16808edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
mNo edit summary
Overthink (talk | contribs)
autopatrolled
2,723 edits
Undo revision 230160 by Domin (talk) please give a better reason
Tag: Undo
 
(14 intermediate revisions by 6 users not shown)
Line 1: Line 1:
{{novelty}}{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|16808}}
{{ED intro}}


16808edo is distinctly [[consistent]] and highly accurate through the 35-odd-limit, and can be used as a [[interval size measure|measure of interval size]] (the [[jinn]]) for most intervals which occur in practice. It is a very, very strong 31-limit division, and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak]], [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak integer]] and [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral edo]]. In the [[23-limit|23-]], [[29-limit|29-]] and [[31-limit]] it has the lowest [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] up until [[148418edo|148418]]; in the 17- and 19-limit up until [[20203edo|20203]]; though in the 13-limit it is beaten out by smaller edos {{EDOs| 5585, 6079, 8269, 8539, 13112 and 14618 }}.
16808edo's step size is sometimes called a '''jinn''', a term proposed by [[Gene Ward Smith]]<ref>[https://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref>, when used as an [[interval size unit]].


Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out 123201/123200 and 1990656/1990625; in the 17-limit 194481/194480 and 336141/336140; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.
== Theory ==
16808edo is distinctly [[consistent]] and highly accurate through the [[35-odd-limit]], being [[consistency #Generalization|consistent to distance 2]]. It is a very, very strong [[31-limit]] system, and a [[zeta peak edo|zeta peak]], [[zeta peak integer edo|zeta peak integer]] and [[zeta integral edo]]. In the [[23-limit|23-]], [[29-limit|29-]] and 31-limit it has the lowest [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] up until [[148418edo|148418]]; in the [[17-limit|17-]] and [[19-limit]] up until [[20203edo|20203]]; though in the [[13-limit]] it is beaten out by smaller edos {{EDOs| 5585, 6079, 8269, 8539, 13112 and 14618 }}. As such, its step size can be used as an [[interval size unit]] (the jinn) for most intervals which occur in practice.
 
Its [[3/2|perfect fifth]] ultimately comes from [[2101edo]], so it not only has two [[chain of fifths|circles of fifths]] ([[hemipyth]]), but ''eight'', giving itself another edge over similar systems.
 
Among the enormous list of 31-limit [[comma]]s it [[tempering out|tempers out]], the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out [[123201/123200]] and 1990656/1990625; in the 17-limit [[194481/194480]] and [[336141/336140]]; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|16808|prec=5|columns=11}}
{{Harmonics in equal|16808|columns=11}}
{{Harmonics in equal|16808|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 16808edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.
16808 has subset edos 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which [[22edo]] and [[764edo]] are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns. [[33616edo]], which doubles it, corrects its harmonics 37, [[43/1|43]], and [[47/1|47]] to near-just qualities.
 
== Intervals ==
Below the intervals of the 35-odd-limit [[tonality diamond]] are tabulated, with the sizes listed in both [[cent]]s and jinns. The worst error occurs for 33/25 and 50/33, which is less than 1/4 of a jinn off. The measure in jinns can be rounded to the next integer to find the corresponding [[degree]] of 16808edo.
 
