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| == Approximation to JI == | | == Approximation to JI == |
| === Selected just intervals by error === | | === Selected just intervals by error === |
| The following table shows how [[15-odd-limit intervals]] are represented in 16edo (ordered by absolute error).
| | {{Q-odd-limit intervals|16}} |
| | |
| {| 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., in [[cent]]s)
| |
| |-
| |
| | [[12/11]], [[11/6]]
| |
| | 0.637
| |
| |-
| |
| | [[13/10]], [[20/13]]
| |
| | 4.214
| |
| |-
| |
| | '''[[8/7]], [[7/4]]'''
| |
| | '''6.174'''
| |
| |-
| |
| | [[13/11]], [[22/13]]
| |
| | 10.790
| |
| |-
| |
| | '''[[5/4]], [[8/5]]'''
| |
| | '''11.314'''
| |
| |-
| |
| | [[13/12]], [[24/13]]
| |
| | 11.427
| |
| |-
| |
| | [[15/11]], [[22/15]]
| |
| | 11.951
| |
| |-
| |
| | [[9/7]], [[14/9]]
| |
| | 14.916
| |
| |-
| |
| | [[11/10]], [[20/11]]
| |
| | 15.004
| |
| |-
| |
| | '''[[16/13]], [[13/8]]'''
| |
| | '''15.528'''
| |
| |-
| |
| | [[6/5]], [[5/3]]
| |
| | 15.641
| |
| |-
| |
| | [[7/5]], [[10/7]]
| |
| | 17.488
| |
| |-
| |
| | [[9/8]], [[16/9]]
| |
| | 21.090
| |
| |-
| |
| | [[14/13]], [[13/7]]
| |
| | 21.702
| |
| |-
| |
| | [[15/13]], [[26/15]]
| |
| | 22.741
| |
| |-
| |
| | '''[[11/8]], [[16/11]]'''
| |
| | '''26.318'''
| |
| |-
| |
| | '''[[4/3]], [[3/2]]'''
| |
| | '''26.955'''
| |
| |-
| |
| | [[11/9]], [[18/11]]
| |
| | 27.592
| |
| |-
| |
| | [[15/14]], [[28/15]]
| |
| | 30.557
| |
| |-
| |
| | [[10/9]], [[9/5]]
| |
| | 32.404
| |
| |-
| |
| | [[14/11]], [[11/7]]
| |
| | 32.492
| |
| |-
| |
| | [[7/6]], [[12/7]]
| |
| | 33.129
| |
| |-
| |
| | [[18/13]], [[13/9]]
| |
| | 36.618
| |
| |-
| |
| | [[16/15]], [[15/8]]
| |
| | 36.731
| |
| |}
| |
| {{15-odd-limit|16}}
| |
|
| |
|
| It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it very discordant, although playing this in the context of a larger chord, and with specialized timbres, can make this less noticeable. | | It's worth noting that the 525-cent interval is almost exactly halfway in between 4/3 and 11/8, making it very discordant, although playing this in the context of a larger chord, and with specialized timbres, can make this less noticeable. |