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| * This section will ''not'' replace any "n-edo and octave stretch" pages. Still, add this section to the relevant edo page, but also link to the "n-edo and octave stretch" page at the top of this section, using the see also Template, eg: <nowiki>"{{See also|36edo and octave stretch}}"</nowiki>. | | * This section will ''not'' replace any "n-edo and octave stretch" pages. Still, add this section to the relevant edo page, but also link to the "n-edo and octave stretch" page at the top of this section, using the see also Template, eg: <nowiki>"{{See also|36edo and octave stretch}}"</nowiki>. |
| * It is okay to add only the descriptive text and collapsed harmonic tables to an edo page initially, and to add the full comparison table at a later date; this should make life easier for editors on mobile devices who might want to help but find tables difficult to edit. | | * It is okay to add only the descriptive text and collapsed harmonic tables to an edo page initially, and to add the full comparison table at a later date; this should make life easier for editors on mobile devices who might want to help but find tables difficult to edit. |
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| = Example (36edo, table on top) =
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| == Octave stretch or compression ==
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| What follows is a comparison of stretched- and compressed-octave 36edo tunings.
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| {| class="wikitable sortable center-all"
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| |-
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| ! rowspan="2" | Tuning !! rowspan="2" | Step size<br>(cents) !! colspan="6" | Prime error (cents)
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| ! rowspan="2" | Mapping of primes 2–13 (steps)
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| ! rowspan="2" | Octave stretch
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| |-
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| ! 2 !! 3 !! 5 !! 7 !! 11
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| ! 13
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| |-
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| ! 21edf
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| | 33.426
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| | +3.3 || +3.3 || −12.0 || +7.2 || −6.5 || +5.1
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| | 36, 57, 83, 101, 124, 133
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| | +0.275%
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| |-
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| ! 57edt
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| | 33.368 || +1.2 || 0.0 || +16.6 || +1.3 || −13.7 || −2.6
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| | 36, 57, 84, 101, 124, 133
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| | +0.001%
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| |-
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| ! 155zpi
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| | 33.346
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| | +0.6 || −1.0 || +15.1 || −0.5 || −16.0|| −5.0
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| | 36, 57, 83, 101, 124, 133
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| | +0.0005%
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| |-
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| ! 36edo
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| | '''33.333'''
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| | '''0.0''' || '''−2.0''' || '''+13.7''' || '''−2.2''' || '''+15.3''' || '''−7.2'''
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| | '''36, 57, 84, 101, 125, 133'''
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| | '''0%'''
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| |-
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| ! 13-limit WE
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| | 33.302
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| | −1.1 || −3.7 || +11.1 || −5.3 || +11.4 || −11.4
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| | 36, 57, 84, 101, 125, 133
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| | -0.0009%
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| ! 11-limit WE
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| | 33.286
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| | −1.7 || −4.7 || +9.7 || −6.9 || +9.4 || −13.5
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| | 36, 57, 84, 101, 125, 133
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| | -0.00142%
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| |}
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| ; [[21edf]]
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| * Step size: 33.426{{c}}
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| * Octave size: 1203.3{{c}}
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| {{Harmonics in equal|21|3|2|columns=12|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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| 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 primes up to 11 within ''12.0{{c}}''. The tuning 21edf does this.
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| ; [[57edt]]
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| * Step size: 33.368{{c}}
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| * Octave size: 1201.2{{c}}
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| {{Harmonics in equal|57|3|1|columns=12|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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| 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 primes up to 11 within ''16.6{{c}}''. Five almost-identical tunings do this: 57edt, [[101ed7]], [[zpi|155zpi]], and the [[TE]] and [[WE]] 2.3.7.13 subgroup WE tunings of 36edo.
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| ; Pure-octaves 36edo
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| * Step size: 33.333{{c}}
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| * Octave size: 1200.0{{c}}
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| Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''.
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| ; [[TE|11-limit TE 36edo]]
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| * Step size: 33.287{{c}}
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| * Octave size: 1198.3{{c}}
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| {{Harmonics in cet|33.287|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}}
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| {{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim WE-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 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings.
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| = Example (36edo, table on bottom) = | | = Example (36edo, table on bottom) = |