g melodic minor might make more sense than c major (harmonic series)

Does G melodic minor relate more to the harmonic series of C than most scales?

The harmonic series of C refers to the overtones generated when you play a fundamental C. These overtones are naturally occurring and help define what we perceive as consonance. The harmonic series of C includes notes like:

C  (1st harmonic, fundamental)
C  (2nd harmonic, octave)
G  (3rd harmonic, perfect fifth)
C  (4th harmonic)
E  (5th harmonic, major third)
G  (6th harmonic)
Bb (7th harmonic, but it’s flatter than equal temperament)
C  (8th harmonic)
D  (9th harmonic)
E  (10th harmonic)
F# (11th harmonic, sharper than in equal temperament)
G  (12th harmonic)
A  (13th harmonic)
Bb (14th harmonic, again a bit flat)
B  (15th harmonic)
C  (16th harmonic)

Now, the G melodic minor scale is:

G - A - Bb - C - D - E - F#

Compare this to the harmonic series of C:

It shares G, C, E, A, Bb, F#, and even D appears early in the series.

The G melodic minor scale includes several of the prominent early overtones from the harmonic series of C, particularly:

G   (3rd, 6th, 12th harmonics)
E   (5th, 10th)
Bb  (7th and 14th, though slightly off)
C   (1st, 2nd, 4th, 8th, 16th)
D   (9th)
F#  (11th harmonic-ish — although not exact in equal temperament)

Conclusion

Yes, G melodic minor does align more closely with the harmonic series of C than many other scales — especially because it includes many partials (or close approximations of them), including the somewhat oddballs like F# (11th) and Bb (7th/14th), which are rare in most diatonic scales.

So in a way, G melodic minor “echoes” the color of the C harmonic series more than, say, a C major scale does. It's an excellent observation if you're exploring spectral relationships or tuning theory.