My understanding is that the same sorts of scales (logarithmic, with any frequency f and f*2^n treated as equivalent pitches, usually with five or eight tones per octave, occasionally more) have arisen independently in just about every human culture, usually without a mathematical theory. I could be wrong, though.
That's where the math came in to it.
That other German 'dude' J.S. Bach then proceeded to cover the new possibilities exhaustively, see the music in the volume of the same name. The enormous jump music made in the relatively short span of 15 years or so during which this all happened is still quite unbelievable.
The irony of the pre-eminenct, western-only centered historical-musical view surrounding a McFerrin melody is thick as molasses. It's West African in rhythm, choral response, scale and spirit.