Xenharmonic Wiki

34zpi: Difference between revisions

← Older editNewer edit →
VisualWikitext
Contribution (talk | contribs)
autopatrolled
2,880 edits
No edit summary
Contribution (talk | contribs)
autopatrolled
2,880 edits
No edit summary
Line 31: Line 31:


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2 left-3 center-4"
|-
| colspan="3" style="text-align:left;" | JI ratios are comprised of 16-integer limit ratios,<br>and are stylized as follows to indicate their accuracy:
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* Normal: relative error < 25 %
* <small>Small:</small> relative error < 33.333 %
* <small><small>Small Small:</small></small> relative error < 41.667 %
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
| style="text-align:right;" | <center>'''12edo'''</center><br>[[9/8|Whole tone]] = 2 steps<br>[[256/243|Limma]] = 1 step<br>[[2187/2048|Apotome]] = 1 step
|-
! Degree
! Cents
! Ratios
! Ups and Downs Notation
|-
| 0
| 0.000
|
| P1
|-
| 1
| 99.807
| '''[[16/15]]''', [[15/14]], <small>[[14/13]]</small>, <small><small>[[13/12]]</small></small>
| m2
|-
| 2
| 199.614
| <small><small><small>[[12/11]]</small></small></small>, <small><small>[[11/10]]</small></small>, [[10/9]], '''<u>[[9/8]]'''</u>, <small>[[8/7]]</small>, <small><small><small>[[15/13]]</small></small></small>
| M2
|-
| 3
| 299.422
| <small>[[7/6]]</small>, '''[[13/11]]''', '''[[6/5]]''', <small><small><small>[[11/9]]</small></small></small>
| m3
|-
| 4
| 399.229
| <small><small>[[16/13]]</small></small>, '''[[5/4]]''', [[14/11]], <small><small>[[9/7]]</small></small>
| M3
|-
| 5
| 499.036
| <small><small><small>[[13/10]]</small></small></small>, '''<u>[[4/3]]'''</u>, <small><small>[[15/11]]</small></small>
| P4
|-
| 6
| 598.843
| <small><small><small>[[11/8]]</small></small></small>, '''[[7/5]]''', [[10/7]], <small><small>[[13/9]]</small></small>, <small><small><small>[[16/11]]</small></small></small>
| A4, d5
|-
| 7
| 698.650
| '''<u>[[3/2]]'''</u>
| P5
|-
| 8
| 798.457
| <small><small>[[14/9]]</small></small>, '''[[11/7]]''', '''[[8/5]]''', <small><small><small>[[13/8]]</small></small></small>
| m6
|-
| 9
| 898.265
| '''[[5/3]]''', <small><small>[[12/7]]</small></small>
| M6
|-
| 10
| 998.072
| <small>[[7/4]]</small>, '''<u>[[16/9]]'''</u>, [[9/5]]
| m7
|-
| 11
| 1097.879
| <small><small><small>[[11/6]]</small></small></small>, <small>[[13/7]]</small>, '''[[15/8]]'''