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ {{nowrap|35-odd-limit intervals}}
! Interval
! Size in cents
! Size in jinns
|-
| 36/35
| 48.7700
| 683.110
|-
| 35/34
| 50.1840
| 702.914
|-
| 34/33
| 51.6820
| 723.899
|-
| 33/32
| 53.273
| 746.176
|-
| 32/31
| 54.964
| 769.868
|-
| 31/30
| 56.767
| 795.114
|-
| 30/29
| 58.692
| 822.073
|-
| 29/28
| 60.751
| 850.923
|-
| 28/27
| 62.961
| 881.872
|-
| 27/26
| 65.337
| 915.158
|-
| 26/25
| 67.900
| 951.056
|-
| 25/24
| 70.672
| 989.885
|-
| 24/23
| 73.681
| 1032.020
|-
| 23/22
| 76.956
| 1077.903
|-
| 22/21
| 80.537
| 1128.055
|-
| 21/20
| 84.467
| 1183.104
|-
| 20/19
| 88.801
| 1243.802
|-
| 19/18
| 93.603
| 1311.066
|-
| 18/17
| 98.955
| 1386.024
|-
| 35/33
| 101.867
| 1426.813
|-
| 17/16
| 104.955
| 1470.075
|-
| 33/31
| 108.237
| 1516.045
|-
| 16/15
| 111.731
| 1564.983
|-
| 31/29
| 115.458
| 1617.187
|-
| 15/14
| 119.443
| 1672.996
|-
| 29/27
| 123.712
| 1732.795
|-
| 14/13
| 128.298
| 1797.031
|-
| 27/25
| 133.238
| 1866.214
|-
| 13/12
| 138.573
| 1940.941
|-
| 38/35
| 142.373
| 1994.177
|-
| 25/23
| 144.353
| 2021.905
|-
| 12/11
| 150.637
| 2109.923
|-
| 35/32
| 155.140
| 2172.989
|-
| 23/21
| 157.493
| 2205.958
|-
| 34/31
| 159.920
| 2239.944
|-
| 11/10
| 165.004
| 2311.159
|-
| 32/29
| 170.423
| 2387.055
|-
| 21/19
| 173.268
| 2426.906
|-
| 31/28
| 176.210
| 2468.110
|-
| 10/9
| 182.404
| 2554.868
|-
| 29/26
| 189.050
| 2647.954
|-
| 19/17
| 192.558
| 2697.090
|-
| 28/25
| 196.198
| 2748.087
|-
| 9/8
| 203.910
| 2856.099
|-
| 35/31
| 210.104
| 2942.857
|-
| 26/23
| 212.253
| 2972.961
|-
| 17/15
| 216.687
| 3035.058
|-
| 25/22
| 221.309
| 3099.808
|-
| 33/29
| 223.696
| 3133.232
|-
| 8/7
| 231.174
| 3237.978
|-
| 31/27
| 239.171
| 3349.982
|-
| 23/20
| 241.961
| 3389.062
|-
| 38/33
| 244.240
| 3420.989
|-
| 15/13
| 247.741
| 3470.026
|-
| 22/19
| 253.805
| 3554.961
|-
| 29/25
| 256.950
| 3599.010
|-
| 36/31
| 258.874
| 3625.968
|-
| 7/6
| 266.871
| 3737.972
|-
| 34/29
| 275.378
| 3857.131
|-
| 27/23
| 277.591
| 3888.120
|-
| 20/17
| 281.358
| 3940.892
|-
| 33/28
| 284.447
| 3984.155
|-
| 13/11
| 289.210
| 4050.864
|-
| 32/27
| 294.135
| 4119.851
|-
| 19/16
| 297.513
| 4167.166
|-
| 25/21
| 301.847
| 4227.864
|-
| 31/26
| 304.508
| 4265.141
|-
| 6/5
| 315.641
| 4421.082
|-
| 35/29
| 325.562
| 4560.044
|-
| 29/24
| 327.622
| 4588.895
|-
| 23/19
| 330.761
| 4632.864
|-
| 40/33
| 333.041
| 4664.791
|-
| 17/14
| 336.130
| 4708.054
|-
| 28/23
| 340.552
| 4769.992
|-
| 11/9
| 347.408
| 4866.027
|-
| 38/31
| 352.477
| 4937.034
|-
| 27/22
| 354.547
| 4966.022
|-
| 16/13
| 359.472
| 5035.009
|-
| 21/17
| 365.825
| 5123.996
|-
| 26/21
| 369.747
| 5178.920
|-
| 31/25
| 372.408
| 5216.197
|-
| 36/29
| 374.333
| 5243.155
|-
| 5/4
| 386.314
| 5410.967
|-
| 44/35
| 396.178
| 5549.138
|-
| 34/27
| 399.090
| 5589.926
|-
