I think it would be a good idea to make just a list
with all possible Triadic Upper Structures 
PS I don’t understand when 6 stay 6 (flat or #) and when becomes 13.
Check this out:
To my understanding, 6 stays 6 when you have a 6th (major or minor) chord (1356) or 6/9 chord.
6 becomes 13th when it is an extention of a 7th chord.
But I’m not a jazz/fusion guy so I may be mistaken… 
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Honestly, I think a much better way to do this is just to understand the big top-level categories first and only worry about their sub-variations as you need them for actual playing.
As Frank Gambale says in our recent interview with him, he really only thinks about six chord families, to keep things simple. Frank’s system boils down to major, minor, dominant, min7b5, altered, and diminished. That’s it. Any chord he plays fits into one of those buckets for him. There might be a few different flavors of each, but thinking about the world as divided up into a few basic items first is going to dramatically simplify how you connect stuff together.
For example, to address your question, something like maj6 goes into your “major” bucket. You want a more happy happy sound? Try a maj6. You want a more neutral sound? Use a major chord.
The 13 chords go in your “dominant” bucket. You want an aggressive sound, with an obvious tritone flavor, do dom7. You want a softer sound, try a dom13. They’re variations of the same color.
In other words, I’m not worrying about which things get flatted or sharped. The 6 and 13 generally don’t get altered that way anyway. Instead I’m asking, hey what color am I looking for here. If it’s dominant, which one? Then I play it.
You’re thinking in families and the slight variation of the family you want. That’s I think the most practical way to do this.
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This reminds me of Joe Pass’ system. If I remember correctly, he thinks of chords only in terms of major, minor, and dominant. (Altered, diminished, augmented, whatnot is all dominant to him) My memory is a bit rusty but I’m sure he talked about that in one of his video lessons and in at least one book that I had.
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Absolutely, he says this on both his REH video and his Hot Licks (I think) video. I wrote that and then deleted it while I was typing one of those paragraphs and forgot to add it back in.
From our interviews, Oz Noy also says this, Olli Soikkeli as well - most all of the great improv type players we have interviewed all think in very simple terms. They may not always articulate things as clearly as Frank is boiling it down here, and as Joe does in those lessons, but it seems pretty clear that thinking in terms of a simplified number of choices is very common.
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I agree that for soloing it’s better to think in major, minor, or dominant. But exploring upper triads comes in handy for composing and chord substitutions. Like if you’re working on a piece with a plain old Cm you can try swapping it for a Eb6, AbM7, Am7b5, or F9 since they all share a triad and see where that takes you.
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For sure. Tal Farlow said in an interview once he just takes whatever the actual shape is, whatever the notes are, on the top few strings, and arpeggiates that. The interviewer was like, uh, really?? Tal had no shortage of harmony knowledge so this was clearly not a cop-out. I think he was just saying, that’s one easy way you can do this.
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I actually did all this theory work earlier this summer- analyzing all types of triads, 7th chords, and Quartal Harmony against a fixed root (in my case G). I took notes on the subject and made a cheat sheat for Major, Minor and Dominant sounds for what chords I can superimpose. Once I find those papers I will take pictures and upload them.
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It’s a 6th when it replaces a chord tone (usually the 7th) and a 13th when it’s an extension. If I see “maj6” on a chart, I would not typically play a 7th. If I see “maj13”, I would include a 7th, although I would not be happy with the notation choice – to me, it’s insufficiently clear, but that’s another story.
Figuring out the triads over bass notes isn’t too tough.
You’ve got 48 triads (maj, min, dim, augmented in all 12 keys). You could add other 3 note structures, too, but that’s a good start. Take a root note (C, or whatever).
Get rid of all the triads that already have a C in them (all the C triads, Fmajor, Aminor, etc) since it’s just a triad with a doubled note.
Make a note of all the structures that are really just 7th chords, like Em/C (Cmaj7). Don’t necessarily get rid of them – it can be useful to think of 7th chords in terms of triads. But if you’ve gone through 7th chords, you should be familiar with these structures.
So the remaining structures will be new chord voicings. Some of them will have clear applications. Some of them might not have any apparent application. Some of them will be ambiguous. Most people start out with voicings where there’s a clear separation between the bass note in the triad, but don’t be afraid to play inversions where the ‘bass note’ is no longer the lowest note.
Another approach is to find different scales that serve as options for improvisation over a chord, and then derive triads from them. Guys like Bill Evans really liked Db and Eb triads over a G7 chord, which comes from Ab melodic minor (or a G altered scale). There are tons of triads in the diminished scale. You get the idea.
