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Non Functional Harmony is a topic generally discussed among composers; not so much as something improvising guitarists include in their vocabulary of soloing techniques. But as more and more of my own playing is exploring harmonic guidelines that parallel but don't always adhere to a written set of changes, there's a lot more possibility to explore chord progression that has different considerations determining note choice.
Some of these include voice leading, an awareness of vertical tension and controlling dissonance/consonance over the course of a progression, decisions on the amount of harmonic suspension within a song form based improvisation, questions of how to assemble a new chordal vocabulary based on dissonance and richness, terms outlined by Herb Pomeroys arranging methods.
Herb Pomeroy, a great arranger and composer developed a hierarchy of intervals which he felt created specific amounts of tension. When the cumulative vertical dissonance (accumulated from stacking these intervals) is taken as a whole, it's an overall effect of total dissonance/richness index that can be quantitatively controlled from one chord to another.
Intervals of most tension: 1/2 steps, Major 7th, baths
Intervals of decreasingly less tension: Whole steps, Minor 7th, Natural 9th
Intervals of less tension: Perfect 4th and 5th
Intervals or even less tension: Tritones
Intervals of the least tension: All 3rds and 6ths
Now I was passed this by Mick, who got it from Herb. He's quantified these into a point system which I may get into at a later post. But I wanted to start a general discussion of non functional harmony, in composition, in free improvisation, in soloing and in changes based improvisation, and first see what some of the members' take on this topic might be. And then in the course of this, explore and maybe work or study some of the Pomeroy material.
This is also related to a thread on Pezanelli hybrid triads over bass notes posted a while back.
I know this is not the usual gear discussion, but I thought for those who love expanding your harmonic possibilities as much as some love expanding their guitar collections, we might share some really hip ideas to get excited over.
Finally, a very recent discussion with Mick:
"That Pomeroy material is really rich, I've begun to explore it and it's changing the way I see harmony"
"How?"
"Chord choices have just become infinitely more complex. How long did you work with this material after Herb introduced it to you?"
"About 50 years"
"Oh"
Any questions or ideas from the community are encouraged for this thread. Please keep an open mind of encouragement for the curious and inquisitive. Thanks
David
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02-24-2015 11:24 PM
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Awesome thread.Guys check the last post on the David Valdez great blog Casa Valdez Studios
There's links to amazing Pomeroy stuff on pdf's.
Thank you for thread TruthHertz.
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Great topic. Just got Mick and Tim's book and it is a major work in harmony. Look forward to this discussion. Always thought Ralph Towner was a master at this. His compositions approach 20th century classical vocabulary more than traditional "jazz" harmony.
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Interesting ... Can you elaborate little on how you might apply this sort of stuff? Just creating more impressionistic, modal, sort of voicings?
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Interesting discussion about consonant and dissonant intervals, though it is not clear to me how this functions in a practical playing sense beyond being sensitive in terms of adding colors to your music. Not sure if this is the point, but I do find that I am very aware of the impact of the addition of intervals to a basic chord structure.
An example would be one of my favorite devices which is to the #5 or the minor 2nd to a dominant V7 chord, as in a progression in C : ....Dm7 - G7alt (or the tritone Dbmaj7, eg). These types of intervals in a solo guitar chord melody style approach give that subtle color that incorporates good voice leading and sophistication to an arrangement. I don't think of that as a "modal" approach so much as voice leading.
Jay
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I think as a topic of discussion, we hit upon the very many approaches to jazz improvisation, a confusing and mysterious discussion in itself. Even throughout my own development as a guitarist, there have been so many different rule sets and disciplines that have shaped myself, students and seasoned players alike.
At one end of the spectrum I see jazz as assimilation of melodic patterns in strictly prescribed harmonic situations (transcribing and playing over standard form with genre appropriate lexicon) and at the other end are people like Joe Morris, Cecil Taylor, or Keith Jarrett, using very controlled sets of rules in the creation of the forms as a part of the soloing process.