| 29/23
| 401.303
| 5620.915
|-
| 24/19
| 404.442
| 5664.884
|-
| 19/15
| 409.244
| 5732.149
|-
| 33/26
| 412.745
| 5781.186
|-
| 14/11
| 417.508
| 5847.895
|-
| 23/18
| 424.364
| 5943.930
|-
| 32/25
| 427.373
| 5986.065
|-
| 9/7
| 435.084
| 6094.078
|-
| 40/31
| 441.278
| 6180.836
|-
| 31/24
| 443.081
| 6206.082
|-
| 22/17
| 446.363
| 6252.051
|-
| 35/27
| 449.275
| 6292.840
|-
| 13/10
| 454.214
| 6362.023
|-
| 30/23
| 459.994
| 6442.988
|-
| 17/13
| 464.428
| 6505.085
|-
| 38/29
| 467.936
| 6554.221
|-
| 21/16
| 470.781
| 6594.071
|-
| 46/35
| 473.135
| 6627.040
|-
| 25/19
| 475.114
| 6654.769
|-
| 29/22
| 478.259
| 6698.818
|-
| 33/25
| 480.646
| 6732.242
|-
| 4/3
| 498.045
| 6975.950
|-
| 35/26
| 514.612
| 7207.998
|-
| 31/23
| 516.761
| 7238.102
|-
| 27/20
| 519.551
| 7277.182
|-
| 23/17
| 523.319
| 7329.954
|-
| 42/31
| 525.745
| 7363.940
|-
| 19/14
| 528.687
| 7405.144
|-
| 34/25
| 532.328
| 7456.141
|-
| 15/11
| 536.951
| 7520.890
|-
| 26/19
| 543.015
| 7605.825
|-
| 48/35
| 546.815
| 7659.061
|-
| 11/8
| 551.318
| 7722.127
|-
| 40/29
| 556.737
| 7798.023
|-
| 29/21
| 558.796
| 7826.873
|-
| 18/13
| 563.382
| 7891.109
|-
| 25/18
| 568.717
| 7965.835
|-
| 32/23
| 571.726
| 8007.971
|-
| 46/33
| 575.001
| 8053.853
|-
| 7/5
| 582.512
| 8159.054
|-
| 38/27
| 591.648
| 8287.017
|-
| 31/22
| 593.718
| 8316.005
|-
| 24/17
| 597.000
| 8361.974
|-
| 17/12
| 603.000
| 8446.026
|-
| 44/31
| 606.282
| 8491.995
|-
| 27/19
| 608.352
| 8520.983
|-
| 10/7
| 617.488
| 8648.946
|-
| 33/23
| 624.999
| 8754.147
|-
| 23/16
| 628.274
| 8800.029
|-
| 36/25
| 631.283
| 8842.165
|-
| 13/9
| 636.618
| 8916.891
|-
| 42/29
| 641.204
| 8981.127
|-
| 29/20
| 643.263
| 9009.977
|-
| 16/11
| 648.682
| 9085.873
|-
| 35/24
| 653.185
| 9148.939
|-
| 19/13
| 656.985
| 9202.175
|-
| 22/15
| 663.049
| 9287.110
|-
| 25/17
| 667.672
| 9351.859
|-
| 28/19
| 671.313
| 9402.856
|-
| 31/21
| 674.255
| 9444.060
|-
| 34/23
| 676.681
| 9478.046
|-
| 40/27
| 680.449
| 9530.818
|-
| 46/31
| 683.239
| 9569.898
|-
| 52/35
| 685.388
| 9600.002
|-
| 3/2
| 701.955
| 9832.050
|-
| 50/33
| 719.354
| 10075.758
|-
| 44/29
| 721.741
| 10109.182
|-
| 38/25
| 724.886
| 10153.231
|-
| 35/23
| 726.865
| 10180.960
|-
| 32/21
| 729.219
| 10213.929
|-
| 29/19
| 732.064
| 10253.779
|-
| 26/17
| 735.572
| 10302.915
|-
| 23/15
| 740.006
| 10365.012
|-
| 20/13
| 745.786
| 10445.977
|-
| 54/35
| 750.725
| 10515.160
|-
| 17/11
| 753.637
| 10555.949
|-
| 48/31
| 756.919
| 10601.918
|-
| 31/20
| 758.722
| 10627.164
|-
| 14/9
| 764.916
| 10713.922
|-
| 25/16
| 772.627
| 10821.935
|-
| 36/23
| 775.636
| 10864.070
|-
| 11/7
| 782.492
| 10960.105
|-
| 52/33
| 787.255
| 11026.814
|-
| 30/19
| 790.756
| 11075.851
|-
| 19/12
| 795.558
| 11143.116
|-
| 46/29
| 798.697
| 11187.085
|-
| 27/17
| 800.910
| 11218.074
|-
| 35/22
| 803.822
