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.