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| == Octave stretch or compression == | | == Octave stretch or compression == |
| 15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | | 15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. Shrunk-octaves versions of 15edo include [[equal tuning|50ed10]], [[47zpi]] and [[ed12|54ed12]]. |
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| ; 15edo
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| * Step size: 80.000{{c}}, octave size: 1200.0{{c}}
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| Pure-octaves 15edo approximates all harmonics up to 12 within 36.1{{c}}.
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| {{Harmonics in equal|15|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 15edo}}
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| {{Harmonics in equal|15|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 15edo (continued)}}
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| ; [[equal tuning|52ed11]]
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| * Octave size: 1197.5{{c}}
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| Compressing the octave of 15edo by around 2.5{{c}} results in improved primes 3, 5 and 13, but worse primes 2, 7 and 11. This approximates all harmonics up to 12 within 28.1{{c}}. The tuning 52ed11 does this.
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| {{Harmonics in equal|52|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 52ed11}}
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| {{Harmonics in equal|52|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 52ed11 (continued)}}
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| ; [[WE|15et, 11-limit WE tuning]]
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| * Step size: 79.770{{c}}, octave size: 1196.5{{c}}
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| Compressing the octave of 15edo by around 3.5{{c}} results in improved primes 3, 5 and 13, but worse primes 2, 7 and 11. This approximates all harmonics up to 12 within 25.0{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this.
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| {{Harmonics in cet|79.770|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 15et, 11-limit WE tuning}}
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| {{Harmonics in cet|79.770|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 15et, 11-limit WE tuning (continued)}}
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| ; [[equal tuning|50ed10]]
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| * Octave size: 1195.1{{c}}
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| Compressing the octave of 15edo by around 4{{c}} results in improved primes 3, 5 and 13, but worse primes 2, 7 and 11. This approximates all harmonics up to 12 within 23.0{{c}}. The tuning 50ed10 does this.
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| {{Harmonics in equal|50|10|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 50ed10}}
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| {{Harmonics in equal|50|10|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 50ed10 (continued)}}
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| ; [[zpi|47zpi]]
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| * Step size: 79.715{{c}}, octave size: 1195.7{{c}}
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| Compressing the octave of 15edo by around 4.5{{c}} results in improved primes 3, 5 and 13, but worse primes 2, 7 and 11. This approximates all harmonics up to 12 within 22.4{{c}}. The tuning 47zpi does this.
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| {{Harmonics in cet|79.715|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 47zpi}}
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| {{Harmonics in cet|79.715|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 47zpi (continued)}}
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| ; [[ed12|54ed12]]
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| * Octave size: 1195.0{{c}}
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| Compressing the octave of 15edo by around 5{{c}} results in improved primes 3, 5 and 13, but worse primes 2, 7 and 11. This approximates all harmonics up to 12 within 20.0{{c}}. The tuning 54ed12 does this.
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| {{Harmonics in equal|54|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 54ed12}}
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| {{Harmonics in equal|54|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 54ed12 (continued)}}
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| == Scales== | | == Scales== |