Approximating π Using Lower Pi-artials

Last month I offered a post for Pi Day. The idea of intoning the number π as a melody that matches the opening of its infinite decimal (or septimal, duodecimal, etc.) representation remains dependent upon this choice of base. An intonation less dependent on such is simply π as the frequency ratio between two numbers: it sounds like a slightly flat minor thirteenth.

Three years ago my April post demonstrated how to approximate the natural logarithm (e) using musical ratios. This time around I suggest a method to do so for π, using the Wallis product.