Stan Willis on Combining Keys: 2 + 2 equals 4

[Nate Miller]

I am curious how many of you have encountered this idea before and where you came across it.

I learned this from Stan Willis, who was a piano player who played with Art Farmer in San Francisco in the 1950s. Stan never got famous, and he's not anywhere to be found on the interwebs, but that doesn't diminish any of the lessons I learned from him.

So what's all this got to do with "2+2=4?"

Stan used to always say, "2+2=4"

what he means is that when you play in 2 keys at the same time, the result is more than either of the parts individually.

We all know that the upper structures of the 9th 11th and 13th come from triads over triads. A Dmaj triad over a Cmaj7 chord will give you the upper structure of the Cmaj13

but that's child's play

Piano players do have an advantage in playing in 2 keys at once since they have two hands

On guitar some of the things I do to try and manifest this idea is to play a run of diatonic triads but in the middle of the run I slip into the other key so maybe something like this (all triads from C major and Db major):

G Gb fmin Ebmin Dmin C -. where the run starts and ends in triads from the key of C but the middle of the run uses triads from Db. Naturally, you can combine any 2 keys, and you can arpeggiate this sort of thing in single lines, too.

Another idea is to play triads of one key with a bassline from the other key

also, you could use something like a stagger concept and start with a 4 note harmonic structure. The bottom 2 notes come from one key and the top 2 notes from the other, then move that interval structure up and down the scale keeping the proper key signatures in the top and bottom (if that made any sense)

and even in a single line...consider the fragment C - Db - Ab- G- E. Parker does stuff like this a lot. the notes in this bop lick come from a C triad combined with a Db triad


so anyway, my question is: have any of you run across ideas like this before, and where did you encounter them?

[docbop]

I agree except for calling it two keys, it probably is, but to me I think more in terms of Polychords. Then the piano player I've been studying the Barry Harris-like stuff with his terminology is "borrow from". So one hand is playing the diatonic chords and the other is "borrowing notes" from another related scale.

So guess this is another example of two people going to same gig, just taking different streets.

[Nate Miller]

Barry Harris does do this sort of thing. That idea of "borrowing from" is probably easier to think in than the way Stan laid it out for me. I'll see if I can't dig up some of his material and give it a look over

Regarding polychords, I think that way of thinking of this sort of thing is valid. I know piano players think that way a lot. If there is any difference, it is subtle and academic. I think the main difference would be that the triads set against each other would be from 2 specific keys and the resulting upper structure of the series of chords would be whatever it came out to be.

I used the term "series" rather than "progression" because a lot of times that you actually get to use this sort of thing in solo guitar is when the harmony is relatively static for a few beats, so your chords may not be actually working towards any particular goal and may just be filling space.

[docbop]

Barry Harris does do this sort of thing. That idea of "borrowing from" is probably easier to think in than the way Stan laid it out for me. I'll see if I can't dig up some of his material and give it a look over

Regarding polychords, I think that way of thinking of this sort of thing is valid. I know piano players think that way a lot. If there is any difference, it is subtle and academic. I think the main difference would be that the triads set against each other would be from 2 specific keys and the resulting upper structure of the series of chords would be whatever it came out to be.

I used the term "series" rather than "progression" because a lot of times that you actually get to use this sort of thing in solo guitar is when the harmony is relatively static for a few beats, so your chords may not be actually working towards any particular goal and may just be filling space.

I've been working on the series too. I'm no solo guitar player, but have be working on simple creating chord melodies for tunes I study and using the series in same way. Series is finding it way into my single line playing and I like how it adds more the lines.

[Nate Miller]

another aspect of this key on key stuff is to remember that in any diatonic key, there are 7 notes that are in the key and 5 notes that are out of the key.

So in the key of C major the notes that are out are Db.Eb,Gb,Ab, and Bb

for you folks playing along at home, keep track of which of those 5 notes that are out you have played so far in your solo.

Each time you play another one of the 5 notes out, you narrow down the number of keys that you could be inferring

So in C, say we have played Bb and Gb already and we are about to use a Db. So when you harmonize that Db, is it a Db major or a Db minor triad?

Well, if you want to imply Gb, you should go with a major triad.

If however, you wish to imply the key of B over the key of C, then a minor triad is the choice to make. you'll end up introducing an Ab, too in this example and at that point the only note left you haven't played is Eb

as you can imagine, I play like I get paid by the note

so I post this as an example of the thinking process. If you were juxtaposing two keys that were only a couple of accidentals away from each other (like C maj and D maj) then you would want to stay well clear of the 3 notes that are not common to either key (Eb,Ab, and Bb)

anyway...some more thoughts on playing key on key

[christianm77]

It's really funny, but I've been thinking and practicing this stuff a lot lately.

