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== Approximation to JI ==
== Approximation to JI ==
=== Interval mappings ===
The following tables show how 16-integer limit ratios are represented in 34zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.


{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Intervals by direct approximation (even if inconsistent)
|+ style="white-space: nowrap;" | 16-integer limit ratios in 34zpi by direct approximation
|-
|-
! Ratio
! Ratio
Line 305: Line 309:
|-
|-
| [[4/3]]
| [[4/3]]
| -0.991
| +0.991 ¢
| -0.993
| +0.993 %
|-
|-
| [[8/3]]
| [[8/3]]
| +1.323
| -1.323 ¢
| +1.325
| -1.325 %
|-
|-
| [[16/9]]
| [[16/9]]
| -1.982
| +1.982 ¢
| -1.986
| +1.986 %
|-
|-
| '''[[2/1]]'''
| '''[[2/1]]'''
| '''+2.314'''
| '''-2.314 ¢'''
| '''+2.318'''
| '''-2.318 %'''
|-
|-
| [[15/1]]
| [[15/1]]
| -2.669
| +2.669 ¢
| -2.674
| +2.674 %
|-
|-
| [[3/2]]
| [[3/2]]
| +3.305
| -3.305 ¢
| +3.311
| -3.311 %
|-
|-
| [[16/3]]
| [[16/3]]
| +3.637
| -3.637 ¢
| +3.644
| -3.644 %
|-
|-
| [[9/8]]
| [[9/8]]
| +4.296
| -4.296 ¢
| +4.304
| -4.304 %
|-
|-
| [[4/1]]
| [[4/1]]
| +4.628
| -4.628 ¢
| +4.637
| -4.637 %
|-
|-
| [[15/2]]
| [[15/2]]
| -4.983
| +4.983 ¢
| -4.992
| +4.992 %
|-
|-
| '''[[3/1]]'''
| '''[[3/1]]'''
| '''+5.619'''
| '''-5.619 ¢'''
| '''+5.629'''
| '''-5.629 %'''
|-
|-
| [[10/1]]
| [[10/1]]
| -5.974
| +5.974 ¢
| -5.985
| +5.985 %
|-
|-
| [[9/4]]
| [[9/4]]
| +6.609
| -6.609 ¢
| +6.622
| -6.622 %
|-
|-
| [[8/1]]
| [[8/1]]
| +6.941
| -6.941 ¢
| +6.955
| -6.955 %
|-
|-
| [[15/4]]
| [[15/4]]
| -7.296
| +7.296 ¢
| -7.311
| +7.311 %
|-
|-
| [[6/1]]
| [[6/1]]
| +7.932
| -7.932 ¢
| +7.948
| -7.948 %
|-
|-
| '''[[5/1]]'''
| '''[[5/1]]'''
| '''-8.287'''
| '''+8.287 ¢'''
| '''-8.303'''
| '''+8.303 %'''
|-
|-
| [[9/2]]
| [[9/2]]
| +8.923
| -8.923 ¢
| +8.941
| -8.941 %
|-
|-
| [[16/1]]
| [[16/1]]
| +9.255
| -9.255 ¢
| +9.273
| -9.273 %
|-
|-
| [[15/8]]
| [[15/8]]
| -9.610
| +9.610 ¢
| -9.629
| +9.629 %
|-
|-
| ''[[13/11]]''
| ''[[13/11]]''
| ''-10.212''
| ''+10.212 ¢''
| ''-10.232''
| ''+10.232 %''
|-
|-
| [[12/1]]
| [[12/1]]
| +10.246
| -10.246 ¢
| +10.266
| -10.266 %
|-
|-
| [[5/2]]
| [[5/2]]
| -10.601
| +10.601 ¢
| -10.622
| +10.622 %
|-
|-
| [[9/1]]
| [[9/1]]
| +11.237
| -11.237 ¢
| +11.259
| -11.259 %
|-
|-
| [[10/3]]
| [[10/3]]
| -11.592
| +11.592 ¢
| -11.614
| +11.614 %
|-
|-
| [[16/15]]
| [[16/15]]
| +11.924
| -11.924 ¢
| +11.947
| -11.947 %
|-
|-
| [[5/4]]
| [[5/4]]
| -12.915
| +12.915 ¢
| -12.940
| +12.940 %
|-
|-
| [[5/3]]
| [[5/3]]
| -13.906
| +13.906 ¢
| -13.933
| +13.933 %
|-
|-
| [[14/5]]
| [[14/5]]
