Xenharmonic Wiki

User:BudjarnLambeth/Sandbox2: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
 
(19 intermediate revisions by the same user not shown)
Line 1: Line 1:
Quick link
== Approximations of odd harmonics ==
 
{{harmonics in equal|1|intervals=odd|columns=7}}
[[User:BudjarnLambeth/Draft related tunings section]]
{{harmonics in equal|2|intervals=odd|columns=7}}
 
{{harmonics in equal|3|intervals=odd|columns=7}}
== Octave stretch or compression ==
{{harmonics in equal|4|intervals=odd|columns=7}}
18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
{{harmonics in equal|5|intervals=odd|columns=7}}
 
{{harmonics in equal|6|intervals=odd|columns=7}}
; 18edo
{{harmonics in equal|7|intervals=odd|columns=7}}
* Step size: 66.667{{c}}, octave size: 1200.0{{c}}  
{{harmonics in equal|8|intervals=odd|columns=7}}
Pure-octaves 18edo approximates all harmonics up to 15 within 31.4{{c}}.
{{harmonics in equal|9|intervals=odd|columns=7}}
{{Harmonics in equal|18|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18edo}}
{{harmonics in equal|10|intervals=odd|columns=7}}
{{Harmonics in equal|18|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18edo (continued)}}
{{harmonics in equal|11|intervals=odd|columns=7}}
 
{{harmonics in equal|12|intervals=odd|columns=7}}
; [[WE|18et, 13-limit WE tuning]]
{{harmonics in equal|13|intervals=odd|columns=7}}
* Step size: 66.291{{c}}, octave size: 1193.2{{c}}
{{harmonics in equal|14|intervals=odd|columns=7}}
Compressing the octave of 18edo by around 7{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 25.3{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{harmonics in equal|15|intervals=odd|columns=7}}
{{Harmonics in cet|66.291|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning}}
{{harmonics in equal|16|intervals=odd|columns=7}}
{{Harmonics in cet|66.291|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning (continued)}}
{{harmonics in equal|17|intervals=odd|columns=7}}
 
{{harmonics in equal|18|intervals=odd|columns=7}}
; [[zpi|61zpi]]
{{harmonics in equal|19|intervals=odd|columns=7}}
* Step size: 66.228{{c}}, octave size: 1192.1{{c}}
{{harmonics in equal|20|intervals=odd|columns=7}}
Compressing the octave of 18edo by around 8{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 28.9{{c}}. The tuning 61zpi does this.
{{harmonics in equal|21|intervals=odd|columns=7}}
{{Harmonics in cet| 66.228 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 61zpi}}
{{harmonics in equal|22|intervals=odd|columns=7}}
{{Harmonics in cet| 66.228 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 61zpi (continued)}}
{{harmonics in equal|23|intervals=odd|columns=7}}
 
{{harmonics in equal|24|intervals=odd|columns=7}}
; [[65ed12]]
{{harmonics in equal|25|intervals=odd|columns=7}}
* Octave size: 1191.3{{c}}
{{harmonics in equal|26|intervals=odd|columns=7}}
Compressing the octave of 18edo by around 9{{c}} results in improved primes 3, 5, 7 and 13, but a worse primes 2. This approximates all harmonics up to 15 within 31.4{{c}}. The tuning 65ed12 does this.
{{harmonics in equal|27|intervals=odd|columns=7}}
{{Harmonics in equal|65|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 65ed12}}
{{harmonics in equal|28|intervals=odd|columns=7}}
{{Harmonics in equal|65|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 65ed12 (continued)}}
{{harmonics in equal|29|intervals=odd|columns=7}}
 
{{harmonics in equal|30|intervals=odd|columns=7}}
; [[47ed6]]
{{harmonics in equal|31|intervals=odd|columns=7}}
* Step size: NNN{{c}}, octave size: 1188.0{{c}}
{{harmonics in equal|32|intervals=odd|columns=7}}
Compressing the octave of 18edo by around 12{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 15 within 29.9{{c}}. The tuning 47ed6 does this.
{{harmonics in equal|33|intervals=odd|columns=7}}
{{Harmonics in equal|47|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 47ed6}}
{{harmonics in equal|34|intervals=odd|columns=7}}
{{Harmonics in equal|47|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 47ed6 (continued)}}
{{harmonics in equal|35|intervals=odd|columns=7}}
{{harmonics in equal|36|intervals=odd|columns=7}}
{{harmonics in equal|37|intervals=odd|columns=7}}
{{harmonics in equal|38|intervals=odd|columns=7}}
{{harmonics in equal|39|intervals=odd|columns=7}}
{{harmonics in equal|40|intervals=odd|columns=7}}
{{harmonics in equal|41|intervals=odd|columns=7}}
{{harmonics in equal|42|intervals=odd|columns=7}}
{{harmonics in equal|43|intervals=odd|columns=7}}
{{harmonics in equal|44|intervals=odd|columns=7}}
{{harmonics in equal|45|intervals=odd|columns=7}}
{{harmonics in equal|46|intervals=odd|columns=7}}
{{harmonics in equal|47|intervals=odd|columns=7}}
{{harmonics in equal|48|intervals=odd|columns=7}}
{{harmonics in equal|49|intervals=odd|columns=7}}
{{harmonics in equal|50|intervals=odd|columns=7}}
{{harmonics in equal|51|intervals=odd|columns=7}}
{{harmonics in equal|52|intervals=odd|columns=7}}
{{harmonics in equal|53|intervals=odd|columns=7}}
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox2"