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I was watching this video where a guy plays Super Mario Bros 2 Overworld theme.

I was wondering if at 0:17s is this a walking bass line or is this counterpoint? and how do you know?

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Ultimately, it's both.

Counterpoint comes from the Latin punctum contra punctum, which just means "note against note." In other words, "counterpoint" is really just a relationship between multiple musical lines. Depending on the musical style, there is a spectrum of rule strictness; a motet by Palestrina, for instance, has much more strict rules than two contrapuntal voices in post-tonal jazz.

The section at 0:17 is a walking bass line. And by virtue of it being played simultaneously with another part, it is in counterpoint with the right hand. As such, this walking bass line is also an example of a contrapuntal relationship between multiple voices.

The two concepts are very much separate, but a walking bass line will typically be counterpointed against another voice, and as such will typically be an example of both concepts.

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