It's interesting that it's coming up so much on the forum...

This sort of thing has been going on before bop to as far as I can tell...

The obvious example, mentioned elsewhere is the melody of Honeysuckle, but another example...

Stompin' at the Savoy - over Db, the melody notes are Ab Bb C F - which is 5 6 7 and 2, or looking at it a different way, a pentatonic cell built on the 5th - 1 2 3 5 on the V, but working over the I chord. I noticed the same use of pentatonics a while ago in Wayne Shorter's solo on Yes or No over the Dmaj7 chord, but never thought to look for the same thing in a swing era tune, because obviously using pentatonic modes is a modern thing, right? :-)

The same usage crops up in Django's soloing. (As do many harmonic devices that are meant to be 'post-bop.')

I doubt it was terribly worked out theoretically, and suspect it based on the ears, which is the beauty of these pentatonic and triad based approaches regardless of the era of the music.

I'm wondering if it isn't the same layered concept of jazz polyrhythm only applied to harmony?

[bako]

I did.

I would say I first consciously encountered bi-tonal sounds as a listener in the music of Stravinsky.
Later I read about it in books and articles chronicling the evolving details of the tools and methods employed
by 20th century composers.

On my own, I've engaged in experiments exploring what additional sound language can be found by
the interaction of 2 or more keys/modes.

One game focused on progressions. Essentially I lined up all 28 modes in a parallel fashion and conceived
of the whole collection as a single massive harmonic grid from which to draw possible chord choices from.
Although there are many interesting sounds to be discovered, I felt that I needed to tighten up my skills navigating sequential and simultaneous chord pairs in order to be able to use this material in real time.

2 + 2 chord tones from each chord was another idea that I played around with.
Since I was mixing from 2 keys, that meant then there are also multiple ways to organize
bi-tonal chord scales. These could also be voice led through progression cycles.

I like also intermingling triad pairs, either incomplete 4 notes dyad arpeggios or in a 6 note scenario
(one note per string arpeggiated, the results were not conducive for solid chords)

Anyway, my pursuit of this material can best be described as an intermittent work in progress.

consider the fragment C - Db - Ab- G- E. Parker does stuff like this a lot. the notes in this bop lick come from a C triad combined with a Db triad

These notes can also seen as F harmonic minor. While these observations are interesting and perhaps useful,
it's not the same as knowing how Parker conceived of what he was doing.

[christianm77]

I did.

I would say I first consciously encountered bi-tonal sounds as a listener in the music of Stravinsky.
Later I read about it in books and articles chronicling the evolving details of the tools and methods employed
by 20th century composers.

Obviously music doesn't exist in a vacuum, but I wouldn't be surprised if these polychord practices evolved seperately in jazz... Monk used to say the same about the whole tone scale IRC...

[Nate Miller]

you know, I'm not convinced there was parallel development. I say that because Stan talked a lot about Debussy. As a piano player, he was aware of his music. He took a lot of ideas from Debussy. I remember he talked about him a lot when he taught me how he saw upper structures


a couple years later when the movie "Round Midnight" came out, Dex had a scene where he said essentially the same thing.

I think the old guys saw what they were doing as pushing the envelope of 7th chord harmony. Classical music by the early 20th century was all crazy, it was the late romantic and impressionist composers that were the state of 7th chord harmonic development, and it was that they were building on

anyway, that's my take on it.

[christianm77]

you know, I'm not convinced there was parallel development. I say that because Stan talked a lot about Debussy. As a piano player, he was aware of his music. He took a lot of ideas from Debussy. I remember he talked about him a lot when he taught me how he saw upper structures


a couple years later when the movie "Round Midnight" came out, Dex had a scene where he said essentially the same thing.

I think the old guys saw what they were doing as pushing the envelope of 7th chord harmony. Classical music by the early 20th century was all crazy, it was the late romantic and impressionist composers that were the state of 7th chord harmonic development, and it was that they were building on

anyway, that's my take on it.

Many jazzers were definitely interested in Debussy (the earliest maybe the guy who composed Limehouse Blues, also Bix was a fan) but I'm not so sure among all jazz players of all socio economic backgrounds - while I know Bird was interested in Stravinsky, Schoenberg and Varese later on, I always get the impression that his early up bringing was Kansas City Swing, with a smattering of Tatum, and that was his primary language... The classical influences came later.

That might be rubbish of course.

I'm always interested in knowing the connection between seventh chord harmony in Impressionism and jazz though - have you checked this out?

