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Whereas Chromatic and WholeTone scales are kind of simple in construction,
the Diminished Scale has a slight complexity to it.
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The first complexity is that there are 2 ways to view the pattern:
Whole-Half and Half-Whole depending on how you start the sequence -- see
patterns above. Also note that the patterns contain each other: there is a
W H W pattern inside of H W H W H. In other words, they are the same scale,
but starting from an adjacent note.
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The second complexity is that the Diminished Scale contains all sorts of
combinations of intervals. The Half-Whole scale gives you a choice of
intervals for the third, fifth, and seventh tones of a chord. The third can
be either major or minor. The fifth can be either perfect or diminished.
The seventh can be either minor (which is also dominant) or diminished.
Thus you can obtain the following triads; major, minor or diminished. You
can also derive any of the following seventh chords; Dominant 7, Minor 7,
Minor 7 (b5), or Diminished 7. Conversely, the half-whole diminished scale
can be played over any of these chords!
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The third complexity is that part about there being only 3 diminished
scales. The C-diminished scale contains the same notes as the Eb, Gb, and A
-diminished scales.
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So, C-Eb-Gb-A spells:
- the C dim7 chord
- the Eb dim7 chord (Eb-Gb-A-C)
- the Gb dim7 chord (Gb-A-C-Eb)
- the A dim7 chord (A-C-Eb-Gb)
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(Note: You might want to revisit section C of
Lesson 9 by Grant Green for more information on diminished chords.)
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Lets look at a few examples of diminished scale usage and discuss some of
its other "features."
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The Whole-Half and Half/Whole patterns for the Dim Scale looks like this:
|-----|-----|-----|-----|--H--|--W--|-----|--H--|--W--
|-----|-----|-----|--H--|--W--|-----|--H--|--W--|-----
|-----|-----|--H--|--W--|-----|--H--|--W--|-----|-----
|-----|--H--|--W--|-----|--H--|--W--|-----|-----|-----
|--H--|--W--|-----|--H--|--W--|-----|-----|-----|-----
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To play a Half/Whole, start anywhere, on a "H"
To play a Whole/Half, start anywhere, on a "W"
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Notice that if you use four notes to a string, the pattern will "creep" to
the right. If you use three notes to a string, the pattern will creep to
the left, like this;
|-----|-----|-----|--H--|--W--|-----|--W--|-----|-----|-----
|-----|-----|-----|--W--|-----|--H--|--W--|-----|-----|-----
|-----|-----|-----|-----|--H--|--W--|-----|--H--|-----|-----
|-----|-----|-----|-----|--W--|-----|--H--|--W--|-----|-----
|-----|-----|-----|-----|-----|--H--|--W--|-----|--H--|-----
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Check out the two strips of interval patterns of minor2-P4 construction.
Or, you can do this:
|-----|-----|-----|--H--|--W--|-----|--H--|-----|-----|-----
|-----|-----|-----|--W--|-----|--H--|--W--|-----|-----|-----
|-----|-----|--W--|-----|--H--|--W--|-----|--H--|-----|-----
|-----|-----|-----|--H--|--W--|-----|--H--|-----|-----|-----
|-----|-----|-----|--W--|-----|--H--|--W--|-----|-----|-----
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Notice that this is a pattern that repeats after every three strings; it's
basically the '3 notes per string' pattern, but with an extra note thrown
onto the third string of the pattern to keep it from creeping too far to
the left!
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A little more compact in position, but complex in pattern.
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Good Rule of Thumb:
Whole-Half --- for playing over diminished chords
Half Whole --- for playing over altered dominant chords [1]
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Example: Play the vii dim7 over the V7 chord:
Key of C: vii dim7 = B dim7 = B D F Ab
and
the V7 of C is G7 = G B D F
then
the B dim7 has many common notes (B D F), and contains a funky b2 (b9) the
Ab, as well. Play the B dim7 over the G7 (or G7b9).
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How about the B half-whole scale? It contains:
B C D D# F F# G# A
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Which are related to G7 as:
3 4 5 #5 dom7 7 b9 9
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Removing the 3, 5, dom7 which are already in the G7 chord, you get:
4 #5 b9 9
---OR---
Play the G half/whole over G7 and get the following cool notes:
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G half/whole:
- G Ab Bb B C# D E F, or
- 1 b2 b3 3 #4 5 6 dom7 relative to G7, or
- " b9 #9 " #11" 13 " (some heavy alterations to G7, but cool sounding if done right)
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In classical music, the dim7 is used as a Dominant Preparation (just before
the closing V7-I cadence, a big diminished chord/scale/arpeggio segment is
inserted for added buildup).
The Allman Brothers, Dead, and Phish use the dim7 this way as well.
