They are more like ordinals than "math" numbers the way you're thinking. It's the fifth scale degree, not 5 of something.
The 11/12 contradiction, or seven notes in an octave too, is just because it's essentially 1-indexed. Interestingly indian classical music is distantly related through the shared proto-indo-european cultural history but counts it differently. They call the octave the saptak, etymologically related to the "sept" root for seven in romance languages.
The 11/12 contradiction, or seven notes in an octave too, is just because it's essentially 1-indexed. Interestingly indian classical music is distantly related through the shared proto-indo-european cultural history but counts it differently. They call the octave the saptak, etymologically related to the "sept" root for seven in romance languages.