5L 3s (tritave-equivalent)

From Xenharmonic Wiki
Jump to navigation Jump to search
5L 3s<3/1>
Brightest mode LLsLLsLs
Period 3/1
Range for bright generator 3\8edt (713.2¢) to 2\5edt (760.8¢)
Range for dark generator 3\5edt (1,141.2¢) to 5\8edt (1,188.7¢)
Parent MOS 3L 2s<3/1>
Daughter MOSes 8L 5s<3/1>, 5L 8s<3/1>
Sister MOS 3L 5s<3/1>
Equal tunings
Supersoft (L:s = 4:3) 11\29edt (721.4¢)
Soft (L:s = 3:2) 8\21edt (724.6¢)
Semisoft (L:s = 5:3) 13\34edt (727.2¢)
Basic (L:s = 2:1) 5\13edt (731.5¢)
Semihard (L:s = 5:2) 12\31edt (736.2¢)
Hard (L:s = 3:1) 7\18edt (739.6¢)
Superhard (L:s = 4:1) 9\23edt (744.2¢)

This MOS belongs to a temperament which has Bohlen-Pierce as its index-2 subtemperament. In addition to being concordant, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio.

Generator tetrachord g in cents

hekts

2g 3g 4g Comments
2\5 1 0 1 760.782

520

1521.564

1040

380.391

260

1141.173

780

27\68 13 1 13 755.188

516.1765

1510.376

1032.353

363.609

248.529

1118.797

764.706

2g=12/5 minus quarter comma near here
25\63 12 1 12 754.744

515.873

1509.488

1031.746

362.277

247.619

1117.021

763.492

23\58 11 1 11 754.2235

515.517

1508.447

1031.0345

360.716

246.551

1114.939

762.069

21\53 10 1 10 753.605

515.094

1507.21

1030.189

358.859

245.283

1112.464

760.378

19\48 9 1 9 752.857

514.583

1505.714

1029.167

356.617

243.75

1109.474

758.333

17\43 8 1 8 751.936

513.9535

1503.871

1027.907

353.852

241.8605

1105.788

755.814

15\38 7 1 7 750.771

513.158

1501.543

1026.316

350.36

239.474

1101.132

752.632

28/71 13 2 13 750.067

512.676

1500.1335

1025.352

348.245

238.028

1098.312

750.704

41\104 19 3 19 749.809

512.5

1499.618

1025

347.4725

237.5

1097.282

750

3g=11/3 near here
13\33 6 1 6 749.255

512.121

1498.51

1024.242

345.81

236.364

1095.065

748.485

24\61 11 2 11 748.31

511.475

1496.62

1022.951

342.976

234.426

1091.286

745.902

35\89 16 3 16 747.96

511.236

1495.92

1022.472

341.924

233.708

1089.884

744.944

5+√29 2 5+√29 747.648

511.023

1495.297

1022.046

340.99

233.069

1088.638

744.092

4g=45/8 near here
11\28 5 1 5 747.197

510.714

1494.393

1021.429

339.635

232.143

1086.831

742.857

20\51 9 2 9 745.865

509.804

1491.729

1019.608

335.639

229.412

1081.504

739.216

29\74 13 3 13 745.361

509.4595

1490.721

1018.919

334.127

228.378

1079.488

737.838

38/97 17 4 17 745.096

509.278

1490.192

1018.557

333.332

227.835

1078.428

737.113

2+√5 1 2+√5 754.051

509.2475

1490.101

1018.495

333.197

227.742

1078.247

736.99

47\120 21 5 21 744.932

509.167

1489.865

1018.333

332.842

227.5

1077.7745

736.667

9\23 4 1 4 744.243

508.696

1488.487

1017.391

330.775

226.087

1075.018

734.783

L/s = 4
34\87 15 4 15 743.293

508.046

1486.586

1016.092

327.923

224.138

1071.216

732.184

4g=39/7 near here
25\64 11 3 11 742.951

507.8125

1485.902

1015.625

326.899

223.4375

1069.85

731.25

16\41 7 2 7 742.226

507.317

1484.453

1014.634

324.724

