Here are the triads and chords:
Major, minor, sus2 and sus4 triads and chords.
Major 7th, flat 7th and minor 7th chords.
9th, min 9th, maj 9th, 11th, min 11th, maj 11th, 13th, min 13th, maj 13th chords.
All other chords fall into the series of chords with 'added' notes or chords with altered notes.
Added chords
Chords with 'added' notes are just what they sound like. They are usually written as something like Cadd2, Cadd4 etc.
Simply start with the 'base' chord (C in this example) and add the appropriate note. You can of course add to any 'base' chord whether it's major or minor or whatever.
Be sure you understand the difference between add2 and sus2 chords, and add4 and sus4 chords - the sus chords have the 3rd replaced with another note. The 'add' chords simply add to the triad, so Cadd2 would be:
Cadd2 = C triad + 2nd = 1st, 2nd, maj 3rd, 5th
Csus2 = Csus2 triad = 1st, 2nd, 5th
Similarly there is an important difference between 'add9' and '9' chords. A C9 chord must have the flat 7th in it (see above), but the Cadd9 chord will not - it's just a C major triad with a 9th added.
You can carry on adding as many notes as you want. If you play around with alternative tunings you could quite easily come across chords like Aadd2add4, but most of the time you'll just have one added note.
You can of course add a note to a chord that isn't a simple major or minor chord - you can have things like Csus4add9 etc.
Altered chords
These are chords with chromatic alterations. The 5th, 2nd, 4th, 9th etc can all be chromatically altered - i.e. moved up or down by a semitone (half step).
Examples of this are chords like E7#9 and E7b9. The 9th of a normal E9 chord has been sharpened in the E7#9, and flattened in the E7b9.
So what are the notes for these?
Well, starting with the 'E7' bit:
E7 = 1st, maj 3rd, 5th, flat 7th = E, G#, B, D
Now add the #9 (count up 15 semitones from E) - G.
So E7#9 = E G# B D G.
Similarly E7b9 = E G# B D F.
There are a few different ways to write these chords.
'-' and '+' signs are sometimes used to mean 'flat' and 'sharp' respectively, but 'b' and '#' are used as well.
You might even see 'dim' and 'aug' (diminished and augmented) used too for the same thing.
So E7#9 could be written as E7+9 or E7aug9, and E7b9 could be written as E7-9 or E7dim9.
With these chromatically altered chords there is almost no limit on the number of chords you can create - most of these will be used in jazz, but some (like the E7#9) appear quite a lot in rock music too.
To work out the notes to these types of chord it's best to start with the 'basic' chord, then add the chromatic notes to this. So, as above for E7#9, start with E7, then add the #9.
You may find several chromatic notes in one chord - like A13b5b9 - treat it just the same way - build up the A13 chord, then swap the 5th and 9th for the flat 5th and flat 9th.
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