Chord Construction Part 11: Diminished Chords and Symmetrical Intervals

We spoke a bit about Diminished Triads in Part 2 of this series. With our understanding on stacking Major and Minor 3rd's we can find
some interesting things in relation to this chord and to further our study of it.

An interval is diminished if it is narrowed. A diminished chord is one which contains a diminished interval. More specifically we
will deal with the Diminished 5th in this topic.

Up to this point we've been building chords based on the Major Scale, and with a few adjustments to the scale (the 3's and 7's) we
were able to extend these chords to the "13" chord by stacking 3rd's until we started repeating ourselves. And in turn creating three
Extended Chord Families.

The Diminished Triads aren't really based on the Major scale directly and they fall out of the patterns we saw developing with
Extended Chord Families, but still they use the familiar idea of stacking 3rd's.

Diminished Chords are "Symmetrical Chords" and are built from "Symmetrical Scales".

Symmetrical Chords and Scales mean the chord or scale is built from a repetitive sequence of Intervals that are always the same
distance from each other.

A sequence of all Half-steps could be called Symmetrical since each note progresses using nothing but Half-steps.

A sequence of all Whole-step could be called Symmetrical since each note progresses using nothing but Whole-steps.

Another Symmetrical pattern could be W H W H W H W H W H W... or H W H W H W H W H W...or again WWWWWWWW or HHHHHHHH....see how each
of these is a repetitive pattern or a sequence of Intervals...because of this they can each be called Symmetrical.

Let's see how the Diminished chord is built from Symmetrical Scales.

The Diminished Chord

Diminished chords are actually built from a Symmetrical scale...either a Whole-Half Tone scale (W-H scale), or a Half-Whole Tone
scale (H-W scale).

Let's look at these two scales from the Root note of C, along with the distance between each note so we can see the Interval
sequence/pattern develop (be aware of the Enharmonic names):

W-H Scale:    C        D        Eb        F        Gb        G#        A        B        C
W       H         W       H          W         H        W        H

H-W Scale:    C        C#        D#        E        F#        G        A        Bb        C
H         W          H       W         H        W        H        W

This should show you the symmetrical lay out of these two scales.

We have learned that a Diminished Triad has this formula:

R b3 b5

Let's look at the distance between each note:

R <--One and a Half Steps--> b3 <-One and a Half Steps--> b5

or

R <--m3--> b3 <--m3--> b5

See a pattern developing? Each of the notes so far are a Symmetrical pattern of repeating m3 Intervals.

And, you also want to notice that these three Intervals are also "every other note in the scale" so far (regardless of which one of
those Symmetrical scales you use). Remember to pay attention to the Enharmonic names.

So, even though we are using a different scale, other than the Major Scale, to build the Diminished Triad we are still just stacking
3rd's within these scales.

It does happen on occasion that a Diminished Triad is used on it's own, as is...but, just as we extended Major, Minor, and Dominant
chords, we can also extend the Diminished Triad.

The Diminished Triad can only really be extended to a 7th, and I'll show you where the limitation lies.

Keeping with our Symmetrical pattern let's continue the sequence of m3's until we start repeating ourselves:

R <--One and a Half Steps--> b3 <-One and a Half Steps--> b5 <--One and a Half Steps--> bb7 <--One and a Half Steps--> R

or

R <--m3--> b3 <--m3--> b5 <--m3--> bb7 <--m3-->R

See how we end up at the Root again? If we continued with our One and a Half Step Symmetrical pattern we'd end up repeating the same
notes/Intervals. Hopefully you can see that.

Ok, what's with the bb7???

Well, we know to "extend" a chord we need an Extended Family foundation of a Root, some type of 3rd, a 5, and some type of 7...this
will build a foundation of some type of "seven chord", remember?

Let's look at a Cdim7 with the Intervals and the note names:

R <--m3--> b3 <--m3--> b5 <--m3--> bb7 <--m3-->R
C                 Eb                 Gb                  A                  C

Ok, why is the A note a bb7 instead of a 6/13?

Well, the easiest way to put it is, when stacking notes for chords our logical order is R 3 5 7 etc...so to extended the Diminished
chord it will consist of a R b3 b5 and bb7.

I'm going to run that by you again...

The technical reason why that Interval is a bb7 instead of a 6/13...

Starting at the A note and counting every other note, or every 3rd note, until you repeat yourself. What notes do you get?

C Eb Gb A C

When building chords from a scale the first three "3rd's" should be a R 3 5 and 7, right? Well, for the Diminished chord it's a Root,
a b3, a b5, and a bb7 (it's a M7 flatted once to a b7, then flatted again to a bb7).