221.951

1066.95

728.268

23\59 10 3 10 741.44

506.78

1482.88

1013.56

322.365

220.34

1063.805

727.12

3+√13 2 3+√13 741.289

506.676

1482.577

1013.352

321.911

220.028

1063.2

726.705

30\77 13 4 13 741.021

506.4935

1482.043

1012.987

321.109

219.4805

1062.131

725.974

pi 1 pi 740.449

506.102

1480.898

1012.204

319.392

218.3065

1056.841

724.409

L/s = pi
7\18 3 1 3 739.649

505.556

1479.298

1011.111

316.992

216.667

1056.642

722.222

L/s = 3
68\175 29 10 29 739.045

505.143

1478.091

1010.286

315.181

215.429

1054.227

720.571

3g=18/5 near here
61/157 26 9 26 738.976

505.0955

1477.952

1010.191

314.973

215.287

1053.949

720.382

54\139 23 8 23 738.889

505.036

1477.778

1010.072

314.712

215.108

1053.601

720.144

47\121 20 7 20 738.776

504.959

1477.552

1009.917

314.373

214.876

1053.149

719.835

40\103 17 6 17 738.623

504.854

1477.247

1009.709

313.915

214.563

1052.538

719.4175

33\85 14 5 14 738.406

504.706

1476.812

1009.412

313.263

214.1765

1051.669

718.882

26\67 11 4 11 738.072

504.478

1476.144

1008.955

312.261

213.433

1050.333

717.91

e 1 e 737.855

504.329

1475.71

1008.6585

311.61

212.988

1049.465

717.317

L/s = e
19\49 8 3 8 737.493

504.082

1474.986

1008.163

310.523

212.245

1048.016

716.3265

3g=18/5 minus quarter comma near here
50\129 21 8 21 737.192

503.876

1474.384

1007.752

309.621

211.628

1046.812

715.504

131\338 55 21 55 737.148

503.846

1474.296

1007.692

309.49

211.5385

1046.638

715.385

212\547 89 34 89 737.138

503.839

1474.276

1007.678

309.459

211.517

1046.597

715.3565

81\209 34 13 34 737.121

503.828

1474.243

1007.6555

309.409

211.483

1046.53

715.311

31\80 13 5 13 737.008

503.75

1474.015

1007.5

309.068

211.25

1046.075

715

12\31 5 2 5 736.241

503.226

1472.481

1006.452

306.767

209.677

1043.007

712.903

1+√2 1 1+√2 735.542

502.748

1471.084

1005.497

304.6715

208.245

1040.214

710.994

Silver false father
17\44 7 3 7 734.846

502.273

1469.693

1004.5455

302.584

206.818

1037.41

709.091

22\57 9 4 9 734.088

501.754

1468.176

1003.509

300.309

205.263

1034.397

707.0175

27\70 11 5 11 733.611

501.429

1467.222

1002.857

298.879

204.286

1032.49

705.714

32\83 13 6 13 733.284

501.205

1466.568

1002.41

297.897

203.6145

1031.181

704.819

2g=7/3 near here
5\13 2 1 2 731.521

500

1463.042

1000

292.609

200

1024.13

700

48\125 19 10 19 730.35

499.2

1460.701

998.4

289.097

197.6

1019.448

696.8

3g=39/11 near here
43\112 17 9 17 730.215

499.107

1460.43

998.214

288.69

197.321

1018.905

696.429

38\99 15 8 15 730.043

498.99

1460.087

997.98

288.175

196.97

1018.218

695.96

33\86 13 7 13 729.82

498.837

1459.64

997.674

287.505

196.512

1017.325

695.349

4g=27/5 near here
28\73 11 6 11 729.547

498.63

1459.034

997.26

286.596

195.89

1016.113

694.5205

23\60 9 5 9 729.083

498.333

1458.1655

996.667

285.293

195

1014.376

693.333

41\107 16 9 16 728.7865

498.131

1457.563

996.262