I wanted to look at this thread as something beyond the grab and lick approach, not that there's anything inherently bad about that, but for those who are expanding what constitutes improvisational music, having harmonic control and architectural vision in a solo is a very different thought process from accomplishing a perfect II V I in Bb.
Does anybody work with The Advancing Guitarist? Somewhere in the pg 60-70 section (I don't have one with me) he talks about 4 part types of chords. It might be a good place to start an analysis and observation of 4 part types, not as functional diatonic puzzle pieces, but to look at them and listen to the amount of dissonance each type of chord might hold, and to start a lexicon of chords with that awareness.
Chew it over, and spit out any observations or reactions. I think discussion makes the best grounds for discovery.
David
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There's the core of the question I had when I worked with these ideas from a compositional perspective: That's all fine and good but what about when I'm playing "tunes"?
Originally Posted by pamosmusic
Well one answer is it's key to work with people who have a similar sensibility, the voicings, the rhythmic space, the ability to musically allow or comment on something that has its own direction is REALLY important. I'll relate a musical experience I was fortunate to be witness to recently. It was a quartet, and for one chorus of a standard form, the guitarist (Dave Tronzo) began to develop an idea early on, the bassist was with him and in support suspended the root movement of the song form. Yes, the form was still there in rhythm, everyone knew the phrase architecture, the transition from song segment, but the solo had a development and tension of its own. And when the final turnaround came around, everyone fell into it like they'd been running the changes all along. It was breathtaking. And begs the question: How much liberty do you allow in a solo, and how much do you need from those around you. Including the audience.
If you're going to build your own road beside an existing one, having command of harmonic content is a really useful skill.
I hope this addresses your question a little bit, and of course it's just one tiny answer to what the topic can reveal.
Still an ongoing question for me too
David
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It does ... I've been working on some intervallic voicings recently as well. good for ammunition in less tonal situations. I haven't been as deep into it as you seem to be but it's extremely interesting and you get a lot of cool voicings by stacking intervals instead of coming from a functional tertian kind of place. If you can make voicings by stacking three notes a fourth apart then why not three notes a seventh and a sixth apart? Very cool colors. Again ... Correct me if I've completely misunderstood where this sort of thing is intended to be going
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Yes, that's the idea. If you look at different intervals, they have a certain amount of tension, a certain amount of "richness weight" if you may. And you can effect the overall weight by knowing the contributions of the individual intervals. Now if you develop the skill to be aware of "weight" AND function, then some interesting things can happen. Originally Posted by pamosmusic
That's what the chart can help with, chose intervals with more dissonant value, or less, and put together chords that have sound qualities you may want to employ. It's very different from strings of drop 2 chords that merely work to enforce the change. It's another parameter of awareness that can help you develop a very unique sound all your own...that kind of "What is he THINKING?" kind of sound.
David
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Very good thread, I've been using interesting, unusual intervals to create unconventional harmony for a while, getting others players to use them is the hardest part, so the progress of this thread will be very interesting.
Curiosity and exploration are my main improvisational ingredients.
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As soon as I read the thread it reminded me of Hindemith interval rankings.
He wrote about it in "the musical craft" book. From least to most tension.
I found this DENSITY DEGREE THEORY
pretty amazing to get your facts straights. (I don't agree with couple of things but the graphs is a cool idea)Last edited by Takemitsu; 02-25-2015 at 01:47 PM.
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Thanks, Takemitsu, I'm going to check that out really thoroughly. A while ago, Jack Pezanelli also made a chart of 12 qualities of tension derived from triads over bass notes. He was working with acoustical engineers at MIT to come up with a hybrid chord tension chart. That's outlined in another thread somewhere on this forum.
It's great to see how these things have been the focus of different composers, and exciting to see this thinking used by some of us in the improvisational guitar family.
So much of this takes time to work out, technically, so much longer to begin to assimilate into the fingers, ear and in practice. But I've heard some guitarists with a high degree of mastery in these or similar ideas and it really does make one of the differences between older school sounds and, for lack of a better term, more modern harmony.
