4L 5s (3/1-equivalent): Difference between revisions

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Dave Keenan (talk | contribs)
autopatrolled, emailconfirmed
1,671 edits
Inserted the name of the 3.5.7 rank-2 temperament, BPS (Bohlen-Pierce-Stearns)
mNo edit summary
Line 81: Line 81:
| |  
| |  
| |  
| |  
| colspan="2" | 475.489
| colspan="2" | 475.488…
325
325
| | 0
| | 0
Line 93: Line 93:
| |  
| |  
| | 8/33
| | 8/33
| | 461.08
| | 461.080…
315.1515
315.{{overline|1=15}}
| | 403.445
| | 403.445…
275.758
275.{{overline|1=75}}
| | 57.635
| | 57.635…
39.394
39.{{overline|1=39}}
| |  
| |  
|-
|-
Line 108: Line 108:
| | 7/29
| | 7/29
| |  
| |  
| | 459.093
| | 459.092…
313.793
313.793…
| | 393.508
| | 393.507…
268.9655
268.965…
| | 65.585
| | 65.584…
44.828
44.827…
| |  
| |  
|-
|-
Line 123: Line 123:
| |  
| |  
| | 13/54
| | 13/54
| | 457.878
| | 457.878…
312.963
312.{{overline|1=962}}
| | 387.435
| | 387.435…
264.815
264.{{overline|1=814}}
| | 70.428
| | 70.442…
48.148
48.{{overline|1=148}}
| |  
| |  
|-
|-
Line 138: Line 138:
| |  
| |  
| |  
| |  
| | 456.469
| | 456.469…
312
312
| | 380.391
| | 380.391…
260
260
| | 76.078
| | 76.078…
52
52
| |  
| |  
Line 153: Line 153:
| |  
| |  
| | 17/71
| | 17/71
| | 455.398
| | 455.397…
311.267
311.267…
| | 375.033
| | 375.033…
256.338
256.338…
| | 80.364
| | 80.364…
54.9295
54.929…
| |  
| |  
|-
|-
Line 168: Line 168:
| | 11/46
| | 11/46
| |  
| |  
| | 454.815
| | 454.815…
310.8695
310.869…
| | 372.122
| | 372.121…
254.348
254.347…
| | 82.694
| | 82.693…
56.522
56.521…
| |  
| |  
|-
|-
Line 183: Line 183:
| |  
| |  
| | 16/67
| | 16/67
| | 454.198
| | 454.198…
310.448
310.447…
| | 369.036
| | 369.036…
252.239
252.238…
| | 85.162
| | 85.162…
58.209
58.208…
| |  
| |  
|-
|-
Line 198: Line 198:
| |  
| |  
| |  
| |  
| | 452.846
| | 452.846…
309.524
309.523…
| | 362.277
| | 362.277…
247.619
247.619…
| | 90.569
| | 90.569…
61.905
61.904…
| |  
| |  
|-
|-
Line 213: Line 213:
| |  
| |  
| | 19/80
| | 19/80
| | 451.714
| | 451.714…
308.75
308.75
| | 356.617
| | 356.616…
243.75
243.75
| | 95.098
| | 95.097…
65
65
| |  
| |  
Line 228: Line 228:
| | 14/59
| | 14/59
| |  
| |  
| | 451.311
| | 451.311…
308.4745
308.474…
| | 354.602
| | 354.601…
242.373
242.372…
| | 96.71
| | 96.709…
66.102
66.101…
| |  
| |  
|-
|-
Line 243: Line 243:
| |  
| |  
| | 23/97
| | 23/97
| | 450.979
| | 450.979…
308.247
308.247…
| | 352.94
| | 352.940…
241.234
241.234…
| | 98.039
| | 98.038…
67.01
67.010…
| |  
| |  
|-
|-
Line 258: Line 258:
| |  
| |  
| |  
| |  
| | 450.463
| | 450.463…
307.895
307.894…
| | 350.36
| | 350.360…
239.474
239.473…
| | 100.103
| | 100.102…
68.421
68.421…
| |  
| |  
|-
|-
Line 273: Line 273:
| |  
| |  
| | 22/93
| | 22/93
| | 449.925
| | 449.924…
307.527
307.526…
| | 347.669
| | 347.669…
237.634
237.634…
| | 102.256
| | 102.255…
69.8925
69.892…
| |  
| |  
|-
|-
Line 288: Line 288:
| | 13/55
| | 13/55
| |  
| |  
| | 449.553
| | 449.553…
307.273
307.{{overline|1=27}}
| | 345.81
| | 345.810…
236.364
236.{{overline|1=36}}
| | 103.743
| | 103.743…
70.909
70.{{overline|1=90}}
| |  
| |  
|-
|-
Line 303: Line 303:
| |  
| |  
| | 17/72
| | 17/72
| | 449.073
| | 449.072…
306.944
306.9{{overline|1=4}}
| | 343.4085
| | 343.408…
234.722
234.7{{overline|1=2}}
| | 105.664
| | 105.664…
72.222
72.{{overline|1=2}}
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| |  
|-
|-
Line 318: Line 318:
| |  
| |  
| |  
| |  
| | 448.421
| | 448.420…
306.499
306.498…
| | 340.148
| | 340.148…
232.494
232.493…
| | 108.2725
| | 108.272…
74.005
74.005…
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| |  
|-
|-
Line 333: Line 333:
| |  
| |  
| |  
| |  
| | 447.518
| | 447.518…
305.882
305.882…
| | 335.639
| | 335.639…
229.412
229.411…
| | 111.88
| | 111.879…
76.471
76.470…
| | Canonical BP scales are between here...
| | Canonical BP scales are between here...
|-
|-
Line 348: Line 348:
| |  
| |  
| | 19/81
| | 19/81
| | 446.137
| | 446.137…
304.938
304.938…
| | 328.733
| | 328.733…
224.691
224.691…
| | 117.405
| | 117.404…
80.247
80.246…
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| |  
|-
|-
Line 363: Line 363:
| | 15/64
| | 15/64
| |  
| |  
| | 445.771
| | 445.770…
304.6875
[[Tel:304.6875|304.6875]]
| | 326.8985
| | 326.898…
223.4375
[[Tel:223.4375|223.4375]]
| | 118.872
| | 118.872…
81.25
81.25
| |  
| |  
Line 378: Line 378:
| |  
| |  
| |  
| |  
| | 445.533
| | 445.533…
304.525
304.525…
| | 325.711
| | 325.710…
222.626
222.625…
| | 119.822
| | 119.822…
81.899
81.899…
| |  
| |  
|-
|-
Line 393: Line 393:
| |  
| |  
| | 26/111
| | 26/111
| | 445.503
| | 445.502…
304.5045
304.{{overline|1=504}}
| | 325.559
| | 325.559…
222.5225
222.{{overline|1=522}}
| | 119.943
| | 119.943…
81.982
81.{{overline|1=981}}
| |  
| |  
|-
|-
Line 408: Line 408:
| |  
| |  
| |  
| |  
| | 445.138
