User:BudjarnLambeth/Sandbox2: Difference between revisions
| Line 11: | Line 11: | ||
; [[WE|7et, 2.3.11.13 WE]] | ; [[WE|7et, 2.3.11.13 WE]] | ||
* Step size: 171.993{{c}}, octave size: 1204.0{{c}} | * Step size: 171.993{{c}}, octave size: 1204.0{{c}} | ||
Stretching the octave of 7edo by around | Stretching the octave of 7edo by around 4{{c}} results in much improved primes 3, 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 75.0{{c}}. The 2.3.11.13 WE tuning and 2.3.11.13 [[TE]] tuning both do this. | ||
{{Harmonics in cet|171.993|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE}} | {{Harmonics in cet|171.993|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE}} | ||
{{Harmonics in cet|171.993|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE (continued)}} | {{Harmonics in cet|171.993|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE (continued)}} | ||
| Line 17: | Line 17: | ||
; [[18ed6]] | ; [[18ed6]] | ||
* Step size: 172.331{{c}}, octave size: 1206.3{{c}} | * Step size: 172.331{{c}}, octave size: 1206.3{{c}} | ||
Stretching the octave of 7edo by around | Stretching the octave of 7edo by around 6{{c}} results in much improved primes 3, 5 and 7, but much worse primes 11 and 14. This approximates all harmonics up to 16 within 48.7{{c}}. The tuning 18ed6 does this. | ||
{{Harmonics in equal| | {{Harmonics in equal|18|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6}} | ||
{{Harmonics in equal| | {{Harmonics in equal|18|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6 (continued)}} | ||
; [[WE|7et, 2.3.5.11.13 WE]] | ; [[WE|7et, 2.3.5.11.13 WE]] | ||
* Step size: 172.390{{c}}, octave size: 1206.7{{c}} | * Step size: 172.390{{c}}, octave size: 1206.7{{c}} | ||
Stretching the octave of 7edo by around | Stretching the octave of 7edo by around 7{{c}} results in much improved primes 3, 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 85.7{{c}}. Its 2.3.5.11.13 WE tuning and 2.3.5.11.13 [[TE]] tuning both do this. | ||
{{Harmonics in cet|172.390|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE}} | {{Harmonics in cet|172.390|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE}} | ||
{{Harmonics in cet|172.390|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE (continued)}} | {{Harmonics in cet|172.390|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE (continued)}} | ||
| Line 29: | Line 29: | ||
; [[zpi|15zpi]] | ; [[zpi|15zpi]] | ||
* Step size: 172.495{{c}}, octave size: 1207.5{{c}} | * Step size: 172.495{{c}}, octave size: 1207.5{{c}} | ||
Stretching the octave of 7edo by around | Stretching the octave of 7edo by around 7.5{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 7 and 13. This approximates all harmonics up to 16 within 84.0{{c}}. The tuning 15zpi does this. | ||
{{Harmonics in cet|172.495|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi}} | {{Harmonics in cet|172.495|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi}} | ||
{{Harmonics in cet|172.495|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi (continued)}} | {{Harmonics in cet|172.495|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi (continued)}} | ||
| Line 35: | Line 35: | ||
; [[11edt]] | ; [[11edt]] | ||
* Step size: 172.905{{c}}, octave size: 1210.3{{c}} | * Step size: 172.905{{c}}, octave size: 1210.3{{c}} | ||
Stretching the octave of 7edo by around NNN{{c}} results in improved primes | Stretching the octave of 7edo by around NNN{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 7 and 13. This approximates all harmonics up to 16 within 83.6{{c}}. The tuning 11edt does this. | ||
{{Harmonics in equal|11|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt}} | {{Harmonics in equal|11|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt}} | ||
{{Harmonics in equal|11|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt (continued)}} | {{Harmonics in equal|11|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt (continued)}} | ||