Theory On Tap
Lesson 12: Symmetrical & synthetic scales
plus other random junk

Introduction

This lesson is on "Symmetrical" scales although we will also touch a little on Synthetic scales. The Major Scale and its modes make up the largest portion of frequently used note-series and there are also some variations (harmonic and melodic minor, and their modes) which get a lot of usage. However, there are some "miscellaneous" scales which although less common, can be quite useful. These include the so-called "Symmetrical" scales named as such because they are set up using repeated series of intervals. The easiest one is the Chromatic Scale.

Symmetrical Scales

A. The Chromatic Scale

The Chromatic scale is a set of continued half-steps. The formula is

 H H H H H H H H H H H H 

In theory, there is only one chromatic scale (C); all other chromatic scales could be considered to be modes of the first.

The name is taken from the Greek Chromos meaning "color" -- many musicians think of chromaticism as adding color to their playing. My favorite way to use chromaticism is to "fill in" the pentatonic pattern with half-steps:

Now, this is an exaggerated example, but you get the picture. Look at all the half-steps. You can chromaticise any scale or scale fragment this way. A Pure chromatic scale looks like this:

Another way is to slide the first two notes on each string which puts the whole thing in one (big) position:

B. The WholeTone Scale

The WholeTone Scale consists of successive whole-steps (1 whole step = 2 Frets). The sound is "dreamy" -- in TV shows and movies, when a person is daydreaming or having a (memory) flashback, or in a state of wonder or amazement, you will almost always hear the WholeTone Scale in the soundtrack. In the introduction to Stevie Wonder's "You Are the Sunshine of My Life," where Stevie plays an ascending WholeTone scale harmonized in major thirds.

In theory, there are only 2 WholeTone Scales (C and C♯), with all others being modes of these two.

The WholeTone Scale has 6 notes instead of the usual 7:

W W W W W W

The WholeTone scales plays out like this:

or this:

To me, they are both unruly. WholeTone Scales are usually used sparingly -- for short segments. A good example is the Django Reinhardt's Improvisation 1 (played by Stephane Wrembel here). Particularly in the starting section of the song. This song also uses a lot of chromaticism so it's a good video to study to see how you can emply these two nebulous scales to make interesting transitions.

Neither the Chromatic nor WholeTone Scale produces a good sense of key-center. Play long sequences (ascending/decending/mixed) over one bass note and this will be clear. It produces a nice effect, in that you can temporarily suspend the key of your piece.

C. The Diminished Scale

The Diminished Scale is a repeating series of alternating whole and half steps:

 H W H W H W H W  aka Half/Whole

 W H W H W H W H  aka Whole/Half

In theory, there are only 3 Diminished Scales (C C♯ D) with all others being modes of these 3.

And, notice that this scale has 8 notes instead of the usual 7. The "extra" note comes from the fact that both the 3 and ♭3 are in it.

Whereas Chromatic and WholeTone scales are kind of simple in construction, the Diminished Scale has a slight complexity to it.

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.

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 (♭5), or Diminished 7. Conversely, the half-whole diminished scale can be played over any of these chords!

The third complexity is that part about there being only 3 diminished scales. The C-diminished scale contains the same notes as the E♭, G♭, and A -diminished scales.

So, C-E♭-G♭-A spells:

• the C dim7 chord
• the E♭ dim7 chord (E♭-G♭-A-C)
• the G♭ dim7 chord (G♭-A-C-E♭)
• the A dim7 chord (A-C-E♭-G♭)

(Note: You might want to revisit section C of Lesson 9 by Grant Green for more information on diminished chords.)

Lets look at a few examples of diminished scale usage and discuss some of its other "features."

The Whole-Half and Half/Whole patterns for the Dim Scale looks like this:

To play a Half/Whole, start anywhere, on a "H"
To play a Whole/Half, start anywhere, on a "W"

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;

Check out the two strips of interval patterns of minor2-P4 construction. Or, you can do this:

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! A little more compact in position, but complex in pattern.

