Diminished Scales

Recall that we defined a scale as:
a group of notes within an octave (and any octaves of those notes) usually played one at a time.

We can describe (define) a scale in any of these ways:
- by letters (representing specific pitches)
- by numbers (representing specific intervals)
- by step pattern (describing intervals from note to note)

So for example the major scale (ionian mode) can be described/ defined as/by: C-D-E-F-G-A-B-C (in the key of C), 1,2,3,4,5,6,7, and W-W-1/2-W-W-W-1/2.

We define a diminished scale as a scale containing the notes (intervals) 1,b3,b5. (In other words, using the notes in the scale we can construct a diminished chord off the root note)

From either diminished (W-1/2) scale = W-1/2-W-1/2-W-1/2-W-1/2,
or C (W-1/2) = C,D,Eb,F,Gb,Ab,Bbb,B we can find the intervals (from the root note) to be 1,2,b3,4,b5,b6,bb7,7.

Looking at the numbers, we can deduce that the diminished (W-1/2) scale is a diminished scale. that is, it contains the notes 1,b3,b5.

We define a mode as a scale within a family of scales that are related by their step patterns. We can derive the modes of a scale by moving the first step of a step pattern to the end, and repeating until we return to the first scale we started with.

The diminished scales are a family consisting of two modes:

W-1/2-W-1/2-W-1/2-W-1/2 = W-1/2
1/2-W-1/2-W-1/2-W-1/2-W = 1/2-W

This lesson we will look at both scales in the family, and consider the semi-symmetric nature of such scales.

So Starting with the W-1/2 scale, lets look at some patterns (moveable shapes) with which we can play the diminished (W-1/2) scale.

|-1|--|-2|b3|--|-4|b5|--|b6|bb7|--|-7|-1|
|--|b6|bb7|--|-7|-1|--|-2|b3|--|-4|b5|--|
|b3|--|-4|b5|--|b6|bb7|--|-7|-1|--|-2|b3|
|--|-7|-1|--|-2|b3|--|-4|b5|--|b6|bb7|--|
|-4|b5|--|b6|bb7|--|-7|-1|--|-2|b3|--|-4|
|-1|--|-2|b3|--|-4|b5|--|b6|bb7|--|-7|-1|


W-1/2 scale "E-shape" (root note on the 6th string)
|-7-|-1-|---|-2-|b3-|
|b5-|---|b6-|bb7|---|
|-2-|b3-|---|-4-|---|
|bb7|---|-7-|-1-|---|
|---|-4-|b5-|---|b6-|
|-7-|-1-|---|-2-|b3-|

W-1/2 scale "D-shape" (root note on the 4th string)
|---|-2-|b3-|---|-4-|
|---|bb7|---|-7-|-1-|
|---|-4-|b5-|---|b6-|
|-7-|-1-|---|-2-|b3-|
|b5-|---|b6-|bb7|---|
|---|-2-|b3-|---|-4-|

W-1/2 scale "C-shape" (root note on the 5th string)
|---|-4-|b5-|---|b6-|
|---|-1-|---|-2-|b3-|
|---|b6-|bb7|---|-7-|
|-2-|b3-|---|-4-|b5-|
|bb7|---|-7-|-1-|---|
|---|-4-|b5-|---|b6-|

W-1/2 scale "A-shape" (root note on the 5th string)
|b5-|---|b6-|bb7|---|
|---|-2-|b3-|---|-4-|
|bb7|---|-7-|-1-|---|
|---|-4-|b5-|---|b6-|
|-7-|-1-|---|-2-|b3-|
|b5-|---|b6-|bb7|---|

W-1/2 scale "G-shape" (root note on the 6th string)
|bb7|---|-7-|-1-|---|
|---|-4-|b5-|---|b6-|
|-1-|---|-2-|b3-|---|
|---|b6-|bb7|---|-7-|
|-2-|b3-|---|-4-|b5-|
|bb7|---|-7-|-1-|---|

By combining two or three shapes together we can come up with lead patterns ( a way of moving up and down the neck in a scale rather than just across the neck). So you could learn these as a way to travel between two unconnected shapes (just one example of their use).

