The Riemann zeta function and tuning: Difference between revisions
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\abs{ \zeta(s) }^2 = \sum_{n,d} \frac{\cos\left(t \ln\left({\tfrac{n}{d}}\right)\right)}{(nd)^{\sigma}}</math> | \abs{ \zeta(s) }^2 = \sum_{n,d} \frac{\cos\left(t \ln\left({\tfrac{n}{d}}\right)\right)}{(nd)^{\sigma}}</math> | ||
Finally, by making the mysterious substitution {{nowrap|''t'' {{=}} {{sfrac|2π|ln(2)}} ''x''}}, the musical implications of the above will start to reveal themselves: | Finally, by making the mysterious substitution {{nowrap|''t'' {{=}} {{sfrac|2π|ln(2)}}''x''}}, the musical implications of the above will start to reveal themselves: | ||
<math> \displaystyle | <math> \displaystyle | ||