| | 445.138…
304.255
304.255…
| | 323.737
| | 323.737…
221.277
221.276…
| | 121.401
| | 121.401…
82.989
82.978…
| |  
| |  
|-
|-
Line 423: Line 423:
| |  
| |  
| | 29/124
| | 29/124
| | 444.812
| | 444.812…
304.032
304.032…
| | 322.105
| | 322.105…
220.161
220.161…
| | 122.705
| | 122.706…
83.871
83.870…
| | Golden BP is near here
| | Golden BP is near here
|-
|-
Line 438: Line 438:
| | 18/77
| | 18/77
| |  
| |  
| | 444.613
| | 444.612…
303.896
303.896…
| | 321.109
| | 321.109…
219.4805
219.480…
| | 123.5035
| | 123.503…
84.416
84.415…
| |  
| |  
|-
|-
Line 453: Line 453:
| |  
| |  
| | 25/107
| | 25/107
| | 444.382
| | 444.382…
303.738
303.738…
| | 319.955
| | 319.955…
218.692
218.691…
| | 120.427
| | 120.426…
85.047
85.046…
| |  
| |  
|-
|-
Line 468: Line 468:
| |  
| |  
| |  
| |  
| | 443.7895
| | 443.789…
303.333
303.{{overline|1=3}}
| | 316.9925
| | 316.992…
216.667
216.{{overline|1=6}}
| | 126.797
| | 126.797…
86.667
86.{{overline|1=6}}
| |  
| |  
|-
|-
Line 483: Line 483:
| |  
| |  
| | 24/103
| | 24/103
| | 443.174
| | 443.173…
302.913
302.912…
| | 313.915
| | 313.914…
214.563
214.563…
| | 129.26
| | 129.259…
88.3495
88.349…
| |  
| |  
|-
|-
Line 498: Line 498:
| | 17/73
| | 17/73
| |  
| |  
| | 442.921
| | 442.921…
302.74
302.739…
| | 312.65
| | 312.650…
213.699
213.698…
| | 130.271
| | 130.270…
89.041
89.041…
| |  
| |  
|-
|-
Line 513: Line 513:
| |  
| |  
| | 27/116
| | 27/116
| | 442.696
| | 442.696…
302.586
302.586…
| | 311.527
| | 311.527…
212.931
212.931…
| | 131.169
| | 131.169…
89.65
89.655…
| |  
| |  
|-
|-
Line 528: Line 528:
| |  
| |  
| |  
| |  
| | 442.315
| | 442.315…
302.326
302.325…
| | 309.621
| | 309.620…
211.628
211.627…
| | 132.6945
| | 132.694…
90.698
90.697…
| |  
| |  
|-
|-
Line 543: Line 543:
| |  
| |  
| | 23/99
| | 23/99
| | 441.868
| | 441.868…
302.02
302.{{overline|1=02}}
| | 307.387
| | 307.386…
210.101
210.{{overline|1=10}}
| | 134.482
| | 134.481…
91.919
91.{{overline|1=91}}
| |  
| |  
|-
|-
Line 558: Line 558:
| | 13/56
| | 13/56
| |  
| |  
| | 441.525
| | 441.525…
301.786
301.785…
| | 305.671
| | 305.671…
208.929
208.928…
| | 135.854
| | 135.853…
92.857
92.857…
| |  
| |  
|-
|-
Line 573: Line 573:
| |  
| |  
| | 16/69
| | 16/69
| | 441.033
| | 441.033…
301.449
301.449…
| | 303.21
| | 303.210…
207.246
207.246…
| | 137.823
| | 137.822…
94.203
94.202…
| |  
| |  
|-
|-
Line 588: Line 588:
| |  
| |  
| |  
| |  
| | 438.913
| | 438.912…
300
300
| | 292.6085
| | 292.608…
200
200
| | 146.304
| | 146.304…
100
100
| | ...and here
| | ...and here
Line 605: Line 605:
| |  
| |  
| | 17/74
| | 17/74
| | 436.935
| | 436.935…
298.649
298.{{overline|1=648}}
| | 282.723
| | 282.723…
193.243
193.{{overline|1=243}}
| | 154.2125
| | 154.212…
105.405
105.{{overline|1=405}}
| |  
| |  
|-
|-
Line 620: Line 620:
| | 14/61
| | 14/61
| |  
| |  
| | 436.514
| | 436.514…
298.361
298.360…
| | 280.616
| | 280.616…
191.803
191.803…
| | 155.897
| | 155.897…
106.557
106.557…
| |  
| |  
|-
|-
Line 635: Line 635:
| |  
| |  
| | 25/109
| | 25/109
| | 436.228
| | 436.228…
298.165
298.165…
| | 279.186
| | 279.186…
190.826
190.825…
| | 157.042
| | 157.042…
207.339
207.339…
| |  
| |  
|-
|-
Line 651: Line 651:
| |  
| |  
| | 435.865
| | 435.865
297.917
297.91{{overline|1=6}}
| | 277.368
| | 277.368…
189.583
189.58{{overline|1=3}}
| | 158.496
| | 158.496…
108.333
108.{{overline|1=3}}
| |  
| |  
|-
|-
Line 665: Line 665:
| |  
| |  
| | 30/131
| | 30/131
| | 435.562
| | 435.562…
297.71
297.709…
| | 275.856
| | 275.856…
188.55
188.549…
| | 159.706
| | 159.706…
109.16
109.160…
| |  
| |  
|-
|-
Line 680: Line 680:
| | 19/83
| | 19/83
| |  
| |  
| | 435.387
| | 435.387…
297.59
297.590…
| | 274.981
| | 274.981…
187.952
187.951…
| | 160.406
| | 160.405…
109.639
109.638…
| |  
| |  
|-
|-
Line 695: Line 695:
| |  
| |  
| | 27/118
| | 27/118
| | 435.193
| | 435.193…
297.458
297.457…
| | 274.0105
| | 274.010…
187.288
187.288…
| | 161.183
| | 161.182…
110.1695
110.169…
| |  
| |  
|-
|-
Line 710: Line 710:
| |  
| |  
| |  
| |  
| | 434.733
| | 434.732…
297.143
297.142…
| | 271.707
| | 271.707…
185.714
185.714…
| | 163.025
| | 163.024…
111.429
111.428…
| |  
| |  
|-
|-
Line 725: Line 725:
| |  
| |  
| | 29/127
| | 29/127
| | 434.305
| | 434.304…
296.85
296.850…
| | 269.568
| | 269.568…
184.252
184.251…
| | 164.736
| | 164.736…
112.598
112.598…
| |  
| |  
|-
|-
Line 740: Line 740:
| | 21/92
| | 21/92
| |  
| |  
| | 434.142
| | 434.141…
596.739
596.739…
| | 268.7545
| | 268.754…
183.696
183.695…
| | 165.387
| | 165.387…
113.0435
113.043…
| |  
| |  
|-
|-
Line 755: Line 755:
| |  
| |  
| | 34/149
| | 34/149
| | 434.003
| | 434.003…
296.644
296.644…
| | 268.061
| | 268.060…
183.2215
183.221…
| | 165.942
| | 165.942…
113.423
113.422…
| | Golden Lambda scale is near here
| | Golden Lambda scale is near here