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People are different, my mental structure requires a formula and method.
Everything must be organized and clear,no randomness resulting from unconsciousness.
Why this note and not another one,why in this place and not in another etc
Like 1 Hīnayāna,2 Vajrayāna,3 Mahāyāna.
1 - play anything if your ears like what you hear
2 - scales and chords, rules of construction
3 - academic level for professionals about improvisation,composition and arrangement
This is a good method for beginners but very amateur and unprofessional
therefore, only for beginners Tal “Hīnayāna” Farlow ;D
Up to this point I understand what you wrote,the rest is difficult
Could you present it to me in graphic form as a schematic drawing? 
Fmaj/C is just Fmaj. It already has a C in the triad (FAC), so it’s just a triad with a doubled note.
Emin/C can be thought of as a Cmaj7 (CEGB). It’s a 7th chord, but I wouldn’t ‘discard’ it. It’s useful to think of 7th chords in terms of triads, and a lot of piano players think this way.
Something like Gmaj/C is its own unique structure (CGBD). Maybe you could call it “Cmaj9 no 3rd”, but it’s probably just easier to think of G/C.
So you go through all 48 possibilities and categorize them. Make your own diagram. It’ll be more valuable if you go through the process yourself.
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Exactly my point. Everyone’s brain requires structure. To be clear, I’m not suggesting you ignore what the notes are or why they are present. You still need to learn that. I’m just suggesting a more efficient structure for doing so, i.e. chord families. Because now in addition to chord structure you’re also associating similarities in sound which gives you an additional dimension to learn. If you prefer, it’s actually more structure, not less.
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6th chords are interesting to me in that by focusing on maj7th chords, I completely missed the sound of certain passages. Where chordscale theory is concerned it’s easy to overlook that the symbols represent sounds/scales/notes/avoid-notes and, with some exception, not voicings per se. Very different from conventional first position “grip” playing.
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Below is a list of common vs uncommon use of 9, 11, and 13 over the basic seventh chord (Variants of 1 3 5 7) types. Using that it’s possible to make a list of triads created from 9, 11, 13, or 7, 9, 13, or 11, 13, 1, etc and see if it would be within conventional use, bright, or ‘uncommon’ (which is neither bad not good, just less used.)
Quick Summary of common uses for extensions/tensions on 7th chords
Maj7:
1 3 5 7
most common: 9, 13
bright: #11
In more modern use: #9
Maj7#5 is not uncommon. Often not voiced with any 9, or 13 options.
Not as common: b9, natural 11, b13.
Min7:
1 3 5 b7
most common: 9, 11
bright: 13.
In more modern use: #11, b13
Not as common: b9
m7b5 (half diminished):
1 b3 b5 b7
most common: 11
bright: 9
Not as common: b9, b13, 13
Diminished Seventh:
1 b3 b5 bb7
9, 11, b13, and 7 are all possible but be mindful of clashing with melody as well as general context
Not as common: b9 or b7
–
Dominant seventh
1 3 5 b7 - (5 is often sharp, flat, or omitted)
Tensions and extensions for dominant chords are more complex.
Dominant seventh as the V7 in a V7 to I motion (another way to say would be, dominant resolving up a fourth as in G7 to C, D7 to G, A7 to D, etc):
Most common: 9 and 13 are common
More tension, but still very common: b9, #9, b5, #5 (b13)
A combination of b9 and 13 is also common in this context.
A combination of 9 and #5 is also common.
A combination of 9 and #11 is not common in this context
A combination of #11 and 13 is not common in this context
Dominant seventh as a I7, II7, IV7, bVII or when resolving down a half step (acting as a subV7) and otherwise any dominant that is not directly acting as a V7
Most common: 9, #11, 13
Note that #11 and b5 are the same note - "enharmonic equivalent" - but the #11/b5 note combined with 9 and 13 has a different function and sound than when combined with b9/#9, and #5.
Also common: #9
Less common, but still used depending in context: b9, #5
–
Minmaj7
1 b3 5 7
Most common: 9
bright/questionable: 13
In more modern use: #11
Not as common: b9, b13
Min6:
1 b3 5 6
most common: 9
Less common: b9, 11, #11, b13
7Sus4:
1 4 5 b7
Most common: 9, 13
Bright: major third
Modern: b9 (especially with 13)
Less common: #9, #11, b13
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13 vs 6, and triad list
The difference is whether there is presence of some type of 7th.
