The add2 chord is very similar to the add9 chord; the notes are in fact the same, but the difference is that the add2 and the add9 notes belong to different octaves. A common major chord includes the first, the third and the fifth notes in its scale. By adding the second note, you get an add2 chord.
So if C major is used as an example, what happen is that C, E and G changes to C, D, E and G.
Notice that sometimes the exactly same fingerings are used for add9 chords. The ambition is to present two different chords with the correct order of notes, but you will be okay if you use an add2 chord instead of Add9 or vice versa.
To explain the difference between these, we could compare Eadd2 with Eadd9. The added note is in this case F#. In Eadd2, the F# is played as the third tone when strumming down strokes. In Eadd9 the F# tone is played as the last tone when strumming down strokes. The difference is in other words small, you can hear some change in the timbre, but if you feel you don't want to memorize both shapes it's alright to use the same shape in all situations when any Eadd chord is indicated.
Sometimes these chords are just referred to with the number two in the chord name, as C2, D2, E2 and so on.
The Badd2 chord has no easy fingering. An alternative to the pictured chord is X2464X. Dadd2 can also be played as XX4230 (Dadd2/F#).
Chord progressions with add2 chord
Some examples of progressions using add2 chords:
C - Cadd2 – Fadd2
C – Cadd2 – D
Aadd2 – D6 – Emaj7
Minor add chords
Less common is the minor add chords.
The minor add2 is close related to the minor add9 and are in a sense equivalent. Yet, if you are meticulous with the sound, you probably want the added tone closer to the root note when choosing minor add2 instead for minor add9.
Chord progressions with minor add chord
A progression using minor add2 chords:
Em – Emadd2 – Am – Amsus4
Existing, but quite uncommon is the related add4.
Some examples in short notation: