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I know you're half joking, but you're twisting my words. I said, there's no such thing as a 9,#11,13 triad. All triads are 1,3,5 by definition.

It's an interesting idea. It personally doesn't work for me. I've already learned all the upper extensions, so I just think of them directly rather than add what I consider another layer of obfuscation by breaking parts of chords into triads of other chords. I feel the same way about modes. They don't help me navigate chord progressions very much in the heat of the moment. I prefer to think of them on their own terms rather than some mode of the tonic. Anyway, that's just how my brain works (or doesn't).

I admit, I've never read any of the books listed here so far, so I could be way off base. But I think techniques like this turn improv into mindless finger flapping. Take some patterns that happen to fit the harmony and play them as fast as possible without regard to melody, voice leading, emotion, harmonic function, tension and release. Yes, they can sound sort of good. But what's the point if they don't mean anything. The difference between a really memorable, moving and meaningful phrase (lick) and a random collection of notes that fit the harmony is the difference between actual music and monkeys on a typewriter.

Sorry, I'll get off my soapbox now.
I'm not twisting your words so much as trying to show you how restricting your thinking is. A triad is any collection of three notes arranged by 3rds. Many people understand chord extensions in harmony by viewing them as stacked triads, and there's nothing incorrect about that.
 

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I'm not twisting your words so much as trying to show you how restricting your thinking is. A triad is any collection of three notes arranged by 3rds. Many people understand chord extensions in harmony by viewing them as stacked triads, and there's nothing incorrect about that.
That's where we disagree. The definition of a triad is 1, 3, 5, not just any 3 chord tones in thirds. So it's not my thinking that's restricting. It's the definition of triad that's restricting. If you prefer to define triads more generally that's cool, but it's not technically correct. It would be correct to call your concept of a triad a "3 note chord" because that encompasses many more types of chords and intervals than just triads. You know how they say all squares are rectangles, but not all rectangles are squares? That's because a square is a very specific type of rectangle. A triad is a very specific type of 3 note chord which consists of 1, 3, 5 only.

Even when you think of harmony as stacked triads, they're still 1, 3, 5 with respect to a given root. So a Cmaj9#11 could be thought of as a C maj triad and a B min triad stacked, not a C maj triad and G maj 7 triad built on 3, 5, 7. The latter does not meet the definition of a triad (1, 3, 5), so I would say it's not the "correct" way to think about it. But if it works for you, then continue to think about it however you want.

Lastly, it's this rigid definition of triad that makes the triad pairs concept simple. If you change the definition to something more general, then it's no longer simple because of instead of just 2 types of triads (maj and min), you now have dozens (maj, min, dim, aug, half-diminished, etc.).
 

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That's where we disagree. The definition of a triad is 1, 3, 5, not just any 3 chord tones in thirds. So it's not my thinking that's restricting. It's the definition of triad that's restricting. If you prefer to define triads more generally that's cool, but it's not technically correct. It would be correct to call your concept of a triad a "3 note chord" because that encompasses many more types of chords and intervals than just triads. You know how they say all squares are rectangles, but not all rectangles are squares? That's because a square is a very specific type of rectangle. A triad is a very specific type of 3 note chord which consists of 1, 3, 5 only.

Even when you think of harmony as stacked triads, they're still 1, 3, 5 with respect to a given root. So a Cmaj9#11 could be thought of as a C maj triad and a B min triad stacked, not a C maj triad and G maj 7 triad built on 3, 5, 7. The latter does not meet the definition of a triad (1, 3, 5), so I would say it's not the "correct" way to think about it. But if it works for you, then continue to think about it however you want.

Lastly, it's this rigid definition of triad that makes the triad pairs concept simple. If you change the definition to something more general, then it's no longer simple because of instead of just 2 types of triads (maj and min), you now have dozens (maj, min, dim, aug, half-diminished, etc.).
The 9, #11, and 13th of C are a triad. Not a C triad, but they comprise, without doubt, beyond discussion, a triad. If you don't like thinking that way, great, think another way. I like triads and especially triad pairs for the sounds they open up, not because they simplify improvisation.
 

