the two dimensions of harmony (man)

[Groyniad]

there are two dimensions of the harmonic world we all love so much (it seems to me)

1. the change itself

2. the sound that changes (into another sound)

-----

i put all my energy into 1 for the longest time. i took my dm7 and i took my g7 and i focused all my attention on what happened to the dm7 when it changed into the g7.

root - stays where it is to become the fifth of g7
3rd - stays where it is to become the 7th of g7 - or moves up a tone to become the tonic
5th - moves down a tone to become the tonic of g7 - or - up a tone to become the 3rd of g7
7th - moves down a semi-tone to become the 3rd of g7 or a tone to become the fifth

these 'movements' (why quotes?) are the most important harmonic events that happen when 2 moves to 5

if you check and see what happens when 5 moves to 1 you will see that it is all EXACTLY THE SAME (wow wow wow wow wow)

every change 'across a fifth' consists in these primary harmonic 'changes' (the quotes are because when the tonic becomes the fifth the absolute pitch is unchanged and only the harmonic function of the note changes etc. etc.)

-----

this stuff is great - and i hear its absence in a lot of even very high level playing

but recently i've been putting all my energy into the other harmonic dimension

-----

we need to unpack the harmony WITHIN a given sound and not just the harmony generated by a change from one sound to another:

we do this by building triads on 1,3,5 and 7 of a given sound.

it turns out that for mainstream be-bop at least there are two sounds above all that you need to get to know this well.

m7 and m6 (or melodic minor)

each one of the four triads that you build from the chord tones of e.g. a m7 sound is a harmonic dimension of the SAME sound. its hard to use them all - but they do give open up the possibility of creating harmonic structure WITHIN a given sound not just BETWEEN two sounds.

i have found this to be absolutely critical in learning how to improvise effectively. i think mainstream bebop requires knowledge of both kinds of harmonic structure.

it is amazing to open up real harmonic differences WITHIN a given sound - it makes constructing rhythmically effective ideas much much easier.

[BigDaddyLoveHandles]

Can you be more concrete and give an example?

[Groyniad]

examples?

well you can think of the transition between one chord and another - and use that as a structuring principle for your lines

and/or you can break the sound of a single chord up into four dimensions revolving around four triads - built on the 1,3,5 and 7 of the chord

1,3,5
3,5,7
5,7,9
7,9,11

the general point is that there are TWO ways to find harmonic 'material' for soloing not just one.

nowadays i think people put too much energy into extending a given sound and not enough into the changes between sounds - and that leaves their lines sounding too unstructured and 'open' (to my ear)

but i've only recently discovered how to extend a given sound by finding the triads built into it and using those triads to build phrases. any phrase you can play revolving round 1,3,5 you can also play revolving around 3,5,7 etc. (of the SAME chord)

so just as you can play a phrase over the 2 chord and then repeat that phrase over the 1 chord

you can play a phrase using the triad built on the 3rd note of the 2 chord and then repeat that phrase using the triad built on the 5th note of the 2 chord. so you get harmonic 'movement' but WITHIN a sound not between two sounds

with BOTH these harmonic dimensions to exploit you have a lot of stuff to use to construct interesting lines

[Nate Miller]

yea, the sort of voice leading you are talking about is what chord tone soloing is all about.

that's basically how I play, with some other stuff thrown in. I think in triads mostly, too.

you might enjoy exploring this idea...when you have a note outside the key, what keys does that new note imply?

what triads could you borrow from those implied keys?

if you built a triad on a note outside the key, would that triad be major or minor? what key(s) are implied by either choice?

that's some questions to get you exploring in the right direction.

I got that triads out of the key stuff from Stan Willis and Jack Petersen, so its for real

[christianm77]

there are two dimensions of the harmonic world we all love so much (it seems to me)

1. the change itself

2. the sound that changes (into another sound)

-----

i put all my energy into 1 for the longest time. i took my dm7 and i took my g7 and i focused all my attention on what happened to the dm7 when it changed into the g7.

root - stays where it is to become the fifth of g7
3rd - stays where it is to become the 7th of g7 - or moves up a tone to become the tonic
5th - moves down a tone to become the tonic of g7 - or - up a tone to become the 3rd of g7
7th - moves down a semi-tone to become the 3rd of g7 or a tone to become the fifth

these 'movements' (why quotes?) are the most important harmonic events that happen when 2 moves to 5

if you check and see what happens when 5 moves to 1 you will see that it is all EXACTLY THE SAME (wow wow wow wow wow)

every change 'across a fifth' consists in these primary harmonic 'changes' (the quotes are because when the tonic becomes the fifth the absolute pitch is unchanged and only the harmonic function of the note changes etc. etc.)

