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| = [[7edo]] =
| | {{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}} |
| == Octave stretch or compression ==
| | {{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}} |
| What follows is a comparison of stretched- and compressed-octave 7edo tunings.
| | {{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}} |
| | | {{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}} |
| ; 7edo
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| * Step size: 171.429{{c}}, octave size: 1200.0{{c}}
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| Pure-octaves 7edo approximates all harmonics up to 16 within NNN{{c}}.
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| {{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)}} | |
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| ; [[WE|7et, 2.3.11.13 WE]]
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| * Step size: 171.993{{c}}, octave size: 1204.0{{c}}
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| 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.
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| {{Harmonics in cet|171.993|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.11.13 WE}}
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| {{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)}} | |
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| ; [[18ed6]]
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| * Step size: 172.331{{c}}, octave size: 1206.3{{c}}
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| 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.
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| {{Harmonics in equal|18|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6}}
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| {{Harmonics in equal|18|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 18ed6 (continued)}} | |
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| ; [[WE|7et, 2.3.5.11.13 WE]]
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| * Step size: 172.390{{c}}, octave size: 1206.7{{c}}
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| 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.
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| {{Harmonics in cet|172.390|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 7et, 2.3.5.11.13 WE}}
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| {{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)}}
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| ; [[zpi|15zpi]]
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| * Step size: 172.495{{c}}, octave size: 1207.5{{c}}
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| 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.
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| {{Harmonics in cet|172.495|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi}}
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| {{Harmonics in cet|172.495|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 15zpi (continued)}}
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| ; [[11edt]]
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| * Step size: 172.905{{c}}, octave size: 1210.3{{c}}
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| 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.
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| {{Harmonics in equal|11|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt}}
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| {{Harmonics in equal|11|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 11edt (continued)}}
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