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The Major scale is not the only scale type from which we can extract related chords.
We can repeat the process described above for any scale type, in any key. Each different scale type yields a different pattern of related chords.
For example, C Melodic Minor differs from C Major in having a third note of Eb, rather than E. Thus the first related chord we find is Cm (=C+Eb+G) rather than Cmaj.

In fact, this one different note changes several of the related chords, as you see from the table below.

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