Chords with missing 3rds or 5ths

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Most classically trained musicians tend to think in terms of triads.  They look for the three main notes of a chord (1, 3, and 5).  However, the more advanced your chords get, the more likely it is that either the 3 or 5 (or both) will be missing from your chords.  Here is an example:

This is a Amin7 chord even though the 5th (E) is not there.  G does not belong in the Amin triad but is the 7th of the chord.

Here is a tip for you.  When you want to identify a chord, start with the assumption that the bass note is the name of the chord and go from there.  You can identify all other notes in their relation to the root.  If you do that, chords like this one will not fool you:

This is C major chord.  The bass note is a C, and you can also easily see the E and G.  The other two notes are the major 7th and a 9th.  Technically, you could label this chord Emin7/C, but CMaj7(9) makes more sense to me. (I will explain what a major 7th is later and how it is different from the more common dominant 7th.)