theory epiphany

Bill McCloskey · Post by **Bill McCloskey** » 15 Dec 2010 5:00 pm

Had one of those nice little theory epiphany's you get now and then, where something simple helps you visualize something you've had trouble keeping in your head.

All because of this simple youtube video. This guy was doing a little lesson on Diminished chords and what he said finally clicked something in me: So we have a dimished chord - stacked 3rds. Which means that there are only 3 diminished chords you need to learn to cover them all .

If you lower any one note, it doesn't matter which, you have a dominant seventh chord. So lets take 1 of the 3 diminished chords: D F Ab B. Lower the B to Bb and you have a Bb dominant chord. Lower the D to C# you have a C# Dominant Chord, etc. So now modulating from one key to the next becomes simple. Let's say I want to modulate from the key of C to the key of A. I can go C to G7 to Ab dim (the G goes up one note) - to E dominant 7 (lower the f one note) to A. I started improvising on the trumpet and it was just so much fun to improvise around these modulations cause they all sound good.

Here is another visualization:
C
(C)D(E)F(G)A(B)
to G7
C(D)E(F)(G)A(B)
To Ab dim
(D)(F)(G#)(B)
to E7
(D)(E)(G#)(B)
to A
(A)B(C#)D(E)F(G#)

Anyway, it helped me.

It occurred to me that if you started a theory course by starting on diminished chords, it might be so much easier for people to visualize everything else. Lot easier to start with 3 of something than 12 of something.

Jim Cohen · Post by **Jim Cohen** » 15 Dec 2010 5:05 pm

Hey, I like that! I'm gonna play around with that. Where's the icon for little light bulb going on?

Post by **Dave Mudgett** » 15 Dec 2010 7:57 pm

I think this really lays out nicely on 6-string guitar, and I uncovered it quite accidentally just noodling around some time ago, only to find out that Pat Martino made a whole theory out of this kind of stuff. Here are a few references if you want to check it out:

http://mto.societymusictheory.org/issue ... apuzzo.pdf

http://chordmelody.org/doc/martinochordfamily.doc

http://www.jazzguitarpro.com/martinos_dim7_insights

and of course Pat's own website

http://www.patmartino.com/

the latter two of which have links to this guitar player article from several years back:

http://www.patmartino.com/Articles/Guit ... l_2004.pdf

You cannot go wrong studying anything Pat has to say about music.

Bill McCloskey · Post by **Bill McCloskey** » 16 Dec 2010 5:11 am

Great stuff Dave. I'll dig into that.

I posted this on a trumpet forum as well and to answer a question I created this follow up message, which I'll post here as well:

Let me see if I can explain it in a little clearer a way.

First, there are many ideas and uses for the information I discuss. I'm still digging in and thinking about it. But let's use a simple example for what this means specifically to trumpet playing and improvisation.

unlike other instruments like a guitar, which can take a chord shape and move it up and down the neck to get different chords of the same family, trumpet players don't have a visual crutch like that. I have to memorize all 12 triads, all 12 dominant 7 chords, all minor 6th chords, etc. That is a lot of chords to keep in your head and bring up in a moments notice. A lot of work, a lot of practice to make these chords available to you without thinking. Wouldn't it be great if there was a system to help make it easier. There is: by using diminished 7th chords. Why? Let me explain.

A diminished 7th chord is a stack of minor thirds put on top of each other. A minor third distance is 3 notes on the chromatic scale from the note before. Here is the chromatic scale repeated twice:

C C# D Eb E F F# G G# A Bb B C C# D Eb E F F# G G# A Bb B C

If you take every 3rd note (the notes of the diminished chord) you get a repeating pattern:

C Eb F# A C Eb F# A which repeats forever. C Eb F# A repeat over and over as a stack of minor thirds. So what does this tell you;

For one it means it doesn't matter where you start: Eb F# A C are the same 4 notes but starting on a different note. In other words Those 4 notes are the same but have 4 different names: Eb Dim 7, F# dim 7, A dim 7, and C dim 7 are four names for the very same chord. So NOW I don't have to memorize 12 diminished chords, I have to memorize 3. C Eb F# A is one, C# E G Bb is another, and D F Ab B, is the third. Those are the only 3 diminished 7th chords in the world, but they encompass all 12 chords. So I memorize those 3 chords and where they lie on the trumpet and now i can play any 12 diminished 7th chords, only having memorized 3.

