7edo: Difference between revisions

Line 483:

== Octave stretch or compression ==

[[Stretched and compressed tuning|Stretched-octaves]] tunings such as [[11edt]], [[18ed6]] or [[~~Ed257/128 #7ed257/128~~|~~7ed257/128~~]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for [[11-limit]] harmonies, then these are good choices to make that easier.

[[Stretched and compressed tuning|Stretched-octaves]] tunings such as [[11edt]], [[18ed6]] or [[zpi|15zpi]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for full [[11-limit]] harmonies, then these are good choices to make that easier.

~~; 7edo~~

* Step size: 171.429{{c}}, octave size: 1200.000{{c}}

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

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

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

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

* Step size: 171.993{{c}}, octave size: 1203.948{{c}}

~~Stretching the octave of 7edo by around 3.9{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 7 and 13. The 2.3.11.13 WE tuning and 2.3.11.13 [[TE]] tuning both do this.~~

~~{{Harmonics in cet|171.992645|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 7et, 2.3.11.13 WE}}~~

~~{{Harmonics in cet|171.992645|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7et, 2.3.11.13 WE (continued)}}~~

~~; [[18ed6]]~~

* Step size: 172.331{{c}}, octave size: 1206.316{{c}}

~~Stretching the octave of 7edo by around 6.3{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 7 and 13. The tuning 18ed6 does this.~~

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

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

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

* Step size: 172.390{{c}}, octave size: 1206.728{{c}}

~~Stretching the octave of 7edo by around 7.3{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 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|172.389769|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE}}~~

~~{{Harmonics in cet|172.389769|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE (continued)}}~~

~~; [[zpi|15zpi]]~~

* Step size: 172.495{{c}}, octave size: 1207.471{{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. The tuning 15zpi does this.~~

~~{{Harmonics in cet|172.495886|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 15zpi}}~~

~~{{Harmonics in cet|172.495886|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 15zpi (continued)}}~~

~~; [[11edt]]~~

* Step size: 172.905{{c}}, octave size: 1210.335{{c}}

~~Stretching the octave of 7edo by around 10.3{{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|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 11edt}}~~

~~{{Harmonics in equal|11|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edt (continued)}}~~

== Instruments ==

@@ Line 483: / Line 483: @@
 == Octave stretch or compression ==
-[[Stretched and compressed tuning|Stretched-octaves]] tunings such as [[11edt]], [[18ed6]] or [[Ed257/128 #7ed257/128|7ed257/128]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for [[11-limit]] harmonies, then these are good choices to make that easier.
+[[Stretched and compressed tuning|Stretched-octaves]] tunings such as [[11edt]], [[18ed6]] or [[zpi|15zpi]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for full [[11-limit]] harmonies, then these are good choices to make that easier.
-; 7edo
-* Step size: 171.429{{c}}, octave size: 1200.000{{c}}
-Pure-octaves 7edo approximates the 2nd, 3rd, 11th and 13th harmonics well for its size, but it is arguable whether it approximates 5 – if it does it does so poorly. It does not approximate 7.
-{{Harmonics in equal|7|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 7edo}}
-{{Harmonics in equal|7|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7edo (continued)}}
-; [[WE|7et, 2.3.11.13 WE]]
-* Step size: 171.993{{c}}, octave size: 1203.948{{c}}
-Stretching the octave of 7edo by around 3.9{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 7 and 13. The 2.3.11.13 WE tuning and 2.3.11.13 [[TE]] tuning both do this.
-{{Harmonics in cet|171.992645|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 7et, 2.3.11.13 WE}}
-{{Harmonics in cet|171.992645|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7et, 2.3.11.13 WE (continued)}}
-; [[18ed6]]
-* Step size: 172.331{{c}}, octave size: 1206.316{{c}}
-Stretching the octave of 7edo by around 6.3{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 7 and 13. The tuning 18ed6 does this.
-{{Harmonics in equal|18|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18ed6}}
-{{Harmonics in equal|18|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18ed6 (continued)}}
-; [[WE|7et, 2.3.5.11.13 WE]]
-* Step size: 172.390{{c}}, octave size: 1206.728{{c}}
-Stretching the octave of 7edo by around 7.3{{c}} results in much improved primes 3, 5 and 11, but much worse primes 2, 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|172.389769|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE}}
-{{Harmonics in cet|172.389769|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE (continued)}}
-; [[zpi|15zpi]]
-* Step size: 172.495{{c}}, octave size: 1207.471{{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. The tuning 15zpi does this.
-{{Harmonics in cet|172.495886|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 15zpi}}
-{{Harmonics in cet|172.495886|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 15zpi (continued)}}
-; [[11edt]]
-* Step size: 172.905{{c}}, octave size: 1210.335{{c}}
-Stretching the octave of 7edo by around 10.3{{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|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 11edt}}
-{{Harmonics in equal|11|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edt (continued)}}
 == Instruments ==