Pitch Interactions with Beat and Meter
Pitch elements (such as melodies and harmonies) interact with the beat and meter in particular ways. For example, a fermata indicates that a note or rest should be continued longer than its notated duration, which means that the beat must be paused for a brief time.
When a soloist is permitted to use rubato, he will often slow down the tempo on the peak (highest note) of a phrase to emphasize the climax, or will slow down just before a cadence to prolong the listeners' anticipation of a harmonic and melodic resolution. When his melody descends, a soloist will sometimes speed up, emulating the way an object will gain momentum as it falls.
In terms of meter, both melodies and harmonies follow certain patterns. Melodies often fit neatly within the measures defined by the meter. To put it another way, the lengths of the melodic phrases are compatible with the meter of the piece. Particularly in vocal music, it is very common to find 4-measure phrases, one after the other.
Meter and Phrase Length
melody of "Twinkle, Twinkle Little Star" showing 4-measure phrase lengths
Harmonic Rhythm and Lead Sheets
Harmonies also fit with meters in certain ways. The rate at which harmonies change is known as harmonic rhythm. Just as the rhythms of melodies can fit into the meter, harmonic rhythms often do too. Harmonic rhythm is particularly clear on a lead sheet. A lead sheet is a type of sheet music that shows the melody of a tune as well as the harmonies that should accompany that melody. Lead sheets are very common in jazz and are occasionally used in popular music and elsewhere.
excerpt from "Summertime" by George Gershwin
As you can see in the example above, the melody is notated on the staff and chord symbols are placed above the staff to indicate harmonies. The chord symbols used in lead sheets are different from the Roman numeral system that is often used to analyze chord progressions. The Roman numeral system is used to show the relationships between chords (i and V, for example), but does not tell us which specific pitches appear in those chords (although you can figure this out if you know the key of the piece). For lead sheets, the name of the root pitch is given, which allows us to determine all the specific pitches of the chord (E = E major chord, which consists of E, G-sharp, and B). The other numbers, letters, and symbols that appear in chord symbols tell us the quality of the chord (major, minor, augmented, diminished), additional notes that should be added to the chord (often the pitch that is a 7th above the root), and alterations that should be made to the pitches in the chord (inserting sharps, flats, or naturals).