David
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well, it seems to me that a theory like this would have to consider:
- choosing a pitch collection, whether that's the entire chromatic scale or some sort of limited pitch group (scales, modes, various collections). what kind of collections would lend themselves to different types of chordal possibilities? is there a way to classify or quantify these sorts of possibilities so that they become more manageable?
- classifying chords by their intervallic makeup. from what i understand, this is what Pomeroy was doing, and if Mick has found a way to more precisely quantify it, it can only help our understanding
- voice leading these types of chords. the Alamanacs would cover a huge amount of this material, but an understanding of tension/dissonance within chord voicings would add a new dimension to this, particularly when voice leading between different "families" of chords (drop 2s, drop 3s, TBN I, 4th voicings, etc)
my immediate thought is that a better understanding of the tension/dissonance in individual chords and how it shifts and transforms through voice-leading could be a huge step towards creating music with the drama and flow of major/minor tonal music in a variety of different approaches (modal, polymodal, chromatic, etc) where tension/release is less obvious
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I'm keep reading the thread and i don't know why but while thinking 'bout this stuff
my mind is more and more into Ran Blake and his playing
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I never heard of Ran Blake and so checked out his youtubes, what wonderful music! Originally Posted by neshkadrums
I'm keep reading the thread and i don't know why but while thinking 'bout this stuff
my mind is more and more into Ran Blake and his playing
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Big presence around these parts. Originally Posted by neshkadrums
I'm keep reading the thread and i don't know why but while thinking 'bout this stuff
my mind is more and more into Ran Blake and his playing
David
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On language:
If a series of harmonies can move to one another in a musical way, is that not functional in some way
within a broader definition of the word?
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X C G# B E X ..... X Db F Bb Eb X ..... G X F# B E X ..... Ab X F Bb D X
X D A C# F X ..... X Eb A D F# X ..... X F C E G X
Observations:
Simple chromatic lead line: E Eb E D F F# G
If I take C as the centric focal point (which has not been established yet) then the melody
progresses from the 3rd (E) to the 5th (G). A tonal move within the chromatic environment.
The chord tones include all 12 notes
The root motion in pairs progresses in 5ths C - G - D
C, G and D each have an upper chromatic neighbor chord C Db - G Ab - D Eb with the exception being the Fma9.
I hear the last chord as major because of the presence of A natural in the 2 preceding chords.
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One area that I've messed around with (which is far short of having gained control of) is trying to conceive of all the modal collections of harmonies as one larger pool of chord possibilities.
How is that different than the chromatic scale? In some ways it's not but it can be viewed in smaller compartmentalized chunks that is easier for my brain and ears to take in.
Another undeveloped interest of mine is chord pairs and scale pairs and the subsequent chord/scale pairs.
In small increments as I grow, these elements (in my mind at least) become functional.
From this perspective, nonfunctional translates to not yet understood.
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I'm very curious to hear about the explorations of other forum members, and learn more details
about the work of Herb Pomeroy and other great thinkers like him.
Thanks David for initiating this discussion. I hope it continues.
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Yes!! Your entire response is an excellent springboard for an overwhelmingly large discussion on the improvisational landscape and how it's changed since Mile's work with his second quintet. Originally Posted by dasein
The individual players need to form a consensus on the harmonic rulebook, and I'm thinking chromatic scale, as was the nature of Pomeroy's system in relationship to diatonicism as we know it, but also thinking polychords, hybrids and schillinger scales certainly are appropriate. It's agreement, direction, intention and sound that determines. But here, I was thinking of tensions within the chord, the chromaticism in relationship to the individual intervals, ALL relationships within the chord structure taken collectively as a whole.
Mick quantified intervallic scale on a 1-4 system. 0 points being a more consonant, or less rich interval, and 4 having the most amount of dissonant "richness". Originally Posted by dasein
4 points for Intervals of most tension: 1/2 steps, Major 7th, baths
3 points for Intervals of decreasingly less tension: Whole steps, Minor 7th, Natural 9th
2 points for Intervals of less tension: Perfect 4th and 5th
1 point for Intervals or even less tension: Tritones
0 points for Intervals of the least tension: All 3rds and 6ths
So each voicing is given an index based on the average of points for each intervallic relationship:
SATB 4 part voicing would be made of
BT= points for that interval
BA= points for that interval
BS= points for that interval
TA= points for that interval
TS= points for that interval
AS= points for that interval
Total points / relationships= average index. That's the tension in that chord. You can see that the alteration of one voice can change the index, make it more or less dense.
