|
|
| Line 1: |
Line 1: |
| {{Infobox ET}} | | {{Infobox ET}} |
| {{ED intro}} It corresponds to 52.9645 [[edo]], which is closely related to [[53edo]] but with the whole tone instead of the octave tuned pure. | | {{ED intro}} |
|
| |
|
| == Harmonics == | | == Theory == |
| {{Harmonics in equal | | 9ed9/8 corresponds to 52.9645…[[edo]], which is closely related to [[53edo]] but with the whole tone instead of the octave tuned pure. Like [[53edo]], 9ed9/8 is [[consistent]] to the [[integer limit|10-integer-limit]]. |
| | steps = 9 | | |
| | num = 9 | | === Harmonics === |
| | denom = 8 | | {{Harmonics in equal|9|9|8}} |
| }} | | {{Harmonics in equal|9|9|8|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 9ed9/8 (continued)}} |
| {{Harmonics in equal | |
| | steps = 9 | |
| | num = 9 | |
| | denom = 8 | |
| | start = 12 | |
| | collapsed = 1 | |
| }} | |
|
| |
|
| == Intervals == | | == Intervals == |
| Line 20: |
Line 13: |
| |- | | |- |
| ! # | | ! # |
| ! Cents Value | | ! Cents |
| ! Ratio | | ! Ratio |
| |- | | |- |
| Line 243: |
Line 236: |
| | (9/8)<sup>6</sup> = 531441/262144 | | | (9/8)<sup>6</sup> = 531441/262144 |
| |} | | |} |
|
| |
| == Approximation to JI ==
| |
| === 15-odd-limit mappings ===
| |
| The following table shows how [[15-odd-limit intervals]] are represented in 9ed9/8 (ordered by absolute error).
| |
|
| |
| {| class="wikitable center-all"
| |
| |-
| |
| |+ Direct approximation (even if inconsistent)
| |
| |-
| |
| ! Interval(s)
| |
| ! Error (abs, [[cent|¢]])
| |
| |-
| |
| | [[9/8]]
| |
| | 0.000
| |
| |-
| |
| | [[3/2]], [[4/3]]
| |
| | 0.402
| |
| |-
| |
| | [[26/15]]
| |
| | 0.679
| |
| |-
| |
| | [[15/8]], [[5/3]]
| |
| | 0.749
| |
| |-
| |
| | [[16/9]]
| |
| | 0.803
| |
| |-
| |
| | [[13/10]]
| |
| | 1.081
| |
| |-
| |
| | [[5/4]], [[10/9]]
| |
| | 1.150
| |
| |-
| |
| | [[15/13]]
| |
| | 1.482
| |
| |-
| |
| | [[6/5]], [[16/15]]
| |
| | 1.552
| |
| |-
| |
| | [[20/13]]
| |
| | 1.884
| |
| |-
| |
| | [[9/5]], [[8/5]]
| |
| | 1.954
| |
| |-
| |
| | [[13/8]], [[13/9]]
| |
| | 2.231
| |
| |-
| |
| | [[13/12]]
| |
| | 2.633
| |
| |-
| |
| | [[16/13]], [[18/13]]
| |
| | 3.034
| |
| |-
| |
| | [[24/13]]
| |
| | 3.436
| |
| |-
| |
| | [[12/7]]
| |
| | 4.206
| |
| |-
| |
| | [[22/13]]
| |
| | 4.524
| |
| |-
| |
| | [[9/7]], [[8/7]]
| |
| | 4.607
| |
| |-
| |
| | [[7/6]]
| |
| | 5.009
| |
| |-
| |
| | [[13/11]]
| |
| | 5.327
| |
| |-
| |
| | [[7/4]], [[14/9]]
| |
| | 5.411
| |
| |-
| |
| | [[10/7]]
| |
| | 5.758
| |
| |-
| |
| | [[22/15]]
| |
| | 6.006
| |
| |-
| |
| | [[15/14]]
| |
| | 6.159
| |
| |-
| |
| | [[11/10]]
| |
| | 6.408
| |
| |-
| |
| | [[7/5]]
| |
| | 6.561
| |
| |-
| |
| | [[15/11]]
| |
| | 6.809
| |
| |-
| |
| | [[13/7]]
| |
| | 6.838
| |
| |-
| |
| | [[28/15]]
| |
| | 6.963
| |
| |-
| |
| | [[11/6]]
| |
| | 7.156
| |
| |-
| |
| | [[20/11]]
| |
| | 7.211
| |
| |-
| |
| | [[11/9]], [[11/8]]
| |
| | 7.558
| |
| |-
| |
| | [[14/13]]
| |
| | 7.642
| |
| |-
| |
| | [[12/11]]
| |
| | 7.960
| |
| |-
| |
| | [[18/11]], [[16/11]]
| |
| | 8.361
| |
| |-
| |
| | [[14/11]]
| |
| | 9.688
| |
| |-
| |
| | [[11/7]]
| |
| | 10.491
| |
| |}
| |
|
| |
| [[Category:Equal-step tuning]]
| |
| [[Category:Edonoi]]
| |
| [[Category:Whole tone]]
| |