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= Title1 =
== Approximations of odd harmonics ==
{{Harmonics in equal|40|10|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
{{harmonics in equal|1|intervals=odd|columns=7}}
{{Harmonics in equal|7|3|2|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}  
{{harmonics in equal|2|intervals=odd|columns=7}}
{{Harmonics in equal|19|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}  
{{harmonics in equal|3|intervals=odd|columns=7}}
{{Harmonics in equal|31|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in ZPINAME}}
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= Title2 =
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== Octave stretch or compression ==
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What follows is a comparison of stretched- and compressed-octave 41edo tunings.
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; [[zpi|184zpi]] / [[WE|41et, 11-limit WE tuning]]
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* Step size: 29.277{{c}}, octave size: NNN{{c}}
{{harmonics in equal|11|intervals=odd|columns=7}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 11-limit WE tuning and 11-limit [[TE]] tuning both do this. So does 184zpi, whose octave is identical to WE within 0.02{{c}}.
{{harmonics in equal|12|intervals=odd|columns=7}}
{{Harmonics in cet|29.277|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 41et, 11-limit WE tuning}}
{{harmonics in equal|13|intervals=odd|columns=7}}
{{Harmonics in cet|29.277|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 41et, 11-limit WE tuning (continued)}}
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; 41edo
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* Step size: 29.268{{c}}, octave size: 1200.0{{c}}  
{{harmonics in equal|17|intervals=odd|columns=7}}
Pure-octaves 41edo approximates all harmonics up to 16 within NNN{{c}}. The octaves of its compressed tuning [[147ed12]] differ by only 0.1{{c}} from pure. The octaves of its 13-limit [[WE]] and [[TE]] tuning differ by less than 0.1{{c}} from pure.
{{harmonics in equal|18|intervals=odd|columns=7}}
{{Harmonics in equal|41|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 41edo}}
{{harmonics in equal|19|intervals=odd|columns=7}}
{{Harmonics in equal|41|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 41edo (continued)}}
{{harmonics in equal|20|intervals=odd|columns=7}}
 
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; [[147ed12]] / [[106ed6]] / [[65edt]]
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* 147ed12 — step size: 29.265{{c}}, octave size: 1199.87{{c}}
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* 106ed6 — step size: 29.264{{c}}, octave size: 1199.69{{c}}
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* 65edt — step size: 29.261{{c}}, octave size: 1199.81{{c}}
{{harmonics in equal|25|intervals=odd|columns=7}}
Compressing the octave of 41edo by around 0.2{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tunings 147ed12, 106ed6 and 65edt do this.
{{harmonics in equal|26|intervals=odd|columns=7}}
{{Harmonics in equal|106|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 106ed6}}
{{harmonics in equal|27|intervals=odd|columns=7}}
{{Harmonics in equal|106|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 106ed6 (continued)}}
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