This sounds A LOT like Allan Holdsworth’s music, both harmonically and rhythmically.
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Certainly does now that I think about it! Besides Goodrick and Miller being aware of the man’s style, kind of makes sense as Holdsworth thought in terms of families of notes, and his voicings were derived from the same.
Thanks to this topic I got interested in the book and ordered it yesterday. Hope it arrives soon and we’ll see how it affects my self-esteem (I currently consider myself as a man whose knowledge of music theory is quite good) 
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I found GMC to a be a fascinating concept. I’ve been using it for many years-since I got the book-both for myself and in my teaching. It’s not something one gets in one sitting, should be digested slowly. Myself I have not yet started working with nor the clusters neither the quatrals in a regular fashion! But, just dealing with the triads is so much fun and gives so rich harmonic results-and triads is something everyone knows, right? It’s just a different angle in how to use them. And this is why I consider it to be very suitable method-provided it’s taken slowly-to introduce extended modal harmony to non jazz players.
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Could you maybe explain it in simple terms? Are there any diagrams you use to explain it?
Sure. I will use only the triads to demonstrate, for the sake of simplicity.
For any given 7 note mode, if you leave out the root you’re left with 6 notes. Those 6 notes can be grouped in 2 groups of 3 notes each. Since we’re only discussing triads, each of those groups will be a triad. For any given mode, these triads are built on the second and third degree of the mode. Here’s an example:
Mode: C Lydian
Remaining notes after leaving out the root: D E F# G A B
Triads on the second and third degree of C Lydian are: Dmaj (D F# A) and Em(E G B)
So, the idea is, when you play the two triads in succession over the root(played, say, by the bass) you get the full modality of the specific chord-in this case C Lydian. Try it and you will see it creates a certain kind of motion and a very appealing richness of sound.
Now, you can apply the concept over a chord progression. First step is to assign a mode to each chord. Next, you look for the triads built on the second and third degree of each. Here’s a simple example:
The progression: G7-Cmaj7, a simple v-i.
Scales assigned: for G7, G Lydian b7. For Cmaj7, C Lydian.
Triads for G Lydian b7: A maj and B dim
Triads for C Lydian: D maj and E min
So, what you do is, comp over each chord using the corresponding triads in succession.
Just to wrap it up, the 3note structures that give the 6 notes of any mode, minus the root, can be of other kind, not just triads. Namely, 7th chords with no 3rd, 7th chords with no 5th, quatral chords and clusters. The book goes in great depth with all of them, both in closed and open position. But, like I said, one needs to take it slowly. I mean, the closed triads by themselves are so much fun-and not too hard.
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Thank you so much.
So, in any progression, a chord has it’s own scale from which the triads come from?
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Yes, you have to assign a mode to each chord for GMC to work. That’s the case even if the modes come from the same parent scale. Say, in the case of a Dm7-G7-Cmaj7, (ii-v-i in C) you could have D Dorian-G Mixolydian-C Ionian-all coming from C major scale, still you have to think in those terms in order for the concept to work.
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Thanks again. If I think of anything I’ll give you a shout. You have explained it to me more clear than the book did!
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Glad some lightbulbs went on for you, @aliendough. Wonderful when a key piece of information falls into place. Let the explorations commence!
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Lydian b7 ? g,a,b,c#,d,e,f ?
Language barrier makes it difficult for me to understand, maybe some pictures?
in the key of C,c ionian,d dorian etc f lydian instead clydian 
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Is the book really not available where you are? “Lydian b7” 1 2 3 #4 5 6 b7
Yes, G Lydian b7 is G A B C# D E F. The structure of the scale is as stated by RockStarJazzCat.
I’m not sure about what you mean after that. Just to clarify, v-i in the key of C is G7-Cmaj7. There is a great number of scales to play over each chord. For G7 could be G Mixolydian, G Mixolydian b13, G alt, G WT, G HW etc. Each scale adds a different set of tensions/extensions. The same for CMaj7. Could be C Ionian, C Lydian, C Lydian aug etc. Different tensions/extensions, different color. F Lydian has nothing to do with this example.
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Ok ok but this is how I understand it
for C ionian scale I have Dm and Em chords with C in bass
for D dorian scale I have Em and Fmaj chords with D in bass etc,right?
and for G mixo scale I have Am,Bdim,+ D#m and Fdim (triton sub.) chords
with G in the bass?
And now what next,we have two triads with tonics in the bass ( for each scales).
So?
You’re spot on about C Ionian and D Dorian! But, and this is crucial in understanding how things work in jazz harmony, what scales you choose to play over a given chord type is really up to you. Playing D Dorian, G Mixolydian and C Ionian over Dm7-G7-CMaj7 is one option but not the only one-and frankly not even the best or most used. For each chord type there are numerous options, different scales that expand or alter the basic sound of the chord in different ways. You can think the Cmaj7 as Cma7/#11, Maj7/#9, Maj7/#5 etc. Each one of these comes from-and calls for-a different scale to use for melodic improvisation and, with regards of GMC, gives a different set of triads to work with.
Regarding the altered sound you hint at in your example about G7…in this case we would think in terms of the G altered scale( that’s the 7th mode of Ab Melodic Minor) and the correct triads would be Abm and Bbm.
It’s a great concept, but requires a good understanding of chord/scales relationships.
But what is the formula?
Two chords,on ii & iii degree of scale,with tonic i in the lowest voice?
Exactly. The root on the bass and two triads built on the ii and iii of any given scale.
And now how can we use this formula musically
to avoid sounding like ordinary exercises?
Let’s start with the c ionian,lydian and mixo - it is not superimposing?
Interesting topic. I was tooling around on the piano yesterday after reading this thread. It’s a thing my teachers brushed upon a little bit in music school but I didn’t really dig into it up until this point.
With some practice and patience it could be a great way to find some obscure voicings and stray away from root-focused playing.
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Uh, by rewriting their book for you? Don’t mean to be a jerk, but that’s the value of their exploration, the musical examples, etudes, play-alongs. You are not getting the full picture avoiding the other chord types they explore, which was the elegance of Goodrick’s discovery. Bringing disparate chord type study together with the simple observation.
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