71zpi: Difference between revisions
Contribution (talk | contribs) |
Contribution (talk | contribs) No edit summary |
||
| Line 1,985: | Line 1,985: | ||
|} | |} | ||
== Record on the Riemann zeta function with prime 2 removed == | |||
'''[[71zpi]]''' sets a height record on the Riemann zeta function with prime 2 removed. The previous record is [[53zpi]] and the next one is [[93zpi]]. It is important to highlight that the optimal equal tunings obtained by excluding the prime numbers 2 from the Riemann zeta function differs slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function. | |||
{| class="wikitable" | |||
! colspan="6" |Unmodified Riemann zeta function | |||
! colspan="5" |Riemann zeta function with prime 2 removed | |||
|- | |||
! colspan="3" | Tuning | |||
! colspan="1" |Strength | |||
! colspan="2" |Closest EDO | |||
! colspan="2" |Tuning | |||
! colspan="1" |Strength | |||
! colspan="2" |Closest EDO | |||
|- | |||
!ZPI | |||
!Steps per octave | |||
!Step size (cents) | |||
! colspan="1" | Height | |||
!EDO | |||
!Octave (cents) | |||
!Steps per octave | |||
!Step size (cents) | |||
! colspan="1" |Height | |||
!EDO | |||
!Octave (cents) | |||
|- | |||
|[[53zpi]] | |||
| 16.3979501311478 | |||
|73.1798786069366 | |||
|2.518818 | |||
| [[16edo]] | |||
|1170.87805771099 | |||
| 16.4044889390925 | |||
|73.1507092025500 | |||
|4.100909 | |||
|[[16edo]] | |||
|1170.41134724080 | |||
|- | |||
|[[71zpi]] | |||
|20.2248393119540 | |||
|59.3329806724710 | |||
| 3.531097 | |||
|[[20edo]] | |||
|1186.65961344942 | |||
|20.2459529213541 | |||
|59.2711049295348 | |||
|4.137236 | |||
|[[20edo]] | |||
|1185.42209859070 | |||
|- | |||
| [[93zpi]] | |||
| 24.5782550666850 | |||
|48.8236449961234 | |||
|2.810487 | |||
|[[25edo]] | |||
|1220.59112490308 | |||
|24.5738316304204 | |||
|48.8324335434323 | |||
|4.665720 | |||
|[[25edo]] | |||
|1220.81083858581 | |||
|} | |||
[[Category:Zeta peak indexes]] | [[Category:Zeta peak indexes]] | ||