| 11258.862
|-
| 8/5
| 813.686
| 11397.033
|-
| 29/18
| 825.667
| 11564.845
|-
| 50/31
| 827.592
| 11591.803
|-
| 21/13
| 830.253
| 11629.080
|-
| 34/21
| 834.175
| 11684.004
|-
| 13/8
| 840.528
| 11772.991
|-
| 44/27
| 845.453
| 11841.978
|-
| 31/19
| 847.523
| 11870.966
|-
| 18/11
| 852.592
| 11941.973
|-
| 23/14
| 859.448
| 12038.008
|-
| 28/17
| 863.870
| 12099.946
|-
| 33/20
| 866.959
| 12143.209
|-
| 38/23
| 869.239
| 12175.136
|-
| 48/29
| 872.378
| 12219.105
|-
| 58/35
| 874.438
| 12247.956
|-
| 5/3
| 884.359
| 12386.918
|-
| 52/31
| 895.492
| 12542.859
|-
| 42/25
| 898.153
| 12580.136
|-
| 32/19
| 902.487
| 12640.834
|-
| 27/16
| 905.865
| 12688.149
|-
| 22/13
| 910.790
| 12757.136
|-
| 56/33
| 915.553
| 12823.845
|-
| 17/10
| 918.642
| 12867.108
|-
| 46/27
| 922.409
| 12919.880
|-
| 29/17
| 924.622
| 12950.869
|-
| 12/7
| 933.129
| 13070.028
|-
| 31/18
| 941.126
| 13182.032
|-
| 50/29
| 943.050
| 13208.990
|-
| 19/11
| 946.195
| 13253.039
|-
| 26/15
| 952.259
| 13337.974
|-
| 33/19
| 955.760
| 13387.011
|-
| 40/23
| 958.039
| 13418.938
|-
| 54/31
| 960.829
| 13458.018
|-
| 7/4
| 968.826
| 13570.022
|-
| 58/33
| 976.304
| 13674.768
|-
| 44/25
| 978.691
| 13708.192
|-
| 30/17
| 983.313
| 13772.942
|-
| 23/13
| 987.747
| 13835.039
|-
| 62/35
| 989.896
| 13865.143
|-
| 16/9
| 996.090
| 13951.901
|-
| 25/14
| 1003.802
| 14059.913
|-
| 34/19
| 1007.442
| 14110.910
|-
| 52/29
| 1010.950
| 14160.046
|-
| 9/5
| 1017.596
| 14253.132
|-
| 56/31
| 1023.790
| 14339.890
|-
| 38/21
| 1026.732
| 14381.094
|-
| 29/16
| 1029.577
| 14420.945
|-
| 20/11
| 1034.996
| 14496.841
|-
| 31/17
| 1040.080
| 14568.056
|-
| 42/23
| 1042.507
| 14602.042
|-
| 64/35
| 1044.860
| 14635.011
|-
| 11/6
| 1049.363
| 14698.077
|-
| 46/25
| 1055.647
| 14786.095
|-
| 35/19
| 1057.627
| 14813.823
|-
| 24/13
| 1061.427
| 14867.059
|-
| 50/27
| 1066.762
| 14941.786
|-
| 13/7
| 1071.702
| 15010.969
|-
| 54/29
| 1076.288
| 15075.205
|-
| 28/15
| 1080.557
| 15135.004
|-
| 58/31
| 1084.542
| 15190.813
|-
| 15/8
| 1088.269
| 15243.017
|-
| 62/33
| 1091.763
| 15291.955
|-
| 32/17
| 1095.045
| 15337.925
|-
| 66/35
| 1098.133
| 15381.187
|-
| 17/9
| 1101.045
| 15421.976
|-
| 36/19
| 1106.397
| 15496.934
|-
| 19/10
| 1111.199
| 15564.198
|-
| 40/21
| 1115.533
| 15624.896
|-
| 21/11
| 1119.463
| 15679.945
|-
| 44/23
| 1123.044
| 15730.097
|-
| 23/12
| 1126.319
| 15775.980
|-
| 48/25
| 1129.328
| 15818.115
|-
| 25/13
| 1132.100
| 15856.944
|-
| 52/27
| 1134.663
| 15892.842
|-
| 27/14
| 1137.039
| 15926.128
|-
| 56/29
| 1139.249
| 15957.077
|-
| 29/15
| 1141.308
| 15985.927
|-
| 60/31
| 1143.233
| 16012.886
|-
| 31/16
| 1145.036
| 16038.132
|-
| 64/33
| 1146.727
| 16061.824
|-
| 33/17
| 1148.318
| 16084.101
|-
| 68/35
| 1149.816
| 16105.086
|-
| 35/18
| 1151.230
| 16124.890
|-
| 2
| 1200.000
| 16808.000
|}
 