Let's take a step further. I have my 3 chords memorized. Now all I have to do is take one of those diminished chords and lower ANY one note to get 4 Dominant 7th chords.

Take our first diminished chord (1 of 3): C Eb F# A. By lowering anyone of these notes I'll have 4 different dominant 7th chords:

Lower the C to B: you get a B7th chord: B Eb F# A
Lower the Eb to D: you get D7th chord: C D F# A is a D7th chord (start it on D and you have D F# A C)
Lower the F# to F you have a f7th chord: C D F A
Lower the A to a Ab you have Ab7th chord: C D F Ab

Now instead of having to memorize 4 different diminished chords and 4 different 7th chords, I only have to memorize 1 chord and everything is created off of that. That saves a lot of brain work. Especially when you think, it doesn't end there: I also have the 4 triads that are part of the 7th chords: B Eb F#, D F# A, F A C, Ab C Eb.

Now here is something to really blow your mind: raise any one note and you have a minor 6th chord. Raise the C to a C# and you have a F# minor 6th: C# Eb F# A (in the proper order: F# A C# Eb)
Raise the Eb to E, you have an A minor 6th: C E F# A, raise the F# to a G, you have a Cm6th: C Eb G A and raise the A to a Bb you have a Eb minor 6th: C Eb F# Bb.

Wow, now by just memorizing ONE chord, a diminished chord, I now have the following chords under my belt:
Cdim7
Ebdim7
F# dim7
A dim7
B triad
D triad
F triad
Ab triad
B7
D7
F7
Ab7
Cmin6
Ebm6
F#m6
Am6

That is a lot of chords to have by memorizing one chord.

I'll explain the modulation thing later. Absorb that first.

Mike Neer · Post by **Mike Neer** » 16 Dec 2010 7:23 am

I love music theory stuff, always have.

I highly recommend Slonimsky's Thesaurus of Melodic Scales and Patterns. It covers this stuff in great depth, although you will have to figure out how to apply it through what seems to be a completely foreign language. I bought it about 25 years ago and it took me a while to really understand the harmonic applications. Yusef Lateef has written the book The Repository of Melodic Scales and Patterns which simplifies things a little and gears it for the jazz musician, but uses many of the same types of patterns.

Scott Shewbridge · Post by **Scott Shewbridge** » 16 Dec 2010 8:12 am

Very nice stuff Bill. On six string, some of the dominant seventh voicings that come out using this technique are not obvious at first and make for some very juicy transitional chords. Thanks for sharing this, it fits very well with things I am trying to learn and I really appreciate it.

Bill Hatcher · Post by **Bill Hatcher** » 16 Dec 2010 2:14 pm

Mike Neer wrote:I love music theory stuff, always have.

I highly recommend Slonimsky's Thesaurus of Melodic Scales and Patterns. It covers this stuff in great depth, although you will have to figure out how to apply it through what seems to be a completely foreign language. I bought it about 25 years ago and it took me a while to really understand the harmonic applications.

mike i have had that book for longer than that. have not really worked on it, but one thing i did that really helped, is to just sequence the patterns with a keyboard or a computer. play them back over and over and then play some bass notes on your guitar and you will be surprised how the patterns will start to sound good in certain tonal centers.

Mike Neer · Post by **Mike Neer** » 16 Dec 2010 6:27 pm

Bill Hatcher wrote: mike i have had that book for longer than that. have not really worked on it, but one thing i did that really helped, is to just sequence the patterns with a keyboard or a computer. play them back over and over and then play some bass notes on your guitar and you will be surprised how the patterns will start to sound good in certain tonal centers.

The coolest thing is many of the patterns you can recognize from hearing others play them. I broke the book out again about a year ago and I've been slowly incorporating some of the patterns into my playing, mostly on altered dominant chords.

