Sample Scale Analysis

Sample Scale Analysis from Book

Harmonic Minor Scale:

When we harmonized the diatonic major scale (Ionian mode), one of the things we learned was that the most important chord in establishing the overall feeling of a key center was the dominant seventh chord, built on the fifth degree of the scale. When we examined cadences, we noted that the strongest harmonic movement is the transition from that V chord to the I (it isn’t called Perfect Cadence for nothing). Recall, also, our discussion about how the minor seventh of the natural minor scale forced the V chord to be a minor seventh instead of the more desirable dominant seventh. Well, that was the impetus behind the development of the Harmonic Minor scale.

Diatonic Major Scale

Natural Minor Scale

Harmonic Minor Scale

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Table 6-1

As we can see in Table 6-1, the Harmonic Minor scale addresses this problem by substituting a major seventh for the natural minor’s minor seventh. While this resolves the cadence problem by returning the V chord to a dominant seventh, it introduces an augmented interval between the b6 and the 7. This interval is responsible for giving the Harmonic Minor scale its exotic sound.

Table 6-2 illustrates the first mode of the Harmonic Minor scale in twelve keys:

1	2	b3	4	5	b6	7
C	D	Eb	F	G	Ab	B
C#	D#	E	F#	G#	A	B#
D	E	F	G	A	Bb	C#
Eb	F	Gb	Ab	Bb	Cb	D
E	F#	G	A	B	C	D#
F	G	Ab	Bb	C	Db	E
F#	G#	A	B	C#	D	E#
G	A	Bb	C	D	Eb	F#
Ab	Bb	Cb	Db	Eb	Fb	G
A	B	C	D	E	F	G#
Bb	C	Db	Eb	F	Gb	A
B	C#	D	E	F#	G	A#

Table 6-2

Here’s a basic fingering pattern:

Strings:	E	A	D	G	B	E
(Eighth fret)	R	4		b3	5	R
			7		b6
	2	5	R	4		2
	b3	b6				b3
			2		7

Table 6-3

Well, let’s get down to business and start harmonizing this new scale.

I Chord:

C Major Scale:

Harm. Min. 1^st deg.:

Results:

Table 6-4

Starting with the first degree and stacking thirds, we see that we have a 1-b3-5-7. This is a m(maj7). We see, therefore, that we can use the Harmonic Minor scale over a m(maj7) chord whose root is the same as that of the scale. In the key of C this would be a Cm(Maj7).

II Chord:

D Major Scale:

Harm. Min. 2^nd Deg.:

Results:

Table 6-5

By comparing the notes of our Harmonic Minor scale, starting at the second degree (D), with the normal step/half-step pattern of a diatonic major scale beginning at the same note, we discover that the resulting chord is a m7(b5), also known as a half-diminished. Thus, we can play the Harmonic Minor scale over a half-diminished chord whose root is two semitones above that of the scale; that is, we’d play a C Harmonic Minor over a Dm7(b5) chord.

III Chord:

Eb Major Scale:

Harm. Min. 3^rd Deg.:

Results:

Table 6-6

The third degree of our Harmonic Minor scale is Eb, a minor third. As before, we compare the Harmonic Minor mode starting at the third note of the scale with the diatonic major scale starting at the same note, in this case, Eb. The result, as shown in Table 6-6, is a Maj7(#5) chord. Hence, we use the Harmonic Minor scale over a major seventh augmented chord whose root is a minor third (three semitones) above that of the scale. In the key of C, we’d play a C Harmonic Minor scale over an EbMaj7(#5) chord.

IV Chord:

F Major Scale:

Harm. Min. 4^th Deg.:

Results:

Table 6-7

The lowered third and lowered seventh make this a minor seventh chord. The #4 will also work well against this minor tonality. We can apply a Harmonic Minor scale to a minor seventh chord whose root is a perfect fourth (five semitones) above that of the scale; that is, we’d use a C Harmonic Minor scale over an Fm7.

V Chord:

G Major Scale:

Harm. Min. 5^th Deg.:

Results:

Table 6-8

The natural third and flatted seventh mean we have a dominant seventh chord--hardly surprising since this is the very reason the Harmonic Minor scale was formulated. We can apply a Harmonic Minor scale to a dominant seventh chord whose root is a perfect fifth (seven semitones) above that of the scale. In C, we’d play a C Harmonic Minor scale over a G7, or a G7(b9).

