User:BudjarnLambeth/5- to 10-tone scales in 47zpi: Difference between revisions

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Mentioned that zeta 15edo is the same scale as 47zpi
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The Riemann Siegel Z function has a local maximum close to 15.0535. One way to interpret this is to say that "15.0535edo" is the [[zeta]] stretched version of [[15edo]]. This gives us a tuning very similar to 15edo, but with closer approximations of most just intervals, especially [[3/2]].
The Riemann Siegel Z function has a local maximum close to 15.0535. One way to interpret this is to say that "15.0535edo" is the [[zeta]] stretched version of [[15edo]]. This gives us a tuning very similar to 15edo, but with closer approximations of most just intervals, especially [[3/2]].
Another way to describe this tuning is [[47zpi]], the 47th [[zeta peak index]] tuning.




Revision as of 23:13, 29 March 2024

The Riemann Siegel Z function has a local maximum close to 15.0535. One way to interpret this is to say that "15.0535edo" is the zeta stretched version of 15edo. This gives us a tuning very similar to 15edo, but with closer approximations of most just intervals, especially 3/2.


Another way to describe this tuning is 47zpi, the 47th zeta peak index tuning.


This article lists some 5- to 10-note scales in 15.0535edo. The tuning of each scale degree is given in cents.


Augmented[6] MOS

  • 318.863
  • 398.578
  • 717.441
  • 797.157
  • 1116.020
  • 1195.735


Equipentatonic (Approximated from 5edo)

  • 239.147
  • 478.294
  • 717.441
  • 956.5881
  • 1195.735


Firedance (this is the original/default tuning)

  • 239.147
  • 558.010
  • 717.441
  • 956.588
  • 1195.735


Magnetosphere (approximated from Hexany 1728)

  • 159.431
  • 398.578
  • 717.441
  • 956.588
  • 1195.735


Monsoon (this is the original/default tuning)

  • 239.147
  • 478.294
  • 717.441
  • 1036.304
  • 1195.735


Porcupine[6] MOS

  • 398.578
  • 558.010
  • 717.441
  • 876.872
  • 1036.304
  • 1195.735


Rockpool (this is the original/default tuning)

  • 79.716
  • 398.578
  • 478.294
  • 717.441
  • 956.588
  • 1195.735


In case you wish to create your own scales from 15.0535edo, here is the full list of intervals available:

  • 79.716
  • 159.431
  • 239.147
  • 318.863
  • 398.578
  • 478.294
  • 558.010
  • 637.725
  • 717.441
  • 797.157
  • 876.872
  • 956.588
  • 1036.304
  • 1116.020
  • 1195.735

See also




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