be played over the Lydian Dominant (IV degree) mode of the Jazz Melodic Minor scale.


5.3 Dominant Pentatonic Scale

C D E G Bb CW W *



Chord type:

Fig.5.3.1: Dominant Pentatonic scale modes in the key of C.

Formula:

I

Degree:

D E G Bb C DW * WII

E G Bb C D E* * WIII

G Bb C D E G* W WIV

Bb C D E G BbW W *V

*

*

W

W

W

W

W

W

*

*

NOTE: [*] “Minor Third” (m3).

Major, m7 included.

Suspended, m7 included.

Diminished, m7 included.

Minor, no m7/M7.

Major, no m7/M7

Fig.5.3.1 shows all modes of the Dominant Pentatonic scale. Same as the Major Pentatonic, the Dominant

Pentatonic scale has only 5 notes including two “m3” steps that span three semi-tones as also shown in the Fig.5.3.2

and Fig.5.3.3. Unlike the Major Pentatonic, however, the Dominant Pentatonic scale includes the Minor Seventh (m7/

“10”) and not the neutral Major Sixth (M6/“9”).

Exercise 5.3.1: Show that the Dominant Pentatonic scale can be played over the following scales:

• Major: V degree Mixolydian mode.

• Melodic Minor: IV and V degree modes.

• Harmonic Minor: none.

In jazz progressions, a Dominant Pentatonic can be used for “Tritone Substitution”: there, a dominant chord is

sometimes replaced with the chord of the same type that is rooted three whole tones away (e.g., B-Major Dominant

Pentatonic can be played over F7 chord). The idea behind the Tritone Substitution is that the two chords (e.g., F7 and

B7) have two common notes (A and D#) corresponding the their strongest intervals (M3 and m7, albeit reverted).

Strings:

E

B

G

D

A

E

5fr 12fr8fr

Fig.5.3.2: C-Major Dominant Pentatonic scale (canonical position).

3fr

W-W-m3-m3-W

20

4

10

2

7

0

0

4

7

2

10

E

B

G

D

A

E

Fig.5.3.3: C-Major Dominant Pentatonic scale (full).

5fr 12fr8fr3fr 10fr

0

4

7

2

0

7

4

0

7

2

2

4

0

7

0

4

2

0

7

2

4

7

2

4

0

4

7

2

0

7

15fr

W-W-m3-m3-W

10

10

10

10

10

10

1010


6. Blues Scales

In Fig.6.1 and Fig.6.2 we show two scales common in blues and jazz. Both scales are simple extensions of the

Pentatonic scale adding notes that would be considered dissonant outside of blues/jazz.

Minor Blues scale (Fig.6.1):

• Adds the “Blue Note” (d5 interval or “6” in Integer Notation) to the Minor Pentatonic (V degree mode of the

Major Pentatonic scale).

• It can be used to play over both major and minor chords.

• It can be played over the complete I-IV-V chord progression.

• See also: “Appendix: I-IV-V Blues Progression”.

Major Blues scale (Fig.6.2):

• The Minor Third (“3”) is added to the Major Pentatonic (I degree mode of the Major Pentatonic scale).

• Used only for major chords.

In Fig.6.3, we show a 9-note scale that covers the two previously mentioned blues scales (the minor one from Fig.6.1

and the major from Fig.6.2).

30

5

10

3

7

0

0

5

7

3

10

30

5

10

3

7

0

0

5

7

3

10

Fig.6.1: Minor Pentatonic vs. Minor Blues scale (canonical position).

6

20

4

9

2

7

0

0

4

7

2

9

20

4

9

2

7

0

0

4

7

2

9

Fig.6.2: Major Pentatonic vs. Major Blues scale (canonical position).

3

3

6

3Pentatonic

scale

Pentatonic

scale

Blues

scale

Blues

scale


2

9

0

0

2

9

0

7

2

Fig.6.3: Nonatonic (9-tone) blues scale.

7

4

4

3

10

3

10

5

5

3

6

6

NOTE: The shown blues scale includes:

- Minor Pentatonic { 0 , 3 , 5 , 7 , 10 }

- Major Pentatonic { 0 , 2 , 4 , 7 , 9 }

- “Blue Note” (6)

6

6

7. Diminished Scale

The Diminished scale shown in Fig.7.1 comes in two flavors:

• Half-Whole (a.k.a. Half Step / Whole Step)

• Whole-Half (a.k.a. Whole Step / Half Step)

In both modes, the scale include includes alternating half-step (“H”) and whole-step (“W”) intervals; the only

difference is what the very first interval is (H or W).

In the Fig.7.2 and Fig.7.3, we shed some light on the scale’s construction. Shown in Fig.7.2 is Adim7 chord and its

inversions that (as characteristic for dim7 chords) repeat every three frets (three semi-tones). Integer Notation is used

to label individual chord notes. The white dots correspond to the root note “A” in different positions. (NOTE: When

discussing “symmetrical” scales, we will typically employ examples in the key of A; this is done merely for the

presentation convenience since such scales exhibit characteristic repetitive fretboard patterns.)

The Half-Whole Diminished scale is constructed by interleaving another instance of a “dim7” chord (A#dim7). In

Fig.7.3, those added notes are interleaved and shown as shaded dots. (NOTE: For simplicity of this introduction, we

show the scale’s positions on 4 strings only; eventually, we will we will include the low-E and A strings as well.)

Using the Integer Notation, we can compute all notes in the shown Half-Whole Diminished scale:

{ 0 , 3 , 6 , 9 } + ({ 0 , 3 , 6 , 9 } + { 1 , 1 , 1 , 1}) = { 0 , 3 , 6 , 9 } + { 1 , 4 , 7 , 10 } = { 0 , 1 , 3 , 4 , 6 , 7 , 9 , 10 }

Strings:

E

B

G

D

A

E

0

2fr 5fr 8fr 11fr

0 0

9

6

3

Adim7

Fig.7.2: Adim7 chord and its inversions.

NOTE: Using Integer Notation, “dim7”

chords are represented as { 0 , 3 , 6 , 9 }. In

terms of intervals, this is the same as

adding “Major Sixth” (M6) to the

“Diminished Triad” consisting of “Perfect

Unison” (P1), “Minor Third” (m3) and

“Diminished Fifth” (d5).

A B C D E F G AH W H W H W HHalf-Whole

A B C D E F G B AW H W H W H WWhole-Half



Scale:

Fig.7.1: Diminished scales.

Formula:

W

H

Strings:

E

B

G

D

A

E

6

3

0

9

9

6

3

0

0

9

6

3

3

0

9

6

7

4

1

10

10

7

4

1

1

10

7

4

4

1

10

7

5fr 7fr

minimal

repeated pattern

5fr 8fr4-fret

3-notes-per-string

overlapping pattern

Fig.7.3: Half-Whole Diminished scale in the key of A. H-W-H-W-H-W-H-W


Strings:

E

B

G

D

A

E

2fr 5fr 8fr 11fr

0

0

0

0

7. Diminished Scale (Cont.)

0

5fr 8fr

4-fret pattern.

5fr 8fr

4-fret pattern.

4-fret pattern.4-fret pattern.

