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

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Listed the original source of the scales as requested on the XA Discord
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m BudjarnLambeth moved page 5- to 10-tone scales in 47zpi to User:BudjarnLambeth/5- to 10-tone scales in 47zpi: Quality is not yet up to main space standards
 
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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]].
This article lists some 5- to 10-note scales in [[47zpi]] (also known as 15.0535edo, 1ed79.716c, or 79.716cET). The tuning of each scale degree is given in [[cents]].




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




Atoll (this is the original/default tuning)
[[Firedance]] (this is the original/default tuning)
*79.716
* 239.147
*398.578
* 558.010
*478.294
* 717.441
*717.441
* 956.588
*956.588
* 1195.735
*1195.735




[[Aurora scale|Aurora]] (approximated from [[Hexany 1728]])
[[Magnetosphere scale|Magnetosphere]] (approximated from [[Hexany 1728]])


* 159.431
* 159.431
Line 21: Line 34:
* 956.588
* 956.588
* 1195.735
* 1195.735
[[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




Monsoon (this is the original/default tuning)
Monsoon (this is the original/default tuning)
*239.147
* 239.147
*478.294
* 478.294
*717.441
* 717.441
*1036.304
* 1036.304
*1195.735
* 1195.735




[[Porcupine]][6] MOS
[[Porcupine]][6] MOS
*398.578
* 398.578
*558.010
* 558.010
*717.441
* 717.441
*876.872
* 876.872
*1036.304
* 1036.304
*1195.735
* 1195.735




Rockpool (this is the original/default tuning)
Rockpool (this is the original/default tuning)
*398.578
* 79.716
*478.294
* 398.578
*717.441
* 478.294
*956.588
* 717.441
*1195.735
* 956.588
* 1195.735




In case you wish to create your own scales from 15.0535edo, here is the full list of intervals available:
In case you wish to create your own scales from 15.0535edo, here is the full list of intervals available:
*79.716
* 79.716
*159.431
* 159.431
*239.147
* 239.147
*318.863
* 318.863
*398.578
* 398.578
*478.294
* 478.294
*558.010
* 558.010
*637.725
* 637.725
*717.441
* 717.441
*797.157
* 797.157
*876.872
* 876.872
*956.588
* 956.588
*1036.304
* 1036.304
*1116.020
* 1116.020
*1195.735
* 1195.735


= See also =
= See also =
* [[The Riemann Zeta Function and Tuning]]
* [[Zeta peak index]] (zpi)
* [[The Riemann zeta function and tuning]]




Line 99: Line 89:




* [[5- to 10-tone scales in 30edo]]
* [[5- to 10-tone scales in 60edo]]
* [[5- to 10-tone scales in 60edo]]
* [[5- to 10-tone scales in 84edo]]
* [[5- to 10-tone scales in 84edo]]
Line 110: Line 99:


[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:15edo]]
[[Category:Zeta]]
[[Category:5-tone scales]]
[[Category:5-tone scales]]
[[Category:6-tone scales]]
[[Category:6-tone scales]]
[[Category:15edo]]
{{Todo| cleanup | review }}

Latest revision as of 03:45, 4 September 2025

This article lists some 5- to 10-note scales in 47zpi (also known as 15.0535edo, 1ed79.716c, or 79.716cET). 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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