What is a melodic interval?

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A melodic interval is the distance between two pitches heard in succession, meaning one after the other as you move through a melodic line. This focuses on how a melody moves from one note to the next over time. When two pitches sound at the same time, that’s a harmonic interval, which relates to chords and harmony rather than a single melodic motion. The other descriptions either refer to a general interval concept, or to simultaneity, or to notes in a chord, none of which capture the sequential nature of a melodic interval. So, describing two pitches that occur in succession matches the idea of a melodic interval.