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| == Octave stretch or compression == | | == Octave stretch or compression == |
| What follows is a comparison of stretched- and compressed-octave 36edo tunings.
| | If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6{{c}}. Several almost-identical tunings do this: [[57edt]], [[93ed6]], [[101ed7]], [[zpi|155zpi]], and the 2.3.7.13-subgroup [[TE]] and [[WE]] tunings of 36et. |
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| ; [[21edf]]
| | Compressing the octave of 36edo by 1-2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. The 11- and 13-limit [[TE]] tunings of 36et both do this, as do their respective [[WE]] tunings. |
| * Step size: 33.426{{c}}, octave size: 1203.351{{c}}
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| Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all harmonics up to 16 within 13.4{{c}}. The tuning 21edf does this.
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| {{Harmonics in equal|21|3|2|columns=11|collapsed=true}}
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| {{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}}
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| ; [[57edt]]
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| * Step size: 33.368{{c}}, octave size: 1201.235{{c}}
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| If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all harmonics up to 16 within 16.6{{c}}. Several almost-identical tunings do this: 57edt, [[93ed6]], [[101ed7]], [[zpi|155zpi]], and the 2.3.7.13-subgroup [[TE]] and [[WE]] tunings of 36et.
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| {{Harmonics in equal|57|3|1|columns=11|collapsed=true}}
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| {{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}}
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| ; 36edo
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| * Step size: 33.333{{c}}, octave size: 1200.000{{c}}
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| Pure-octaves 36edo approximates all harmonics up to 16 within 15.3{{c}}.
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| {{Harmonics in equal|36|2|1|intervals=integer|columns=11|collapsed=true}}
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| {{Harmonics in equal|36|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 36edo (continued)}}
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| ; [[TE|36et, 13-limit TE tuning]]
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| * Step size: 33.304{{c}}, octave size: 1198.929{{c}}
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| Compressing the octave of 36edo by about 1{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all harmonics up to 16 within 11.6{{c}}. The 11- and 13-limit TE tunings of 36et both do this, as do their respective WE tunings.
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| {{Harmonics in cet|33.303596|columns=11|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et}}
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| {{Harmonics in cet|33.303596|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 13-limit TE tuning of 36et (continued)}}
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| ; [[TE|36et, 11-limit TE tuning]]
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| * Step size: 33.287{{c}}, octave size: 1198.330{{c}}
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| {{Harmonics in cet|33.287|columns=11|collapsed=true|title=Approximation of harmonics in 11lim TE-tuned 36edo}}
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| {{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim TE-tuned 36edo (continued)}}
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| Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 16 within 13.4{{c}}. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.
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| {| class="wikitable sortable center-all mw-collapsible mw-collapsed" | | {| class="wikitable sortable center-all mw-collapsible mw-collapsed" |