== References ==
<references />
 
[[Category:16808edo| ]] <!-- main article -->
[[Category:Interval size measures]]

Latest revision as of 00:14, 13 May 2026

← 16807edo 16808edo 16809edo →
Prime factorization 23 × 11 × 191
Step size 0.0713946 ¢ 
Fifth 9832\16808 (701.951 ¢) (→ 1229\2101)
Semitones (A1:m2) 1592:1264 (113.7 ¢ : 90.24 ¢)
Consistency limit 35
Distinct consistency limit 35

16808 equal divisions of the octave (abbreviated 16808edo or 16808ed2), also called 16808-tone equal temperament (16808tet) or 16808 equal temperament (16808et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 16808 equal parts of about 0.0714 ¢ each. Each step represents a frequency ratio of 21/16808, or the 16808th root of 2.

16808edo's step size is sometimes called a jinn, a term proposed by Gene Ward Smith[1], when used as an interval size unit.

Theory

16808edo is distinctly consistent and highly accurate through the 35-odd-limit, being consistent to distance 2. It is a very, very strong 31-limit system, and a zeta peak, zeta peak integer and zeta integral edo. In the 23-, 29- and 31-limit it has the lowest relative error up until 148418; in the 17- and 19-limit up until 20203; though in the 13-limit it is beaten out by smaller edos 5585, 6079, 8269, 8539, 13112 and 14618. As such, its step size can be used as an interval size unit (the jinn) for most intervals which occur in practice.

Its perfect fifth ultimately comes from 2101edo, so it not only has two circles of fifths (hemipyth), but eight, giving itself another edge over similar systems.

Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out 123201/123200 and 1990656/1990625; in the 17-limit 194481/194480 and 336141/336140; in the 19-limit 43681/43680, 89376/89375 and 104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

Prime harmonics

Approximation of prime harmonics in 16808edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0035 +0.0023 -0.0015 -0.0090 +0.0007 -0.0054 -0.0118 -0.0021 +0.0040 -0.0094
Relative (%) +0.0 -5.0 +3.3 -2.2 -12.7 +0.9 -7.5 -16.6 -2.9 +5.5 -13.2
Steps
(reduced) 		16808
(0) 		26640
(9832) 		39027
(5411) 		47186
(13570) 		58146
(7722) 		62197
(11773) 		68702
(1470) 		71399
(4167) 		76032
(8800) 		81653
(14421) 		83270
(16038)
Approximation of prime harmonics in 16808edo (continued)
Harmonic 37 41 43 47 53 59 61 67 71 73 79
Error Absolute (¢) -0.0351 +0.0190 +0.0244 +0.0336 +0.0081 -0.0332 +0.0119 +0.0123 +0.0036 +0.0306 +0.0038
Relative (%) -49.2 +26.6 +34.2 +47.1 +11.3 -46.4 +16.7 +17.3 +5.0 +42.9 +5.3
Steps
(reduced) 		87560
(3520) 		90050
(6010) 		91205
(7165) 		93362
(9322) 		96275
(12235) 		98875
(14835) 		99684
(15644) 		101959
(1111) 		103365
(2517) 		104039
(3191) 		105954
(5106)

Subsets and supersets

16808 has subset edos 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which 22edo and 764edo are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns. 33616edo, which doubles it, corrects its harmonics 37, 43, and 47 to near-just qualities.

Intervals

Below the intervals of the 35-odd-limit tonality diamond are tabulated, with the sizes listed in both cents and jinns. The worst error occurs for 33/25 and 50/33, which is less than 1/4 of a jinn off. The measure in jinns can be rounded to the next integer to find the corresponding degree of 16808edo.