By construction, the scale in Fig.7.3 has several interesting properties:

[1] As shown it Fig.7.1, the Diminished scale is a “symmetrical scale” since it divides the octave in (four) equal parts.

The same minimal pattern repeats every three frets. As shown in Fig.7.3, using only 4 strings, no minimal repeated

pattern spanning 3 frets includes all 8 notes from the scale, however; this can be accomplished by using the 4-fret 3-

notes-per-string overlapping pattern (that itself has a repeat rate of 3).

[2] The same pattern repeats on alternating strings (i.e., identical frets are used on E and G strings; same for B and D).

[3] The scale includes both the Major Triad ({ 0 , 4 , 7 }) and the Minor Triad ({ 0 , 3 , 7 }). But, since everything

repeats every 3 frets, there have to be actually 4 Major Triads and 4 Minor Triads included in one octave of any Half-

Whole Diminished scale. By repeated addition of { 3 , 3 , 3 , 3 } (using “modulo 12” arithmetic) we can discover the

following Major Triads:

- A = { 0 , 4 , 7 } ; C = { 3 , 7, 10 } ; D# = { 6, 10, 1 } ; F# = { 9 , 1 , 4 }

Similarly, for Minor Triads:

- Am = { 0 , 3 , 7 } ; Cm = { 3 , 6, 10 } ; D#m = { 6, 9, 1 } ; F#m = { 9 , 0 , 4 }

Shown in Fig.7.4 are all notes that belong to the Half-Whole Diminished scale (all as white dots) with, for orientation,

three A chord instances overlaid on top (black dots). The scale is typically used to add tension over Dominant

Seventh chords. Notice that the scale includes both Third intervals: “m3” (“3” in Integer Notation) and “M3” (“4”).

Also, some notes do not naturally belong to the key of A and, when played, may sound dissonant at first (e.g., m2 or

“1” in Integer Notation), but work really well over Altered chords like A13b9 shown in Fig.7.4. (See also:

“Appendix: I-vi-ii-V Progression”).

Fig.7.4: Half-Whole Diminished scale in the key of A with A chords overlaid (black dots).

3

0

0

9

6

3

10

7

4

1

1

10

5fr

(detail)

5fr 8fr

4-fret pattern.

9

4

1

5fr

10

0

A13b9

Exercise 7.1: Construct the Whole-Half Diminished scale in the key of A by interleaving Adim7 and Bdim7. Show

the repeated 4-fret pattern similar to the detail shown in Fig.7.4 and label all positions using the Integer Notation.

Analyze the pattern in terms of its harmonic components. The scale’s use is mostly limited to playing over dim7

chords.


7. Diminished Scale (Cont.)

Things get more interesting (and only slightly more complicated) when the two remaining strings (low-E and A) are

included. Shown in Fig.7.5 and Fig.7.6 are two common ways to play the Diminished scale over roughly two and

three octaves, respectively.

Due to its rich harmonic content, the scale’s use is common in jazz. But the scale’s repeated nature and its friendly

fingering pattern also makes it popular among the guitar “shredders”.

Strings:

E

B

G

D

A

E 1 3

9

4

6 7

3

0

0

9

6

3

10

7

4

1

1

10

6fr 9fr

Alternating 3-notes-

per-string patterns

(W-H, H-W)

0

Strings:

E

B

G

D

A

E 1 3

9

4

6 7

0

6

3

0

9

6

10

1

7

4

1

10

7

5fr 12fr

5-fret 4-notes-per-string

repeated pattern (H-W-H)

0

8fr

3

9

4

10

5fr 8fr

Alternating 3-notes-

per-string patterns

(W-H, H-W)

Identical two alternating 3-note-per-

string patterns are used on (E-B),

(G-D) and (A-E) strings, but with

one shift (when moving between D

and A):

- W-H (a.k.a. 1-3-4 fingering)

- H-W (a.k.a. 1-2-4 fingering)

Lead/root note makes this a Half-Whole

Diminished scale in the key of A.

(If omitted, the remainder would be a

Whole-Half Diminished scale in A# key.)

Same 4-tone pattern

(H-W-H) played

shifted on all strings,

but with an extra shift

when moving

between B and G.

Fig.7.5: “In-place” Half-Whole Diminished scale over 2 octaves.

Fig.7.6: “Advancing” Half-Whole Diminished scale over 3 octaves.

Trivia 7.1: The “Petrushka” scale ({ 0 , 1, 4 , 6 , 7 , 10 }) is a subset of the Half-Whole Diminished scale. It is based

on a dissonant chord (C and F# Major Triads played on top of each other) used by Stravinsky.


8. Whole Tone Scale

A B C D E F G Am3 H m3 H m3 HAugmented



Scale:

Fig.8.1: Whole Tone scale and Augmented scale.

Formula:

A B C D E F G AW W W W W WWhole Tone

Fig.8.1 describes the Whole Tone scale and the Augmented scale. Both hexatonic (6-note) scales are “symmetrical”

in that they divide the octave in equal parts (6 and 3 parts, respectively). As discussed below, they are constructed in a

similar fashion, but they sound very different.

In Fig.8.2 and Fig.8.3, we shed some light on the Whole Tone scale’s construction. Shown in Fig.8.2 is A+ chord and

its inversions that (as characteristic for “augmented/+” chords) repeat every four frets (four semi-tones). Integer

Notation is used to label individual notes. The white dots correspond to the root note “A” in different positions.

Strings:

E

B

G

D

A

E2fr 5fr 8fr 11fr

0

8

4

0

A+

Fig.8.2: A+ chord and its inversions.

NOTE: Using Integer Notation,

“augmented/+” chords are represented as

{ 0 , 4 , 8 }. In terms of intervals, this is

the same as raising the “Perfect Fifth”

(P5) of the Major Triad to the

“Augmented Fifth” (A5).

Fig.8.3: Whole Tone scale in the key of A. W-W-W-W-W-W

Strings:

E

B

G

D

A

E

2fr 5fr 8fr 11fr

0

8

4

0

8

4

0

8

4

0

8

4

10

6

2

10

10

6

2

10

2

10

6

2

2

10

6

2

6

2

10

6


The Whole Tone scale is constructed by interleaving another instance of an “augmented” chord (B+). In Fig.8.3,

those added notes are interleaved and shown as shaded dots. (NOTE: For simplicity of this introduction, we show the

scale’s positions on 4 strings only; eventually, we will we will include the low-E and A strings as well.) Using the

Integer Notation, we can compute all notes in the Whole Tone scale:

{ 0 , 4 , 8 } + ({ 0 , 4 , 8 } + { 2 , 2 , 2 }) = { 0 , 4 , 8 } + { 2 , 6 , 10 } = { 0 , 2 , 4 , 6 , 8 , 10 }

As shown it Fig.8.1, the Whole Tone scale is a “symmetrical scale” since it divides the octave in (six) equal parts.

The same minimal pattern repeats every two frets. Since all intervals are identical, there is no leading tone. No Major

or Minor Triads are included in the scale that is used to add tension while improvising over Dominant Seventh

chords. Included in the scale are both tones that alter the Perfect Fifth (“6” and“8”).