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The 9, #11, and 13th of C are a triad. Not a C triad, but they comprise, without doubt, beyond discussion, a triad. If you don't like thinking that way, great, think another way. I like triads and especially triad pairs for the sounds they open up, not because they simplify improvisation.
Absolutely. It's not any sort of C triad by any stretch. It's a D maj triad, which I agree with 100%.

It's not as useful for me to think of it as a D triad as it is just to remember what the 9, #11 and 13 are because I have to remember all these other rules about where on the circle of 5ths the related triads are and all of that. Too much thinking and too many things to remember for my old, slow brain.
 

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Lastly, it's this rigid definition of triad that makes the triad pairs concept simple. If you change the definition to something more general, then it's no longer simple because of instead of just 2 types of triads (maj and min), you now have dozens (maj, min, dim, aug, half-diminished, etc.).
I'm with you in that I don't like to think of chord extensions as triads because I prefer to think of them in relation to the actual chord root (to which they are extensions). Just less confusing, for me. Maybe not for some and it's fine how you think about it as long as it works for you.

However, my understanding of triads is that they aren't limited to maj & min. I think there are 4 possibilities:

maj: 1 3 5
min: 1 b3 5
dim: 1 b3 b5
aug: 1 3 #5

(I don't think you can have a half-dim triad because that requires a 7th chord)
 

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There is a great course on Coursera, by Dariusz Terefenko, called "The Blues: Understanding and Performing an American Art Form". The course covers all the background about harmonies and improvisation. In contrast to many courses, it is lively presented with Dariusz on the piano, joined by other musicians on a lesson-by-lesson basis. I found this course extremely helpful and a lot of fun. And.... it is free!

The link to the course site is here: The Blues: Understanding and Performing an American Art Form
 

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A very general question that a local sax player asked me. Any suggestions on some "basic" books? Thanks.

"Hey John, i'm trying to get better at jazz improvisation especially with triads. Do you know of a good book I can buy to work on that kind of stuff? I want to be able to do the straightahead."
I highly recommend 2 relatively recent books from a UK Jazz Educator Buster Birch. The 2nd one would probably match your local player's ask ...

(1) Beginner Jazz Soloing for Saxophone & Clarinet: The beginner's guide to jazz improvisation for woodwind instruments - on Amazon here (UK link) [focused on improvising with the pentatonic scale]

(2) Rhythm Changes Soloing for Saxophone & Clarinet: The Guide to Chord Tone Soloing on Rhythm Changes for Jazz Saxophone and Clarinet (Amazon)

What I love about these books is the step by step process, with practice exercises and backing tracks, that take you from the basics forward, isolating one element of the jazz improvisation mix at a time so that you can focus on something more manageable. The 2nd book is focused on chord tone soloing, all he way from practicing the chords and rhythm to embellishments such as enclosures and on to tri-tone chord substitutions to give you more options. Buster also has been running a series of online jazz workshops which I've started to catch up on (here).

Hope this helps
 

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I highly recommend 2 relatively recent books from a UK Jazz Educator Buster Birch. The 2nd one would probably match your local player's ask ...

(1) Beginner Jazz Soloing for Saxophone & Clarinet: The beginner's guide to jazz improvisation for woodwind instruments - on Amazon here (UK link) [focused on improvising with the pentatonic scale]

(2) Rhythm Changes Soloing for Saxophone & Clarinet: The Guide to Chord Tone Soloing on Rhythm Changes for Jazz Saxophone and Clarinet (Amazon)

What I love about these books is the step by step process, with practice exercises and backing tracks, that take you from the basics forward, isolating one element of the jazz improvisation mix at a time so that you can focus on something more manageable. The 2nd book is focused on chord tone soloing, all he way from practicing the chords and rhythm to embellishments such as enclosures and on to tri-tone chord substitutions to give you more options. Buster also has been running a series of online jazz workshops which I've started to catch up on (here).

Hope this helps
I'm sure those are great books. But I think it's unlikely either of them would talk about triad pairs like the OP is looking for. I've only seen it presented in a few books as an advanced concept, not in any beginner books. If you have the books, can you confirm whether triad pairs is covered or not?
 
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