| -14.017
| +14.017 ¢
| -14.044
| +14.044 %
|-
|-
| [[8/5]]
| [[8/5]]
| +15.229
| -15.229 ¢
| +15.258
| -15.258 %
|-
|-
| [[11/7]]
| [[11/7]]
| -15.965
| +15.965 ¢
| -15.996
| +15.996 %
|-
|-
| [[6/5]]
| [[6/5]]
| +16.220
| -16.220 ¢
| +16.251
| -16.251 %
|-
|-
| [[7/5]]
| [[7/5]]
| -16.331
| +16.331 ¢
| -16.362
| +16.362 %
|-
|-
| [[10/9]]
| [[10/9]]
| -17.211
| +17.211 ¢
| -17.244
| +17.244 %
|-
|-
| [[16/5]]
| [[16/5]]
| +17.543
| -17.543 ¢
| +17.577
| -17.577 %
|-
|-
| [[14/11]]
| [[14/11]]
| +18.279
| -18.279 ¢
| +18.315
| -18.315 %
|-
|-
| [[12/5]]
| [[12/5]]
| +18.534
| -18.534 ¢
| +18.569
| -18.569 %
|-
|-
| [[10/7]]
| [[10/7]]
| +18.645
| -18.645 ¢
| +18.681
| -18.681 %
|-
|-
| [[9/5]]
| [[9/5]]
| +19.524
| -19.524 ¢
| +19.562
| -19.562 %
|-
|-
| [[15/14]]
| [[15/14]]
| +19.636
| -19.636 ¢
| +19.674
| -19.674 %
|-
|-
| [[15/7]]
| [[15/7]]
| +21.949
| -21.949 ¢
| +21.992
| -21.992 %
|-
|-
| [[14/1]]
| [[14/1]]
| -22.304
| +22.304 ¢
| -22.347
| +22.347 %
|-
|-
| '''[[7/1]]'''
| '''[[7/1]]'''
| '''-24.618'''
| '''+24.618 ¢'''
| '''-24.666'''
| '''+24.666 %'''
|-
|-
| ''[[13/7]]''
| ''[[13/7]]''
| ''-26.177''
| ''+26.177 ¢''
| ''-26.228''
| ''+26.228 %''
|-
|-
| [[7/2]]
| [[7/2]]
| -26.932
| +26.932 ¢
| -26.984
| +26.984 %
|-
|-
| [[14/3]]
| [[14/3]]
| -27.923
| +27.923 ¢
| -27.977
| +27.977 %
|-
|-
| ''[[14/13]]''
| ''[[14/13]]''
| ''+28.491''
| ''-28.491 ¢''
| ''+28.546''
| ''-28.546 %''
|-
|-
| [[7/4]]
| [[7/4]]
| -29.246
| +29.246 ¢
| -29.302
| +29.302 %
|-
|-
| [[7/3]]
| [[7/3]]
| -30.237
| +30.237 ¢
| -30.295
| +30.295 %
|-
|-
| [[8/7]]
| [[8/7]]
| +31.560
| -31.560 ¢
| +31.621
| -31.621 %
|-
|-
| [[11/5]]
| [[11/5]]
| -32.296
| +32.296 ¢
| -32.359
| +32.359 %
|-
|-
| [[7/6]]
| [[7/6]]
| -32.551
| +32.551 ¢
| -32.614
| +32.614 %
|-
|-
| [[14/9]]
| [[14/9]]
| -33.542
| +33.542 ¢
| -33.606
| +33.606 %
|-
|-
| [[16/7]]
| [[16/7]]
| +33.874
| -33.874 ¢
| +33.939
| -33.939 %
|-
|-
| [[11/10]]
| [[11/10]]
| -34.610
| +34.610 ¢
| -34.677
| +34.677 %
|-
|-
| [[12/7]]
| [[12/7]]
| +34.864
| -34.864 ¢
| +34.932
| -34.932 %
|-
|-
| [[9/7]]
| [[9/7]]
| +35.855
| -35.855 ¢
| +35.925
| -35.925 %
|-
|-
| [[13/9]]
| [[13/9]]
| +37.775
| -37.775 ¢
| +37.848
| -37.848 %
|-
|-
| [[15/11]]
| [[15/11]]
| +37.915
| -37.915 ¢
| +37.988
| -37.988 %
|-
|-
| [[13/12]]
| [[13/12]]
| +38.765
| -38.765 ¢
| +38.840
| -38.840 %
|-
|-
| [[16/13]]
| [[16/13]]
| -39.756
| +39.756 ¢
| -39.833
| +39.833 %
|-
|-
| '''[[11/1]]'''
| '''[[11/1]]'''
| '''-40.584'''
| '''+40.584 ¢'''
| '''-40.662'''
| '''+40.662 %'''
|-
|-
| [[13/6]]
| [[13/6]]
| +41.079
| -41.079 ¢