[Nate Miller]

I'm always interested in knowing the connection between seventh chord harmony in Impressionism and jazz though - have you checked this out?

absolutely. I took a major in theory when I was in music school. Debussy uses a lot of big extended 7th chord harmonies. Aside from Debussy, there's other composers in the classical guitar repertoire from that era, too.

Villa-Lobos's work has a lot of 7th chord harmony, so does Albiniz , Tarrega, ..a lot of the late 19th early 20th century guitar repertoire

the guitar repertoire is particularly interesting for us because of the choices we have to make in how we voice big extended harmonies. It's especially in Villa-Lobos's work I run into all these "old friend" chords I've been playing in rhythm sections since I was a kid

now mind you, a transcription of a Joe Pass chord solo will blow the pants off of most of the long haired stuff, but in the interest of examining the connections from late 19th century harmony to the music we play, its interesting to look through that era of the classical guitar repertoire

[Jonah]

If we speak about harmony I try to see music as whole piece in respect of harmony... I mean if there's 11th chord and in the context it works as 11th chord - I do not see it as a set of triads... (though this could bw a way to organize performance simpler - but it's not harmonic analysis)..

I think in jazz it is often mixed up: real harmonic analyzys with performer's approach to harmony from pov of organization of performnance... we can think of playing bass line from one key and triads from another but as a result there will be kind of 'listner's perception' - who only hears resultutive music.. in that concern I believe any musician is first of all a listner...

same thing with polytonality...
to me it's really seldom when there are really two keys sounding at the same time... because in this case composer/or inprovizer should use additional means to prevent two harmonic flows merge into one harmony...
Like Stravinsky used different rythmic structures for example - so that you immidiately noticed two harmonic layers in different keys... or it could be separated by arrangement... or stylistic separation... like Mahler did sometimes... or late in 20th century Schnittke...
To me one of the most interesting and natural use of polytonality was in Charles Ives' music but again it was mostly stressing stylistic contrasts...

[cosmic gumbo]

We all know that the upper structures of the 9th 11th and 13th come from triads over triads. A Dmaj triad over a Cmaj7 chord will give you the upper structure of the Cmaj13

but that's child's play

Actually, isn't it a Dmin triad over a Cma7 chord that gives you Cmaj13? That's a triad over a 4 note 7th chord, so I'm not grasping the triad over triad thing. I'm totally at a loss at what 2+2=4 represents.

[christianm77]

Actually, isn't it a Dmin triad over a Cma7 chord that gives you Cmaj13? That's a triad over a 4 note 7th chord, so I'm not grasping the triad over triad thing. I'm totally at a loss at what 2+2=4 represents.

No, you would use D major, because the F# is more compatible with the sound of the C major triad than an F. You are basically evoking C lydian.

[JonR]

Actually, isn't it a Dmin triad over a Cma7 chord that gives you Cmaj13?

I'd see "Cmaj13" as indicating C E G B (D) A. No F in the chord, and an optional 9th. 11th (F) omitted because of confusing dissonances with the E below, and also with the B.

A D major triad over Cmaj7 ought to be called Cmaj13#11. A D triad over a C triad would also be lydian, but would lack the 7th implied by "maj". C69#11 maybe?

I'm totally at a loss at what 2+2=4 represents.

I've not heard the concept either, and was a little surprised it referred to a polychord or polytonal concept.
To me it suggests something rhythmic or formal: call and response, the way song forms tend to be duple (2-bar phrases, 4-bar lines, 8-bar sections); that kind of thing.
As outlined above, why not calll it 1+1 = 2? Makes more sense in context.

[Jonah]

o, you would use D major, because the F# is more compatible with the sound of the C major triad than an F. You are basically evoking C lydian.

To my understanding Cmaj13 contains all natural sounds - here =Ionian... arpegiated I in see major shows it

though 11th in this case would be most probably omited...

And Lydian would be Cmaj13#11... like arpegiated IV in G major

or I miss something?

[Nate Miller]

those of you who are saying that you see things as 11 or 13 chords and you view this as simpler, are of course correct.


you are missing something, though. You see, the way you look at it is the way jazz is taught, which is why you are correct, but that's not the way the old guys went about it. I know, I got it from the horse's mouth as it were. I'm old enough to have had the opportunity to play with guys from the bop era.

and right or wrong, I play jazz my way, which is the way I learned from my mentors, that 2 + 2 = 4. I would expect you to play jazz your way in the way you learned as well.

But this gets right to the heart of the matter. Remember me talking about being stuck in the 50s? That my style is an anachronism?