If we have a C7, Cmaj7, or Cm7 chord and add an A, we’ll call that a 13th.
If we have a C major triad or C minor triad and add an A, we’ll call that a 6th.
It comes from the concept that with 7th chord type of harmony, things are built in thirds: 1, 3, 5, 7, 9, 11, 13, then back to 1. Just a categorization/organizational thing.
For what it’s worth, I did make a list of all possible major and minor triads against a C bass note and what their harmonic implication would be, but it doesn’t exactly answer your question and it’s possible the shorthand won’t be of much use to you. Though between this post and my previous one hopefully you can put it all together:
Triads over da bass notes
Db/C = C phrygian
D/C = C lydian/maj7#11
Eb/C = It’s a Cm7
E/C = It’s a Cmaj7#5
F/C = It’s an inverted F triad
F#/C = cool for C7b5b9
G/C = Cma9 no 3
Ab/C = It’s an inverted Ab triad
A/C = cool for C13b9
Bb/C = C7sus4
B/C = Cdimmaj7 or Cminmaj7#11 or Cmaj7#9#11
C#m/C = C7#5b9
Dm/C = C7sus4 or it’s just an inverted Dm7
Ebm/C = Cm7b5, in the right context could be C7b5#9
Em/C = It’s a Cmaj7
Fm/C = It’s an inverted Fm triad
F#m/C = can work for C13b5b9
Gm/C = nice C7sus sound (personal fav)
Abm/C = don’t know about this one! Kind of implying V7alt, G7alt
Am/C = It’s an inverted Am triad
Bbm/C = C7sus4b9
Bm/ C = Cmaj9#11, can work over minor chords too because there’s no third.
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@nasierszyca, adding to what @JakeEstner said, with “7th chord harmony,” in the case of a maj6 chord, the sixth may be considered as acting as a chord tone and it would be odd to use a number an octave up. The categorization/organizational thing can obscure the function in practice.
Folks confused about this will benefit from hearing the difference. Play any four note major 7th chord. Then drop the maj7 down to the maj6. Go back and forth between the two structures listening for stability/finality. In the case of tonic min6th chords, the maj7th, while present in the chordscale, may also sound completely inappropriate when played as part of the voicing in context.
Sometimes function is expressed from the root of the scale, and sometimes from the scale expressed as a stack of thirds as Jake illustrates. When 6’ is functioning as a chord tone we call it a “sixth.” When as a tension on a dominant seventh chord, it’s called a 13th.
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When 6’ is flatted or sharped, it’s no longer acting as chord tone in tonic major or minor chord, so you are less likely to see b6 or #6 than you are to see #5, b13, or b7. It’s good that you brought up sixth chords too, because as you see from the list of triads over bass notes, one may miss an essential sound. It’s present enharmonically, albeit in inversion.
Am7 / C —> A C E G / C —> A C E G —> C/A —> Cmaj6 in third inversion
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yeah @RockStarJazzCat it’s an important thing to see with sixth chords, not to confuse things further, that they are also seventh chords if we name the 6 as the root.
So yeah C E G A = Cmaj6, A is the 6th, reordered as ACEG it’s Am7, so they are just inversions of each other
Similarly, C Eb G A is Cm6 and Am7b5. I’ve heard that calling a chord an Am7b5 is a relatively new practice and in the first half or so of the 20th century the chord would more often be called Cm/A or Cm6/A.
To my ears it’s always sort of a point of ambiguity, especially on a voicing like C, A, E, low to high. It’s more simply a minor triad in inversion, but it is often used as a type of C major sound, C6, even though there’s no fifth. Brian Wilson/Beach Boys were really big on the major 6th sound.
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Yeah @JakeEstner, the subject of the thread being about structures that yield certain sounds that relate to other harmonic concepts, it can easily get complicated beyond practical use sonically.
@nasierszyca, here’s a concept from Barry Harris that will reinforce the idea of the sixth as a chord tone. Try running the following scale up and down with a swing feel…
C D E F G G# A Ab G F E D C
Contrast that with running the following scale…
C D E F G A Bb A G F E D C
…the latter mixolydian scale contains no chromaticism with regard to its related parent key (F major). Nevertheless the former, with a chromatic passing tone, captures the sound of a jazz tonic major scale better than the way people would typically run it…
C D E F G A B C B A G F E D C
(I’ve been singing all of these with solfege syllables so writing them out with note names feels decidely weird. I likely made a typo or two.)
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