The Whole Tone scale playing patterns are extremely regular. Basically, the same whole-step pattern is present on

each string; it repeats interleaved/shifted except when aligned between G and B strings. In Fig.8.4(a), we show an “in-

place” playing pattern; a 3-notes-per-string “advancing” pattern is shown in Fig.8.4(b). The patterns can be used in

any fret position (perhaps with some repeated notes).

8. Whole Tone Scale (Cont.)

Strings:

E

B

G

D

A

E 0 2

10

4

6 8

0

10

86

2

0

(b) “Advancing” Whole Tone scale playing pattern.

Fig.8.4: Whole Tone scale playing patterns (segment).

2

64 8

4

10

Trivia 8.1: The “Prometheus” scale ({ 0 , 2, 4 , 6 , 9 , 10 }) is an “almost whole-tone” scale. It is based on

Scriabin’s ascending “mystic chord” sequence { C , F# , Bb , E , A , D }. (Something like C13b5 chord.)

(a) “In-place” Whole Tone scale pattern.

0 2 4

6 8

0

10

6

2

4

10

4

8

0 2


Like the Whole Tone scale, the Augmented scale is a result of interleaving two Augmented Triads. The scale is

“symmetrical” in that it divides the octave in three equal parts. In Fig.9.1, we show how the Augmented scale is

constructed from back-to-back (not equidistant) instances of the Augmented Triad.

While the Whole Tone scale includes only Augmented Triads, the Augmented scale has a very rich harmonic content.

Based on the its Integer Notation ({ 0 , 3 , 4 , 7 , 8 , 11 }, we see that both the Major and Minor Triad are included

(actually, three of each since the scale repeats every four frets). As illustrated in Fig.9.2, the scale also includes three

full M7 chords of the form ({ 0 , 4 , 7 , 11 }); of course, the corresponding mM7 chords (including m3 instead of M3)

are present as well. There are no Dominant Seventh chords, however. The scale is applicable to chords like AM7#5

(also shown in Fig.9.1) and is used mostly in jazz.

The pattern shown in Fig.9.1 consists of 2-note wide diagonals separated by two empty frets and it looks somewhat

playing-unfriendly. In practice, the Augmented scale could be played by applying and connecting triadic patterns or

seventh chord arpeggios. For example, { 0 , 4 , 7 } with the root note played on the D string and the other two notes

on the G string can be followed by { 4 , 8 , 11 } on G/B strings and { 8 , 0 , 3 } on B/E strings.

Exercise 9.1: Identify and play the Augmented scale that covers the following chords: C, Cm, C+, CM7, CmM7 and

CM7#5. Show that the scale covers the same chord types in E and G#.

9. Augmented Scale

Augmented Triad pattern { 0 , 4 , 8 }

over 6 strings. Strings:

E

B

G

D

A

E

Fig.9.1: Augmented scale in the key of A (segment).

Fig.9.2: Augmented scale segment with M7 chord overlay.

0

4

0

8

8

4

3

7

3

11

11

7

8

4

0

0

8

11

3

11

7

3

3

8

4

0

7

7

0

m3-H-m3-H-m3-H

11

0

4

4

7

4

7

11

11

4

7

11

7

0

7

Strings:

E

B

G

D

A

E

11

4

4

7

4

8

4

0

0

8

4

8

4

0

0

8

A B C D E F G Am3 H m3 H m3 HAugmented



Scale:

Fig.8.1 (reprint): Whole Tone scale and Augmented scale.

Formula:

A B C D E F G AW W W W W WWhole Tone

5fr

AM7#5

0

8

4

11

5fr


10. Overview

Major: I (Ionian), IV (Lydian)

Scale:Chord Type:

Harmonic Minor: I

CM7

CmM7

Major: II (Dorian), III (Phrygian), VI (Aeolian/Natural Minor)

Cm7

Major: V (Mixolydian)

C7

Fig.10.1: Common scales classified.

Harmonic Major: I

Pentatonic: I (Major)

Harmonic Minor: V (Phrygian Dominant)

Jazz Melodic Minor: IV (Lydian Dominant), VII (Altered Dominant)

Pentatonic: I (Major)

Whole Tone

Half-Whole Diminished

Jazz Melodic Minor: I

Jazz Melodic Minor: II (Dorian b9)

In Fig.10.1, we classify scales discussed in earlier sections. All chord types use the common tonic (C). For each scale,

we list applicable scale degrees. The list is not an exhaustive one.

Double Harmonic Major: IV (Hungarian Minor)

Major: VII (Locrian)Cm7b5

Jazz Melodic Minor: VI (Locrian #2)

Double Harmonic Major: I

Augmented

Augmented

Pentatonic: V (Minor)

Harmonic Minor: IV (Dorian #4)

Harmonic Major: IV (Lydian b3)


Dominant Pentatonic

11.1 Appendix: Common Major Scale Progressions

In Fig.11.1.1, we list some common chords progression that could be played over using the same Major scale. For the

sake of example, we assume the key of C, but we also describe individual progressions in generalized terms

applicable to any key; we also provide the key of each song as originally recorded.

C-Major scale = { C , D , E , F , G , A , B }

As shown in Fig.2.1.3, we can associate the following seventh chords with the C-Major scale modes:

CM7 — Dm7 — Em7 — FM7 — G7 — Am7 — Bm7b5

We annotate the associated chords using roman numerals indicating a particular chord’s root distance (in terms of

intervals) from the scale’s root. An uppercase Roman numeral indicates a major chord; lowercase Roman numerals

are used for minor chords. A simplified triad-based view of the Major scale is:

I — ii — iii — IV — V — vi — vii(dim)

(But remember that V is the only Dominant Seventh chord in the scale.) Similarly, the Natural Minor (VI degree

Aeolian mode) scale chords are:

i — ii(dim) - bIII — iv — v — bVI — bVII

We use the same representation for other Major scale modes—e.g., the V degree Mixolydian:

I — ii — iii(dim) — IV — v — vi — bVII

Comment:Chords

(Major Scale):

Progression:

IV, V F-G I-II (Lydian mode).

“Jane Says”, Jane’s Addiction (1988, orig. G-Lydian).

G-F I-bVII (Mixolydian mode).

“Fire on the Mountain”, Grateful Dead (1978, orig. B-Mixolydian)

ii, V G-Dm I-v (Mixolydian mode).

“Wharf Rat”, Grateful Dead (1971, orig. A-Mixolydian)

I, iii, IV, V C–Em–F-G I-iii-IV-V (Ionian mode).

“Midnight Train to Georgia”, Gladys Knight and the Pips (1973). “Crocodile Rock”, Elton John

(1972), includes both I-vi-IV-V (intro) and I-iii-IV-V, both in G-Major.

I, IV, V , vi C–Am–F-G I-vi-IV-V (Ionian mode).

The 50s progression a.k.a. “Stand by Me” (1961) progression.

C–G–Am-F I-V-vi-IV (Ionian mode).

“No Woman No Cry”, Bob Marley and the Wailers (1974). “Let It Be”, The Beatles (1970).

I, ii, IV, V Dm–F–C-G i-bIII-bVII-IV (Dorian mode).

“Knockin’ on Heavens Door”, Bob Dylan (1973, orig. G-Major: G-D-Am G-D-C).

I, IV, V G-F-C I-bVII–IV (Mixolydian mode).