| M7
|-
| 12
| 1197.686
| '''<u>[[2/1]]'''</u>
| P1 +1 oct
|-
| 13
| 1297.493
| [[15/7]], <small><small>[[13/6]]</small></small>
| m2 +1 oct
|-
| 14
| 1397.301
| <small>[[11/5]]</small>, '''<u>[[9/4]]'''</u>, <small><small>[[16/7]]</small></small>
| M2 +1 oct
|-
| 15
| 1497.108
| <small>[[7/3]]</small>, [[12/5]]
| m3 +1 oct
|-
| 16
| 1596.915
| '''[[5/2]]'''
| M3 +1 oct
|-
| 17
| 1696.722
| <small><small><small>[[13/5]]</small></small></small>, '''<u>[[8/3]]'''</u>
| P4 +1 oct
|-
| 18
| 1796.529
| <small><small><small>[[11/4]]</small></small></small>, '''[[14/5]]'''
| A4 +1 oct, d5 +1 oct
|-
| 19
| 1896.336
| '''<u>[[3/1]]'''</u>
| P5 +1 oct
|-
| 20
| 1996.144
| [[16/5]], <small><small><small>[[13/4]]</small></small></small>
| m6 +1 oct
|-
| 21
| 2095.951
| '''[[10/3]]'''
| M6 +1 oct
|-
| 22
| 2195.758
| <small>[[7/2]]</small>
| m7 +1 oct
|-
| 23
| 2295.565
| <small><small><small>[[11/3]]</small></small></small>, '''<u>[[15/4]]'''</u>
| M7 +1 oct
|-
| 24
| 2395.372
| '''<u>[[4/1]]'''</u>
| P1 +2 oct
|-
| 25
| 2495.180
| <small><small><small>[[13/3]]</small></small></small>
| m2 +2 oct
|-
| 26
| 2594.987
| '''[[9/2]]'''
| M2 +2 oct
|-
| 27
| 2694.794
| <small>[[14/3]]</small>
| m3 +2 oct
|-
| 28
| 2794.601
| '''<u>[[5/1]]'''</u>
| M3 +2 oct
|-
| 29
| 2894.408
| '''<u>[[16/3]]'''</u>
| P4 +2 oct
|-
| 30
| 2994.215
| <small><small><small>[[11/2]]</small></small></small>
| A4 +2 oct, d5 +2 oct
|-
| 31
| 3094.023
| '''<u>[[6/1]]'''</u>
| P5 +2 oct
|-
| 32
| 3193.830
| <small><small><small>[[13/2]]</small></small></small>
| m6 +2 oct
|-
| 33
| 3293.637
|
| M6 +2 oct
|-
| 34
| 3393.444
| [[7/1]]
| m7 +2 oct
|-
| 35
| 3493.251
| '''<u>[[15/2]]'''</u>
| M7 +2 oct
|-
| 36
| 3593.059
| '''<u>[[8/1]]'''</u>
| P1 +3 oct
|-
| 37
| 3692.866
|
| m2 +3 oct
|-
| 38
| 3792.673
| '''[[9/1]]'''
| M2 +3 oct
|-
| 39
| 3892.480
|
| m3 +3 oct
|-
| 40
| 3992.287
| '''<u>[[10/1]]'''</u>
| M3 +3 oct
|-
| 41
| 4092.094
|
| P4 +3 oct
|-
| 42
| 4191.902
| <small><small>[[11/1]]</small></small>
| A4 +3 oct, d5 +3 oct
|-
| 43
| 4291.709
| '''[[12/1]]'''
| P5 +3 oct
|-
| 44
| 4391.516
| <small><small><small>[[13/1]]</small></small></small>
| m6 +3 oct
|-
| 45
| 4491.323
|
| M6 +3 oct
|-
| 46
| 4591.130
| [[14/1]]
| m7 +3 oct
|-
| 47
| 4690.937
| '''<u>[[15/1]]'''</u>
| M7 +3 oct
|-
| 48
| 4790.745
| '''[[16/1]]'''
| P1 +4 oct
|}


