What is a term for 3 or more musical pitches sounded simultaneously?

Typically, when two or more pitches are sounded together, we identify the sound as "harmony". Depending on the character of this harmony, we can further describe the sound as "consonant" (meaning, "sounding good together"), or "dissonant".

Consonant harmonies typically consist of the perfect intervals (unisons, octaves, fourths, and fifths), as well as thirds and sixths (major and minor).

Dissonant intervals range from strong dissonances (such as the minor second and major seventh, as well as the augmented fourth), to lesser dissonances such as the minor seventh.