What types of chords are used in classical music?

[gabriels]

I know M7 chords like C-E-G-B are rarely used in classical music, whereas m7 like C-Eb-G-Bb more used and dominant chords like C-E-G-Bb much more used than m7.

What are the types of chords used in classical music? Are chords with 6th, 4th, 2nd, 9th, 11th, 13th, 15th, sus2, sus4, aug used? How often?

Besides, I would like to know specifically what notes are usually removed from the chords. For example, C-E-G-B-D could be written as C-B-D.

[lelle]

All of those chords appear in classical music, frequency depends on era. More colorful chords appear with increasing frequency in the romantic era. But even Bach could get to some pretty crunchy harmonies along the way. In traditional harmony, they will be seen as dissonances that need to be resolved to consonant (or at least more consonant) chords. You'll often arrive to certain more dissonant chords via traditional voice leading, and at the very least resolve them via voice leading. And even if you make an excursion into tension and dissonance, you eventually resolve everything back to basic triads without decoration.

The note you can most commonly leave out is the fifth, because it's the root and the third that gives a particular chord its fundamental character.

By the time of Debussy these rules started to be broken more and more, and composers started using unresolved dissonance and depart from functional harmony and traditional voice leading alltogether.

[brogers70]

I know M7 chords like C-E-G-B are rarely used in classical music, whereas m7 like C-Eb-G-Bb more used and dominant chords like C-E-G-Bb much more used than m7.

It's true that major seventh chords are not used that much in the classical period, but it's not never. There's a very memorable circle of fifths progression in Mozart's K332 piano sonata that uses a couple of them to good effect (in the third and fourth measures of the excerpt here).