“Sweet Home Alabama”, Lynyrd Skynyrd (1974, orig. D-Mixolydian)

ii, iii, vi Em-Dm-Am v-iv-i (Aeolian mode).

Dm-Em-Am iv-v-i (Aeolian mode).

Dm–C-G i-bVII-IV (Dorian mode).

“Down in the Hole”, Alice in Chains (1992, orig. includes both A-Dorian and D-Dorian).

I, ii, IV, V G-Dm-F-C I-v-bVII-IV (Mixolydian mode).

“Cinnamon Girl”, Neil Young (1969, orig. D-Mixolydian).

I, ii, V

Fig.11.1.1: Common Major scale progressions.

I, ii, V , vi C–Am–Dm-G I-vi-ii-V (Ionian mode).

“Cheek to Cheek”, Fred Astaire (“Top Hat” movie, 1935). “Blue Moon” (1934, e.g., M. Torme,

F. Sinatra, Glenn Miller Band).


11.2 Appendix: Modulation

Mode:

Bm-Aeolian (Natural Minor)

Em-Dorian

E-Mixolydian

D-Ionian

Chord:

Bm

Em

E

D

F#-Phrygian Dominant

A-Major Pentatonic

F#

A

G-LydianG

F#-Phrygian Dominant F#

Scale:

D-Major (VI degree)

D-Major (II degree)

A-Major (V degree)

D-Major (I degree)

Harmonic B-Minor (V degree)

A-Major (I degree)

D-Major (IV degree)

Harmonic B-Minor (V degree)

Fig.11.2.1: Modes and scales used in “Hotel California”.

As shown in Fig.11.1.1, a piece of music can be written in such a way that it uses only notes from one scale (e.g., a

song “in the key of C” would use the notes from the C-Major scale) and the same scale can be used to play over all

chords of the progression. This, however, limits the number of notes and chords available for a composition and we

reprint an earlier table (Fig.2.1.3) to illustrate this point. From the table, we can conclude that a chord progression

having more than one Dominant Seventh chord cannot be played over using the same Major scale; in the key of C, for

example, G7 is the only such chord—the other two major chords from the scale (CM7 and FM7) include M7 (not m7).

We can also observe that a Major scale can cover up to 3 major chords, but not more than that. And a song written in

the Aeolian mode cannot use E7 as a dominant chord for its Am tonic while staying in the same Natural Minor scale.

In the following section, we will analyze an example where multiple key changes occur within the chord progression.

Example 11.2.1: “Hotel California”, The Eagles (1977).

Chords: Bm-F#-A-E-G-D-Em-F#

The song’s dominant key is D-Major (Bm-Aeolan a.k.a. Natural Minor mode) with several transitions to the

Harmonic Minor as well as the A-Major key. The scales/modes corresponding to individual chords are shown in

Fig.11.2.1. A chromatic descent (B - A# - A - G# - G - F#) behind the first 6 chords provides the foundation for the

progression. (Notice that A#, G# and F# notes are the Thirds from the corresponding F#, E and D chords.)

The V chord of the Natural Minor scale is a minor one, so F# (the 2nd and the 8th/final chord of the progression) is

played over using the Harmonic Minor (Phrygian Dominant, the V degree major mode of the Harmonic B-Minor).

Mode:

Ionian

Triad Chord:

C

Locrian Bdim

Lydian F

Aeolian Am

Degree:

I

VII

IV

VI

Dorian Dm

Phrygian Em

II

III

Mixolyidan GV

Seventh Chord:

CM7

Bm7b5

FM7

Am7

Dm7

Em7

G7

Fig.2.1.3 (reprint): Chords associated with the C-Major scale modes.


D / DM7

C#dim / C#m7b5

G / GM7

Bm / Bm7

Em / Em7

F#m / F#m7

A / A7

A / AM7

G#dim / G#m7b5

D / DM7

F#m / F#m7

Bm / Bm7

C#m / C#m7

E / E7

I

VII

IV

VI

II

III

V

D

C#

G

B

E

F#

A

A

G#

D

F#

B

C#

E

I

VII

IV

VI

II

III

V

Fig.11.2.2: Comparison of D-Major and A-Major Scales: (a) notes, (b) triad/seventh chords.

(a) (b)

D-Major: A-Major:Degree: D-Major: A-Major:Degree:

DB

E

A

D

F#

B

B

E

F#

D

A

Fig.11.2.3: “Hotel California” progression over B-Minor Pentatonic.

7fr

D

F#

B

E

D

A

C#

C#

G#

D

F#

B

E

D

G

C#

C#

A#

D

F#

B

E

D

AG

C#

C#

D-Major A-Major Harmonic B-Minor

Pentatonic B-Minor

Strings:

E

B

G

Strings:

E

B

G

D

A

E

11.2 Appendix: Modulation (Cont.)

The modulation from D-Major key to A-Major key happens on the third chord of the progression (A). In Fig.11.2.2,

we compare the two scales. We see that 6-of-7 notes are common (A, B, C#, D, E, F#), the only difference being G-

vs-G# note. We also highlight that the two scales share four triadic chords (D, F#m, A and Bm). The common A chord

is used as a “pivot chord” to transition between D-Major and A-Major keys. Notice, however, that the corresponding

7th chords (i.e., a triad plus m7/M7 interval) differ between the two scales: A7 (in D-Major) suggests the Mixolydian

mode, while AM7 (in A-Major) suggests the Ionian mode—if not sure, one could simply play only the notes common

to both scales or a mode-agnostic A-Major Pentatonic. After this, the fourth chord of the progression (E) is played in

the changed key of A-Major. (Notice that D-Major includes Em and not E). The next three chords in the progression

(G, D and Em) are played in the original D-Major key again; the return from the A-Major is smooth since the landing

G-Lydian mode shares all notes except for its root (G).

In Fig.11.2.3, we show how the above analysis could translate to a simple playing pattern. To reflect the Natural

Minor mode, we use the Pentatonic B-Minor that includes 5-of-6 chord roots (the G note is missing). The only

(occasionally) “bad” note is “A” that gets shifted to “A#” in the Harmonic Minor context, but otherwise the shown

pentatonic could be played over the whole progression. The C# note can also be included as it belongs to all three

scales. A few additional notes could be selectively played (G-vs-G# and A-vs-A#) providing extra color and melodic

space. Notice how seemingly complex changes of modes and scales amount to merely tweaking a note here-and-

there. In the end, the enduring quality of the “Hotel California” guitar solo lies in its memorable melody combined

with effective phrasing (e.g., string bending) and dramatic effect (e.g., the closing chromatically-descending sequence

of triplets).


Example 11.2.2: “Rock Steady”, Sting (1987).

Chords: Am7-F7 (orig: Bbm7–Gb7)

In Fig.11.1.1, we list several standard progressions where Am and F can be played over using a common C-Major

scale. There (and in many other examples from rock music[1]), however, the underlying harmony is based on a minor

seventh chord (VI degree Aeolian mode) and a major seventh chord (IV degree Lydian mode).

A chord progression quite common in jazz and blues consists of Am7 and a dominant-seventh F7 chord. These two

chords, however, cannot co-exist in any major scale. Let’s assume that Am7 is played as Dorian mode (G-Major’s II

degree).

