I've noticed that in most, nearly all, popular music, the part that the singer sings usually follows the same pattern. Each bar has an emphasized note, and the same three notes are repeated in a specific pattern over and over.
Middle, High, Middle, Low, Middle, High, Middle, Low...
For example, Amazing Grace, C is the middle note, E above that is the high note, and G below the C is the low note. The whole melody is mostly C E C G C E C G C etc etc.
Is there a name for this pattern?
Also, is it always I III I V I III I V I III?