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| For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. See also the [[22edo]] page. | | For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. See also the [[22edo]] page. |
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| |
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| == JI approximation == | | == Approximation to JI == |
| | |
| === 15-odd-limit interval mappings === | | === 15-odd-limit interval mappings === |
| The following table shows how [[15-odd-limit intervals]] are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | | The following table shows how [[15-odd-limit intervals]] are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. |
| {| class="wikitable center-all mw-collapsible mw-collapsed"
| |
| |+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)
| |
| |-
| |
| ! Interval, complement
| |
| ! Error (abs, ¢)
| |
| ! Error (rel, %)
| |
| |-
| |
| | [[7/6]], [[12/7]]
| |
| | 0.204
| |
| | 0.5
| |
| |-
| |
| | ''[[15/11]], [[22/15]]''
| |
| | ''3.617''
| |
| | ''8.1''
| |
| |-
| |
| | '''[[13/8]], [[16/13]]'''
| |
| | '''3.917'''
| |
| | '''8.8'''
| |
| |-
| |
| | [[5/3]], [[6/5]]
| |
| | 4.530
| |
| | 10.2
| |
| |-
| |
| | [[9/5]], [[10/9]]
| |
| | 4.626
| |
| | 10.4
| |
| |-
| |
| | [[7/5]], [[10/7]]
| |
| | 4.734
| |
| | 10.7
| |
| |-
| |
| | [[13/7]], [[14/13]]
| |
| | 5.035
| |
| | 11.3
| |
| |-
| |
| | [[13/12]], [[24/13]]
| |
| | 5.239
| |
| | 11.8
| |
| |-
| |
| | ''[[11/9]], [[18/11]]''
| |
| | ''8.148''
| |
| | ''18.3''
| |
| |-
| |
| | '''[[7/4]], [[8/7]]'''
| |
| | '''8.952'''
| |
| | '''20.1'''
| |
| |-
| |
| | '''[[3/2]], [[4/3]]'''
| |
| | '''9.156'''
| |
| | '''20.6'''
| |
| |-
| |
| | [[9/7]], [[14/9]]
| |
| | 9.360
| |
| | 21.1
| |
| |-
| |
| | [[13/10]], [[20/13]]
| |
| | 9.770
| |
| | 22.0
| |
| |-
| |
| | ''[[11/10]], [[20/11]]''
| |
| | ''12.774''
| |
| | ''28.7''
| |
| |-
| |
| | '''[[5/4]], [[8/5]]'''
| |
| | '''13.686'''
| |
| | '''30.8'''
| |
| |-
| |
| | [[15/14]], [[28/15]]
| |
| | 13.891
| |
| | 31.3
| |
| |-
| |
| | [[13/9]], [[18/13]]
| |
| | 14.395
| |
| | 32.4
| |
| |-
| |
| | ''[[11/6]], [[12/11]]''
| |
| | ''17.304''
| |
| | ''38.9''
| |
| |-
| |
| | ''[[11/7]], [[14/11]]''
| |
| | ''17.508''
| |
| | ''39.4''
| |
| |-
| |
| | '''[[11/8]], [[16/11]]'''
| |
| | '''17.985'''
| |
| | '''40.5'''
| |
| |-
| |
| | [[9/8]], [[16/9]]
| |
| | 18.312
| |
| | 41.2
| |
| |-
| |
| | [[15/13]], [[26/15]]
| |
| | 18.926
| |
| | 42.6
| |
| |-
| |
| | ''[[15/8]], [[16/15]]''
| |
| | ''21.602''
| |
| | ''48.6''
| |
| |-
| |
| | [[13/11]], [[22/13]]
| |
| | 21.901
| |
| | 49.3
| |
| |}
| |
| {{15-odd-limit|27}} | | {{15-odd-limit|27}} |
| | {{15-odd-limit|27.1|title=15-odd-limit intervals by 27e val mapping}} |
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| === Selected 17-limit intervals === | | === Selected 17-limit intervals === |