Line 772: Line 772:
| |  
| |  
| |  
| |  
| | 433.779
| | 433.779…
296.491
296.491…
| | 266.941
| | 266.941…
182.456
182.456…
| | 166.838
| | 166.838…
114.035
114.035…
| | 18\7*30\11=7
| | 18\7*30\11=7
|-
|-
Line 787: Line 787:
| |  
| |  
| | 31/136
| | 31/136
| | 433.534
| | 433.533…
296.3235
296.323…
| | 265.714
| | 265.714…
181.618
181.617…
| | 167.8195
| | 167.819…
114.706
114.705…
| |  
| |  
|-
|-
Line 802: Line 802:
| | 18/79
| | 18/79
| |  
| |  
| | 433.356
| | 433.356…
296.2025
296.202…
| | 264.829
| | 264.829…
181.013
181.012…
| | 168.528
| | 168.527…
115.189
115.189…
| |  
| |  
|-
|-
Line 817: Line 817:
| |  
| |  
| | 23/101
| | 23/101
| | 433.1185
| | 433.118…
296.04
296.039…
| | 263.637
| | 263.637…
180.198
180.198…
| | 169.484
| | 169.481…
115.842
115.841…
| |  
| |  
|-
|-
Line 832: Line 832:
| |  
| |  
| |  
| |  
| | 432.2625
| | 432.262…
295.4545
295.{{overline|1=45}}
| | 259.3575
| | 259.357…
177.273
177.{{overline|1=27}}
| | 172.905
| | 172.905…
118.182
118.{{overline|1=18}}
| |  
| |  
|-
|-
Line 847: Line 847:
| |  
| |  
| | 22/97
| | 22/97
| | 431.371
| | 431.371…
294.845
294.845…
| | 254.901
| | 254.901…
174.227
174.226…
| | 176.47
| | 176.470…
120.619
120.618…
| |  
| |  
|-
|-
Line 862: Line 862:
| | 17/75
| | 17/75
| |  
| |  
| | 431.11
| | 431.109…
294.667
294.{{overline|1=6}}
| | 253.594
| | 253.594…
173.333
173.{{overline|1=3}}
| | 177.516
| | 177.515…
121.333
121.{{overline|1=3}}
| |  
| |  
|-
|-
Line 877: Line 877:
| |  
| |  
| | 29/128
| | 29/128
| | 430.912
| | 430.911…
294.531
294.531…
| | 252.603
| | 252.603…
172.626
172.656…
| | 178.308
| | 178.308…
121.875
121.875
| |  
| |  
Line 892: Line 892:
| |  
| |  
| |  
| |  
| | 430.631
| | 430.631…
294.334
294.339…
| | 251.202
| | 251.201…
171.698
171.698…
| | 179.43
| | 179.429…
122.6415
122.641…
| |  
| |  
|-
|-
Line 907: Line 907:
| |  
| |  
| | 31/137
| | 31/137
| | 430.369
| | 430.369…
294.161
294.160…
| | 249.892
| | 249.891…
170.803
170.802…
| | 180.4775
| | 180.477…
123.358
123.357…
| |  
| |  
|-
|-
Line 922: Line 922:
| | 19/84
| | 19/84
| |  
| |  
| | 430.204
| | 430.204…
294.048
294.047…
| | 249.066
| | 249.065…
170.238
170.238…
| | 181.139
| | 181.138…
123.8095
123.809…
| |  
| |  
|-
|-
Line 937: Line 937:
| |  
| |  
| | 26/115
| | 26/115
| | 430.007
| | 430.007…
293.913
293.913…
| | 248.081
| | 248.081…
169.565
169.565…
| | 181.927
| | 181.926…
124.348
124.347…
| |  
| |  
|-
|-
Line 952: Line 952:
| |  
| |  
| |  
| |  
| | 429.474
| | 429.473…
293.548
293.548…
| | 245.4135
| | 245.413…
167.742
167.741…
| | 184.06
| | 184.060…
125.8065
125.806…
| |  
| |  
|-
|-
Line 967: Line 967:
| |  
| |  
| | 23/102
| | 23/102
| | 428.872
| | 428.872…
293.137
293.137…
| | 242.406
| | 242.406…
165.686
165.686…
| | 186.466
| | 186.466…
127.451
127.450…
| |  
| |  
|-
|-
Line 982: Line 982:
| | 16/71
| | 16/71
| |  
| |  
| | 428.6095
| | 428.609…
292.958
292.957…
| | 241.093
| | 241.092…
164.789
164.788…
| | 187.517
| | 187.516…
128.169
128.169…
| |  
| |  
|-
|-
Line 997: Line 997:
| |  
| |  
| | 25/111
| | 25/111
| | 428.368
| | 428.368…
292.793
292.{{overline|1=792}}
| | 239.886
| | 239.886…
163.964
163.{{overline|1=963}}
| | 188.482
| | 188.482…
128.829
128.{{overline|1=828}}
| |  
| |  
|-
|-
Line 1,012: Line 1,012:
| |  
| |  
| |  
| |  
| | 427.94
| | 427.939…
292.5
292.5
| | 237.744
| | 237.744…
162.5
162.5
| | 190.1955
| | 190.195…
130
130
| |  
| |  
Line 1,027: Line 1,027:
| |  
| |  
| | 20/89
| | 20/89
| | 427.406
| | 427.405…
292.135
292.134…
| | 235.073
| | 235.073…
160.674
160.674…
| | 192.3325
| | 192.332…
131.461
131.460…
| |  
| |  
|-
|-
Line 1,042: Line 1,042:
| | 11/49
| | 11/49
| |  
| |  
| | 426.9695
| | 426.969…
291.837
291.836…
| | 232.892
| | 232.892…
159.184
159.183…
| | 194.077
| | 194.077…
132.653
132.653…
| |  
| |  
|-
|-
Line 1,057: Line 1,057:
| |  
| |  
| | 13/58
| | 13/58
| | 426.3
| | 426.300…
291.379
291.379…
| | 229.546
| | 229.546…
156.897
156.896…
| | 196.754
| | 196.753…
134.483
134.482…
| |  
| |  
|-
|-
Line 1,072: Line 1,072:
| |  
| |  
| |  
| |  
| | 422.657
| | 422.656…
288.889
288.{{overline|1=8}}
| colspan="2" | 211.328
| colspan="2" | 211.328…
144.444
144.{{overline|1=4}}
| | Separatrix of Lambda and Anti-Lambda scales
| | Separatrix of Lambda and Anti-Lambda scales
|-
|-
Line 1,085: Line 1,085:
| |  
| |  
| | 13/59
| | 13/59
| | 419.075
| | 419.074…
286.441
286.440…
| | 225.656
| | 225.655…
154.237
154.237…
| | 193.419
| | 193.419…
132.203
132.203…
| |  
| |  
|-
|-
Line 1,100: Line 1,100:
| | 11/50
| | 11/50
| |  
| |  
| | 418.43
| | 418.430…
286
286
| | 228.235
| | 228.234…
156
156
| | 190.1955
| | 190.195…
130
130
| |  
| |  
Line 1,115: Line 1,115:
| |  
| |  
| | 20/91
| | 20/91
| | 418.01
| | 418.012…
285.714
285.714…
| | 229.907
| | 229.906…
157.143
157.142…
| | 188.105
| | 188.105…
128.571
128.571…
| |  
| |  
|-
|-
Line 1,130: Line 1,130:
| |  
| |  
| |  
| |  
| | 417.502
| | 417.502…
285.365
285.365…
| | 231.946
| | 231.945…
158.537
158.536…
| | 185.557
| | 185.556…
126.829
126.829…
| |  
| |  
|-
|-
Line 1,145: Line 1,145:
| |  
| |  
| | 25/114
| | 25/114
| | 417.095
| | 417.095…
285.088
285.087…
| | 233.573
| | 233.573…
159.649
159.649…
| | 183.522
| | 183.521…
125.439
125.438…
| |  
| |  
|-
|-
Line 1,160: Line 1,160:
| | 16/73
| | 16/73
| |  
| |  
| | 416.867
| | 416.866…
284.9315
284.931…
| | 234.488
| | 234.487…
160.273
160.273…
| | 182.379
| | 182.379…
124.6575
124.657…
| |  
| |  
|-
|-
Line 1,175: Line 1,175:
| |  
| |  
| | 23/105
| | 23/105
| | 416.619
| | 416.618…
284.762
284.761…
| | 235.48
| | 235.480…
160.952
160.952…
| | 181.139
| | 181.138…
123.8095
123.809…
| |  
| |  
|-
|-
Line 1,190: Line 1,190:
| |  
| |  
| |  
| |  
| | 416.053
| | 416.052…
284.375
284.375
| | 237.744
| | 237.744…
162.5
162.5
| | 178.308
| | 178.308…
121.875
121.875
| |  