Good Rule of Thumb:

• Whole-Half --- for playing over diminished chords
• Half Whole --- for playing over altered dominant chords [1]

Key of C: vii dim7 = B dim7 = B D F A♭
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 ♭2 (♭9) the A♭, as well. Play the B dim7 over the G7 (or G7♭9).

How about the B half-whole scale? It contains:
B C D D♯ F F♯ G♯ A
Which are related to G7 as:
3 4 5 ♯5 dom7 7 ♭9 9
Removing the 3, 5, dom7 which are already in the G7 chord, you get:
4 ♯5 ♭9 9
---OR---
Play the G half/whole over G7 and get the following cool notes:
G half/whole:

• G A♭ B♭ B C♯ D E F, or
  
• 1 ♭2 ♭3 3 ♯4 5 6 dom7 relative to G7, or
  
• " ♭9 ♯9 " ♯11" 13 " (some heavy alterations to G7, but cool sounding if done right)
  

D. The Augmented Scale

The Augmented Scale a set of alternating Augmented 2nds and minor 2nds
(an augmented 2nd is the same as a ♭3).

Its formula is:

   1 ♭3 3 5 ♯5 7 (a 6-note scale)

   1 → ♭3  = aug2
  ♭3 →  3  = m2
   3 →  5  = aug2
   5 → ♯5  = m2
  ♯5 →  7  = aug2
  

The pattern is:

This pattern involves putting the aug2 interval on the same string, and the dim2 between strings. If you reverses it, it becomes:

Which is easy to finger, but still creeps to the left. To make it stay in one place, add these notes:

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!

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:

  1 ♭2 2 ♭3 3 4 ♭5 (1)

  C D♭ D E♭ E F G♭ (C) (bunch of small steps + one big step)
  

Basically anything OTHER than the scales we already use. A good way is to start with a common scale, then just change one note.

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).

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.)

However you arrive at your 7 notes of choice, fine. Let's pick the following at random:

C D♭ E F G♭ A B♭
1 ♭2 3 4 ♭5 6 ♭7

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.

This will give us a set of chords, and a set of modes to play over them, with all the right notes!

The 1 chord is:	C E G♭ B♭	or 1 3 ♭5 dom7	or C7♭5
2	is: D♭ F A C	or 1 3 ♯5 7	or D♭M7♯5
3	is: E G♭ B♭ D♭	or 1 ♭♭3 ♭5 dim7	or ? (Edim7 9)
4	is: F A C E	or 1 3 5 dom7	or F7
5	is: G♭ B♭ D♭ F	or 1 3 5 7	or G♭M7
6	is: A C E G♭	or 1 ♭3 5 dim7	or Adim7nat5
7	is: B♭ D♭ F A	or 1 ♭3 5 7	or B♭min-M7

Now for the payoff: construct a tune using chord formulas:

I IV I V IV I (Blues-from-Venus)

but putting in the Synthetic chords, and playing the Synthetic modes over them. (Go back to Lesson 1 and reapply it all). This can sound BAD, but never train-wreck-bad. More like not-playing-with-a-full-deck-bad. Listen to Zappa and Vai. I have done a tune where we broke into a Synthetic Jam in the middle. This will really wake up the audience.

Have fun and Keep-on-Tappin!
-- Will and Rick

**Thanks to Wayne Wylupski and Scott Homan for helpful information and suggestions**

Reference

1. Haslip, Jimmy, The Melodic Bass Library, James Haslip Publishing, Miami Florida, 1991, p. 70
2. Haerle, Dan, The Jazz Language, Studio 224, Hialeah, Florida, 1980, p. 34-36
3. Persichetti, Vincent, Twentieth Century Harmony, W W Norton and Company, New York, 1961, p. 43-45

copyright © 1995 rick bellinger, Will Pirkle