Xenharmonic Wiki

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

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,295 edits
m Remove todo from user page
 
(16 intermediate revisions by 3 users not shown)
Line 1: Line 1:
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
[[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]]
[[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
*239.147
*478.294
*717.441
*1036.304
*1195.735
 
 
[[Porcupine]] Hexatonic
*398.578
*558.010
*717.441
*876.872
*1036.304
*1195.735
 
 
Rockpool
*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:
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]]
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/5-_to_10-tone_scales_in_47zpi"