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m BudjarnLambeth moved page 5- to 8-tone scales in zeta stretched 15edo to 5- to 10-tone scales in zeta stretched 15edo: I had originally made these pages “5 to 8 tone scales” because I misremembered reading that there was something special about scales with 5 to 8 tones. On one of the wikifuture/wishlist pages, Inthar listed highlighting 5 to 10 tone scales as a goal, which I agree is a good idea, so I’m converting these articles to focus on 5 to 10 tone scales instead, in service of t...
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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 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




[[Aurora scale|Aurora]]
[[Firedance]] (this is the original/default tuning)
* 239.147
* 558.010
* 717.441
* 956.588
* 1195.735
 
 
[[Magnetosphere scale|Magnetosphere]] (approximated from [[Hexany 1728]])


* 159.431
* 159.431
Line 23: Line 36:




[[Augmented]]
Monsoon (this is the original/default tuning)
*318.863
* 239.147
*398.578
* 478.294
*717.441
* 717.441
*797.157
* 1036.304
*1116.020
* 1195.735
*1195.735




[[Blacksmith|Equipentatonic]]
[[Porcupine]][6] MOS
*239.147
* 398.578
*478.294
* 558.010
*717.441
* 717.441
*956.5881
* 876.872
*1195.735
* 1036.304
* 1195.735




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




Monsoon
In case you wish to create your own scales from 15.0535edo, here is the full list of intervals available:
*239.147
* 79.716
*478.294
* 159.431
*717.441
* 239.147
*1036.304
* 318.863
*1195.735
* 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]]




[[Porcupine]] Hexatonic
* [[Augmented]]
*398.578
* [[Blackwood]]
*558.010
* [[Porcupine]]
*717.441
*876.872
*1036.304
*1195.735




Rockpool
* [[5- to 10-tone scales in 60edo]]
*398.578
* [[5- to 10-tone scales in 84edo]]
*478.294
* [[5- to 10-tone scales in 91edo]]
*717.441
* [[5- to 10-tone scales in 96edo]]
*956.588
*1195.735




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


[[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 }}
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