Without digging into any math myself, I find it curious that it's 1/12th longer. That specific ratio, 1/12th, is also the basis for the Equal Temperament system

Without digging into any math myself, I find it curious that it's 1/12th longer. That specific ratio, 1/12th, is also the basis for the Equal Temperament system for tuning Western musical instruments ("12-tone Equal Temperament, specifically), which also represents a harmonic series. https://en.wikipedia.org/wiki/Equal_temperament https://en.wikipedia.org/wiki/Equal_temperament