35-odd-limit intervals
Interval Size in cents Size in jinns
36/35 48.7700 683.110
35/34 50.1840 702.914
34/33 51.6820 723.899
33/32 53.273 746.176
32/31 54.964 769.868
31/30 56.767 795.114
30/29 58.692 822.073
29/28 60.751 850.923
28/27 62.961 881.872
27/26 65.337 915.158
26/25 67.900 951.056
25/24 70.672 989.885
24/23 73.681 1032.020
23/22 76.956 1077.903
22/21 80.537 1128.055
21/20 84.467 1183.104
20/19 88.801 1243.802
19/18 93.603 1311.066
18/17 98.955 1386.024
35/33 101.867 1426.813
17/16 104.955 1470.075
33/31 108.237 1516.045
16/15 111.731 1564.983
31/29 115.458 1617.187
15/14 119.443 1672.996
29/27 123.712 1732.795
14/13 128.298 1797.031
27/25 133.238 1866.214
13/12 138.573 1940.941
38/35 142.373 1994.177
25/23 144.353 2021.905
12/11 150.637 2109.923
35/32 155.140 2172.989
23/21 157.493 2205.958
34/31 159.920 2239.944
11/10 165.004 2311.159
32/29 170.423 2387.055
21/19 173.268 2426.906
31/28 176.210 2468.110
10/9 182.404 2554.868
29/26 189.050 2647.954
19/17 192.558 2697.090
28/25 196.198 2748.087
9/8 203.910 2856.099
35/31 210.104 2942.857
26/23 212.253 2972.961
17/15 216.687 3035.058
25/22 221.309 3099.808
33/29 223.696 3133.232
8/7 231.174 3237.978
31/27 239.171 3349.982
23/20 241.961 3389.062
38/33 244.240 3420.989
15/13 247.741 3470.026
22/19 253.805 3554.961
29/25 256.950 3599.010
36/31 258.874 3625.968
7/6 266.871 3737.972
34/29 275.378 3857.131
27/23 277.591 3888.120
20/17 281.358 3940.892
33/28 284.447 3984.155
13/11 289.210 4050.864
32/27 294.135 4119.851
19/16 297.513 4167.166
25/21 301.847 4227.864
31/26 304.508 4265.141
6/5 315.641 4421.082
35/29 325.562 4560.044
29/24 327.622 4588.895
23/19 330.761 4632.864
40/33 333.041 4664.791
17/14 336.130 4708.054
28/23 340.552 4769.992
11/9 347.408 4866.027
38/31 352.477 4937.034
27/22 354.547 4966.022
16/13 359.472 5035.009
21/17 365.825 5123.996
26/21 369.747 5178.920
31/25 372.408 5216.197
36/29 374.333 5243.155
5/4 386.314 5410.967
44/35 396.178 5549.138
34/27 399.090 5589.926
29/23 401.303 5620.915
24/19 404.442 5664.884
19/15 409.244 5732.149
33/26 412.745 5781.186
14/11 417.508 5847.895
23/18 424.364 5943.930
32/25 427.373 5986.065
9/7 435.084 6094.078
40/31 441.278 6180.836
31/24 443.081 6206.082
22/17 446.363 6252.051
35/27 449.275 6292.840
13/10 454.214 6362.023
30/23 459.994 6442.988
17/13 464.428 6505.085
38/29 467.936 6554.221
21/16 470.781 6594.071
46/35 473.135 6627.040
25/19 475.114 6654.769
29/22 478.259 6698.818
33/25 480.646 6732.242
4/3 498.045 6975.950
35/26 514.612 7207.998
31/23 516.761 7238.102
27/20 519.551 7277.182
23/17 523.319 7329.954
42/31 525.745 7363.940
19/14 528.687 7405.144
34/25 532.328 7456.141
15/11 536.951 7520.890
26/19 543.015 7605.825
48/35 546.815 7659.061
11/8 551.318 7722.127
40/29 556.737 7798.023
29/21 558.796 7826.873
18/13 563.382 7891.109
25/18 568.717 7965.835
32/23 571.726 8007.971
46/33 575.001 8053.853
7/5 582.512 8159.054
38/27 591.648 8287.017
31/22 593.718 8316.005
24/17 597.000 8361.974
17/12 603.000 8446.026
44/31 606.282 8491.995
27/19 608.352 8520.983
10/7 617.488 8648.946
33/23 624.999 8754.147
23/16 628.274 8800.029