-----

this stuff is great - and i hear its absence in a lot of even very high level playing

but recently i've been putting all my energy into the other harmonic dimension

-----

we need to unpack the harmony WITHIN a given sound and not just the harmony generated by a change from one sound to another:

we do this by building triads on 1,3,5 and 7 of a given sound.

it turns out that for mainstream be-bop at least there are two sounds above all that you need to get to know this well.

m7 and m6 (or melodic minor)

each one of the four triads that you build from the chord tones of e.g. a m7 sound is a harmonic dimension of the SAME sound. its hard to use them all - but they do give open up the possibility of creating harmonic structure WITHIN a given sound not just BETWEEN two sounds.

i have found this to be absolutely critical in learning how to improvise effectively. i think mainstream bebop requires knowledge of both kinds of harmonic structure.

it is amazing to open up real harmonic differences WITHIN a given sound - it makes constructing rhythmically effective ideas much much easier.

I think it's entirely possible to play bebop entirely using variations of the major/dominant sound (including the backdoor dominant #1) - this is what I've been working on for the past few months, and its amazing how far just that gets you.

The melodic minor/m6 is more like special use...

Anyway, with bop/straightahead I've got it down to three main harmonic movements:

V7-I (where I is major, minor or dominant) - applies to vanilla dominants, ii V I's,
bVII7-I - applies to minor V-I's, ii-V-I's, iv-I, bVII-I (of course), iv-bVII7-I etc
IV7-I - the blues cadence - applies to IV7-I, IV-#ivo7-I, io7-I, VII7alt-I etc

So really that three resolutions - up a fourth, up a step and down a fourth.

In the second and third case you can use a #1 dominant for smoother movement back into the I. It's not everything, but it covers 80% of the progressions you play through. Anything you are likely to apply to dominants - bebop scales, family of four, mixolydians, lydian dominants, tritone substitutes, diminished scales, any and all of the Barry Harris language patterns - if practiced on these three progressions should prepare for playing through a most standards progressions. I believe most good bebop players have clocked this to some extent.

(And for this reason, we can easily identify progression that bop players don't like: II7-vi-I (or II7-bVII7-I - that jump of a major third...) This progression very common in pre-war repertoire and standards, not common in post war bop so much (AFAIK) and good bop players often don't like it. I find it a struggle myself, I'm meant to be practicing it this week...)

Anyway - happy to give analytical examples if you like.

[Boston Joe]

examples?

well you can think of the transition between one chord and another - and use that as a structuring principle for your lines

and/or you can break the sound of a single chord up into four dimensions revolving around four triads - built on the 1,3,5 and 7 of the chord

1,3,5
3,5,7
5,7,9
7,9,11

the general point is that there are TWO ways to find harmonic 'material' for soloing not just one.

nowadays i think people put too much energy into extending a given sound and not enough into the changes between sounds - and that leaves their lines sounding too unstructured and 'open' (to my ear)

but i've only recently discovered how to extend a given sound by finding the triads built into it and using those triads to build phrases. any phrase you can play revolving round 1,3,5 you can also play revolving around 3,5,7 etc. (of the SAME chord)

so just as you can play a phrase over the 2 chord and then repeat that phrase over the 1 chord

you can play a phrase using the triad built on the 3rd note of the 2 chord and then repeat that phrase using the triad built on the 5th note of the 2 chord. so you get harmonic 'movement' but WITHIN a sound not between two sounds

with BOTH these harmonic dimensions to exploit you have a lot of stuff to use to construct interesting lines

Hey Groyniad:

This is interesting, and I really want to understand it.

I get what you're saying about building triads on the various chord degrees, but I guess I don't really see how this idea is any different from taking various triads from the scale. So, for example, according to your formula, if you've got a CM7 chord, you've got the following triads built on the chord tones: CMaj, Emin, GMaj, Bdim.

So far, so good?

So the question is, why is this any different from taking triads out of a harmonized major scale? Why wouldn't you also include, say Amin, or DMaj (to get the #11)? What advantage do you get from your conception?