== Approximation to JI ==
== Approximation to JI ==
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Intervals by direct approximation (even if inconsistent)
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[4/3]]
| -0.991
| -0.993
|-
| [[8/3]]
| +1.323
| +1.325
|-
| [[16/9]]
| -1.982
| -1.986
|-
| '''[[2/1]]'''
| '''+2.314'''
| '''+2.318'''
|-
| [[15/1]]
| -2.669
| -2.674
|-
| [[3/2]]
| +3.305
| +3.311
|-
| [[16/3]]
| +3.637
| +3.644
|-
| [[9/8]]
| +4.296
| +4.304
|-
| [[4/1]]
| +4.628
| +4.637
|-
| [[15/2]]
| -4.983
| -4.992
|-
| '''[[3/1]]'''
| '''+5.619'''
| '''+5.629'''
|-
| [[10/1]]
| -5.974
| -5.985
|-
| [[9/4]]
| +6.609
| +6.622
|-
| [[8/1]]
| +6.941
| +6.955
|-
| [[15/4]]
| -7.296
| -7.311
|-
| [[6/1]]
| +7.932
| +7.948
|-
| '''[[5/1]]'''
| '''-8.287'''
| '''-8.303'''
|-
| [[9/2]]
| +8.923
| +8.941
|-
| [[16/1]]
| +9.255
| +9.273
|-
| [[15/8]]
| -9.610
| -9.629
|-
| ''[[13/11]]''
| ''-10.212''
| ''-10.232''
|-
| [[12/1]]
| +10.246
| +10.266
|-
| [[5/2]]
| -10.601
| -10.622
|-
| [[9/1]]
| +11.237
| +11.259
|-
| [[10/3]]
| -11.592
| -11.614
|-
| [[16/15]]
| +11.924
| +11.947
|-
| [[5/4]]
| -12.915
| -12.940
|-
| [[5/3]]
| -13.906
| -13.933
|-
| [[14/5]]
| -14.017
| -14.044
|-
| [[8/5]]
| +15.229
| +15.258
|-
| [[11/7]]
| -15.965
| -15.996
|-
| [[6/5]]
| +16.220
| +16.251
|-
| [[7/5]]
| -16.331
| -16.362
|-
| [[10/9]]
| -17.211
| -17.244
|-
| [[16/5]]
| +17.543
| +17.577
|-
| [[14/11]]
| +18.279
| +18.315
|-
| [[12/5]]
| +18.534
| +18.569
|-
| [[10/7]]
| +18.645
| +18.681
|-
| [[9/5]]
| +19.524
| +19.562
|-
| [[15/14]]
| +19.636
| +19.674
|-
| [[15/7]]
| +21.949
| +21.992
|-
| [[14/1]]
| -22.304
| -22.347
|-
| '''[[7/1]]'''
| '''-24.618'''
| '''-24.666'''
|-
| ''[[13/7]]''
| ''-26.177''
| ''-26.228''
|-
| [[7/2]]
| -26.932
| -26.984
|-
| [[14/3]]
| -27.923
| -27.977
|-
| ''[[14/13]]''
| ''+28.491''
| ''+28.546''
|-
| [[7/4]]
| -29.246
| -29.302
|-
| [[7/3]]
| -30.237
| -30.295
|-
| [[8/7]]
| +31.560
| +31.621
|-
| [[11/5]]
| -32.296
| -32.359
|-
| [[7/6]]
| -32.551
| -32.614
|-
| [[14/9]]
| -33.542
| -33.606
|-
| [[16/7]]
| +33.874
| +33.939
|-
| [[11/10]]
| -34.610
| -34.677
|-
| [[12/7]]
| +34.864
| +34.932
|-
| [[9/7]]
| +35.855
| +35.925
|-
| [[13/9]]
| +37.775
| +37.848
|-
| [[15/11]]
| +37.915
| +37.988
|-
| [[13/12]]
| +38.765
| +38.840
|-
| [[16/13]]
| -39.756
| -39.833
|-
| '''[[11/1]]'''
| '''-40.584'''
| '''-40.662'''
|-
| [[13/6]]
| +41.079
| +41.159
|-
| [[13/8]]
| +42.070
| +42.151
|-
| ''[[13/5]]''
| ''-42.508''
| ''-42.590''
|-
| [[11/2]]
| -42.897
| -42.980
|-
| [[13/3]]
| +43.393
| +43.477
|-
| [[13/4]]
| +44.384
| +44.470
|-
| ''[[13/10]]''
| ''-44.822''
| ''-44.909''
|-
| [[11/4]]
| -45.211
| -45.299
|-
| [[11/3]]
| -46.202
| -46.291
|-
| [[13/2]]
| +46.698
| +46.788
|-
| [[11/8]]
| -47.525
| -47.617
|-
| ''[[11/9]]''
| ''+47.986''
| ''+48.079''
|-
| ''[[15/13]]''
| ''+48.127''
| ''+48.220''
|-
| [[11/6]]
| -48.516
| -48.610
|-
| ''[[12/11]]''
| ''-48.977''
| ''-49.072''
|-
| '''[[13/1]]'''
| '''+49.012'''
| '''+49.106'''
|-
| [[16/11]]
| +49.839
| +49.935
|}


== See also ==
== See also ==
Retrieved from "https://en.xen.wiki/w/34zpi"