VI Chord:

Ab Major Scale:

Harm. Min. 6^th Deg.:

Results:

Table 6-9

As shown in Table 6-9, we can play the Harmonic Minor scale over a Maj7 or Maj7(#11) chord whose root is a minor sixth (eight semitones) above that of the scale. However, we need to be a little cautious of that #2, which will tend to sound like a minor third. This means that we might also play the Harmonic Minor over a m(Maj7) chord. A C Harmonic Minor scale is played over an AbMaj7(#11) chord, or an Abm(Maj7) chord. In either case, we’ll have to be careful of introducing dissonance between the #2 and the 3.

VII Chord:

B Major Scale:

Harm. Min. 7^th Deg.:

Results:

bb7

Table 6-10

A chord with a b3, b5, and bb7 is known as a diminished seventh chord. We can play a C Harmonic Minor over a Bdim7 chord.

Progression

Let’s examine what kind of progression might provide a background for experimenting with our C Harmonic Minor scale. As we’ve seen, the chords we have to work with are:

Cm(Maj7), Dm7(b5), EbMaj7+, Fm7, G7(b9), AbMaj7(#11), Bdim7.

Once again, our goal is to assemble a progression that uses all of these chords, while respecting the rules of cadence. The C scale-tone chords are the Cm(Maj7) (I), the Dm7(b5) (II), the Fm7 (IV), the G7b9 (V) and the Bdim7 (VII). A progression that utilizes these chords is: I-II-IV-I-VII-V-I, or:

Cm(Maj7)-Dm7(b5)-Fm7-Cm(Maj7)-Bdim7-G7(b9)-Cm(Maj7).

That leaves us with the EbMaj7+ and the AbMaj7(#11) to deal with. Let’s start by observing that the diminished chord has an ambiguous root, that is, any of its 4 notes could be considered the root of the chord. Hence, a Bdim=Ddim=Fdim=Abdim.

Let’s consider Eb as a temporary key center. From this perspective:

Fdim (same as Bdim)	=	II
EbMaj7+ (same as D#)	=	III
AbMaj7(#5) (same as G#)	=	IV

Since II-III-IV-II is a permissible sequence, we can therefore replace the Bdim7 with the sequence: Fdim7-EbMaj7+-AbMaj7(#11)-Bdim7, which gives us:

Cm(Maj7)-Dm7(b5)-Fm7-Cm(Maj7)-Fdim7-EbMaj7+-AbMaj7(#11)-Bdim7-G7(b9)-Cm(Maj7).

In Figure 6 we examine 4 bars (14-17) from the example file (see above). In the first bar, playing over a Cm(Maj7), the G note represents a fifth, the and Eb gives us our minor third. The next two notes repeat the first two. Next, the B yields a major seventh, followed by another E. The C is a root tone, followed by another B, which tied into the second bar, where it takes on the function of a b5 in the context of the Fdim7. Continuing in bar 2, we have an Ab, functioning here as the Fdim7’s b3, an F, which gives us the root tone, another b5 (B), and finally, a D, functioning here as a bb7 (6). Hence, bar 2 contains all scale tones in terms of the Fdim7. In bar 3 we’re playing over an EbMaj7(#5). The first note is a root tone (Eb), followed by a D, functioning here as a major seventh. Next we have a B, giving us our #5, followed by another D. Finally, we end bar 3 with a G, yielding a major third in the EbMaj7(#5) context. The last bar starts off with an Ab, functioning as a root tone over the AbMaj7(#11). The G gives us a major seventh, and the final note is another Ab.

1	2	b3	4	5	b6	7
C	D	Eb	F	G	Ab	B
C#	D#	E	F#	G#	A	B#
D	E	F	G	A	Bb	C#
Eb	F	Gb	Ab	Bb	Cb	D
E	F#	G	A	B	C	D#
F	G	Ab	Bb	C	Db	E
F#	G#	A	B	C#	D	E#
G	A	Bb	C	D	Eb	F#
Ab	Bb	Cb	Db	Eb	Fb	G
A	B	C	D	E	F	G#
Bb	C	Db	Eb	F	Gb	A
B	C#	D	E	F#	G	A#

1	2	b3	4	5	b6	7
C	D	Eb	F	G	Ab	B
C#	D#	E	F#	G#	A	B#
D	E	F	G	A	Bb	C#
Eb	F	Gb	Ab	Bb	Cb	D
E	F#	G	A	B	C	D#
F	G	Ab	Bb	C	Db	E
F#	G#	A	B	C#	D	E#
G	A	Bb	C	D	Eb	F#
Ab	Bb	Cb	Db	Eb	Fb	G
A	B	C	D	E	F	G#
Bb	C	Db	Eb	F	Gb	A
B	C#	D	E	F#	G	A#