• Obviously, for F7, a Dominant Pentatonic can be used. (Major Pentatonic would also work, but why drop a

dominant chord’s “m7” in favor of a more neutral “M6”?)

• F7 is also the V chord in the Bb-Major scale, so we can try playing a full F-Mixolydian scale[2].

• But, as shown in Fig.11.2.4, we could also use the Melodic C-Minor where F7 corresponds to the scale’s IV

degree Lydian Dominant mode. This scale seems like a perfect fit, as the Melodic C-Minor and the G-Major have

five common notes shown as shaded fields in Fig.11.2.4(a); the only two F7-specific notes are very strong and

distinctive: F (root/P1) and D# (m7).

In jazz, dominant V chords returning to i are typically played using the Altered scale of the Melodic Minor. (See

also: Fig.3.3.1, “Appendix: ii-V-i Progression” and “Appendix: I-vi-ii-V Progression”). Other types of

dominant chords typically employ the Lydian Dominant scale (e.g., substitute dominant chords created by tritone

substitution).

G

F#

C

E

A

B

D

Bb

A

D#

G

C

D

F

I

VII

IV

VI

II

III

V

Fig.11.2.4: Scales used in Am7-F7 progression.

G-Major: Bb-Major:Degree:

30

5

10

3

7

0

0

5

7

3

10

Fig.11.2.3: “Hotel California” progression over B-Minor Pentatonic.

5fr

A-Dorian

Strings:

E

B

G

D

A

E

11.2 Appendix: Modulation (Cont.)


C

B

F

A

D

D#

G

Melodic

C-Minor:

______________________________________________________________________________________

[1] This list includes famous solos from “Stairway to Heaven” (Led Zeppelin, 1971) and “All Along the Watchtower” (J. Hendrix, 1968).

[2] The Bb note from the F-Mixolydian may sound a bit strange being the “m2” interval of the first chord (Am7).

2

2

9

2

9

74

9

2

7

4

4

9

0

7

2

5fr

F-Lydian Dominant

6

6

6

0

10

10

10

(a)

(b)

74

2

7

4

4

0

7

2

5fr

Dominant F-Pentatonic

0

10

10

10

11.3 Appendix: Relative Minor

For any Major key, its Relative Minor key is 3 semi-tones (3 frets) lower. For example, Am would be the relative

minor of C, and Em would be the relative minor of G.

It is commonly said that a major chord can be played over using the Minor Pentatonic scale in the key of the chord’s

relative minor. This can be observed in the example of C-Major scale shown in Fig.2.1.4 and Fig.2.1.5: there, any

major-mode pattern (e.g., Ionian in its canonical position) is preceded by a minor-mode pattern (e.g., Aeolian) with

the corresponding roots being three frets apart.

Example 11.3.1: Use Em Pentatonic to play over a I-IV-V-I progression in G.

As analyzed in Fig.11.3.1, the same G-Major scale can be used to play over G-C-D chord progression. The figure

also shows the S6 (“Aeolian”) pattern that covers all triads (the shaded notes not belonging to the Em-Minor

Pentatonic). Integer Notation corresponds to the I chord (G). The Em-Pentatonic scale (black dots) could use a few

extra notes (e.g., the shaded “5” corresponding to the C note is missing from the 5-note scale), but the scale would

suffice in certain situations (e.g., to embellish transitions between chords in country music). Notice the root position

(“0”) of the leading G chord—if, for example, the same pattern (S6) is used to play over Em, its root would shift to a

more common “canonical” position (corresponding to “9” in the key of G).

Strings:

E

B

G

D

A

E

S6(Aeo.)

9

4

0

7

2

9

5

11

2

9

4

11

0

7

5

0

Fig.11.3.1: G-C-D-G progression in Relative Minor position.

Fig.11.3.2: C-Major scale (detail).

5fr 8fr 10fr

11

9

4

0

7

2

9

5

11

2

9

4

11

0

7

5

0

4

11

2

9

5

0

7

2

S6

S1

7

54

Analysis:

• G Major scale = { G , A , B , C , D , E , F# }

• G = { G , B , D } // Ionian

• C = { C , E , G } // Lydian

• D = { D , F# , A } // Mixolydian

• Em-Pentatonic = { E , G , A , B , D }

The above discussion merely re-iterates a point that tends to gets overlooked (by beginner players, in particular).

Frequently, drawings depicting scales have a low-E root played by either the first/index or second/middle finger. (So

far, for uniformity and brevity, that was the case most of the time our presentation as well.) In Fig.11.3.2, we show

another route to play 2 octaves of a particular scale from the same root position. One route (corresponding to the

black dots) corresponds to the C-Ionian mode played using the S1 pattern. But, of course, the same scale is available

via the shaded S6 pattern (the “Relative Minor” path). Even if the same notes are played, a particular pattern might be

easier to play or to put a desired emphasis (e.g., bend specific notes, play segments of underlying chords, etc.). This

is true regardless of a major chord’s mode (see Fig.2.1.4 and Fig.2.1.5): the relative minor of S5 pattern (Mixolydian)

would be S3 (Phrygian); for Lydian (S3 pattern shared with Phrygian), the relative minor is S2 (Dorian).


2

9

4

0

7

10

5

0

4

2

9

5

0

7

2

10

4

11.4 Appendix: I-IV-V Blues Progression

9

4

7

2

10

5

0

7

9

4

0

7

2

9

10

5

10

4

7

2

9

4

5

0

10

5

9

4

7

2

10

5

0

7

9

Fig.11.4.2: Blues pattern analyis.

Chord: Scale: Pattern:

MixolydianI

IV

V

Mixolydian

Mixolydian

S5 (“Mixolydian”)

S2 (“Dorian”)

S1 (“Ionian”)

Fig.11.4.1: Blues progression chords (example).

A typical blues progressions consists of I-IV-V Dominant Seventh chords arranged in 12 bars—for example:

4 x A7 — 2 x D7 — 2 x A7 — E7 — D7 — A7 — E7

This progression is used throughout this section and the chords (with some variations suggested) are shown in

Fig.11.4.1. The black dots are the basic chords used in this example, while the lightly shaded ones are related notes

that could be included in some other forms of the same chord. For example, both IV and V chord can be played as

either 7th chords (D7/E7) or 9th chords (D9/E9).

Analysis: There is only one Major scale mode (Mixolydian) that includes m7 and works for Dominant Seventh

chords suggesting we cannot play the same Major scale over the whole progression. Theoretically, we can play over

the I-IV-V blues progression by playing the Mixolydian scale in all corresponding keys: e.g., a simple way would

be to move the same S5 pattern between 5fr (A7), 10fr (D7) and 12fr (E7) positions. In this example, we analyze how

three Mixolydian scales can be all played in the same position (5fr). In Fig.11.4.2, the potential playing patterns are

identified and labeled using Integer Notation based on the root notes corresponding to I, IV and V chords,

respectively. This is important because the four basic notes—the 1st (P1/“0”), the 3rd (m3/“3” or M3/“4”), the 5th (“7”)

and the 7th (“10”)—provide each chord’s identity and safe landings for phrases used in improvisation. Being aware of

underlying chords (Fig.11.4.2) helps understand where “important” note are as chords change.