John Steele (deceased) · Post by **John Steele (deceased)** » 20 Dec 2010 7:24 am

The dominant chord you end up with after lowering one of the notes in the diminished voicing is a 7b9 chord.
There are also many other ways to play it.
Think of the second-last chord in "For The Good Times".
- John

Bill McCloskey · Post by **Bill McCloskey** » 20 Dec 2010 12:50 pm

John, can you give me an example of the 7b9 chord? Maybe I'm being dense, but I'm not sure that is even possible. If you have stacked minor 3rds, how can you have a flat 9 by lowering one note?

David Mason · Post by **David Mason** » 20 Dec 2010 1:19 pm

I have thought of the diminished movement/substitutions as one of the primary gateways to get around weirdly for about 15 years or so - it's a foolproof way to break out of modal monotony. In one of my deep listening & analysis periods, I was quite happy to discover that Jerry Garcia, John McLaughlin and even Miles seemed to agree with me, although with Miles it's pretty hard to identify where his rule-breaking mischief arises from.

The diminished half-whole step stuff becomes pretty boggling in a full C6th setup, especially if you try to stick to open voicings - lifetimes could be spent.... (and your audience probably thinks "The Flinstones" is all too jazzy already)

John Steele (deceased) · Post by **John Steele (deceased)** » 20 Dec 2010 5:15 pm

Hi Bill,
I didn't explain that very well.
Really, the stack of minor thirds on it's own is a 7b9 chord with no root... when you lower one of those, you end up with either the root of the chord, or something else interesting in there.

Try this simple V-I change on C6 -
Hit the root (on the 10th string) first, then strum the four note voicing, and listen to it resolve:
[tab]
....G7b9.......C6.

1------------------
2------------------
3---------------0--
4---------------0--
5-------5(5-----0--
6-------5(6-----0--
7-------5----------
8-------5----------
9------------------
10--5(5-------0----
[/tab]

You will notice that the four note voicing is a perfect stack of minor thirds... however, the root is not in that stack. That's what confuses people.
Really, when you're playing with a bass player, you don't need to play the root - in fact they'd probably prefer you didn't. But for the purposes of explanation I've included it.

In the first chord, the root on the 10 string is a G note, of course. The note produced by the 6th string is Ab - the b9. You will notice the tension in this chord caused by this minor second interval, and how it begs to be resolved. That's the beauty of it.
If you play just those two notes together, it'll sound real gnarly.
[tab]
6---5(6--
7--------
8--------
9--------
10--5(5--
[/tab]
Now, that's not saying that you have to put the root on the bottom and the b9 nearer the top. You can put it anywhere.
Here's an example of lowering one of the notes in that stack of minor thirds in order to get the root - this time, on top. Notice that the b9 note is present, but this time toward the bottom of the voicing... no root on the bottom:

[tab]
...G7b9....C

1-------------
2-------------
3----8L---7---
4----8----7---
5----8(5--7---
6----8(6--7---
7----8----7---
8-------------
9-----------7-
10------------
[/tab]

Beyond "For the Good Times", another tune that makes use of the 7b9 chord as the second last chord is "Whispering".

7b9 chords (and 7#9 chords) are very useful things to know about. They make great V chords in minor keys, where major 9ths (and 13ths) cause problems. The same may be said for III chords.

On the C6 pedal steel, it's a bit of a gift, because you can change any 5 pedal dominant chord (D9 at the open fret) into a 7b9 by simply adding pedal 6. And likewise, you can change any 6 pedal dominant chord (F9 at the open fret) into a 7b9 by simply adding the 5 pedal (although in the case of F, you lose your root on the lowest strings because it raises).

Now for the "something else interesting" comment I made earlier:
Another variation on the 7b9 chord can contain the 13th. Once again, the 13th can be achieved by lowering one of the notes in the stack of minor thirds. Here's an example, again in C:

[tab]
..G7b913...C6

1-------------
2-------------
3---5L----0---
4---5-----0---
5---5(5---0---
6---5(6---0---
7---5---------
8-------------
9-------------
10--5(5---0---
[/tab]

There's all kinds of tension there: The b9 strains against the root on the 10th string, and also the 13th on the top (lowered 3rd string) pushes against the 7th on string 7.

