Extensions
Right now we have triads and seventh chords. But surely we can make chords with more than four notes, right? Of course we can! When additional notes are added onto our basic chord forms, the additional notes are called extensions. Extensions are named after the scale degree which is added.
To review, triads contain the root, 3rd and 5th scale degrees. Seventh chords are the addition of a 7th degree to a triad. That leaves the 2nd, 4th, and 6th degrees as our possible extensions.
The confusing part for most people is why we see chords like C13 or G11 when we only have 7 notes in a scale. Where does 13 or 11 come from? The answer is simple: if there is already a 7th in the chord, the scale numbers continue to increase for continuity. Therefore, the 2nd 4th and 6th become the 9th, 11th, and 13th scale degrees. If there is not a 7th in the chord, however, we simply call the extensions 2nds, 4ths, and 6ths. Basically, if you see a number higher than 7th, the 7th is implied. It is also important to note that if you see a C13, for example, not only is the 7th implied, but also the 9th and the 11th. Unless specifically stated with an "add," all scale degrees below the one given are fair game.
For example: if you want a C7 chord with an A note as well, you would write C7 add 13. In contrast, if you write C13 you in fact are implying a C7 chord with a 9, 11, and 13 in the harmony. Understand that this style of chord playing is heavily geared towards the keyboard. As guitar players, having only six strings, we obviously only have the ability to play 6 notes at a time. It is therefore commonplace for guitar players to play C7 add 13 when they see C13. It is also common to omit the 5th when making complex chords because omitting the 5th has no effect on our chords tonality and it frees up fingers to grab more notes that will impact our chords tonality. As long as you get the root, 3rd, 7th, and the stated extension, you are in business!
Lastly,
If major or minor isn’t stated, it is implied that the extension is over a dominant 7th chord.
C13 = C7 + 9 + 11 + 13 (C E G Bb D F A
If you see minor it is implied that the extension is over a minor 7 chord.
C minor 13 = Cmi7 + 9 + 11 + 13 (C Eb G Bb D F A)
If you see major it is implied that the extension is over a major 7 chord.
C major 13 = Cma7 + 9 +11 + 13 (C E G B D F A)
There are many different chords that can be made and it would be futile to explain every possible option, but below is a chart of extended chords commonly played by guitar players. There will be future lessons on specific ones, but for now, just be sure you understand the concept of extensions, how to notate them, what to call them, and how to build them on the neck.