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Table of zeta-stretched edos: Difference between revisions

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<noinclude>This table lists tuning instructions for [[EDO|equal divisions of the octave]] which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: [[the Riemann zeta function and tuning]].
This table lists tuning instructions for [[EDO|equal divisions of the octave]] which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: [[the Riemann zeta function and tuning]].


No such table could possibly be complete (as there are so many possible edos), so please add tunings of interest as you see fit.
No such table could possibly be complete (as there are so many possible edos), so please add tunings of interest as you see fit.
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=== Calculation instructions ===
=== Calculation instructions ===
How to calculate the third column using the free version of Wolfram Cloud:
How to calculate the third column using the free version of Wolfram Cloud:
# Copy-paste <code>Plot{{!(}}Abs{{!(}}RiemannSiegelZ{{!(}}9.06472028x{{))!}}, {{(}}x, 11.9, 12.1{{)}}{{)!}}</code> into a cell.
# Copy-paste <code><nowiki>Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9, 12.1}]</nowiki></code> into a cell.
# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
# Change "'''11.9'''" and "'''12.1'''" to whatever values you want, e.g. to view the curve around 15edo you might use the values "'''14.9'''" and "'''15.1'''".
# Ensure that cell is still selected
# Ensure that cell is still selected
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=== Table ===
=== Table ===
This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
This is a list of zeta peak-based octave tunings, which includes all EDOs up to 100 and certain noteworthy ones above 100.
</noinclude>{| class="wikitable sortable"
{| class="wikitable sortable"
|+ style="font-size: 105%;" | Zeta-optimal tunings for selected EDOs
|+ style="font-size: 105%;" | Zeta-optimal tunings for selected EDOs
|-
! Tuning !! Associated edo !! No. of steps per 1200 cents !! Step size (cents) !! Tuning of 2/1 (cents) !! Gram point index
! Tuning !! Associated edo !! No. of steps per 1200 cents !! Step size (cents) !! Tuning of 2/1 (cents) !! Gram point index
|-
|-
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|-
|-
| [[5818zpi]] || 684edo || 683.939 || 1.755 || 1200.107 || 5816
| [[5818zpi]] || 684edo || 683.939 || 1.755 || 1200.107 || 5816
|}<noinclude>
|}


== See also ==
== See also ==
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[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:Zeta peak indexes]]
[[Category:Zeta peak indexes]]
</noinclude>
Retrieved from "https://en.xen.wiki/w/Table_of_zeta-stretched_edos"