Structural Analysis
These ideas of structural analysis are Schenkerian in origin, but they can be applied even if one isn't adhering strictly to Schenkerian analysis.
Drone
Here is the first phrase of Dudelsack ("Bagpipe", unknown composer) (YouTube example). In this case, there is a literal drone happening.
Harmonization
But now consider this harmonization of the melody.
Analysis Level 1
Clearly there is no drone. Instead, below is a first-level harmonic analysis.
Analysis Level 2
In m. 1, the strong beats both feature the I chord, while the melody outlines that same chord. The IV chord, then, is clearly a contrapuntal chord connecting I to I, and the vi chord can be viewed as a substitute for I. Thus, the entire first measure can be interpreted as a prolonged tonic harmony. (PT = Passing Tone; APT = Accented Passing Tone.) Similar reasoning allows measure 3 to be interpreted also as a prolonged tonic harmony (ii7 is a passing [i.e., contrapuntal] chord, and iii and vi are substitutes for I).
In measure 2, the V7 chord serves a clearly cadential purpose, while the IV chord on beat 4 is again contrapuntal, connect the beat 3 I chord with the I chord beginning measure 3. Thus measure 2, and measure 4 by similar reasoning, can be interpreted as V7 - I.
This comprises a second-level harmonic/melodic analysis.
Analysis Level 3 – Harmony
Considering the phrase as a whole, there can only be one cadence, and that, naturally, occurs in the final measure. This begs the question of what the V7 chord in measure 2 means – what is its function in the larger phrase. Given the second-level analysis, the measure 2 V7 chord is serving to connect (prolong) the I-chord segments on either side.
Analysis Level 3 – Melody
Given the harmonic structure, one can propose a melodic structure that goes along with it as well as those melodic pitches that support that structure. Ideally, the large-scale melody would be fluid, so here's a proposal. The red notes are the abstract (large-scale) melody, the cyan notes define the principal harmonic pitches, and the small notes are supporting or secondary pitches. (N = Neighbor.)
Full Circle
A formal Schenkerian analysis would look rather different from this, but the basic ideas are present. And looking at the large-scale harmonic analysis, we see that it's nearly the same as the drone from the original version of the piece. In fact, were we to go a step further and remove the requirement of a V-I cadence, then we could view the V7 chord as connecting two segments of I, and our analysis would be exactly the drone version.