Melodies are made up of a stream of short thematic cells. Longer melodic segments are typically made up of these cells.

Motive:

The shortest idea to have detectable closure and identifiable content. Repeated thematically in a melody, repetitions are often modifications of the original idea. Vivid ideas are typically placed in melody while less vivid motives are used in background patterns.

A thematic cell with detectable closure. Used to build sub-phrases and phrases. A melody usually consists of repetitions of one or two motive ideas. A figure is like a motive but has less thematic impact and less distinct closure. Used repetitiously in accompaniments or perpetual motion lines.
See Motive Variants.

Cadence:

Punctuation-like closure, varied in conclusiveness like the comma, semi-colon, colon, period, and so on in language. Standard cadences are authentic (AC), perfect authentic (PAC), semi (SC), plagal (PC), deceptive (DC). An elision occurs if the closing note of one phrase coincides with the first down beat of the following phrase, an overlapping. Cadences articulate form. The punctuation strength of a cadence helps to form the multi-phrase patterns of the melody.

Phrase:

Made up of motives, the shortest idea to have punctuation-like closure (a cadence).

A self-contained melodic unit punctuated by a cadence. In common practice music, most phrases are reducible to a simple harmonic gesture like I-V, or V-I. Phrase are a few bars long (2, 3, 4, etc). Two- and four-bar phrases are common but not the rule. A series of phrases need not be equal in length. Mozart, for example, uses two "shorts" and a "long" in some of his melodies.

Sub-phrase (phraselet):

Some phrases have detectable divisions made of two or so motives. A sub-phrase might consist of two or three motives, or be a particularly long motive with stronger than usual closure.

Phrase extension:

Once the composers establishes a phrase length, it can be extended in the up-beat, body, or cadence portions of the phrase.

Parallel construction:

Ideas of one phrase repeated in another.

Asymmetrical:

Phrases not equal in length.

Repeated phrase:

A phrase followed by its copy or ornamented copy.

Phrase-group:

Any grouping of phrases defined by a terminal cadence. Periods and double periods are phrase groups with special properties. A succession of two or more phrases analgous to a compound sentence in language. Ends in a terminal cadence.

Period:

A special case of a phrase-group. A pair of complementary phrases, in an antecedent-consequent relationship, cadence of first phrase is "open" (HC) and the second is "closed" (AC or PAC).

Double-Period:

Like a repeated period only the cadence of the first consequent phrase is not AC or PAC. first and third and second and fourth phrases in parallel construction.

Analysis Signs for phrase forms through double periods

Awareness of the phrase, its parts, its length, and its relationship to other phrases in the continuity of ideas is extremely important to the creation, interpretation or performance of music.Methods of joining and combining units vary from piece to piece, composer to composer, style to style, and so on. These contribute greatly to the individuality of a melody.

Caveat: Be aware that not all sources agree on the definition of music terms. Indeed some sources may appear to contradict others.