| |  
Line 1,205: Line 1,205:
| |  
| |  
| | 26/119
| | 26/119
| | 415.553
| | 415.553…
284.034
284.033…
| | 239.742
| | 239.742…
163.8655
163.865…
| | 175.811
| | 175.810…
120.168
120.168…
| |  
| |  
|-
|-
Line 1,220: Line 1,220:
| | 19/87
| | 19/87
| |  
| |  
| | 415.3695
| | 415.369…
283.908
283.908…
| | 240.477
| | 240.477…
164.368
164.367…
| | 174.892
| | 174.892…
119.54
119.540…
| |  
| |  
|-
|-
Line 1,235: Line 1,235:
| |  
| |  
| | 31/142
| | 31/142
| | 415.2155
| | 415.215…
283.803
283.802…
| | 241.093
| | 241.092…
164.789
164.788…
| | 174.123
| | 174.122…
119.014
119.014…
| |  
| |  
|-
|-
Line 1,250: Line 1,250:
| |  
| |  
| |  
| |  
| | 414.972
| | 414.972…
283.636
283.{{overline|1=63}}
| | 242.067
| | 242.067…
165.4545
165.{{overline|1=45}}
| | 172.905
| | 172.905…
118.182
118.{{overline|1=18}}
| |  
| |  
|-
|-
Line 1,265: Line 1,265:
| |  
| |  
| | 29/133
| | 29/133
| | 414.712
| | 414.711…
283.459
283.458…
| | 243.107
| | 243.107…
166.165
166.165…
| | 171.605
| | 171.604…
117.293
117.293…
| |  
| |  
|-
|-
Line 1,280: Line 1,280:
| | 17/78
| | 17/78
| |  
| |  
| | 414.528
| | 414.528…
283.333
283.{{overline|1=3}}
| | 243.84
| | 243.840…
166.667
166.{{overline|1=6}}
| | 170.688
| | 170.688…
116.667
116.{{overline|1=6}}
| |  
| |  
|-
|-
Line 1,295: Line 1,295:
| |  
| |  
| | 22/101
| | 22/101
| | 414.287
| | 414.287…
283.168
283.168…
| | 244.806
| | 244.806…
167.327
167.326…
| | 169.481
| | 169.481…
115.842
115.841…
| |  
| |  
|-
|-
Line 1,310: Line 1,310:
| |  
| |  
| |  
| |  
| | 413.4685
| | 413.468…
282.609
282.608…
| | 248.081
| | 248.081…
169.565
169.565…
| | 165.387
| | 165.387…
113.0435
113.043…
| |  
| |  
|-
|-
Line 1,325: Line 1,325:
| |  
| |  
| | 23/106
| | 23/106
| | 412.688
| | 412.688…
282.0755
282.075…
| | 251.202
| | 251.201…
171.698
171.698…
| | 161.487
| | 161.486…
110.377
110.377…
| |  
| |  
|-
|-
Line 1,340: Line 1,340:
| | 18/83
| | 18/83
| |  
| |  
| | 412.472
| | 412.472…
281.928
281.927…
| | 252.066
| | 252.066…
172.289
172.289…
| | 160.406
| | 160.405…
109.639
109.638…
| |  
| |  
|-
|-
Line 1,355: Line 1,355:
| |  
| |  
| | 31/143
| | 31/143
| | 412.312
| | 412.311…
281.818
281.{{overline|1=81}}
| | 252.707
| | 252.707…
172.727
172.{{overline|1=72}}
| | 159.605
| | 159.604…
109.091
109.{{overline|1=09}}
| |  
| |  
|-
|-
Line 1,370: Line 1,370:
| |  
| |  
| |  
| |  
| | 412.09
| | 412.090…
281.667
281.{{overline|1=6}}
| | 253.594
| | 253.594…
173.333
173.{{overline|1=3}}
| | 158.496
| | 158.496…
108.333
108.{{overline|1=3}}
| |  
| |  
|-
|-
Line 1,385: Line 1,385:
| |  
| |  
| | 34/157
| | 34/157
| | 411.888
| | 411.888…
281.529
281.528…
| | 254.402
| | 254.401…
173.885
173.885…
| | 157.487
| | 157.486…
107.643
107.643…
| | Golden Anti-Lambda scale is near here
| | Golden Anti-Lambda scale is near here
|-
|-
Line 1,400: Line 1,400:
| | 21/97
| | 21/97
| |  
| |  
| | 411.7635
| | 411.763…
281.443
281.443…
| | 254.901
| | 254.901…
174.227
174.226…
| | 156.862
| | 156.862…
107.2165
107.216…
| |  
| |  
|-
|-
Line 1,415: Line 1,415:
| |  
| |  
| | 29/134
| | 29/134
| | 411.617
| | 411.617…
281.343
281.343…
| | 255.4865
| | 255.486…
174.627
174.626…
| | 156.131
| | 156.130…
103.716
103.716…
| |  
| |  
|-
|-
Line 1,430: Line 1,430:
| |  
| |  
| |  
| |  
| | 411.2335
| | 411.233…
281.081.
281.{{overline|1=081}}.
| | 257.021
| | 257.020…
175.676
175.{{overline|1=675}}
| | 154.2125
| | 154.212…
105.405
105.{{overline|1=405}}
| |  
| |  
|-
|-
Line 1,445: Line 1,445:
| |  
| |  
| | 27/125
| | 27/125
| | 410.822
| | 410.822…
280.8
280.8
| | 258.666
| | 258.665…
176.8
176.8
| | 152.156
| | 152.156…
104
104
| |  
| |  
Line 1,460: Line 1,460:
| | 19/88
| | 19/88
| |  
| |  
| | 410.649
| | 410.649…
280.682
280.681…
| | 259.3575
| | 259.357…
177.273
177.{{overline|1=27}}
| | 151.292
| | 151.291…
103.409
103.409…
| |  
| |  
|-
|-
Line 1,475: Line 1,475:
| |  
| |  
| | 30/139
| | 30/139
| | 410.494
| | 410.494…
280.5755
280.575…
| | 259.9795
| | 259.979…
177.698
177.697…
| | 150.514
| | 150.514…
102.878
102.877…
| |  
| |  
|-
|-
Line 1,490: Line 1,490:
| |  
| |  
| |  
| |  
| | 410.2255
| | 410.225…
280.392
280.392…
| | 261.053
| | 261.052…
178.431
178.431…
| | 149.173
| | 149.173…
101.961
101.960…
| |  
| |  
|-
|-
Line 1,505: Line 1,505:
| |  
| |  
| | 25/116
| | 25/116
| | 409.904
| | 409.904…
280.172
280.172…
| | 262.339
| | 262.338…
179.31
179.310…
| | 147.5655
| | 147.565…
100.862
100.862……
| |  
| |  
|-
|-
Line 1,520: Line 1,520:
| | 14/65
| | 14/65
| |  
| |  
| | 409.652
| | 409.651…
280
280
| | 263.348
| | 263.347…
180
180
| | 146.304
| | 146.304…
100
100
| |  
| |  
Line 1,535: Line 1,535:
| |  
| |  
| | 17/79
| | 17/79
| | 409.2815
| | 409.281…
279.747
279.746…
| | 264.819
| | 264.819…
181.013
181.012…
| | 144.452
| | 144.452…
98.734
98.734…
| |  
| |  
|-
|-
Line 1,550: Line 1,550:
| |  
| |  
| |  
| |  
| | 407.562
| | 407.561…
278.571
278.571…
| | 271.708
| | 271.707…
185.714
185.714…
| | 135.854
| | 135.853…
92.857
92.857…
| | Boundary of propriety for Anti-Lambda scale
| | Boundary of propriety for Anti-Lambda scale
|-
|-
Line 1,565: Line 1,565:
| |  
| |  
| | 16/75
| | 16/75
| | 405.75
| | 405.750…
277.333
277.{{overline|1=3}}
| | 278.953
| | 278.953…
190.667
190.{{overline|1=6}}
| | 126.797
| | 126.797…
86.667
86.{{overline|1=6}}
| |  
| |  
|-
|-
Line 1,580: Line 1,580:
| | 13/61
| | 13/61
| |  
| |  
| | 405.335
| | 405.334…
277.049
277.049…
| | 280.616
| | 280.616…
191.803
191.803…
| | 124.718
| | 124.718…
85.245
85.245…
| |  
| |  
|-
|-
Line 1,595: Line 1,595:
| |  
| |  
| | 23/108
| | 23/108
| | 405.046
| | 405.045…
276.852
276.{{overline|1=851}}
| | 281.771
| | 281.771…
192.593
192.{{overline|1=592}}
| | 123.275
| | 123.274…
84.259
84.{{overline|1=259}}
| |  
| |  
|-
|-
Line 1,610: Line 1,610:
| |  
| |  
| |  
| |  
| | 404.671
| | 404.671…
