User:BudjarnLambeth/Sandbox2: Difference between revisions

Line 7:

; [[zpi|567zpi]]

* Step size: 12.138{{c}}, octave size: 1201.66{{c}}

Stretching the octave of 99edo by around 1.5{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within 5.54{{c}}. The tuning 567zpi does this.

Stretching the octave of 99edo by around 1.5{{c}} results in improved primes 11, 13, 17, and 19, but worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 5.54{{c}}. The tuning 567zpi does this.

{{Harmonics in cet|12.138|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 567zpi}}

{{Harmonics in cet|12.138|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 567zpi (continued)}}

Line 13:

; [[WE|99et, 13-limit WE tuning]]

* Step size: 12.123{{c}}, octave size: 1200.18{{c}}

Stretching the octave of 99edo by around a fifth of a cent results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within 5.25{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

Stretching the octave of 99edo by around a fifth of a cent results in improved primes 11 and 13, but worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 5.25{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.

{{Harmonics in cet|12.123|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99et, 13-limit WE tuning}}

{{Harmonics in cet|12.123|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99et, 13-limit WE tuning (continued)}}

Line 25:

; [[WE|99et, 7-limit WE tuning]] / [[256ed6]]

* Step size: 12.117{{c}}, octave size: 1199.58{{c}}

Compressing the octave of 99edo by around 0.6{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within 5.71{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So does the tuning 256ed6 whose octave is identical within a thousandth of a cent.

Compressing the octave of 99edo by around 0.6{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.71{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So does the tuning 256ed6 whose octave is identical within a thousandth of a cent.

{{Harmonics in cet|12.117|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99et, 7-limit WE tuning}}

{{Harmonics in cet|12.117|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99et, 7-limit WE tuning (continued)}}

Line 31:

; [[zpi|568zpi]]

* Step size: 12.115{{c}}, octave size: 1199.39{{c}}

Compressing the octave of 99edo by around 0.4{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within 5.68{{c}}. The tuning 568zpi does this.

Compressing the octave of 99edo by around 0.4{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.68{{c}}. The tuning 568zpi does this.

{{Harmonics in cet|12.115|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 568zpi}}

{{Harmonics in cet|12.115|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 568zpi (continued)}}

Line 37:

; [[157edt]] / [[ed5|230ed5]]

* Step size: 12.114{{c}}, octave size: 1199.32{{c}}

Compressing the octave of 99edo by around 0.3{{c}} results in improved primes ~~NNN~~, but worse primes ~~NNN~~. This approximates all harmonics up to 16 within 5.44{{c}}. The tuning 157edt does this. So does 230ed5 whose octave is identical within a hundredth of a cent.

Compressing the octave of 99edo by around 0.3{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.44{{c}}. The tuning 157edt does this. So does 230ed5 whose octave is identical within a hundredth of a cent.

{{Harmonics in equal|157|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 157edt}}

{{Harmonics in equal|157|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 157edt (continued)}}

@@ Line 7: / Line 7: @@
 ; [[zpi|567zpi]]
 * Step size: 12.138{{c}}, octave size: 1201.66{{c}}
-Stretching the octave of 99edo by around 1.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within 5.54{{c}}. The tuning 567zpi does this.
+Stretching the octave of 99edo by around 1.5{{c}} results in improved primes 11, 13, 17, and 19, but worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 5.54{{c}}. The tuning 567zpi does this.
 {{Harmonics in cet|12.138|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 567zpi}}
 {{Harmonics in cet|12.138|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 567zpi (continued)}}
@@ Line 13: / Line 13: @@
 ; [[WE|99et, 13-limit WE tuning]]
 * Step size: 12.123{{c}}, octave size: 1200.18{{c}}
-Stretching the octave of 99edo by around a fifth of a cent results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within 5.25{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
+Stretching the octave of 99edo by around a fifth of a cent results in improved primes 11 and 13, but worse primes 2, 3, 5 and 7. This approximates all harmonics up to 16 within 5.25{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
 {{Harmonics in cet|12.123|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99et, 13-limit WE tuning}}
 {{Harmonics in cet|12.123|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99et, 13-limit WE tuning (continued)}}
@@ Line 25: / Line 25: @@
 ; [[WE|99et, 7-limit WE tuning]] / [[256ed6]]
 * Step size: 12.117{{c}}, octave size: 1199.58{{c}}
-Compressing the octave of 99edo by around 0.6{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within 5.71{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So does the tuning 256ed6 whose octave is identical within a thousandth of a cent.
+Compressing the octave of 99edo by around 0.6{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.71{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So does the tuning 256ed6 whose octave is identical within a thousandth of a cent.
 {{Harmonics in cet|12.117|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 99et, 7-limit WE tuning}}
 {{Harmonics in cet|12.117|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 99et, 7-limit WE tuning (continued)}}
@@ Line 31: / Line 31: @@
 ; [[zpi|568zpi]]
 * Step size: 12.115{{c}}, octave size: 1199.39{{c}}
-Compressing the octave of 99edo by around 0.4{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within 5.68{{c}}. The tuning 568zpi does this.
+Compressing the octave of 99edo by around 0.4{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.68{{c}}. The tuning 568zpi does this.
 {{Harmonics in cet|12.115|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 568zpi}}
 {{Harmonics in cet|12.115|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 568zpi (continued)}}
@@ Line 37: / Line 37: @@
 ; [[157edt]] / [[ed5|230ed5]]
 * Step size: 12.114{{c}}, octave size: 1199.32{{c}}
-Compressing the octave of 99edo by around 0.3{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within 5.44{{c}}. The tuning 157edt does this. So does 230ed5 whose octave is identical within a hundredth of a cent.
+Compressing the octave of 99edo by around 0.3{{c}} results in improved primes 3, 5, 7 and 11, but worse primes 2 and 13. This approximates all harmonics up to 16 within 5.44{{c}}. The tuning 157edt does this. So does 230ed5 whose octave is identical within a hundredth of a cent.
 {{Harmonics in equal|157|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 157edt}}
 {{Harmonics in equal|157|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 157edt (continued)}}