[Groyniad]

Hey Boston Joe

great question

the point is that you want a way to develop one and the same sound - say the 1 sound - so you're working NOT with the diatonic chords made from the notes of e.g. the c major scale - but with the extension of the 1 sound itself. you want to extend it without moving away from it.

as soon as you play a dm7 in C you've moved away from the 1 sound; when you play an em7 in C you move back to it; when you play an f maj 7 you've moved back to the 2 type sound etc. etc.

but we're not trying to reduce the diatonic sequence to something more basic - we're just trying to get everything we can out of 1 and 2 (or 1 and 5 if you like)

it turns out that the phrases you build using these triads can be applied in all sorts of different diatonic situations.

my idea is just that its useful to appreciate that you can think of harmonic structure as something generated across a change between two sounds - or something that already exists within a particular sound. and both are useful for improvisers

[Boston Joe]

Hey Boston Joe

great question

the point is that you want a way to develop one and the same sound - say the 1 sound - so you're working NOT with the diatonic chords made from the notes of e.g. the c major scale - but with the extension of the 1 sound itself. you want to extend it without moving away from it.

as soon as you play a dm7 in C you've moved away from the 1 sound; when you play an em7 in C you move back to it; when you play an f maj 7 you've moved back to the 2 type sound etc. etc.

but we're not trying to reduce the diatonic sequence to something more basic - we're just trying to get everything we can out of 1 and 2 (or 1 and 5 if you like)

it turns out that the phrases you build using these triads can be applied in all sorts of different diatonic situations.

my idea is just that its useful to appreciate that you can think of harmonic structure as something generated across a change between two sounds - or something that already exists within a particular sound. and both are useful for improvisers

OK, but:

1) What about Am? That's a very common I substitute and doesn't figure in your approach, and

2) The Gmajor and Bdim triads are definitely not "1 sounds".

[Boston Joe]

Or are you suggesting something like Em > Bdim > GM > Cm as a sort of I-V-I kind of movement?

[BigDaddyLoveHandles]

Or are you suggesting something like Em > Bdim > GM > Cm as a sort of I-V-I kind of movement?

??? Typo?

[Groyniad]

this is a different - though i'm sure related topic

you can classify all the 7 diatonic chords into 1 sounds and 5 sounds - and this is a great thing to do if you want to simplify your thinking (which is important - and very sophisticated - not simple).

1 = 1,3,6

5 = 2,4,5,7

the reason for this does have to do with what happens when you extend the sounds in the way i'm talking about

but still my main point is that there are 2 kinds of harmonic structure to exploit when you're improvising: within a sound (using triads built on the strong notes of the home sound - 1,3,5,7); and between sounds

these two ways ARE connected - but the point is to keep them separate because it helps you make up groovy ideas to do so.

[Boston Joe]

I was playing around with this last night. I can see how the G and B triads really pull back towards the Cmajor chord tones.

[BigDaddyLoveHandles]

I was playing around with this last night. I can see how the G and B triads really pull back towards the Cmajor chord tones.

B and F and the biggies: B->C and F->E. Note these are the two half steps in the C major scale.

x2x031 -> x3x000

[christianm77]

I divide diatonic chords into the chords with the 4 in and the ones without. That conforms to the tonic/dominant duality although I regard it as more a tonic/subdominant as the role of the seventh doesn't seem terribly important.

So - in C, chords with an F in and those without

tonic = Cmaj7 Em7 Am7 actually in my understanding, I always think of Em as a first inversion C major type chord

Subdominant = G7, Bm7b5, Dm7, Fmaj7
Oh look it's the family of four.

[Groyniad]

interesting to focus on the 4th like that

you get the right result that's for sure

these are the two sounds i'm working on all the time - have been for a long time now

1 and 4 basically - or 1 and 2

and then the mm - or the - mmmmmmm

[joe2758]

g7 and Bm7b5 subdominant in the key of c? pulling toward A minor I guess

[Nate Miller]

g7 and Bm7b5 subdominant in the key of c? pulling toward A minor I guess

that's exactly what's happening. Am still has the notes C and E in it, so the note motion F->E and B->C still holds

[pingu]

yes in C major tunes
having control of the F > E resolution thing is totally crucial ....

chords/ideas with the F are away to me
chords/ideas with the E are home

but then again IV is different to V
happy birthday etc

dunno

[christianm77]

yes in C major tunes
having control of the F > E resolution thing is totally crucial ....

chords/ideas with the F are away to me
chords/ideas with the E are home

but then again IV is different to V
happy birthday etc

dunno

IV is indeed different to V if you are accompanying a soloist or writing a tune, but in jazz improvisation it does appear that IV's can be superimposed on V's without anyone having a problem.

This might be a side issue: but, what I have learned from transcribing is that during the swing and bop eras, jazz musicians regarded cadences as completely interchangeable. V I, ii V I, IV7 I, IVm I, even IV #ivo7 I could all be swapped out and superimposed on each other. The important thing is that a cadence is expressed.

It doesn't even have to be set up or resolved at the same time as the rhythm section (see Parker.)