276.596
276.595…
| | 283.27
| | 283.269…
193.617
193.617…
| | 121.401
| | 121.401…
82.979
82.978…
| |  
| |  
|-
|-
Line 1,625: Line 1,625:
| |  
| |  
| | 27/127
| | 27/127
| | 404.353
| | 404.352…
276.378
276.377…
| | 284.544
| | 284.544…
194.488
194.488…
| | 119.808
| | 119.808…
81.89
81.889…
| |  
| |  
|-
|-
Line 1,640: Line 1,640:
| | 17/80
| | 17/80
| |  
| |  
| | 404.165
| | 404.165…
276.25
276.25
| | 285.293
| | 285.293…
195
195
| | 118.873
| | 118.872…
81.25
81.25
| |  
| |  
Line 1,655: Line 1,655:
| |  
| |  
| | 24/113
| | 24/113
| | 403.955
| | 403.955…
276.106
276.106…
| | 286.135
| | 286.134…
195.575
195.575…
| | 117.82
| | 117.820…
80.531
80.530…
| |  
| |  
|-
|-
Line 1,670: Line 1,670:
| |  
| |  
| |  
| |  
| | 403.445
| | 403.445…
275.758
275.{{overline|1=75}}
| | 288.175
| | 288.175…
196.97
196.{{overline|1=97}}
| | 115.27
| | 115.270…
78.788
78.{{overline|1=78}}
| |  
| |  
|-
|-
Line 1,685: Line 1,685:
| |  
| |  
| | 25/118
| | 25/118
| | 402.957
| | 402.956…
275.424
275.423…
| | 290.129
| | 290.128…
198.305
198.305…
| | 112.828
| | 112.827…
77.119
77.118…
| |  
| |  
|-
|-
Line 1,700: Line 1,700:
| | 18/85
| | 18/85
| |  
| |  
| | 402.767
| | 402.766…
275.294
275.294…
| | 290.887
| | 290.887…
198.8235
198.823…
| | 111.88
| | 111.879…
76.471
76.470…
| |  
| |  
|-
|-
Line 1,715: Line 1,715:
| |  
| |  
| | 29/137
| | 29/137
| | 402.604
| | 402.603…
275.1825
275.182…
| | 291.5405
| | 291.540…
199.27
199.270…
| | 111.063
| | 111.063…
75.912
75.912…
| |  
| |  
|-
|-
Line 1,730: Line 1,730:
| |  
| |  
| |  
| |  
| | 402.337
| | 402.336…
275
275
| | 292.6085
| | 292.608…
200
200
| | 109.728
| | 109.728…
75
75
| |  
| |  
Line 1,745: Line 1,745:
| |  
| |  
| | 26/123
| | 26/123
| | 402.039
| | 402.039…
274.797
274.796…
| | 293.79
| | 293.797…
200.813
200.813…
| | 108.241
| | 108.241…
73.984
73.983…
| |  
| |  
|-
|-
Line 1,760: Line 1,760:
| |  
| |  
| |  
| |  
| | 402.015
| | 402.014…
274.78
274.779…
| | 293.896
| | 293.896…
200.88
200.880…
| | 108.118
| | 108.118…
73.9
73.899…
| |  
| |  
|-
|-
Line 1,775: Line 1,775:
| | 15/71
| | 15/71
| |  
| |  
| | 401.8215
| | 401.821…
274.648
274.647…
| | 294.669
| | 294.669…
201.4085
201.408…
| | 107.152
| | 107.152…
73.239
73.239…
| |  
| |  
|-
|-
Line 1,790: Line 1,790:
| |  
| |  
| | 19/90
| | 19/90
| | 401.524
| | 401.523…
274.444
274.{{overline|1=4}}
| | 295.829
| | 295.859…
202.222
202.{{overline|1=2}}
| | 105.664
| | 105.664…
72.222
72.{{overline|1=2}}
| |  
| |  
|-
|-
Line 1,805: Line 1,805:
| |  
| |  
| |  
| |  
| | 400.412
| | 400.411…
273.684
273.684…
| | 300.309
| | 300.308…
205.263
205.263…
| | 100.103
| | 100.103…
68.421
68.421…
| |  
| |  
|-
|-
Line 1,820: Line 1,820:
| |  
| |  
| |  
| |  
| | 399.692
| | 399.692…
273.193
273.192…
| | 303.1855
| | 303.185…
207.2295
207.229…
| | 96.507
| | 96.506…
65.963
65.963…
| |  
| |  
|-
|-
Line 1,835: Line 1,835:
| |  
| |  
| | 17/81
| | 17/81
| | 399.176
| | 399.175…
272.8395
272.839…
| | 305.252
| | 305.252…
208.642
208.641…
| | 93.924
| | 93.923…
64.1975
64.197…
| |  
| |  
|-
|-
Line 1,850: Line 1,850:
| | 13/62
| | 13/62
| |  
| |  
| | 398.797
| | 398.797…
272.551
272.580…
| | 306.767
| | 306.766…
209.677
209.677…
| | 92.03
| | 92.030…
62.903
62.903…
| |  
| |  
|-
|-
Line 1,865: Line 1,865:
| |  
| |  
| | 22/105
| | 22/105
| | 398.505
| | 398.505…
272.381
272.380…
| | 307.936
| | 307.935…
210.476
210.476…
| | 90.569
| | 90.569…
61.905
61.904…
| |  
| |  
|-
|-
Line 1,880: Line 1,880:
| |  
| |  
| |  
| |  
| | 398.084
| | 398.083…
272.093
272.093…
| | 309.621
| | 309.620…
211.628
211.627…
| | 88.463
| | 88.463…
60.465
60.465…
| |  
| |  
|-
|-
Line 1,895: Line 1,895:
| |  
| |  
| | 23/110
| | 23/110
| | 397.6815
| | 397.681…
271.818
271.{{overline|1=81}}
| | 311.229
| | 311.229…
212.727
212.{{overline|1=72}}
| | 86.4525
| | 86.452…
59.091
59.{{overline|1=09}}
| |  
| |  
|-
|-
Line 1,910: Line 1,910:
| | 14/67
| | 14/67
| |  
| |  
| | 397.423
| | 397.423…
271.641
271.641…
| | 312.261
| | 312.261…
213.433
213.432…
| | 85.162
| | 85.162…
58.209
58.208…
| |  
| |  
|-
|-
Line 1,925: Line 1,925:
| |  
| |  
| | 19/91
| | 19/91
| | 397.1115
| | 397.111…
271.429
271.428…
| | 313.509
| | 313.509…
214.286
214.285…
| | 83.602
| | 83.602…
57.143
57.143…
| |  
| |  
|-
|-
Line 1,940: Line 1,940:
| |  
| |  
| |  
| |  
| | 396.241
| | 396.240…
270.833
270.8{{overline|1=3}}
| | 316.9925
| | 316.992…
216.667
216.{{overline|1=6}}
| | 79.248
| | 79.248
54.167
54.1{{overline|1=6}}
| |  
| |  
|-
|-
Line 1,955: Line 1,955:
| |  
| |  
| | 16/77
| | 16/77
| | 395.211
| | 395.211…
270.13
270.129…
| | 321.109
| | 321.109…
219.4805
219.480…
| | 74.102
| | 74.102…
50.649
50.649…
| |  
| |  
|-
|-
Line 1,970: Line 1,970:
| | 11/53
| | 11/53
| |  
| |  
| | 394.745
| | 394.745…
269.811
269.811…
| | 322.9735
| | 322.973…
220.755
220.754…
| | 71.772
| | 71.771…
49.057
49.056…
| |  
| |  
|-
|-
Line 1,985: Line 1,985:
| |  
| |  
| | 17/82
| | 17/82
| | 394.308
| | 394.307…
269.8512
269.512…
| | 324.724
| | 324.724…
221.951
221.951…
| | 69.584
| | 69.583…
47.561
47.560…
| |  
| |  
|-
|-
Line 2,000: Line 2,000:
| |  
| |  
| |  
| |  
| | 393.508
| | 393.507…
268.9655
268.965…
| | 327.923
| | 327.923…
224.138
224.137…
| | 65.585
| | 65.584…
44.8275
44.827…
| |  
| |  
|-
|-
Line 2,030: Line 2,030:
| | 7/34
| | 7/34
| |  
| |  
| | 391.579
| | 391.578…
267.647
267.647…
| | 335.639
| | 335.639…
229.412
229.411…
| | 55.94
| | 55.939…
38.235
38.235…
| |  
| |  
|-
|-
Line 2,045: Line 2,045:
| |  
| |  
| | 8/39
| | 8/39
| | 390.145
| | 390.144…
266.667
266.{{overline|1=6}}
| | 341.3765
| | 341.376…
233.333
233.{{overline|1=3}}
| | 48.768
| | 48.768
33.333
33.{{overline|1=3}}
| |  
| |  
|-
|-
Line 2,060: Line 2,060:
| |  
| |  
| |  
| |  
| colspan="2" | 380.391
| colspan="2" | 380.391…
260
260
| | 0
| | 0
| |
|}
|}