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D. The Augmented Scale
The Augmented Scale a set of alternating Augmented 2nds and minor 2nds (an
augmented 2nd is the same as a b3). Its formula is:
1 b3 3 5 #5 7 (it is a 6-note scale)
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1 to b3 = aug2
b3 to 3 = m2
3 to 5 = aug2
5 to #5 = m2
#5 to 7 = aug2
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The pattern is:
|-O--|----|----|-O--|----|----|----|----
|----|-R--|----|----|-O--|----|----|----
|----|----|-O--|----|----|-O--|----|----
|----|----|----|-O--|----|----|-O--|----
|----|----|----|----|-R--|----|----|-O--
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This pattern involves puting the aug2 interval on the same string, and the
dim2 between strings. If you reverses it, it becomes:
|-O--|-O--|----|----|----|----|
|----|-O--|-R--|----|----|----|
|----|----|-O--|-O--|----|----|
|----|----|----|-O--|-O--|----|
|----|----|----|----|-O--|-R--|
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Which is easy to finger, but still creeps to the left. To make it stay in
one place, add these notes:
|----|-O--|----|----|-O--|-O--|
|----|-O--|-R--|----|----|-O--|
|----|----|-O--|-O--|----|----|
|----|----|----|-O--|-O--|----|
|----|-O--|----|----|-O--|-R--|
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The pattern on the last string is identical to the pattern on the first
string; thus the whole pattern will repeat from there (if you had an
infinitely wide fret board). It's the above pattern, but with extra notes
added onto the first, forth and fifth strings of the pattern to keep it
from wandering left again. However, take care that the root will be in a
different place in the rest of the pattern!
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Synthetic Scales
The last thing I want to discuss (briefly...) is Synthetic scales. Of all
the possible 7-note scales, we only use a handful of them. And, all but a
few are combinations of W and H steps = Major2 (M2) and minor 2 (m2)
intervals. But, theoretically, you can have any combination, so long as it
is 7 notes. Like this horror:
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1 b2 2 b3 3 4 b5 (1)
C Db D Eb E F Gb (C) (bunch of small steps + one big step)
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Basically anything OTHER than the scales we already use. A good way is to
start with a common scale, then just change one note.
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Another way is to splice "tetrachords" together. What's a tetrachord? It's
simply a string of four sequential notes, usually comprising half of a
scale. A major tetrachord is the first four notes of a major scale. A minor
tetrachord is the first four notes of a minor scale. A major scale is
simply a minor tetrachord stacked on top of a major tetrachord! Also, a
melodic minor tetrachord is a major tetrachord spliced to the end of a
minor tetrachord. (Note that in the above examples, the last note of the
second tetrachord will be the same as the first note of the second
tetrachord. Thus you have eight notes, but only seven distinct pitches. If
you splice two minor tetrachords together, you get a diminished scale, with
eight notes and eight distinct pitches).
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You can splice some tetrachords together in unusual combinations to arrive
at some interesting synthetic scales. If you stack the second half of a
harmonic minor scale on top of a major tetrachord, you get something called
a "Harmonic Major" Scale, which can also be looked at as either a harmonic
minor scale with a raised third or a major scale with a flat sixth. You can
also get some fairly exotic scales like the "Double Harmonic" scale, which
is comprised of two identical tetrachords from the second half of the
harmonic minor scale. (Another popular synthetic scale, the "Hungarian
Minor" Scale, is actually the fourth mode of the double harmonic scale.)
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However you arrive at your 7 notes of choice, fine. Let's pick the
following at random:
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C Db E F Gb A Bb
1 b2 3 4 b5 6 b7
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When you have the notes you want/like/stumble upon, then harmonize the
whole thing up by stacking every other note (just like has been done in
several of these lessons). We are mimicking the way Western harmony works.
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This will give us a set of chords, and a set of modes to play over them,
with all the right notes!
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| The 1 chord is: |
C E Gb Bb |
or 1 3 b5 dom7 |
or C7b5 |
| 2 |
is: Db F A C |
or 1 3 #5 7 |
or DbM7#5 |
| 3 |
is: E Gb Bb Db |
or 1 bb3 b5 dim7 |
or ? (Edim7 9) |
| 4 |
is: F A C E |
or 1 3 5 dom7 |
or F7 |
| 5 |
is: Gb Bb Db F |
or 1 3 5 7 |
or GbM7 |
| 6 |
is: A C E Gb |
or 1 b3 5 dim7 |
or Adim7nat5 |
| 7 |
is: Bb Db F A |
or 1 b3 5 7 |
or Bbmin-M7 |
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Now for the payoff: construct a tune using chord formulas:
I IV I V IV I (Blues-from-Venus)
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but putting in the Synthetic chords, and playing the Synthetic modes over
them. (Go back to Lesson 1 and reapply it all).
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This can sound BAD, but never train-wreck-bad. More like
not-playing-with-a-full-deck-bad. Listen to Zappa and Vai.
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I have done a tune where we broke into a Synthetic Jam in the middle. This
will really wake up the audience.
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Have fun and Keep-on-Tappin!
Will and Rick
**Thanks to Wayne Wylupski and Scott Homan for helpful information and
suggestions**
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REFERENCE
- Haslip, Jimmy, The Melodic Bass Library, James Haslip Publishing, Miami
Florida, 1991, p. 70
- Haerle, Dan, The Jazz Language, Studio 224, Hialeah, Florida, 1980, p. 34-36
- Persichetti, Vincent, Twentieth Century Harmony, W W Norton and
Company, New York, 1961, p. 43-45
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