Lately I have been working with improvising using triad pairs. I like the sound this intervalic approach creates. There are several books which cover this topic but this is the way I think of them.
Start by taking to major triads a major second apart: F triad and G Triad, for example. Play them in a line like the following:
FAC GBD ACF BDG CFA DBG FAC etc.
You will start alternating all of the inversions of the triads and creating an intervalic line. Furthermore these triad pairs can be used over a variety of chords to create different sounds. For example:
F Major 7th: FAC and GBD give the root, 3rd, 5th, 9th, #11th, and 6th (the lydian soud). The triad pair is built on the root of the F major 7th chord.
C major 7th: FAC and GBD give the 5th, 7th, 9th, 4th, 6th, and the root (the major sound). The triad pair is built on the 5th of the C major cord.
D minor 7th: FAC and GBD give the 4th, 6th, root, 3rd, 5th, and 7th (the dorian sound). The triad pair is built on the minor third.
E minor 7th: FAC and GBD give the flat 9th, 4th, flat 6th, 3rd, 5th, and 7th (the phrygian sound). The triad pair is build on the lowered 9th.
A minor 7th: FAC and GBD give the flat 6th, root, 3rd, 7th, 9th, 4th (the aeolian sound). The triad pair is built on the lowered 6th.
F dominant 7th: FAC and GBD give the root, 3rd, 5th, 9th, #11th, and 6th (the lydian dominant sound soud). The triad pair is built on the root of the F major 7th chord.
G dominant 7th: FAC and GBD give the 7th, 9th, 4th, root, 3rd, and 5th (the mixolydian sound). The triad pair is build on the 7th.
B dominant 7th: FAC and GBD give the #4th, 7th, flat 9th, flat 6th, rood, and #9th (the altered sound). The triad pair is build on the #4th.
B half diminished: FAC and GBD give the 5th, 7th, 9th, 6th, rood, and 3rd (the locrain sound). The triad pair is build on the 5th.
There are some ways to use triad pairs. You can get alot of mileage out of pairs of major triads. I amsure that there are other ways to use them but these are the ones that make the most sense to me. Please add your comments or personal approaches to using triad pairs.
Scott, that is an interesting pattern. Since it has eight of the twelve possible notes, it is highly chromatic and I am not sure if it has a specific name but it does give a cool sound. At first glance I thought it was three sets of perfect foruths separated by minor thirds but the Eb in the third group of notes changes this. So, the pattern is not transpositonally equivelant like diminished 7th chords or whole tone scales. Like the major scales, there are twelve different transpositions of this pattern.
As for application, I would probably play it over a C-7 chord or a C7sus4 chord. Lets take a look at the pattern:
C-F-Bb Eb-Ab-Db Gb-B-Eb C-F-Bb
Notice there are three different three note groups. The first one C-F-Bb is made up of the root, fourth, and seventh of C-7 (the fourth sounds really good over a minor chord) and C7sus4.
The second group is the thrid, lowered sixth, and lowered ninth of the C-7; it creates a phrygian sound over the C-7 chord. Over the C7sus4 it provides altered tones (which work because a C7sus4 serves as a dominant chord): Eb is the #9, Ab is the #5, and Db is the b9.
The third group is where things go outside because the B natural clashes with Bb whcich is the 7th of both chords. The Gb clashes with G in the C-7 (G is the fifth of C-7). With the C7sus4 the Gb clashes with the F which is the 4th of the C7sus4 chord. The Eb works with both chords, it is the third of the C-7 and the #9th of the C7sus4.
This is a pattern I would probably use on modal tunes (ones where the chords last for several measures) like Impressions, Maiden Voyage, Mr. Clean, etc. I would recommend using this on modal tunes because you have to resolve a line like this. You would need to resolve this back to where you started so you don't sound like you aren't sure of the harmony. I would also voice lead it to make the movement from group to group sound fluid, for example:
This way you are creating a line that moves outside of the key and clearly resolves back to the original chord.
The E-natural makes it a pattern based on symmetrical division of the octave. The type of lines you will find in Chapter three of The Thesaurus of Scales and Melodic patterns by Nicolas Slonimsky. This pattern is three note sets of perfect fourths all a minor third apart. This pattern (like many of the ones in the Slonimsky book) is transpositionally equivelant, that is whether you start C, Eb, Gb, or A, the pattern is the same. This pattern does make sense to me. It is comletely chromatic as it contain all 12 notes. Essentially, it is a chromatic scale arranged in perfect fourths. I would use it the same way I would the other pattern and use it on C-7 or C7sus4. But, since it incorporates summetrical division of the the octave and transpositonal equivelance, you can use it on Eb-7, Gb-7, and A-7 as well as Eb7sus4, Gb7sus4, and A7sus4. But, since we are dealing with perfect foruths, it falls out of the realm of triad pairs.