Lester Young and Charlie Christian often ignored cadences and played in the home area. There's a good example of CC playing on the I chord using blues phrases while the rhythm section plays ii V for four bars IIRC. There's so much freedom in how you set up and resolve your phrases.

I can't say this enough because it is very counterintuitive to the modern mindset, but it does appear that traditionally melodic improvisation and harmony were two separate areas of study. The structure of Barry Harris's teaching reflects this.

One example he gives is the b7 sub on the tritone - so we sub G7 C with Db7 G and then use the b7 chord of the Db7 scale which is Bmaj7. Barry states that the reason this sounds so pretty is because of the F# over the G7. I agree. I love putting major 7ths on dominant chords.

The role of the leading note was always pretty relaxed in jazz, from the 1920's on. But you wouldn't get free use of major sevenths in chords in the piano or guitar. I suppose on the piano that's two different worlds - the left hand and the right hand. It seems strange, but there's a lot of evidence to support this.

[Reg]

Christian was on to better understanding of connection of sounds.... So generally eventually chords fall into Tonic, subdominant and dominant areas of function. Or what movement tendencies the chord has. Obviously without a reference... the movement has no tendencies.

Some organizations can use more modal concepts... like whether a 4th is in a chord with some type of reference etc...Subdominant with reference to a tonic or a different tonal target.

But generally each of those functional areas... have extended or expanded relationships. That Cmaj7 as a tonic has up and down a diatonic 3rd for functional relationships.... the related minor A-7 and related minor E-7 both have similar functional tendencies... bring in modal interchange and other types of organization.... and now you have extended relationships... Change to notes on top.

You can basically just use the root motion for organizing functional tendencies, because the reference has so much weight.
This allows different organization of relationships to also be going on with the original basic reference... the diatonic up and down a third.

Long story short.... when you become aware of the weight of different functional types of creating harmonic movement, your able to have more options of combining more layers of harmonic movement. There's no real difference whether your doing this melodically or with chords....

You can have more than one level of functional movement going on the same time.... generally when performing in jazz style... that's a basic requirement.

[pingu]

One example he gives is the b7 sub on the tritone - so we sub G7 C with Db7 G and then use the b7 chord of the Db7 scale which is Gbmaj7. Barry states that the reason this sounds so pretty is because of the F# over the G7. I agree. I love putting major 7ths on dominant chords.

thats very interesting chaps
did you mean to say 'Db7 to C' ?

also Db7 comes from the Gb scale and the
b7 chord of that would be E7 ?
also have I got this right ish ?

bit confused but intreaged , I got what you were saying about all those 'something' to I
being interchangeable/superimposable
yeah thats so true

[christianm77]

thats very interesting chaps
did you mean to say 'Db7 to C' ?

also Db7 comes from the Gb scale and the
b7 chord of that would be E7 ?
also have I got this right ish ?

bit confused but intreaged , I got what you were saying about all those 'something' to I
being interchangeable/superimposable
yeah thats so true

It's a typo - I'm talking about Bmaj7 comes from the Db dominant/mixolydian scale. Sorry!

[pingu]

It's a typo - I'm talking about Bmaj7 comes from the Db dominant/mixolydian scale. Sorry!

still confused a bit, sorry
do you mean you play Bmaj7 as a sub for G7 ?

[christianm77]

still confused a bit, sorry
do you mean you play Bmaj7 as a sub for G7 ?

Yes.

G7 'family of four' - G7 Bm7b5 Dm7 Fmaj7

Tritone sub

Db7 'family of four' - Db7 Fm7b5 Abm7 Bmaj7

[Reg]

Standard subs, BH used family relationship names for chord relationship groups

G7 diatonic sub is B-7b5, same notes as G9 with out root or G.

D-7 again standard diatonic sub is Fmaj7, again D-9 without root

Then same process but new reference using the tritone sub of Db7.

So....
D-7 to G7 to Target of Cmaj7. becomes using Diatonic subs,

Fma7 to B-7b5 to Cmaj7... and then the tritone sub version.

Ab-7 to Db7 to Target Cmaj7... in actual use, that would be pretty vanilla, so modal interchange usually comes into play etc... and then the Diatonic subs of the tritone subs,

Bmaj7 to F-7b5 to Cmaj7, again that's pretty straight, so modal changes would generally be used based on actual tune.

The next step is again same process but down a diatonic 3rd... (instead of up a Diatonic 3rd)

So...
D-7 to G7 to Cmaj7, becomes using Diatonic subs down a 3rd,

B-7b5 E-7 to Cmaj7, again MI is usually used. And the tritone sub version down a diatonic 3rd,

F-7b5 to B-7 to Cmaj7