Revision as of 04:26, 25 August 2021

↖ 3L 4s⟨3/1⟩ ↑ 4L 4s⟨3/1⟩ 5L 4s⟨3/1⟩ ↗
← 3L 5s⟨3/1⟩ 4L 5s (3/1-equivalent) 5L 5s⟨3/1⟩ →
↙ 3L 6s⟨3/1⟩ ↓ 4L 6s⟨3/1⟩ 5L 6s⟨3/1⟩ ↘ 
┌╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLss
ssLsLsLsL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 2\9 to 1\4 (422.7 ¢ to 475.5 ¢)
Dark 3\4 to 7\9 (1426.5 ¢ to 1479.3 ¢)
Related MOS scales
Parent 4L 1s⟨3/1⟩
Sister 5L 4s⟨3/1⟩
Daughters 9L 4s⟨3/1⟩, 4L 9s⟨3/1⟩
Neutralized 8L 1s⟨3/1⟩
2-Flought 13L 5s⟨3/1⟩, 4L 14s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 2\9 (422.7 ¢)
Supersoft (L:s = 4:3) 7\31 (429.5 ¢)
Soft (L:s = 3:2) 5\22 (432.3 ¢)
Semisoft (L:s = 5:3) 8\35 (434.7 ¢)
Basic (L:s = 2:1) 3\13 (438.9 ¢)
Semihard (L:s = 5:2) 7\30 (443.8 ¢)
Hard (L:s = 3:1) 4\17 (447.5 ¢)
Superhard (L:s = 4:1) 5\21 (452.8 ¢)
Collapsed (L:s = 1:0) 1\4 (475.5 ¢)

Suggested for use as a "diatonic scale" when playing Bohlen-Pierce is the 9-note Lambda scale, which is the 4L5s MOS. This can be thought of as an MOS generated by a 3.5.7 rank-2 temperament called BPS (Bohlen-Pierce-Stearns) that eliminates only the comma 245/243, so that 9/7 * 9/7 = 5/3.

