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Why does the relative minor begin on the sixth note of the major scale?

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The relative minor begins on the sixth note of the major scale because relative keys are defined by sharing the exact same key signature and the same collection of notes.1

In Western music, a major scale and its relative minor are composed of the same seven pitches, simply starting from a different tonic or initial note. Because the natural minor scale pattern requires a specific sequence of whole and half steps, starting on the sixth degree of a major scale naturally aligns those intervals to create the minor tonality while utilizing the identical set of notes found in the major scale.1

For example, in the C major scale (C-D-E-F-G-A-B-C), the sixth note is A. By starting on A and playing the same notes (A-B-C-D-E-F-G-A), you produce the A natural minor scale. This relationship is a fundamental aspect of modern music theory, distinguishing relative keys from parallel keys, which share the same tonic but have different key signatures.1