Table of zeta-stretched edos: Difference between revisions
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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: [[ | 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: [[Riemann zeta function]]. | ||
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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All of the tunings listed on this page are [[zeta peak index]] tunings, e.g. 1zpi, 2zpi, 3zpi... However, not all zeta peak index tunings are listed here - only those with intervals close to the octave. For a more complete table see: [[zeta peak index]]. | All of the tunings listed on this page are [[zeta peak index]] tunings, e.g. 1zpi, 2zpi, 3zpi... However, not all zeta peak index tunings are listed here - only those with intervals close to the octave. For a more complete table see: [[zeta peak index]]. | ||
== 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. | ||
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=== Record zeta peaks | == Calculation instructions == | ||
The third column of the above table can be calculated using the free version of Wolfram Cloud: | |||
# 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'''". | |||
# Ensure that cell is still selected | |||
# In the menu select Evaluation > Evaluate Cells | |||
== Record zeta peaks == | |||
<pre> | <pre> | ||
0.00000 | 0.00000 | ||
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== See also == | == See also == | ||
* [[Zeta peak index]] | * [[Zeta peak index]] | ||
* [[ | * [[User:Contribution/Gallery of Zeta Peak Indexes at sigma = 1|Zeta Peak Indexes at sigma = 1]] | ||
* [[Riemann zeta function]] | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
[[Category:Zeta peak indexes]] | [[Category:Zeta peak indexes]] | ||