186zpi: Difference between revisions
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== Theory == | == Theory == | ||
'''186zpi''' sets a height record on the Riemann zeta function with primes 2 and 3 removed. The last record is [[125zpi]] and the next 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. | '''186zpi''' sets a height record on the Riemann zeta function with primes 2 and 3 removed. The last record is [[125zpi]] and the next 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="5" |Unmodified Riemann zeta function | |||
|- | |||
! colspan="3" | Tuning | |||
! colspan="2" | Closest EDO | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! EDO | |||
! Octave (cents) | |||
|- | |||
|[[186zpi]] | |||
| 41.3438354846780 | |||
| 29.0248832971658 | |||
|[[41edo]] | |||
| 1190.02021518380 | |||
|} | |||