When you perform a harmonic analysis, you are attempting to explain how a listener hears a harmonic progression and why it sounds either functional or non-functional to that person. To do so, we rely on our understanding of diatonic tendencies and voice-leading to explain likely listener interpretations, in the same way that a composer relies on their musical knowledge to elicit a desired reaction from a listener.
Once we go beyond looking at the fundamental aspects of music – rhythm, intervals, chords, keys, etc. – and begin combining these concepts to analyze function, we must begin to organize music into structures that combine rhythm, pitch, and timbre into complete musical ideas.
A motive is the smallest identifiable fragment of music. It can be a short melodic fragment, a short harmonic progression, a distinct rhythm, or a combination of these things. A composer can take a motive and build an entire work around it through various transformations, but it will always retain some fundamental relationships of pitch, rhythm, or both.
A phrase is the complete musical idea built to support a motive. The most common analogy used to describe a phrase is to compare it to a “musical sentence”. A good written or verbal sentence has a clear beginning, middle, and end. It has a few required structures and often some decorative parts to provide more specific function. This is exactly how a musical phrase works. It has a clear beginning, middle, and end; it has required structures to define its function; and it can be manipulated, decorated, and transformed to relate to the ideas that surround it. Phrases can sometimes be divided into sub-phrases, but these sub-phrases do not function independently; instead, sub-phrases are best thought of as motives with their supporting textures.