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"
{| class="wikitable"
! colspan="5" |Unmodified Riemann zeta function
! colspan="5" |Unmodified Riemann zeta function
! colspan="5" |Riemann zeta function with primes 2 and 3 removed
|-
|-
! colspan="3" | Tuning
! colspan="2" | Closest EDO
! colspan="3" | Tuning
! colspan="3" | Tuning
! colspan="2" | Closest EDO
! colspan="2" | Closest EDO
|-
|-
! ZPI
! Steps per octave
! Step size (cents)
! EDO
! Octave (cents)
! ZPI
! ZPI
! Steps per octave
! Steps per octave
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! Octave (cents)
! Octave (cents)
|-
|-
|[[186zpi]]
| [[186zpi]]
| 41.3438354846780
| 29.0248832971658
| [[41edo]]
| 1190.02021518380
| [[186zpi]]
| 41.3438354846780
| 41.3438354846780
| 29.0248832971658
| 29.0248832971658
|[[41edo]]
| [[41edo]]
| 1190.02021518380
| 1190.02021518380
|}
|}