7

2

0

0

0

10

4

E7

I

IV

V0

2

10

4

7

7

E9

7

10

4fr0

0

A7

10

4

0

7

0

7

7

D7

4

10

7

0

10

0

2

10

4

7

7

D9

4fr 4fr

6fr5fr0

0

4


The presented by-the-book analysis is somewhat complicated and the result may not sound utterly authentic and

convincing. If we superimpose all 3 patterns, we get something almost as extensive as the 9-note blues scale shown in

Fig.6.3; we will return to this scale later in this section.

As an alternative, we investigate using the Minor Blues scale (Fig.6.1) to play over the I-IV-V progression of

major chords. This simple 6-tone scale is frequently used in both blues and jazz. Shown in Fig.11.4.3 are Integer

Notation-based markings for the three chords. We see that the root note is present in all three chords together with the

Minor Seventh (m7 or “10”) thus capturing the Mixolyidian flavor. If we disregard the “blue note” that is dissonant in

all three chords (as d5/m2/M7), the three pentatonic chords could be approximated as:

I = Am7

IV = D9sus4

V = Em7#5

Obviously, this works for minor I/IV/V chords and the neutral IV is also acceptable for a major chord as well. But,

most important, in blues, the “m3” note is typically played bent—frequently, by less that the whole semi-tone step

towards M3—and is not considered dissonant if played within a major context.

Next, in Fig.11.4.4, we observe that two extra notes (shaded dots) can be added to all three chords, ranging from

distinctive blues notes (e.g., M6/“9” in the I/IV chords) to more neutral (like M2/“2”). We can add more color by

incorporating these extra notes as either passing notes or by bending them to the existing scale’s notes. Notice that

what is shown in Fig.11.4.4 is really the Dorian scale with the “Blue Note” added. Next, for emphasis, we could also

selectively play M3 (“4”) in the I chord (in particular when transitioning to the IV chord) and thus completely re-

create the Nonatonic blues scale from Fig.6.3. Nevertheless, a somewhat surprising conclusion is that we could play

I-Dorian over the whole progression.

30

5

10

3

7

0

0

5

7

3

10

Fig.11.4.3: Minor Blues scale over I-IV-V progression of major chords.

6

6

11.4 Appendix: I-IV-V Blues Progression (Cont.)

107

0

5

10

2

7

7

0

2

10

5

1

1

85

10

3

8

0

5

5

10

0

8

3

11

11

30

5

10

3

7

0

0

5

7

3

10

Fig.11.4.4: Adding 2 extra notes to the Minor Blues scale.

6

6

107

0

5

10

2

7

7

0

2

10

5

1

1

85

10

3

8

0

5

5

10

0

8

3

11

11

2

9

9

4

7

2

I IV V

I IV V

2 9 7


2

9

0

0

2

9

0

7

2

Fig.6.3 (reprint): Nonatonic (9-tone) blues scale.

7

4

4

3

10

3

10

5

5

3

6

6

NOTE: The shown blues scale includes:

- Minor Pentatonic { 0 , 3 , 5 , 7 , 10 }

- Major Pentatonic { 0 , 2 , 4 , 7 , 9 }

- “Blue Note” (6)

6

Exercise 11.4.1:

Listen to great blues players and try to play along. The list below is subjective and short, but it certainly features some

of the finest bluesmen of all time. The songs vary in form, with the Allman Brothers straying most from the discussed

I-IV-V structure, but the basic principles still apply. (All songs are pretty easy to find on the Internet, except for the

Hendrix one. A copyright issue? Anyway, worth the effort to track down...)

• “Sweet Sixteen”, B.B. King (~1960).

• “Stormy Monday Blues”, Allman Brothers Band (“At Fillmore East”, 1971).

• “Have You Ever Loved a Woman”, Eric Clapton (“E.C. Was Here”, 1975).

• “Once I Had a Women”, Jimi Hendrix (“Midnight Lightning”, 1975).

Exercise 11.4.2:

“Not My Cross to Bear” (Allman Brothers Band, 1969) has several modal changes in its chord progression:

B - E9 - Em13 - B7 - G#7 - C#7 - F# - ( turnaround: B - B7 - E7 - G - F#7#5#9 )

Identify all key changes and play along.

11.4 Appendix: I-IV-V Blues Progression (Cont.)


11.5 Appendix: ii-V-i Progression

Fig.11.5.1: ii-V-i chord progression.

ii

V

Exercise 11.5.1: For the progression in Fig.11.5.1(a), we can use the same scale (Natural D-Minor, i.e., F-Major) for

i/ii chords:

• Em7b5 = { E , G , Bb , D } // Locrian mode

• Dm7 = { D , F , A , C } // Aeolian mode

• F-Major scale = { F , G , A , Bb , C , D , E }

• Natural D-Minor = { D , E , F , G , A, Bb , C }

The A7 chord (“V” chord of the progression), however, cannot use the Natural D-Minor, because of the presence of

“C#” note. If we raise m7 (Natural Minor) to M7 (Harmonic Minor), we see that we can use the Harmonic D-Minor

scale for the V chord.

• A7 = { A , C# , E , G } //

• Harmonic D-Minor = { D , E , F , G , A , Bb , C# }

Exercise 11.5.2: For the progression in Fig.11.5.1(b), we can use the recipe from Fig. 3.3.1 to play the whole

progression as three Jazz Melodic Minor scales:

• ii chord: G-Minor (VI degree, Locrian #2),

• V chord: Bb-Minor (VII degree, Altered) and

• i chord: D-Minor (I degree).

Exercise 11.5.3: Try also “Tritone Substitution” on A7 by playing the Eb-Major Dominant Pentatonic.

2

0

3

7

2

3

11

7

2

0

9

5

5fr

0

3

11

53

5fr

9

5

3

20

11

0

5

7

7

11

2

0

11

9

3

3

2


Em7b5

(ii)

6fr

Dm7

(i)

5fr5fr

7

0

0

4

10

7

A7

(V)

7

0

7

3

10

7(a)0

6

10

3

5fr

A7#5b9

(V)

Em7b5(ii)

6fr

0

6

10

3

0

10(b)

4fr7

9

0

3

Dm6

(i)

1

8

4

5 9

9

11

3

7

2

5

0

7

11

9

3

0

7

2

5

11

i2

9

3

119

9

11

ii

V

5fr

5

0

3

10

5

8

6

1

10

5

0

3

8

5fr

0

6

1

86

85

4

7

0

1

0

5

7

8

1

10

0

4

1

10

4

4

7

7

2

5

0

7

10

8

3

0

7

2

5

10

i2

8

3

108

NOTE:

“9” is E.

NOTE:

“11” is A.

11.6 Appendix: I-vi-ii-V Progression

A7#5b9

(VI)

8

13

0

4

10

5fr

CM7

(I)

711

4

0

7

73fr

G13b9

(V)

9

13

0

4

10

3fr

Shown in Fig.11.6.1 is one of many ways to play the I-vi-ii-V (e.g., CM7—Am7—Dm7—G7) progression:

CM7 — A7#5b9 — Dm11 — G13b9

Dm11

(ii)

14

0

10

3fr

3

17

Fig.11.6.1: I-vi-ii-V chord progression.