This is a very good temperament on the 3.5.7 subgroup, and additionally is supported by many EDT's (and even EDOs!) besides 13-EDT.

Some low-numbered EDOs that support Lambda are 19, 22, 27, 41, and 46, all of which make it possible to play BP music to some reasonable extent. These EDOs contain not only the Lambda BP diatonic scale, but also the 13-note "Lambda chromatic" MOS scale, or Lambda[13], which can be thought of as a "detempered" version of the 13-EDT Bohlen Pierce scale. This scale may be a suitable melodic substitute for the BP chromatic scale, and is basically the same as how 19-EDO and 31-EDO do not contain 12-EDO as a subset, but they do contain the meantone[12] chromatic scale.

When playing this temperament in some EDO, it may be desired to stretch/compress the tuning so that the tritave is pure, rather than the octave being pure - or in general, to minimize the error on the 3.5.7 subgroup while ignoring the error on 2/1.

One can "add" the octave to Lambda temperament by simply creating a new mapping for 2/1. A simple way to do so is to map the 2/1 to +7 of the ~9/7 generators, minus a single tritave. This is Sensi temperament, in essence treating it as a "3.5.7.2 extension" of the original 3.5.7 Lambda temperament.

List of EDT's supporting Lambda Temperament

Below is a list of the equal-temperaments which contain a 4L+5s scale using generators between 422.7 cents and 475.5 cents.

L=1 s=0 4 edt

L=1 s=1 9 edt (5flat40 7sharp18)

L=2 s=1 13 (5flat7 7flat3)

L=3 s=1 17 (5sharp10 7flat12)

L=3 s=2 22 (~14edo)

L=4 s=1 21

L=4 s=3 31

L=5 s=1 25

L=5 s=2 30 (~19edo) (5sharp3 7flat8)

L=5 s=3 35 (~22edo) (5flat14 7sharp0)

L=5 s=4 40

L=6 s=1 29

L=6 s=5 49 (~31EDO) (5sharp8 7sharp8) (Schism*)

L=7 s=1 33

L=7 s=2 38 (~24edo)

L=7 s=3 43 (~27edo) (5sharp0 7flat6)

L=7 s=4 48 (5flat13 7flat0)

L=7 s=5 53

L=7 s=6 58 5sharp1 7sharp10 (Schism*)

  • Schism, by which I mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L+5s MOS.

[Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the "counterparts" of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, e.g. 12edt and 27edt.]

Generator cents

hekts

L s notes
1/4 475.488…

325

0
8/33 461.080…

315.15

403.445…

275.75

57.635…

39.39

7/29 459.092…

313.793…

393.507…

268.965…

65.584…

44.827…

13/54 457.878…

312.962

387.435…

264.814

70.442…

48.148

6/25 456.469…

312

380.391…

260

76.078…

52

17/71 455.397…

311.267…

375.033…

256.338…

80.364…

54.929…

11/46 454.815…

310.869…

372.121…

254.347…

82.693…

56.521…

16/67 454.198…

310.447…

369.036…

252.238…

85.162…

58.208…

5/21 452.846…

309.523…

362.277…

247.619…

90.569…

61.904…

19/80 451.714…

308.75

356.616…

243.75

95.097…

65

14/59 451.311…

308.474…

354.601…

242.372…

96.709…

66.101…

23/97 450.979…

308.247…

352.940…

241.234…

98.038…

67.010…

9/38 450.463…

307.894…

350.360…

239.473…

100.102…

68.421…

22/93 449.924…

307.526…

347.669…

237.634…

102.255…

69.892…

13/55 449.553…

307.27

345.810…

236.36

103.743…

70.90

17/72 449.072…

306.94

343.408…

234.72

105.664…

72.2

448.420…

306.498…

340.148…

232.493…

108.272…

74.005…

4/17 447.518…

305.882…

335.639…

229.411…

111.879…

76.470…

Canonical BP scales are between here...
19/81 446.137…

304.938…

328.733…

224.691…

117.404…

80.246…

15/64 445.770…

[[1]]

326.898…

[[2]]