36/25 631.283 8842.165
13/9 636.618 8916.891
42/29 641.204 8981.127
29/20 643.263 9009.977
16/11 648.682 9085.873
35/24 653.185 9148.939
19/13 656.985 9202.175
22/15 663.049 9287.110
25/17 667.672 9351.859
28/19 671.313 9402.856
31/21 674.255 9444.060
34/23 676.681 9478.046
40/27 680.449 9530.818
46/31 683.239 9569.898
52/35 685.388 9600.002
3/2 701.955 9832.050
50/33 719.354 10075.758
44/29 721.741 10109.182
38/25 724.886 10153.231
35/23 726.865 10180.960
32/21 729.219 10213.929
29/19 732.064 10253.779
26/17 735.572 10302.915
23/15 740.006 10365.012
20/13 745.786 10445.977
54/35 750.725 10515.160
17/11 753.637 10555.949
48/31 756.919 10601.918
31/20 758.722 10627.164
14/9 764.916 10713.922
25/16 772.627 10821.935
36/23 775.636 10864.070
11/7 782.492 10960.105
52/33 787.255 11026.814
30/19 790.756 11075.851
19/12 795.558 11143.116
46/29 798.697 11187.085
27/17 800.910 11218.074
35/22 803.822 11258.862
8/5 813.686 11397.033
29/18 825.667 11564.845
50/31 827.592 11591.803
21/13 830.253 11629.080
34/21 834.175 11684.004
13/8 840.528 11772.991
44/27 845.453 11841.978
31/19 847.523 11870.966
18/11 852.592 11941.973
23/14 859.448 12038.008
28/17 863.870 12099.946
33/20 866.959 12143.209
38/23 869.239 12175.136
48/29 872.378 12219.105
58/35 874.438 12247.956
5/3 884.359 12386.918
52/31 895.492 12542.859
42/25 898.153 12580.136
32/19 902.487 12640.834
27/16 905.865 12688.149
22/13 910.790 12757.136
56/33 915.553 12823.845
17/10 918.642 12867.108
46/27 922.409 12919.880
29/17 924.622 12950.869
12/7 933.129 13070.028
31/18 941.126 13182.032
50/29 943.050 13208.990
19/11 946.195 13253.039
26/15 952.259 13337.974
33/19 955.760 13387.011
40/23 958.039 13418.938
54/31 960.829 13458.018
7/4 968.826 13570.022
58/33 976.304 13674.768
44/25 978.691 13708.192
30/17 983.313 13772.942
23/13 987.747 13835.039
62/35 989.896 13865.143
16/9 996.090 13951.901
25/14 1003.802 14059.913
34/19 1007.442 14110.910
52/29 1010.950 14160.046
9/5 1017.596 14253.132
56/31 1023.790 14339.890
38/21 1026.732 14381.094
29/16 1029.577 14420.945
20/11 1034.996 14496.841
31/17 1040.080 14568.056
42/23 1042.507 14602.042
64/35 1044.860 14635.011
11/6 1049.363 14698.077
46/25 1055.647 14786.095
35/19 1057.627 14813.823
24/13 1061.427 14867.059
50/27 1066.762 14941.786
13/7 1071.702 15010.969
54/29 1076.288 15075.205
28/15 1080.557 15135.004
58/31 1084.542 15190.813
15/8 1088.269 15243.017
62/33 1091.763 15291.955
32/17 1095.045 15337.925
66/35 1098.133 15381.187
17/9 1101.045 15421.976
36/19 1106.397 15496.934
19/10 1111.199 15564.198
40/21 1115.533 15624.896
21/11 1119.463 15679.945
44/23 1123.044 15730.097
23/12 1126.319 15775.980
48/25 1129.328 15818.115
25/13 1132.100 15856.944
52/27 1134.663 15892.842
27/14 1137.039 15926.128
56/29 1139.249 15957.077
29/15 1141.308 15985.927
60/31 1143.233 16012.886
31/16 1145.036 16038.132
64/33 1146.727 16061.824
33/17 1148.318 16084.101
68/35 1149.816 16105.086
35/18 1151.230 16124.890
2 1200.000 16808.000

References

  1. ↑ Stichting Huygens-Fokker: Logarithmic Interval Measures
Retrieved from "https://en.xen.wiki/index.php?title=16808edo&oldid=230168"