C#dim7

(vi)

6

3

0

63fr

9

5fr3fr

9

4 5

0

11 0

7

2

C-Ionian

(C-Major)

5fr3fr

A-Phrygian

Dominant

(Harmonic

D-Minor)

5fr3fr

D-Dorian

(C-Major)

0

7

3 4

0

10

6

1

G-Diminished

(Half-Whole)

A-Altered

Dominant

(Melodic

Bb-Minor)

Melodic

D-Minor

I

VI

ii

V

The I-vi-ii-V progression in its basic form (e.g., CM7—Am7—Dm7—G7) can be played over using the C-Major

scale since all four chords are seventh chords from the Major scale (see Fig.2.1.3). The version from Fig.11.6.1,

however, has the vi as a major chord (i.e., VI). Also, VI and V are more colorful “altered dominant” chords.

• I and ii chords could still be played using the C-Major (Ionian and Dorian modes, respectively).

• A-Major is a Dominant-V chord w.r.t. D-Minor, so Harmonic Minor can be used for the VI chord.

• The V chord is an altered chord shape covered by an instance of the Diminished scale.

Exercise 11.6.1: Play the progression using the shown scale patterns shown in Fig.11.6.2. Also, repeat the exercise by

playing the scales in different positions.

9

C#dim7 can be played as the vi

chord. If so, notice a chromatic

C—C#—D bass line and that all

four chords can be played in the

same “barre” position (3fr) with

multiple common notes in

adjacent chords. (Note: C#dim7

can be also re-annotated as a

rootless A7b9.)

NOTE: For a bit of an “outside” sound, A and D (VI and

ii) chords could be played over using the Jazz Melodic

Minor as shown below.

Exercise 11.6.2: A simplest, slow and bluesy, solo could

consist of a single E note per chord (e.g., slide or bend into

it for more fun)—this works since the note is present in all

four chords. Next, try a single-G-note solo. (See also Lary

Carlton’s YouTubeTM demo “Soloing Over I-VI-II-V - Blues

Guitar Lessons”.

Fig.11.6.2: I-vi-ii-V progression scales.

1


7

542

9

11

7 9

0

7 8

4

1

10

5

10

875

0

4

10 0

1

1

7

2 3

10

9 10

5

0

5

320

7

9

5 7

3

10

0 1 3 4

6 7 9

5fr3fr

0

8

4

1

10

3

10

86

0

4

10 0

1

1

7

2 3

11

9

11

5

0

5

320

7

9

5 7

6

3 4

0

9

9

7

11 0

2

0

11

4

9

2

11

9

2

7

0

9

4 5

4

7

6

4

D-Minor Pentatonic

G-Minor Pentatonic

Fig.11.7.1: Pentatonic superimposition (examples).

Scale:

D E F A BC-Dorian

C D E F G A BC-Minor Pentatonic

I

I

Relative

degree:

II

V

D F AC-IonianI CM7

Cm7

C D E F G A B

E-Minor PentatonicIII C D F G A BNo P1 (root). M7 included.

Intervals 1/3/5/7 all included.

No m3. No m7.

No m3.

D F A BC-MixolydianI C7

G-Minor PentatonicV C D E F A BNo M3. m7 included.

E

G

C D E F G A B

C D E F G A B

Intervals:

Integer Notation: 0 1 2 3 4 5 6 7 8 9 10 110 1 2 3 4 5 6 7 8 9 10 11

P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7Intervals:

Integer Notation: 0 1 2 3 4 5 6 7 8 9 10 11

P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7

Chord type:

D F G A BC-LocrianI Cm7b5 E

C D F G A BEb-Minor PentatonicIII No P1 (root). E

D E F A BC-AeolianI Cm7

C D E F G A BF-Minor PentatonicIV No P5.

11.7 Appendix: Scale Substitution

As discussed previously, by abstracting out the Major scale’s mode info, the same Major/Minor Pentatonic can be

applied to all major/minor modes of the Major scale; moreover, the Minor Pentatonic is merely a mode (V degree) of

the Major Pentatonic.

The simplicity of the Pentatonic scale makes it easy to play, but it can also sound a bit boring after a while—e.g.,

there is no direct way to express if the underlying major chord is C7 or CM7 (i.e., there is no 7th interval in the I

degree of Major Pentatonic). More variety and color can be provided in two ways: (a) use more complex scales (with

more than 5 notes), or (b) keep using the simple and familiar Pentatonic scale, but superimpose “wrong” Pentatonic

shapes. A superimposed Pentatonic should include certain notes from the basic chord, but also add compatible notes

from the same Major scale where the chord comes from.

Several examples of pentatonic superimposition are shown in Fig.11.7.1. In practice, the “missing” intervals are not a

problem: if needed, they can be played by switching to the “correct” Pentatonic or some other instrument may

provide them (e.g., a band’s bass is likely to play root notes). More important, those missing intervals make the

superimposed sequences less conventional and less predictable. Notice that the superimposed pentatonics in

Fig.11.7.1 do not introduce any wrong (non-scale) notes. Still, a skilled player can create a perception of drifting

“outside” while playing, for example, the D-Minor pentatonic over the C-Dorian mode—we examine this case next

(see Fig.11.7.2).

A-Minor PentatonicVI No M7. Major Pentatonic, V deg.

C D E F G A BA-Minor PentatonicVI No m7. Major Pentatonic, V deg.

C D E F G A BC-Minor PentatonicI Intervals 1/3/5/7 all included.

(a) Pentatonic superimposition applied to major chords.

(b) Pentatonic superimposition applied to minor chords.

(c) Pentatonic superimposition applied to half-diminished chords.


C G

C

C G

C E G

C E G B


D-Minor Pentatonic

G-Minor Pentatonic

C D E F G A BC-Dorian (Bb-Major)

C D E F G A BC-Minor Pentatonic

II

II

III

VI

Cm7

Cm7.

Suspended chord. No m3, no m7.

Suspended chord. No m3.

C D E F G A B

C D E F G A B

Intervals:




P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7

Fig.11.7.2: Pentatonic superimposition (Dorian mode example).

Major

scale

degree:

Assume that Cm7 chord is played over using the C-Dorian scale (the II degree mode of the Bb-Major scale).

Obviously, the C-Minor Pentatonic can be used instead. There are, however, two other pentantonics (D-Minor and G-

Minor) that fit harmonically in the same Bb-Major scale (see Fig.11.7.2). Neither pentatonic includes any “wrong”

(non-scale) notes, but, since some important intervals are missing (m3, m7 or both), the two scales sound very

distinctive. Playing the D-Minor Pentatonic, in particular, can create a perception of drifting “outside”—there, the

obfuscation arises from excluding two most distinctive Cm7 intervals (m3 and m7).

Exercise 11.7.1: Try the substitutions from Fig.11.7.2 over a “Take Five” backing track[1]. (Note: The song was

originally recorded by Dave Brubeck in Ebm7, so the Reader may have to transpose the shown Cm7-based examples).

Exercise 11.7.2: While improvising, pick a short phrase (“lick”) from a Pentatonic scale and take it through multiple

scales shown in Fig.11.7.2 [1].