So, since we need a "7" note we look at it from the perspective of the M7 Interval. When we flat the M7 we end up with the b7, well
if we flat it again (from the M7 perspective) we end up with a bb7 or a double-flatted 7. Hope that makes sense.

There's a lot of common understandings about Diminished Chords:

1. In general terms, the Diminished Triad is not considered "The" Diminished Chord...but only a Diminished "Triad".

What we call "The" Diminished Chord is actually the four note chord or the dim7 chord.

So, when some says "play a C Diminished Chord"...they'll be expecting the four note Diminished 7 chord. If someone wants the three
note Triad they'll say..."play a Diminished Triad".

2. Play this C Diminished chord (remember it's going to be the Cdim7, right?):

--2--
--1--
--2--
--1--
--x--
--x--

Now, move that chord up three frets (One and a Half Steps = m3):

--5--
--4--
--5--
--4--
--x--
--x--

Then three more frets (another One and a Half Steps = m3):

--8--
--7--
--8--
--7--
--x--
--x--

Then three more frets (another One and a Half Steps = m3):

--11--
--10--
--11--
--10--
--x--
--x--

Then three more frets (another One and a Half Steps = m3):

--14--
--13--
--14--
--13--
--x--
--x--

And now we are one Octave higher than the chord we started with. And, if we continue moving it up One and a Half Steps at a time we
will repeat what we just did, only an Octave higher.

Now repeat this while strumming each of the chords fast before continuing on to the next chord. While doing this you should
hear/notice a very familiar sound you may have heard before in certain types of music, maybe while watching a cartoon or something
even. In other words, it's a very distinctive sound.

3. Look at each note in the chords above. If you inspect each string individually you'll notice that each note was moving up One and
a Half Steps, or a sequence of m3's.

And, after further inspection you need to realize that each of those chords above contain THE SAME NOTES, regardless of which one you
play. This is the result of moving each note up the same amount of distance.

Once you see they all contain the same notes, and are all Diminished chords, you should realize that any note in this chord could be
called the Root. Anyone of these chords could be called Ebdim, Adim, Cdim or F#dim. Since each chord contains Eb A C and F#, and the
Intervals are symmetrical, either note in the chord could be the root.

The chords shown above could ALL be thought of as Ebdim chords since they all contain the notes of a Ebdim chord. Or, they could be
thought as any arrangement of Ebdim's, Cdim's, Adim's, or F#dim's...it's your call, they all mean the same chord.

Pretty cool, huh?

4. Well, if you understood the information in #3 then hopefully this will make sense...

If every time we move One and a Half Steps we are playing the same diminished chord...then that really limits the amount of
diminished chords on the fretboard...in theory that is. Let's look at the first chord...

Ebdim:

--2--
--1--
--2--
--1--
--x--
--x--

Naming it from the lowest note in the chord, Eb, we can call this an Ebdim chord and it contains the notes: Eb A C and F# low to
high.

Now, move that chord up the fretboard one fret, only one fret, to the second fret of the D string. You could now call the chord an
Edim, right? And, it contains the notes low to high E A# C# G.

Now, move this chord up one more fret to the third fret of the D string. You could call this chord a Fdim and it contains the notes:
F G# B and D.

Ok, you with me so far??? Cause here's where repetition kicks in...

Move that chord one more fret higher to the 4th fret of the D string. We can call this chord a F#dim, right. It contains the note F#
C Eb and A...wait a minute that's the same note in the first chord we played, so the F#dim could really also be a Cdim, and Ebdim, or

Well, now if we move that chord up the fretboard one more fret to the 5th fret of the D string we'll find a Gdim, but look at the
notes from low to high: G C# E and A#, that's also the notes in the Edim chord we played a couple of steps back, right?

And, if we move that chord one more fret to the 6th fret of the D string we'll find G#dim, which has the notes G# D F B, which is
also the note a few steps back in the Fdim.

Cool, So by knowing three Diminished chords that don't have the same four notes in them, I've in a sense learned all the other
Diminished chord!

That's cool in theory but it's not reality, but it is the reality of the Diminished chord and a cool concept that everyone should
know.

Here's a couple of common movable chord people use to play Diminished chord on the fretboard (the Root is on the lowest string of the
chord):

Eb (also Adim, Cdim, or F#dim):

--2--
--1--
--2--
--1--
--x--
--x--

Cdim (also Ebdim, F#dim, or Adim):

--x--
--4--
--2--
--4--
--3--
--x--

Move these two chords around to play all over the other Diminished Chords.

The other thing to do is to learn the Whole-Half and Half-Whole Tone scales as they are very useful for playing a scale that fits a
Diminished chord.