|--|--|--|--|--|--|--|--|b6|-6|--|-7|-1|
|--|--|--|--|--|--|--|-2|--|-3|4-|b5|--|
|--|--|--|--|--|b6|-6|--|-7|-1|--|--|--|
|--|--|--|--|-2|b3|--|-4|b5|--|--|--|--|
|--|--|--|b6|-6|--|-7|-1|--|--|--|--|--|
|-1|--|-2|b3|--|-4|b5|--|--|--|--|--|--|

|--|--|--|--|--|--|--|--|--|--|--|
|--|--|--|--|--|--|b6|-6|--|-7|-1|
|--|--|--|--|-2|b3|--|-4|b5|--|--|
|--|--|--|b6|-6|--|-7|-1|--|--|--|
|-1|--|-2|b3|--|-4|b5|--|--|--|--|
|--|--|--|--|--|--|--|--|--|--|--|

two adjacent strings:
Seperated by a P4
|---|---|---|b6-|bb7|---|-7-|-1-|
|-1-|---|-2-|b3-|---|-4-|b5-|---|

seperated by a M3
|---|---|b5-|---|b6-|bb7|---|-7-|-1-|
|-1-|---|-2-|b3-|---|-4-|b5-|---|---|

on a single string:

|1|-|2|b3|-|4|b5|-|b6|bb7|-|7|1|

For this lesson, since the scale we are looking at has more than 7 pitches we will consider a different harmonization method than used in previous lessons, although its similar to the pentatonic lessons.

Consider the notes, and some of their enharmonic equivalents.

W-1/2 = 1,2,b3,4,b5(#4),b6(#5),bb7(6),7

Building chords just off the root note gives close to standard chords:
triads: io, i+5, i(6), iosus2, iosus4
seventh chords: io7 (i6b5), imaj7#5, imaj7b5, i6#5
ninth chords: i6/9b5, imaj9#5, imaj9b5, i6/9#5
eleventh chords: imaj11#5, imaj11b5
thirteenth chords: imaj13#5, imaj13b5

Turning to the 1/2-W scale:

From either diminished (1/2-W) scale = 1/2-W-1/2-W-1/2-W-1/2-W,
or C (1/2-W) = C,Db,Eb,Fb,Gb,G,Bbb,Bb we can find the intervals (from the root note) to be 1,b2,b3,3,b5,5,bb7,b7.

Looking at the numbers, we can deduce that the diminished (W-1/2) scale is a diminished scale. that is, it contains the notes 1,b3,b5. It can also be viewed as a major scale (1,3,5), a minor scale (1,b3,5), and a dominant scale (1,3,5,b7).

Lets look at some patterns (moveable shapes) with which we can play the diminished (1/2-W) scale.

|-1|b2|--|b3|-3|--|b5|-5|--|bb7|b7|--|-1|
|-5|--|bb7|b7|--|-1|b2|--|b3|-3|--|b5|-5|
|b3|-3|--|b5|-5|--|bb7|b7|--|-1|b2|--|b3|
|b7|--|-1|b2|--|b3|-3|--|b5|-5|--|bb7|b7|
|--|b5|-5|--|bb7|b7|--|-1|b2|--|b3|-3|--|
|-1|b2|--|b3|-3|--|b5|-5|--|bb7|b7|--|-1|


1/2-W scale "E-shape" (root note on the 6th string)
|---|-1-|b2-|---|b3-|
|b5-|-5-|---|bb7|b7-|
|---|b3-|-3-|---|b5-|
|bb7|b7-|---|-1-|b2-|
|-3-|---|b5-|-5-|---|
|---|-1-|b2-|---|b3-|

1/2-W scale "D-shape" (root note on the 4th string)
|b2-|---|b3-|-3-|---|
|---|bb7|b7-|---|-1-|
|-3-|---|b5-|-5-|---|
|---|-1-|b2-|---|b3-|
|b5-|-5-|---|bb7|b7-|
|b2-|---|b3-|-3-|---|

1/2-W scale "C-shape" (root note on the 5th string)
|-3-|---|b5-|-5-|---|
|---|-1-|b2-|---|b3-|
|-5-|---|bb7|b7-|---|
|---|b3-|-3-|---|b5-|
|bb7|b7-|---|-1-|b2-|
|-3-|---|b5-|-5-|---|