Each stack of minor thirds can be at least 8 different chords. For example, leaving out the root, the first chord in the tab, at the 5th fret with pedals 5 & 6 contains, from the top down the notes
B
Ab
F
D

These four notes can represent four different diminished chords (B,Ab,F and D) but it also represents four different 7b9 chords, without the root: G7b9, Bb7b9, Db7b9 and E7b9.

7b9 chords are a fascinating thing, and you can spend years turning them in the sunlight like a prism, and finding new and cool things about them.

I hope this is a more complete explanation, and I really, really hope you play C6.

- John

John Steele (deceased) · Post by **John Steele (deceased)** » 20 Dec 2010 7:08 pm

And...

You asked for examples, and I only provided one.

7b9 chords often follow half-diminished chords (often called m7b5 chords) in jazz standards. They go hand in glove. An example of it occuring in a melody might be found in the 8th measure of a tune Jim Cohen likes to play, "Desifinado".

I should have mentioned that, although the 7b9 chord is indeed a dominant chord, and functions as such, it does indeed come from the diminished scale.
In our example of G7b9, you start the scale on G and begin going up with a half-step (Ab - the b9), followed by a whole step (A# or Bb - the #9), etc. This is significant.
When you get into dominant chord harmony involving the diminished scale and/or altered scale, you start noticing tunes which employ them in the melody... often using both #9 and the b9.
Examples of this would be the 6th bar of "Blue Bossa". Also the second measure of the bridge of "Everything Happens to Me".

There are lots of ways to voice these chords without strictly using a stack of minor thirds. One of the most beautiful examples in the pedal steel vocabulary was brought to us by Buddy Emmons:

[tab]

..G7#9...G7b9..............C

1-------------------------------
2-------------------------------
3---8(7~~~8---------------------
4---8(7~~~8----8(7~~~8----7-----
5--------------8~~~~~8----7-----
6---8(6~~~8(6-------------7-----
7--------------8~~~~~8----7-----
8-------------------------------
9----------------------------7--
10------------------------------

[/tab]

In the second chord, the b9 is on the top. In the third chord, it has moved to the bottom.

As with all things, there are many other ways to voice the same idea.

- John

p.s. I think it should also be said that the standard C6th setup is more than capable of expressing all these more colourful jazz harmonies only because of a very, very few of the instrument's pioneers - who possessed the ear, interest, and genius to make it part of the capabilities of the tunings. Primary amongst them were Buddy Emmons and Curly Chalker, imho. - J

CrowBear Schmitt · Post by **CrowBear Schmitt** » 21 Dec 2010 2:43 am

Thanx John
i always dig yer contributions

David Mason · Post by **David Mason** » 21 Dec 2010 6:46 am

Several years back I made one of those apocryphal lists - "Songs I have to learn before I die." I went through "Over the Rainbow" and "My Favorite Things" and I saw like uh-oh, by the time I hit "Autumn Leaves" and "Caravan" I was like

"Vee Haff VEYS of MAKINK You Learn 7b9's undt -7b5's, you know...." Nyuck, nyuck.

I made up a handy chart for my music stand:

Edim7= Gdim7= Bbdim7= Dbdim7= Edim7 - resolves a fifth down to:
Ab ------ B ------ D -------- F ------- Ab

Plus the other two combinations, then I fit them onto a half page and taped them up on all my music stands. Cheating, sure, fine. It works backwards too - up a fourth then slide, warp & shimmy - I may be crazier now than before I started.

(but it's the GOOD crazee....)

Rick Schmidt · Post by **Rick Schmidt** » 21 Dec 2010 7:11 am

John Steele.... Brother....Your posts on this thread are downright elegant!

Thanks as always.

Merry Christmas!

Rick

Scott Shewbridge · Post by **Scott Shewbridge** » 21 Dec 2010 8:48 pm

These posts are fantastic and very stimulating. Last night when playing with some of Mr. Steele's ideas, I came across something, but am not sure I'm right about the theory part of it.