| +41.159
| -41.159 %
|-
|-
| [[13/8]]
| [[13/8]]
| +42.070
| -42.070 ¢
| +42.151
| -42.151 %
|-
|-
| ''[[13/5]]''
| ''[[13/5]]''
| ''-42.508''
| ''+42.508 ¢''
| ''-42.590''
| ''+42.590 %''
|-
|-
| [[11/2]]
| [[11/2]]
| -42.897
| +42.897 ¢
| -42.980
| +42.980 %
|-
|-
| [[13/3]]
| [[13/3]]
| +43.393
| -43.393 ¢
| +43.477
| -43.477 %
|-
|-
| [[13/4]]
| [[13/4]]
| +44.384
| -44.384 ¢
| +44.470
| -44.470 %
|-
|-
| ''[[13/10]]''
| ''[[13/10]]''
| ''-44.822''
| ''+44.822 ¢''
| ''-44.909''
| ''+44.909 %''
|-
|-
| [[11/4]]
| [[11/4]]
| -45.211
| +45.211 ¢
| -45.299
| +45.299 %
|-
|-
| [[11/3]]
| [[11/3]]
| -46.202
| +46.202 ¢
| -46.291
| +46.291 %
|-
|-
| [[13/2]]
| [[13/2]]
| +46.698
| -46.698 ¢
| +46.788
| -46.788 %
|-
|-
| [[11/8]]
| [[11/8]]
| -47.525
| +47.525 ¢
| -47.617
| +47.617 %
|-
|-
| ''[[11/9]]''
| ''[[11/9]]''
| ''+47.986''
| ''-47.986 ¢''
| ''+48.079''
| ''-48.079 %''
|-
|-
| ''[[15/13]]''
| ''[[15/13]]''
| ''+48.127''
| ''-48.127 ¢''
| ''+48.220''
| ''-48.220 %''
|-
|-
| [[11/6]]
| [[11/6]]
| -48.516
| +48.516 ¢
| -48.610
| +48.610 %
|-
|-
| ''[[12/11]]''
| ''[[12/11]]''
| ''-48.977''
| ''+48.977 ¢''
| ''-49.072''
| ''+49.072 %''
|-
|-
| '''[[13/1]]'''
| '''[[13/1]]'''
| '''+49.012'''
| '''-49.012 ¢'''
| '''+49.106'''
| '''-49.106 %'''
|-
|-
| [[16/11]]
| [[16/11]]
| +49.839
| -49.839 ¢
| +49.935
| -49.935 %
|}
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 16-integer limit ratios in 34zpi by patent val mapping
|-
! 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 %
|-
| [[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 %'''
|-
| [[7/2]]
| +26.932 ¢
| +26.984 %
|-
| [[14/3]]
| +27.923 ¢
| +27.977 %
|-
| [[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 %
|-
| [[11/2]]
| +42.897 ¢
| +42.980 %
|-
| [[13/3]]
| -43.393 ¢
| -43.477 %
|-
| [[13/4]]
| -44.384 ¢
| -44.470 %
|-
| [[11/4]]
| +45.211 ¢
| +45.299 %
|-
| [[11/3]]
| +46.202 ¢
| +46.291 %
|-
| [[13/2]]
| -46.698 ¢
| -46.788 %
|-
| [[11/8]]
| +47.525 ¢
| +47.617 %
|-
| [[11/6]]
| +48.516 ¢
| +48.610 %
|-
| '''[[13/1]]'''
| '''-49.012 ¢'''
| '''-49.106 %'''
|-
| [[16/11]]
| -49.839 ¢
| -49.935 %
|-
| ''[[12/11]]''
| ''-50.830 ¢''
| ''-50.928 %''
|-
| ''[[15/13]]''
| ''+51.680 ¢''
| ''+51.780 %''
|-
| ''[[11/9]]''
| ''+51.821 ¢''
| ''+51.921 %''
|-
| ''[[13/10]]''
| ''-54.985 ¢''
| ''-55.091 %''
|-
| ''[[13/5]]''
| ''-57.299 ¢''
| ''-57.410 %''
|-
| ''[[14/13]]''
| ''+71.316 ¢''
| ''+71.454 %''
|-
| ''[[13/7]]''
| ''-73.630 ¢''
| ''-73.772 %''
|-
| ''[[13/11]]''
| ''-89.595 ¢''
| ''-89.768 %''
|}
|}


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