One thing that all of these songs have in common, besides the use of a single chord, is great melodies. In the absence of one or more elements, the remaining parts of a song get exposed in a way they otherwise wouldn’t, so these melodies had to be extra good in order to carry the tune.
When it comes to great melody pop writing, it often comes down to melodic development inside of single sections and melodic contrast between song sections. Inside of a single section, it’s a good idea to stick to a single motif and either repeat it a number of times or create slight variations of it through techniques like sequencing, extension, and truncation to name a few.
The opening “Oh—” section in “Single Ladies” consists of the same motif repeated verbatim. The second section, which is the first verse, consists of a single motif that gets repeated twice in the first bar and then is extended in the second bar by flipping the motif back around.
There’s a significant contrast between these two sections, mostly in the length of the phrases and where those phrases are placed in the measures. The opening has a pickup that drops onto the downbeat, creating a wave-like motion across the duration of two measures. In the verse, we’re starting right on the downbeat with shorter phrases, which create a sense of forward motion or acceleration.
The moral of the story here is that you need strong and simple melodies that your listener can latch onto in the absence of harmonic structure, as well as strong contrast between sections so your listener doesn’t get lost as to which part of the song they’re in.
That sounds familiar
Certain genres lend themselves to single chord iterations, specifically for those that are culturally rooted in some sort of groove. For instance, lots of funk music is written above a single chord for the verses, and then when you “take it to the bridge” you also take it to the IV chord. Lots of funk centers around the tonic and has more to do with a pocket, or feel, than anything else. In 12-bar blues, eight out of twelve chords are the tonic chord. There’s a strong sense of home throughout, which makes the V-IV turnaround at the end feel especially momentous.
In a more contemporary sense, lots of songs have verse sections, which only contain a single chord, helping to create contrast and a sense of propulsion when harmonic movement is introduced in the chorus. A great example of this done effectively is “Hanging by a Moment” by Lifehouse. Throughout the verse sections, we’re pinned down by a cello playing the tonic notes while the guitar riff plays a repeated pattern above. The lyrics are “desperate for changing,” and the arrangement of this section supports that notion. The protagonist is “hanging by a moment”—a moment that happens when the chorus section smacks us in the face with the vi and V chords.