Second-species counterpoint (i.e. two-to-one counterpoint) involves two tones in one part to one tone in the other parts.
Strong beats (downbeats) in second species are always consonant. As in first species, imperfect consonances (thirds and sixths) are preferable to to perfect consonances (fifths and octaves).
Dissonant intervals (e.g. dim 5ths, sevenths, etc.) may be used on weak beats (off beats) if they move by a major or minor second.
The following piece is an example of second-species counterpoint in E Phrygian:
And the first eight measures of the next piece is an example of 2:1 counterpoint using the E pentatonic scale.