Not so much, just as a matter of approach and perspective. The almanacs were concerned with voice leading, a horizontal function. This relates to the perception of individual chords that can voice lead but don't necessarily have to; the richness is the guiding principle with each individual vertical chord. And of course you don't want to juxtapose wildly disparate chords (or maybe you do!) by following a dense high index 5 part chord with a major triad… Originally Posted by dasein
These are vertical considerations, chords that might not even be cycling, certainly not necessarily thinking in that way.
Yes. You might be choosing chords in comping for a number of reasons. That's the individual's development and identity. But maybe you run a chord that doesn't really work well, you may not always know why. Now awareness of how it fits numerically with the surrounding chords might give some insight into how it's perceived in a progression. Originally Posted by dasein
How this is used is really up to you. You might begin looking at groups of chords by their indices, and planning progressions with an ear towards controlling tension… that's just one way. That's what I'm hoping we might all contribute.
A few observations on my own notebook:
As I've worked with these and as I am now, my chordal use has become even more sparse. I find space allows the time to savour the qualities and feel of individual chords.
I definitely consider finger style a plus if not a necessity. My voicings are becoming an awareness of intervallic choices and not chord shapes (grab inspired). The chords I'm using are not ones I'd ever sweep through with a pick.
I'm finding improvisational areas where I once thought of just changes. For instance, the first 4.5 bars of ATTYA might be seen as a soundscape for an Ab chordal improvisation area before moving into the key of C. Within this tonal area, you can really play with density as a guiding concept.
Gosh, I hope this makes some sense, and I hope this proves to be fun to some of us. Please do weigh in! I look forward to the discussion!
David
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Interesting that tritone is considered less tension than 4th and 5th.2 points for Intervals of less tension: Perfect 4th and 5th
1 point for Intervals or even less tension: Tritones
0 points for Intervals of the least tension: All 3rds and 6ths
I would also ponder why 3rds and 6ths are less tension than 4ths and 5ths.
Also, is there a difference between #5 and b6 or does one size fit all?
Within each category, there is also a continuum.
As I hear it from least tension to most:
ma7 .... m2 .... b9
ma9 .... b7 .... ma2
etc.
Anyway, one has to draw lines somewhere in the sand to create a measurement system.
When I get a chance, I'll apply to some voicings to see what insight it offers.
Thanks David
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Right on the money with these observations Bako. I'm in the process of commenting on your last post, but there's so much there to say, it'll be a few days. Originally Posted by bako
The tritone is, yes that's the one that always gets everyone. Aside from root position, its appearance within a chord can describe a dominant sound, or have a certain symmetical stability within itself.
The gradations within the point categories is absolutely right. That's Mick's next step, to quantify within the groupings. But for now, they're the category divisions given to him from Herb.
And me too, there's a lot to take in and experiment with. I see the potential for much observation and discovery here.
Thanks Bako
David
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Are there some recordings that you can link which use this type of harmony? Or maybe some examples notated we can try out? I've been playing around with "non-functional" harmony for years, although I'm not sure I've developed a scientific system with it. When I do it, I tend to focus on the voice leading and just let myself get as chromatic and "out" as I like, but then I resolve back into the changes. Doesn't always work out but sometimes I get some amazing sounds out of this simple system.
