7edo: Difference between revisions

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Line 487:

; 7edo

* Step size: 171.429{{c}}, octave size: 1200.0{{c}}

Pure-octaves 7edo approximates ~~all~~ harmonics ~~up to 16 within NNN{{c}}~~.

Pure-octaves 7edo approximates the 2nd, 3rd, 11th and 13th harmonics well for its size, but it's arguable whether it approximates 5 - if it does it does so poorly. It doesn't approximate 7.

{{Harmonics in equal|7|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edo}}

{{Harmonics in equal|7|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edo (continued)}}

Line 493:

; [[WE|7et, 2.3.11.13 WE]]

* Step size: 171.993{{c}}, octave size: 1204.0{{c}}

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.

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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE (continued)}}

Line 499:

; [[18ed6]]

* Step size: 172.331{{c}}, octave size: 1206.3{{c}}

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.

Stretching the octave of 7edo by around 6{{c}} results in much improved primes 3, 5 and 7, but much worse primes 11 and 13. The tuning 18ed6 does this.

{{Harmonics in equal|18|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6}}

{{Harmonics in equal|18|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6 (continued)}}

Line 505:

; [[WE|7et, 2.3.5.11.13 WE]]

* Step size: 172.390{{c}}, octave size: 1206.7{{c}}

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.

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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE (continued)}}

Line 511:

; [[zpi|15zpi]]

* Step size: 172.495{{c}}, octave size: 1207.5{{c}}

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.

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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi (continued)}}

Line 517:

; [[11edt]]

* Step size: 172.905{{c}}, octave size: 1210.3{{c}}

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.

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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt (continued)}}

@@ Line 487: / Line 487: @@
 ; 7edo
 * Step size: 171.429{{c}}, octave size: 1200.0{{c}}
-Pure-octaves 7edo approximates all harmonics up to 16 within NNN{{c}}.
+Pure-octaves 7edo approximates the 2nd, 3rd, 11th and 13th harmonics well for its size, but it's arguable whether it approximates 5 - if it does it does so poorly. It doesn't approximate 7.
 {{Harmonics in equal|7|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edo}}
 {{Harmonics in equal|7|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7edo (continued)}}
@@ Line 493: / Line 493: @@
 ; [[WE|7et, 2.3.11.13 WE]]
 * Step size: 171.993{{c}}, octave size: 1204.0{{c}}
-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.
+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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE (continued)}}
@@ Line 499: / Line 499: @@
 ; [[18ed6]]
 * Step size: 172.331{{c}}, octave size: 1206.3{{c}}
-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.
+Stretching the octave of 7edo by around 6{{c}} results in much improved primes 3, 5 and 7, but much worse primes 11 and 13. The tuning 18ed6 does this.
 {{Harmonics in equal|18|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6}}
 {{Harmonics in equal|18|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6 (continued)}}
@@ Line 505: / Line 505: @@
 ; [[WE|7et, 2.3.5.11.13 WE]]
 * Step size: 172.390{{c}}, octave size: 1206.7{{c}}
-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.
+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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE (continued)}}
@@ Line 511: / Line 511: @@
 ; [[zpi|15zpi]]
 * Step size: 172.495{{c}}, octave size: 1207.5{{c}}
-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.
+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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi (continued)}}
@@ Line 517: / Line 517: @@
 ; [[11edt]]
 * Step size: 172.905{{c}}, octave size: 1210.3{{c}}
-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.
+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. 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=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt (continued)}}