If you've never heard the term UST (upper strucure triads) you probably wouldn't want to read this piece unless your current playing/reading level is intermediate to advanced, in which case: you should read it.
USTs is a great device for improvising and comping. UST is short for Upper Structure Triad which in a few words is a triadic structure that is a subset (substructure) of the "current structure". USTs work really well in any song and/or style but they're not the only structures that can be superimposed against others. In fact, as we will see later, any structure that is a subset of the current structure can be successfully superimposed.
What is a structure? A structure is any collection of pitches. No rules will be imposed to these collections. Any collection is valid. Any subset of that collection is a substructure of that main or source structure.
e.g. The C major scale is a collection of pitches => it's a structure. The notes C-D-F-B are a subset of the C major scales => that set is a substructure of the C major Scale. C-E-G is another subset of the C major scale and is also a triad => it's a triadic substructure of the C major scale.
How do you use these substructures? Actually, it is very simple:
Choose a substructure of the "current structure" and improvise or comp with it.
It sounds easy but: How do you know which one is the "current structure"? and how do you choose a substructure? These are not easy questions to tackle. There are so many factors to account for regarding these matters that the answers to these questions are almost subjective.
Determining the "Current Structure"
In order to find the current structure, one must be able to analyze the harmonic progression of the piece. Assuming the piece is tonal/functional, the analysis should be pretty easy to realize (if you know tonal harmony theory)
In functional harmony every chord has a function which implies a scale that fits best.
For example:
1. The I chord in a major tonal key takes Ionian, since I is always associated to the Ionian scale. In this case Ionian is your "current structure".
2. The V7/ii chord in a major key takes Mixolydian b13, since a V is always asscociated to some form of the Mixolydian scale. In this case, the V7/ii is a dominant of a minor chord that takes Dorian, therefore the 3rd of that chord is minor and the 6th is major which superimposed with the V7/ii chord gives us a 9 an 11 and a b13 => Mixo b13.
Here's an example in C: The ii is D minor which takes Dorian. The V/ii is an A7 chord.
If we look at A7 mixo (A-B-C#-D-E-F#-G) we have A C# E G (1-3-5-b7) as chord tones and B D F# as tensions (or extensions of the chord 9-11-13). Only two of the notes are not in D Dorian: C# and F#. We must keep all chord tones to have an A7 chord, therefore we can't change C# to C, but we can change F# to F (which gives us Mixo b13) and fits D Dorian best.
As you can see it is not too hard to find the associated scale (the "current structure") for a certain function (if you know your harmony and your modes).
Choosing a substructure of the current structure
It's all subjective. Any subset of the current structure is available.
How do you choose?... You use your ears and your taste. Every structure (or substructure) has a color (a sound) produced by the combination of note-intervals embedded in it.
For example: the structure C E (2 note structure) is only an interval of a major 3rd (or 2 if you consider the inversion E to C which is a minor 6th) when played it gives us a color.
Why are triads so often used?... Triads have a very distinct color (sound) that has been invading our ears all our lives, therefore they are recognizable entities even against other structures. We can always tell them apart because we have unconsciously trained our ears to feel at home with them.
