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| Line 1,116: |
Line 1,116: |
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| Tuning file: [[9x4just]] | | Tuning file: [[9x4just]] |
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| == Related equal tunings ==
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| What follows is a comparison of stretched- and compressed-octave 36edo tunings.
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| Of the stretched-octave tunings listed, ''36ed513/256'', with a step size about 33.4 cents, performs best in this comparison, approximating all 11-limit primes with less than 36% relative error (< 12 cents error).
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| Of the compressed-octave tunings listed, ''36ed511/256'', with a step size about 33.25 cents, performs best in this comparison, approximating all 11-limit primes with less than 36% relative error (< 12 cents error).
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| The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. They are 36edo with the octave stretched by less than 1{{c}}. Their main usage is to optimise 36edo for use as a [[dual-n|dual-5]] tuning, while also making slight improvements to 3/1 and 7/1 as well. So if one intends to use both 36edo's vals for 5/1 at once, 57edt or 101ed7 may be worth considering.
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| {| class="wikitable sortable center-all"
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| ! rowspan="2" | Tuning !! rowspan="2" | Step size<br>(cents) !! colspan="5" | Error (% step size) !! colspan="5" | Mapping (# steps)
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| |-
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| ! Prime 2 !! Prime 3 !! Prime 5 !! Prime 7 !! Prime 11 !! Prime 2 !! Prime 3 !! Prime 5 !! Prime 7 !! Prime 11
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| |-
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| ! 154zpi
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| | 33.547 || +23 || +31 || -5 || -41 || +27 || 36 || 57 || 83 || 100 || 124
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| |-
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| ! 36ed257/128
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| | 33.521 || +20 || +26 || -12 || +50 || +15 || 36 || 57 || 83 || 101 || 124
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| |-
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| ! 36ed513/256
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| | 33.427 || +10 || +11 || -35 || +23 || -18 || 36 || 57 || 83 || 101 || 124
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| |-
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| ! 57edt
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| | 33.368 || +4 || 0 || +50 || +5 || -40 || 36 || 57 || 83 || 101 || 124
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| |-
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| ! 101ed7
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| | 33.355 || +2 || -2 || +46 || 0 || -46 || 36 || 57 || 84 || 101 || 124
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| |-
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| ! 155zpi
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| | 33.350 || +2 || -3 || +45 || -1 || -48 || 36 || 57 || 84 || 101 || 124
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| |-
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| ! 36edo
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| | '''33.333''' || '''0'''|| '''-6''' || '''+40''' || '''-6''' || '''+46''' || '''36'''|| '''57'''|| '''84'''|| '''101'''|| '''125'''
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| |-
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| ! 36ed511/256
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| | 33.239 || -10 || -22 || +18 || -35 || +11 || 36 || 57 || 84 || 101 || 125
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| |-
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| ! 156zpi
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| | 33.152 || -20 || -37 || -5 || +38 || -23 || 36 || 57 || 84 || 102 || 125
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| |-
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| ! 36ed255/128
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| | 33.145 || -21 || -38 || -6 || +36 || -25 || 36 || 57 || 84 || 102 || 125
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| |}
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| == Instruments == | | == Instruments == |