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

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Created an article listing some 5 to 8 note scales from zeta stretched 15edo. I noticed in Wikifuture that one of the suggestions was to describe more 5 to 10 note scales, so I thought this may help with that a little.
 
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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 [[Zeta]] 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 8-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




Atoll
Equipentatonic (Approximated from [[5edo]])
79.716
* 239.147
398.578
* 478.294
478.294
* 717.441
717.441
* 956.5881
956.588
* 1195.735
1195.735




Augmented
[[Firedance]] (this is the original/default tuning)
318.863
* 239.147
398.578
* 558.010
717.441
* 717.441
797.157
* 956.588
1116.020
* 1195.735
1195.735




Equipentatonic
[[Magnetosphere scale|Magnetosphere]] (approximated from [[Hexany 1728]])
239.147
478.294
717.441
956.5881
1195.735


* 159.431
* 398.578
* 717.441
* 956.588
* 1195.735


Firedance
239.147
558.010
717.441
956.588
1195.735


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


Monsoon
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


Porcupine Hexatonic
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


Porcupine Symmetric
159.431
318.863
478.294
717.441
876.872
1036.304
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 =
* [[Zeta peak index]] (zpi)
* [[The Riemann zeta function and tuning]]
* [[Augmented]]
* [[Blackwood]]
* [[Porcupine]]


Rockpool
398.578
478.294
717.441
956.588
1195.735


* [[5- to 10-tone scales in 60edo]]
* [[5- to 10-tone scales in 84edo]]
* [[5- to 10-tone scales in 91edo]]
* [[5- to 10-tone scales in 96edo]]


In case you wish to create your own scales from 15.0535edo, here is the full list of intervals available:
 
79.716
* [[5- to 10-tone scales from the modes of the harmonic series]]
159.431
* [[5- to 10-tone scales from the modes of the subharmonic series]]
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


[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:5-tone scales]]
[[Category:6-tone scales]]
[[Category:15edo]]
[[Category:15edo]]
[[Category:Zeta]]
{{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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