186zpi: Difference between revisions

'''186 zeta peak index''' (abbreviated '''186zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 186st [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].

== Theory ==

=== Record on the Riemann zeta function with primes 2 and 3 removed ===

'''186zpi''' sets a height record on the Riemann zeta function with primes 2 and 3 removed. The previous record is [[125zpi]] and the next one is [[565zpi]]. It is important to highlight that the optimal equal tunings obtained by excluding the prime numbers 2 and 3 from the Riemann zeta function differs very slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function.

{| class="wikitable"

|-

! colspan="3" | Tuning

| 30.6006474885974

| 39.2148564976330

| [[31edo]]

| 1215.66055142662

| 30.5974484926723

| 39.2189564527704

| [[31edo]]

| 1215.78765003588

|-

|-

|}