I believe that the way jazz was taught in universities since the 1970s has watered down the harmonic vocabulary. The style I play truly IS a dead language because its no longer being taught. It is frozen in time. Most of the people who practiced it are gone.

It is good to hear that there are other guys out there still grappling with these ideas. That's bop. That's what made it. It was the searching every night for something beautiful from out of nowhere

[christianm77]

those of you who are saying that you see things as 11 or 13 chords and you view this as simpler, are of course correct.


you are missing something, though. You see, the way you look at it is the way jazz is taught, which is why you are correct, but that's not the way the old guys went about it. I know, I got it from the horse's mouth as it were. I'm old enough to have had the opportunity to play with guys from the bop era.

and right or wrong, I play jazz my way, which is the way I learned from my mentors, that 2 + 2 = 4. I would expect you to play jazz your way in the way you learned as well.

But this gets right to the heart of the matter. Remember me talking about being stuck in the 50s? That my style is an anachronism?

I believe that the way jazz was taught in universities since the 1970s has watered down the harmonic vocabulary. The style I play truly IS a dead language because its no longer being taught. It is frozen in time. Most of the people who practiced it are gone.

It is good to hear that there are other guys out there still grappling with these ideas. That's bop. That's what made it. It was the searching every night for something beautiful from out of nowhere

Just trying to play clean and find the pretty notes....

[Jonah]

those of you who are saying that you see things as 11 or 13 chords and you view this as simpler, are of course correct.


you are missing something, though. You see, the way you look at it is the way jazz is taught, which is why you are correct, but that's not the way the old guys went about it. I know, I got it from the horse's mouth as it were. I'm old enough to have had the opportunity to play with guys from the bop era.

and right or wrong, I play jazz my way, which is the way I learned from my mentors, that 2 + 2 = 4. I would expect you to play jazz your way in the way you learned as well.

But this gets right to the heart of the matter. Remember me talking about being stuck in the 50s? That my style is an anachronism?

I believe that the way jazz was taught in universities since the 1970s has watered down the harmonic vocabulary. The style I play truly IS a dead language because its no longer being taught. It is frozen in time. Most of the people who practiced it are gone.

It is good to hear that there are other guys out there still grappling with these ideas. That's bop. That's what made it. It was the searching every night for something beautiful from out of nowhere

I understand what you mean...

But as I said I think we are listners first of all... music is what we hear...

And how we organize our perfomance process as musicians is a different question...
I can think of playing triad over triad or so because it's convinient for my purposes of performance... but resultative sound in most cases is still C11 - that's what I am trying to say...

[Nate Miller]

you know, Jonah, when I started out, it seems like there were lots of players that had their own personal approach and ideas about theory

that was part of being a jazzman...you had your way, I had mine, and sometimes the combination sparked something special, too.

so I have no problem with the way you think about harmony. Its an efficient and practical way.

[bako]

I'm totally at a loss at what 2+2=4 represents.

The way I interpreted this was based on 4 note chords, 2 notes from each chord mixed together.

D over C

CE DF#
EG F#A
GC AD

CE AF#
EG DA
GC F#D

CG AD
EC DF#
GE F#A

CG AF#
EC DA
GE F#D

ect.

[Nate Miller]

2 + 2 = 4 is a metaphor. Stan often spoke in riddles. He always meant more than what he said. He did that so that you had to do some real work yourself to pick up what he was laying down.

what it means is simply this: when you play one key against another, the result is always more than the two keys individually.

that's all it means...there's no significance to the actual numbers, it's not a mathematical expression, it's more like a euphemism

[cosmic gumbo]

2 + 2 = 4 is a metaphor.
what it means is simply this: when you play one key against another, the result is always more than the two keys individually.

Saying 2+2=5 would make more sense as a metaphor, wouldn't it?

So adding Dmaj triad to Cmaj7 gives you the 9, 11, 13?? As has been mentioned, F# would be the #11, not 11....child's play?

[christianm77]

plusgood

[Nate Miller]

Saying 2+2=5 would make more sense as a metaphor, wouldn't it?

So adding Dmaj triad to Cmaj7 gives you the 9, 11, 13?? As has been mentioned, F# would be the #11, not 11....child's play?

You don't get to chose the way your mentor teaches you. 2 + 2 = 4 all day where I'm from. So that's what the man said.

And listen, when you extend a major 7 chord, it is always a #11. the natural 11 is a sus4. So just like I always speak in concert pitch, when I say a maj13 I assume you understand that means a #11

and yes, that really is child's play. It's Jazz 101. The common stuff everybody knows