118.872…

81.25

445.533…

304.525…

325.710…

222.625…

119.822…

81.899…

26/111 445.502…

304.504

325.559…

222.522

119.943…

81.981

11/47 445.138…

304.255…

323.737…

221.276…

121.401…

82.978…

29/124 444.812…

304.032…

322.105…

220.161…

122.706…

83.870…

Golden BP is near here
18/77 444.612…

303.896…

321.109…

219.480…

123.503…

84.415…

25/107 444.382…

303.738…

319.955…

218.691…

120.426…

85.046…

7/30 443.789…

303.3

316.992…

216.6

126.797…

86.6

24/103 443.173…

302.912…

313.914…

214.563…

129.259…

88.349…

17/73 442.921…

302.739…

312.650…

213.698…

130.270…

89.041…

27/116 442.696…

302.586…

311.527…

212.931…

131.169…

89.655…

10/43 442.315…

302.325…

309.620…

211.627…

132.694…

90.697…

23/99 441.868…

302.02

307.386…

210.10

134.481…

91.91

13/56 441.525…

301.785…

305.671…

208.928…

135.853…

92.857…

16/69 441.033…

301.449…

303.210…

207.246…

137.822…

94.202…

3/13 438.912…

300

292.608…

200

146.304…

100

...and here

Boundary of propriety for Lambda scale

17/74 436.935…

298.648

282.723…

193.243

154.212…

105.405

14/61 436.514…

298.360…

280.616…

191.803…

155.897…

106.557…

25/109 436.228…

298.165…

279.186…

190.825…

157.042…

207.339…

11/48 435.865

297.916

277.368…

189.583

158.496…

108.3

30/131 435.562…

297.709…

275.856…

188.549…

159.706…

109.160…

19/83 435.387…

297.590…

274.981…

187.951…

160.405…

109.638…

27/118 435.193…

297.457…

274.010…

187.288…

161.182…

110.169…

8/35 434.732…

297.142…

271.707…

185.714…

163.024…

111.428…

29/127 434.304…

296.850…

269.568…

184.251…

164.736…

112.598…

21/92 434.141…

596.739…

268.754…

183.695…

165.387…

113.043…

34/149 434.003…

296.644…

268.060…

183.221…

165.942…

113.422…

Golden Lambda scale is near here

18\7*30\11=7

13/57 433.779…

296.491…

266.941…

182.456…

166.838…

114.035…

18\7*30\11=7
31/136 433.533…

296.323…

265.714…

181.617…

167.819…

114.705…

18/79 433.356…

296.202…

264.829…

181.012…

168.527…

115.189…

23/101 433.118…

296.039…

263.637…

180.198…

169.481…

115.841…

5/22 432.262…

295.45

259.357…

177.27

172.905…

118.18

22/97 431.371…

294.845…

254.901…

174.226…

176.470…

120.618…

17/75 431.109…

294.6

253.594…

173.3

177.515…

121.3

29/128 430.911…

294.531…

252.603…

172.656…

178.308…

121.875

12/53 430.631…

294.339…

251.201…

171.698…

179.429…

122.641…

31/137 430.369…

294.160…

249.891…

170.802…

180.477…

123.357…

19/84 430.204…

294.047…

249.065…

170.238…

181.138…

123.809…

26/115 430.007…

293.913…

248.081…

169.565…

181.926…

124.347…

7/31 429.473…

293.548…

245.413…

167.741…

184.060…

125.806…

23/102 428.872…

293.137…

242.406…

165.686…

186.466…

127.450…

16/71 428.609…

292.957…

241.092…

164.788…

187.516…

128.169…

25/111 428.368…

292.792

239.886…

163.963

188.482…

128.828

9/40 427.939…

292.5

237.744…

162.5

190.195…

130

20/89 427.405…

292.134…

235.073…

160.674…

192.332…

131.460…

11/49 426.969…

291.836…

232.892…

159.183…

194.077…

132.653…

13/58 426.300…

291.379…

229.546…

156.896…

196.753…

134.482…

2/9 422.656…

288.8

211.328…

144.4

Separatrix of Lambda and Anti-Lambda scales
13/59 419.074…

286.440…

225.655…

154.237…

193.419…

132.203…

11/50 418.430…

286

228.234…

156

190.195…

130

20/91 418.012…

285.714…

229.906…

157.142…

188.105…

128.571…

9/41 417.502…

285.365…

231.945…

158.536…

185.556…

126.829…

25/114 417.095…

285.087…

233.573…

159.649…

183.521…

125.438…

16/73 416.866…

284.931…

234.487…

160.273…

182.379…

124.657…

23/105 416.618…

284.761…

235.480…

160.952…

181.138…

123.809…

7/32 416.052…

284.375

237.744…

162.5

178.308…

121.875

26/119 415.553…

284.033…

239.742…

163.865…

175.810…

120.168…

19/87 415.369…

283.908…

240.477…

164.367…

174.892…

119.540…

31/142 415.215…

283.802…

241.092…

164.788…

174.122…

119.014…

12/55 414.972…

283.63

242.067…

165.45

172.905…

118.18

29/133 414.711…

283.458…

243.107…

166.165…

171.604…

117.293…

17/78 414.528…

283.3

243.840…

166.6

170.688…

116.6

22/101 414.287…

283.168…

244.806…

167.326…

169.481…

115.841…

5/23 413.468…

282.608…

248.081…

169.565…

165.387…

113.043…

23/106 412.688…

282.075…

251.201…

171.698…

161.486…

110.377…

18/83 412.472…

281.927…

252.066…

172.289…

160.405…

109.638…

31/143 412.311…

281.81

252.707…

172.72

159.604…

109.09

13/60 412.090…

281.6

253.594…

173.3

158.496…

108.3

34/157 411.888…

281.528…

254.401…

173.885…

157.486…

107.643…

Golden Anti-Lambda scale is near here
21/97 411.763…

281.443…

254.901…

174.226…

156.862…

107.216…

29/134 411.617…

281.343…

255.486…

174.626…

156.130…

103.716…

8/37 411.233…

281.081.

257.020…

175.675

154.212…

105.405

27/125 410.822…

280.8

258.665…

176.8

152.156…

104

19/88 410.649…

280.681…

259.357…

177.27

151.291…

103.409…

30/139 410.494…

280.575…

259.979…

177.697…

150.514…

102.877…

11/51 410.225…

280.392…

261.052…

178.431…

149.173…

101.960…

25/116 409.904…

280.172…

262.338…

179.310…

147.565…

100.862……

14/65 409.651…

280

263.347…

180

146.304…

100

17/79 409.281…

279.746…

264.819…

181.012…

144.452…

98.734…

3/14 407.561…

278.571…

271.707…

185.714…

135.853…

92.857…

Boundary of propriety for Anti-Lambda scale
16/75 405.750…

277.3

278.953…

190.6

126.797…

86.6

13/61 405.334…

277.049…

280.616…

191.803…

124.718…

85.245…

23/108 405.045…

276.851

281.771…

192.592

123.274…

84.259

10/47 404.671…

276.595…

283.269…

193.617…

121.401…

82.978…

27/127 404.352…

276.377…

284.544…

194.488…

119.808…

81.889…

17/80 404.165…

276.25

285.293…

195

118.872…

81.25

24/113 403.955…

276.106…

286.134…

195.575…

117.820…

80.530…

7/33 403.445…

275.75

288.175…

196.97

115.270…

78.78

25/118 402.956…

275.423…

290.128…

198.305…

112.827…

77.118…

18/85 402.766…

275.294…

290.887…

198.823…

111.879…

76.470…

29/137 402.603…

275.182…

291.540…

199.270…

111.063…

75.912…

11/52 402.336…

275

292.608…

200

109.728…

75

26/123 402.039…

274.796…

293.797…

200.813…

108.241…

73.983…

402.014…

274.779…

293.896…

200.880…

108.118…

73.899…

15/71 401.821…

274.647…

294.669…

201.408…

107.152…

73.239…

19/90 401.523…

274.4

295.859…

202.2

105.664…

72.2

4\19 400.411…

273.684…

300.308…

205.263…

100.103…

68.421…

399.692…

273.192…

303.185…

207.229…

96.506…

65.963…

17/81 399.175…

272.839…

305.252…

208.641…

93.923…

64.197…

13/62 398.797…

272.580…

306.766…

209.677…

92.030…

62.903…

22/105 398.505…

272.380…

307.935…

210.476…

90.569…

61.904…

9/43 398.083…

272.093…

309.620…

211.627…

88.463…

60.465…

23/110 397.681…

271.81

311.229…

212.72

86.452…

59.09

14/67 397.423…

271.641…

312.261…

213.432…

85.162…

58.208…

19/91 397.111…

271.428…

313.509…

214.285…

83.602…

57.143…

5/24 396.240…

270.83

316.992…

216.6

79.248

54.16

16/77 395.211…

270.129…

321.109…

219.480…

74.102…

50.649…

11/53 394.745…

269.811…

322.973…

220.754…

71.771…

49.056…

17/82 394.307…

269.512…

324.724…

221.951…

69.583…

47.560…

6/29 393.507…

268.965…

327.923…

224.137…

65.584…

44.827…

13/63 392.467

265.254

332.087

226.984

60.3795

41.27

7/34 391.578…

267.647…

335.639…

229.411…

55.939…

38.235…

8/39 390.144…

266.6

341.376…

233.3

48.768

33.3

1/5 380.391…

260

0
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