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Hey there Guitarzen-yes that's exactly how it works; not necessarily voice led in this case but that does make a lot of sense. It's initially and primarily an arranging technique, so a lot of applications were not intended for guitar specifically, and included things like 5 part writing for multi instrumentalists, clusters, that kind of thing, but for guitarists, there's plenty too. I'll dig up some examples of experimentations. Originally Posted by Guitarzen
I'd say that as you've been using non-functional harmony all along, we don't need to talk about the why, and your own how is certainly good. You've got lots of options when you're "on the way out" and this system might be helpful when organizing in your own mind just which one you'll choose. You know that the difference in one note of a voicing can make a difference in the way you perceive that chord, and the alteration of another note may result in a huge difference. That's subjective; and this is one way you can put some objectivity in your options. You can now have a tool in your perception of chord options of saying "Oh, that's a 2.4 index, that's nice but now this time around, as I'm approaching a point of peak tension, my 2.6 options might be a good choice". It's also a good awareness with which to set an architecture to the solo.
I hope as you fool around, you might offer up some examples you might not have thought of, especially with the transitions between non-functional areas and returning to the structure of the piece. That's the really interesting area for me right now.
It's still a big experiment for me at this point, so that's why I wanted to throw it out for us all to splash around, community spirit and all. I'll share ideas I discover and look forward to the contributions of all the people here.
I'll say though, one thing I do is combine free improvisation with standard song forms. In doing that, there is the opportunity to create transitional introductions to a piece by following the song form's tonality and points of climax (for example) and not use the changes at that time. Instead, the tonal vocabulary is created through awareness of tension and relaxation in chord choice. I'm finding that non voice led options are not the first things I'd think of (Hey I need to resolve this...) but wow, it does work. The eventual introduction of a piece's given chord structure then comes as a magical transition and what I played looks like an introduction that can be more interesting than the piece itself.
Too, I've worked with Jack Pezanelli's hybrids to this end and Mick's modal compression. And as long as the amount of tension follows in an intended way, it can really have a beautiful result.
Oh well, enough said. I love this stuff because it provides ways out of being trapped by running the same licks over changes with the goal of just getting through the form. 'puts a lot of responsibility and control in the hands of the soloist.
David
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ted greene developed something along these lines..he called it the "V system" (check his web site for breakdowns of this method)..ted studied with George van Epps) so the chord structures are well thought out .. the use of fingers is almost mandatory as a pick would not get the moving voices to be played correctly..
this is a study in composition and counter point..very "Bach" flavored..watching each voice create chords as it moves against the other voices..and the intervals producing very dynamic results..the "chords" seem to be just illusions as the voices are the main attraction..but using chords as spring boards is a way of reference and location..
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The more this discussion goes on, the more profound it's getting. I'm loving it. Originally Posted by wolflen
Yes, historically, up to the time of Debussey, right up to that time, Western music didn't really think in the vertical way we jazzers do. It was very much a horizontal linear concept.
I know jazz guitar is taught in terms of chord shapes placed at points of rhythmic beats in "changes", but thinking in terms of chord texture, linearity, counterpoint, non-functionality… these mark a real plateau in conceptual thinking and a real identifiable change in the way chord melody is approached and chordal playing.
I have the real privilege of playing regularly with someone who has made his life work to master the generalities and subtleties of well thought out vertical and horizontal playing and yes, it can be done in a spontaneous real time situation, and once it's accepted that you learn to access note choice in a progressive (voice led) or textural (chordal progressive) way, the playing field increases a quantum amount.
Very exciting stuff.
David
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jimi Hendrix made chords come alive by "embellishments" adding a 6th or a 9th to a static chord using a trill or hammer on..just those few devices created a "moving voice" that made many guitarists take note and looked to expand that concept-voice leading! Originally Posted by TruthHertz
today there are many players using entire melodic fragments around chord functions to create melodic passages that contain the essence of the chord without having to "form" a chord shape at all..yet the quality and function are clearly defined and established in a harmonic context..and the static feel of a chord is not missed at all..now this is not entirely new..early players-Charlie Christian could do this with some lines and you would hear harmonic movement without a chord being played..later..players like johnny smith and joe pass would take chord melody into another realm ..today there are new concepts being created with added technology..bringing harmonic/melodic unity into a new art form..the work of Stanley Jordan comes to mind..talk about "beyond guitar" his approach makes the most technical players look ancient by comparison..and he isn't even holding a guitar!
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