Next, we will examine replacing certain Dorian scale notes by switching to other related scales (see Fig.11.7.3).

Chord type:

11.7 Appendix: Scale Substitution (Cont.)

______________________________________________________________________________________

[1] Also, listen to and watch George Benson perform “Take Five”. His original recording (1974) and several live versions (e.g., “Musikladen

Extra” appearance in 1978) are available on YouTubeTM. Dave Brubeck’s original version is from 1959.

[2] Exercise 11.7.2 is a neat fusion-sounding trick. A demo (“Scott Henderson Shares Secrets of the Pentatonic Scale”) is available on

YouTubeTM.


An improvisation over the assumed Cm7 chord (in C-Dorian mode) can also include some notes outside of its native

Major scale. By modifying a single note (i.e., playing M7 instead of m7), we can take a slightly dissonant route via

the Melodic C-Minor (CmM7 chord)—see Fig.11.7.3(a). But we can also try playing other minor-type degrees from

the Melodic Minor scale: e.g., II degree mapping to Cm7 or the half-diminished VI degree; in both cases, the

strongest notes from the C-Dorian scales are preserved (P1, m3, m7) and the “outside” effect is produced by one or

two changed intervals. A less obvious approach could drop the root note C as well, but preserve distinctive m3 and

m7 notes from the C-Dorian—one such scale would be the Melodic Minor rooted 8 semi-tones higher (or 4 semi-

tones lower) than the original root note C (i.e., I degree of the Melodic Ab-Minor).

In Fig.11.7.3(b), we also show several substitutions based on various Harmonic scales.

Exercise 11.7.3: Same as Exercise 11.7.1, but try the substitutions from Fig.11.7.3(a) and Fig.11.7.3(b).

Exercise 11.7.4: Same as Exercise 11.7.2, but try it for Melodic Minor scales shown in Fig.11.7.3(a).

Certainly, a creative player is free to crack notes in any way that works in a particular musical context, but playing a

“wrong” scale is a convenient and useful exploration starter tool.

11.7 Appendix: Scale Substitution (Cont.)

C D E F G A BMelodic C-MinorI CmM7. M7 instead of m7.

C D E F G A BMelodic Ab-MinorI AbmM7. No P1. m3 and m7 included.

C D E F G A BMelodic Eb-MinorVI Cm7b5. m3 and m7 included.

C D E F G A BDouble-Harmonic G-MajorIV CmM7. M7 instead of m7.

C D E F G A BMelodic Bb-MinorII Cm7. m3 and m7 included.

C D E F G A BHarmonic G-MinorIV Cm7. m3 and m7 included.

Intervals:




P1 m2 M2 m3 M3 P4 d5 P5 A5 M6 m7 M7

C D E F G A BC-Dorian (Bb-Major)II Cm7

C D E F G A BHarmonic C-MinorI CmM7. M7 instead of m7.

C D E F G A BHarmonic G-MajorIV CmM7. M7 instead of m7.

Fig.11.7.3(a): Melodic Minor-based substitution (examples).

Fig.11.7.3(b): Harmonic scales-based substitution (examples).

Degree: Chord type:

11.8 Appendix: 3NPS Patterns (Major Scale)

In Fig.2.1.5, we presented 5 overlapping patterns that can be used to play the Major scale in any key and mode, but

there are other ways to play the scale. In Fig.11.8.1, we show the three-notes-per-string (3NPS) patterns derived by

starting from the C-Major scale’s notes on the low-E string and advancing by playing three notes on each string. The

3NPS allows for faster playing by simplifying picking and frequently having the same pattern on adjacent strings

(e.g., see patterns I , II and VII below); it requires more finger stretching, however, and is a bit detached from

underlying chords (e.g., a full “open” C-chord shape cannot be discerned under any of the seven shown patterns).

5

0

4

11

2

9

5

0

7

2

4

11

7

2

9

4

5

0

7

2

4

11

7

2

9

4

5

0

5

9

4

11

7

2

9

4

5

0

5

9

4

11

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2

5

0

7

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4

5

9

4

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2

5

0

7

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4

0

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2

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2

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0

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0

7

2

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2

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0

7

5

0

4

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2

9

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5

0

4

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2

9

5

0

7

2

4

117

2

9

0

5fr 12fr8fr3fr 10fr 15fr5fr 12fr8fr3fr 10fr 15fr

5

0

7

2

5

11

4

Fig.11.8.1: C-Major scale played as 3-notes-per-string.

I

II

III

IV

V

VI

VII

Strings:

E

B

G

D

A

E



11.8 Appendix: 3 NPS Patterns (Harmonic Minor Scale)

Fig.11.8.1 shows three-notes-per-string (3NPS) patterns derived by starting from the C-Major scale’s notes on the

low-E string and advancing by playing three notes on each string. In Fig.11.8.2, we derive the Harmonic Major 3NPS

patterns in the following fashion: (i) first, we re-number the notes to make the Natural Minor (VI degree A-Aeolian)

mode the root, and (ii) then, we raise the Natural Minor’s m7 interval (“10” using the Integer Notation) to M7

(“11”)—thus, all notes (excluding the 7th interval) are played in the same position as in the C-Minor’s 3NPS. The V

pattern corresponds to the E-Phrygian Dominant mode and was already presented in Fig.3.2.3(b).

8

3

7

2

5

0

8

3

5

7

2

5

0

7

8

3

5

7

2

5

0

7

8

3

8

0

7

2

5

0

7

8

3

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0

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2

5

8

3

2

0

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8

0

7

2

5

8

3

2

0

7

3

5

0

8

3

2

0

7

3

5

0

8

2

5

0

7

2

3

3

5

0

8

2

5

0

7

2

3

8

3

7

2

5

0

2

8

3

7

2

5

0

8

3

5

7

211

5

0

3

8

3

11

5

8

2

7

Fig.11.8.2: Harmonic A-Minor scale played as 3-notes-per-string.

III

IV

V

VI

VII

I

II

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

11

Strings:

E

B

G

D

A

E




11.8 Appendix: 3NPS Patterns (Melodic Minor Scale)

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0

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7

2

3

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2

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3

5

0

7

2

3

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2

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3

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2

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5

9

3

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3

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9

3

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0

7

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9

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0

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5

11

2

9

3

11

0

7

0

7

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2

9

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11

0

7

5

0

3

11

2

9

11

5

0

3

11

2

9

5

0

7

2

3

117

2

9

0

5

0

7

2

5

11

3

Fig.11.8.3: Melodic C-Minor scale played as 3-notes-per-string.

I

II

III

IV

V

VI

VII

Strings:

E

B

G

D

A

E


In Fig.11.8.1, we presented 3NPS patterns for the C-Major scale. In Fig.11.8.3, we derive the Melodic Minor 3NPS

patterns by lowering the C-Major’s M3 interval (“4” using the Integer Notation) to m3 (“3”)—thus, all notes

(excluding the 3rd interval) are played in the same position as in the C-Major’s 3NPS. Using the 3NPS patterns, the

Melodic Minor requires similar level of finger stretching as the Major scale; there are no repeated patterns on adjacent

strings, however.



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Musical Scales: A Guitar Navigation Kit Ivan Radivojevic...The scales covered in this presentation...

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