|
|
| (20 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: NNN{{c}}, octave size: NNN{{c}}
| | {{harmonics in equal|8|intervals=odd|columns=7}} |
| Pure-octaves 18edo approximates all harmonics up to 16 within NNN{{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 NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{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 NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{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}} |
| * Step size: NNN{{c}}, 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 NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{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}} |
| ; [[WE|18et, 7-limit WE tuning]]
| | {{harmonics in equal|31|intervals=odd|columns=7}} |
| * Step size: 66.148{{c}}, octave size: 1190.7{{c}}
| | {{harmonics in equal|32|intervals=odd|columns=7}} |
| Compressing the octave of 18edo by around 9.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this.
| | {{harmonics in equal|33|intervals=odd|columns=7}} |
| {{Harmonics in cet| 66.148 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning}} | | {{harmonics in equal|34|intervals=odd|columns=7}} |
| {{Harmonics in cet| 66.148 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning (continued)}} | | {{harmonics in equal|35|intervals=odd|columns=7}} |
| | | {{harmonics in equal|36|intervals=odd|columns=7}} |
| ; [[47ed6]]
| | {{harmonics in equal|37|intervals=odd|columns=7}} |
| * Step size: NNN{{c}}, octave size: 1188.0{{c}}
| | {{harmonics in equal|38|intervals=odd|columns=7}} |
| Compressing the octave of 18edo by around 12{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 47ed6 does this.
| | {{harmonics in equal|39|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|40|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|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}} |