I think the m7b5 can act like a Maj7, followed by a 7b9 up a half step acting as the dominant, resolved with another Maj7. For example, my ear likes F#m7b5, G7b9 and C Maj7 (or C6). This makes for some very tasty tight voicings.

Because of this, now I think I can play the m7b5 arpeggio over both I & IV Maj 7 chords and the diminished arpeggio over the V7. To my ear, it seems to perfectly skirt the border between inside and outside playing.

Again really, really great posts all. I'm still learning and might not have it right, but I am very excited about what you are sharing. Sincere thanks.

David Mason · Post by **David Mason** » 22 Dec 2010 6:21 am

If you're familiar with playing scales and notes against a set tone to improve your intonation - Bob Hoffnar had a CD for sale with some sample tone and chords - then you can see the value of exploring superimposed triads and "clashing" chords. I usually use a little Boss RC20XL looper to try this stuff. I think in the old days musicians actually used to play with each other, exploring this stuff - a lot of the Parker/Powell/Gillespie jamming, some of Miles's practice sessions, some of what the Dead did was just play.

From what I can tell just by trying to play music as it's written, the diminished movements (I would include tritone substitution) are right at the heart of jazz chord writing, from the 40's till the 60's at least. Along with 1-4-5 stuff and the diatonic chords. The beboppers superimposed triads to build new melodies with drastically-extended chords, but that's the stuff you don't want to teach the bass player...

(I say that as someone who played more bass than anything, but I knew my place - I thought Stanley Clarke & Jaco Pastorius were actually pretty horrible, or at least they wreaked a lot of havoc, overall).

Certainly Duke Ellington used this stuff a lot and then Bud Powell, it had been piano players leading the charge and it almost takes a "two hand" approach to understand it. Like, chromatic bass lines are a good outcome, but I don't thing you can understand them with only a bass.... There is a big difference between jamming as the only chordal instrument and writing for a big band. I spent some effort going through a bunch of guitar videos - Danny Gatton, Scotty Anderson, Joe Pass, Martin Taylor - and they all did completely different chord substitutions from each other, it was whatever worked.

Pedal steel has the fault that just about everything can be made to sound reasonable playing alone in your bedroom, but a looper loaded with pristine keyboard or guitar chords can teach some harsh lessons. So, nothing is "right" or "wrong", but you do need to figure out context. I wasn't at all surprised to find out that Doug Livingston & Bill Stafford are great piano players too.

John Steele (deceased) · Post by **John Steele (deceased)** » 31 Dec 2010 1:44 pm

Thanks, CB, Rick, all...

my ear likes F#m7b5, G7b9 and C Maj7

I think your F#m7b5 might actually be D9 without the root. That way, it would be a perfect II-V-I change.
- John

Brian McGaughey · Post by **Brian McGaughey** » 1 Jan 2011 9:12 am

Every now and then a gold nugget thread like this pops up. Interesting info to me. I love learning theory and especially chord theory. Thanks all.

Bill, it's funny you mention trumpet. I played trumpet all through school and I use my right hand running through the chromatic fingerings to count intervals in chord construction. I can imagine if a person didn't have that or was not able to visualize the piano keyboard that this stuff can be confusing. I use my right hand to count interval distance all the time. I use the trumpet fingerings even though I haven't picked up a horn for years!

Bill McCloskey · Post by **Bill McCloskey** » 1 Jan 2011 3:10 pm

Thanks Brian - you are right about the muscle memory to counting off intervals. I've told this story somewhere else but when I'm trying to quickly decide which way is right or left, I imagine i have a pencil in my hand and what ever hand has the pencil, that is right.

How ever synapses in the brain are constructed: that method is faster for me than thinking which way is right.

Some with your trumpet fingering. I was thinking tonight how each note on the trumpet is distinct, unlike a stringed instrument: an F# feels a certain way because the fingering the pressure of the lips and breath. And so chords each have their own feel, sound and mood. A c chord is completely different than a D chord in every imaginable way. That is something that people who play stringed instruments miss out on.