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Songs have chord progressions - different chords played in a sequence repeatedly [mostly]. These chords don't belong to a single scale [usually]; they belong to different scales.

As I gather along, learning chords and chord progression is the key to playing songs on piano.

Where does the practice of scales fit in? Does it only help in finding the keys of the chords in the beginning?

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If you're talking about Western music, the chords underlying songs WILL belong to the same key/scale. It is a basic tenet of most of these songs that that happens. Take, for example, a song in Cmaj. The chords that will fit it will have come mainly, if not exclusively, from the Cmaj. scale. As in C,D,E,F,G,A,and B. the 3 majors all use some of these notes, as do the 3 minors. The other chord (Bm7b5) is not so common, but also uses some of these notes, but no others.Occasionally, a tune may modulate, and in C, the extra note is often F#. O.K., it's not in key, but it won't be, because neither is the tune at that place.

Answering the second question - a scale is just an ordered list of the available notes. A bit like a dictionary is a list of words in a particular order, or the alphabet is... I hope you understand.Those notes, just like those chords, will work well in a specific key, so knowing them as a discrete group will help when one plays in that particular key.

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