You probably worked out, the image up there is an example of counterpoint. Well, counterpoint is ruled by one major thing - cadence. A cadence is a series of intervals that end a section of music. However, cadences can be made to clash, and create what is known as a 'dissonated cadential trill'. There are several types of cadence.
1. Perfect Authentic Cadence. This is chords V to I (e.g.: in C it would be G chord to C chord)
3. Imperfect Authentic Cadence. Similar to a PAC, but the V chord can be a diminished vii in first inversion, or the V or I chords ar inverted.
5. Half cadence: any cadence ending on V, whether preceded by ii, IV, or I, or any other chord. Because it sounds incomplete or "suspended", half cadence is considered a weak cadence - the weakest cadence, in fact. A progression of a diminished second in first inversion to V is considered the Phrygian Half Cadence.
6. Plagal cadence: IV to I, also known as the "Amen Cadence" because of its frequent appearance in hymns.
7. Deceptive (or interrupted) cadence: V to any chord except I (typically vi or VI). This is considered a weak cadence because of the "hanging" (suspended) feel it invokes.
Cadences can also be classified by their rhythmic position. A masculine cadence occurs on a strong position, typically the downbeat of a measure. A feminine cadence occurs in a metrically weak position, for instance, after a long appoggiatura (see also feminine ending). Masculine cadences are considered stronger and are generally of greater structural significance. (To avoid offending those sensitive to sex stereotypes, the Society for Music Theory endorses the terms "metrically accented" and "metrically unaccented cadence" in their Guidelines for Nonsexist Language.) Likewise, cadences can be classified as either transient (a pause, like a comma in a sentence, which implies that the piece will go on after a brief lift in the voice) and terminal (more conclusive, like the period or other terminal punctuation, which implies that, at least for the time being, we are done). Most transient cadences are half cadences (which stop momentarily on a dominant chord), though IAC or deceptive cadences are also usually transient, as well as Phrygian cadences. Terminal cadences are usually PAC or sometimes plagal ("Amen") cadences.
Neo-Harmony. You may think it means 'new harmony', which technically it should. However, it in fact represents a certain sequence of notes. It is a sequence in which a certain mode, melody or key is hinted at, but then turned into something else.