One thing I've definitely gained appreciation of from playing jazz is the impressive range of sounds and colours you can achieve with chord extensions. Of course it wasn't always so - I distinctly remember changing keyboard teachers in 2006, and discovering for the first time that the Major 7th was more than just that awful-sounding chord in the keyboard's sequenced accompaniment. A few years later, although I'm by no means a master of chord extensions, there is almost no situation where I don't think to use one.
There are several possible approaches to extending a chord. You might, for example, consider playing a C chord and add an A to get C6, because A is the 6th of C. Alternatively, you might just play an Am7 instead, because it has all the same notes as C6 anyway. This post aims to discuss some of the ways I often think about extending chords.
A fairly simple one to start with. As already mentioned above, playing a chord's relative minor instead automatically adds the 6th - an extension often used in swing, and when you want the chord progression to sound 'finished'. A C chord is CEG, and Am is CEA - you might notice we've lost the 5th (G) here, however we can add that back in by playing Am7 (ACEG).
What happens, however, if you try and do it the other way around? What if, faced with an Am (CEA), you instead play the relative major, C (CEG)? In this case, we've gone the other way, except instead of automatically adding the 6th, we've automatically added the dominant 7th (G). Also instead of losing the 5th, we've actually lost the Root - a rootless chord! These are often used by piano and guitar players in modern jazz, because they help avoid stepping on the bass player's toes, who usually plays the root. As a bonus, let's add the Major 7th to get Cmaj7 (CEGB) - this is the same as a rootless Am9!
I mentioned in a previous post on tritones that a popular way of playing simple jazz chords is to play the 3rd and the Dominant 7th, which are a tritone apart. This gives you a 7th chord right from the start, but you can also get some interesting-sounding chords by adding notes. Below are a few example extensions of C Major:
This way of voicing is popular in jazz organ, where you play the 3rd and 7th with the thumb and index finger and reach up the keyboard to extending notes (this is all in the right hand - the left hand plays a bass line down below. On piano, you'd be able to split this across both hands).
Another approach is to overlay chords on top of each other. If you want an extended C chord, you can play the notes C, E, G, plus any of Bb, D, F and A, depending on whether you want a 7th, 9th, 11th or 13th chord.
Alternatively, you can layer the 'base' 7th chord (C7 - C E G Bb) with its relative II chord (the minor chord two semitones above, i.e. Dm - D F A). Playing these two layered chords gives a fully-voiced C13. You can get different extensions by playing only part of the Dm - you can play only its first two notes (D, F) to get C11, or just the first note (D) to get C9. This way, instead of having to remember all the notes that make up a complex chord, you can just remember two fairly simple chords and layer bits of them together however you want.