1/2-W scale "A-shape" (root note on the 5th string)
|b5-|-5-|---|bb7|b7-|
|b2-|---|b3-|-3-|---|
|bb7|b7-|---|-1-|---|
|-3-|---|b5-|-5-|---|
|---|-1-|b2-|---|b3-|
|b5-|-5-|---|bb7|b7-|

1/2-W scale "G-shape" (root note on the 6th string)
|bb7|b7-|---|-1-|b2-|
|-3-|---|b5-|-5-|---|
|-1-|b2-|---|b3-|---|
|-5-|---|bb7|b7-|---|
|---|b3-|-3-|---|b5-|
|bb7|b7-|---|-1-|b2-|

|--|--|--|--|--|--|--|--|--|-6|b7|--|-1|
|--|--|--|--|--|--|--|--|b3|-3|--|b5|-5|
|--|--|--|--|--|--|-6|b7|--|-1|b2|--|--|
|--|--|--|--|--|b3|-3|--|b5|-5|--|--|--|
|--|--|-5|--|-6|b7|--|-1|b2|--|--|--|--|
|-1|b2|--|b3|-3|--|b5|--|--|--|--|--|--|

|--|--|--|--|--|--|--|--|--|--|--|
|--|--|--|--|--|--|--|-6|b7|--|-1|
|--|--|--|--|--|b3|-3|--|b5|-5|--|
|--|--|-5|--|-6|b7|--|-1|b2|--|--|
|-1|b2|--|b3|-3|--|b5|--|--|--|--|
|--|--|--|--|--|--|--|--|--|--|--|

two adjacent strings:
Seperated by a P4
|---|---|-5-|---|bb7|b7-|---|-1-|
|-1-|b2-|---|b3-|-3-|---|b5-|---|

seperated by a M3
|---|---|---|-5-|---|bb7|b7-|---|-1-|
|-1-|b2-|---|b3-|-3-|---|b5-|---|---|

on a single string:

|1|b2|-|b3|3|-|b5|5|-|bb7|b7|-|1|

Considering the notes, and some of their enharmonic equivalents.

1/2-W = 1,b2,b3,3,b5(#4),5,bb7(6),b7

Building chords just off the root note gives close to standard chords:
triads: io, I, i, Isus2, Isus#4, I(6), I(b5)
seventh chords: io7 (i6b5), i6, I7, I7b5, i7, i7b5, I6, I6b5
ninth chords: i6/b9b5, i6b9, i7b9b5, i7b9, I7b9, I7b9b5, I6b9, I6b9b5
eleventh chords: I7#11b9, i7#11b9
thirteenth chords: I13#11b9, i13#11b9

Since the diminished scales are diminished scales, that is they have a diminished chord built off their root notes, the concept of progressions built off the chords doesn't work as well. There is a lack of stability in the root chords. rather let's consider the symmetric nature of these scales and see what chords we can use these scales with.

Since the step pattern repeats at regular intervals, we don't have to learn 12 scales for each.

We note :
CW-1/2 = EbW-1/2 = GbW1/2 = AW-1/2
DbW-1/2 = EW-1/2 = GW1/2 = BbW-1/2
DW-1/2 = FW-1/2 = AbW1/2 = BW-1/2

(the same relationships hold for 1/2-W).

The first set of chords (written above for W-1/2) can be found on the 1,b3,b5,bb7 for the W-1/2 scale, and the 2nd set of chords can be found on the 2,4,b6,7.

For the 1/2-W scale the second set of chords can be found on the 1,b3,b5,bb7 and the first set can be found on the b2,3,5,and b7.

Where/when does one usually decide to use diminished scales?
- some would use it over the io7 chord in the major scale/key context (play i-diminished (W-1/2 or 1/2-W) over io7)
- you could use the 1/2-W scale over I7 or i7 or im7b5.
- over several chords that fit within a parallel major/minor context. ex. over D7-Dm7b5 (I7-im7b5), or D7-Dm7 (I7-i7) you could play D-1/2-W.
- over io7 - IV7, play the iW-1/2 scale.

Next lesson is on Advanced Rhythm.

Peace,
Christopher Roberts
snglstringtheory@aol.com


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated December 21, 2007
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