284.4045

194.3925

1013.191

692.523

59\154 23 13 23 728.671

498.052

1457.342

996.104

284.058

194.156

1012.729

692.208

3g=99/28 near here
77\201 30 17 30 728.61

498.01

1457.219

996.02

283.874

194.03

1012.483

692.04

95\248 37 21 37 728.5715

497.984

1457.143

995.968

283.7145

193.952

1012.286

691.9355

Golden BP is index-2 near here
18\47 7 4 7 728.408

497.872

1456.817

995.745

283.27

193.617

1011.678

691.49

√3 1 √3 728.159

497.702

1456.318

995.404

282.522

193.106

1010.6815

690.808

4g=27/5 minus third comma near here
31\81 12 7 12 727.909

497.531

1455.817

995.062

281.771

192.593

1009.68

690.1235

13\34 5 3 5 727.218

497.059

1454.436

994.118

279.699

191.1765

1006.917

688.235

34\89 13 8 13 726.59

496.629

1453.179

993.258

277.814

189.888

1004.403

686.517

89\233 34 21 34 726.498

496.5665

1452.996

993.133

277.538

189.7

1004.036

686.266

233\610 89 55 89 726.4845

496.557

1452.969

993.115

277.4985

189.672

1003.983

686.2295

Golden false father
144\377 55 34 55 726.476

496.552

1452.952

993.104

277.473

189.655

1003.95

686.207

55\144 21 13 21 726.441

496.528

1452.882

993.056

277.368

189.583

1003.809

686.111

21\55 8 5 8 726.201

496.364

1452.402

992.727

276.468

189.091

1002.849

685.4545

pi 2 pi 725.736

496.046

1451.472

992.091

275.252

188.137

1000.988

684.183

8\21 3 2 3 724.554

495.238

1449.109

990.476

271.708

185.714

996.226

680.952

Optimum rank range (L/s=3/2) false father

4g=16/3 near here

27\71 10 7 10 723.279

494.366

1446.557

988.732

267.881

183.099

991.16

677.465

46\121 17 12 17 723.057

494.215

1446.115

988.43

267.217

182.645

990.274

676.8595

19\50 7 5 7 722.743

494

1445.486

988

266.274

182

989.017

676

3g=7/2 near here
11\29 4 3 4 721.431

493.103

1442.862

986.207

262.338

179.31

983.77

672.414

25\66 9 7 9 720.4375

492.424

1440.875

984.8485

259.3575

177.273

979.795

669.697

64\169 23 18 23 720.267

492.308

1440.534

984.615

258.848

176.923

979.113

669.231

167\441 60 47 60 720.2415

492.29

1440.483

984.5805

258.7965

176.871

979.001

669.161

437\1154 157 123 157 720.238

492.288

1440.475

984.575

258.758

176.863

978.996

669.151

270\713 97 76 97 720.235

492.286

1440.471

984.572

258.751

176.858

978.987

669.1445

103\272 37 29 37 720.226

492.279

1440.451

984.558

258.722

176.837

978.947

669.116

39\103 14 11 14 720.158

492.233

1440.315

984.466

258.518

176.699

978.676

668.932

14\37 5 4 5 719.659

491.892

1439.317

983.784

257.021

175.676

976.679

667.568

31\82 11 9 11 719.032

491.463

1438.064

982.927

255.14

174.39

974.172

665.844

79\209 28 23 28 718.921

491.388

1437.842

982.775

254.807

174.163

973.728

665.55

206\545 73 60 73 718.904

491.376

1437.808

982.752

254.757

174.138

973.661

665.505

539\1426 191 117 191 718.902

491.3745

1437.803

982.749

254.75

174.123

973.652

665.498

333\881 118 97 118 718.9

491.373

1437.8

982.747

254.745

174.12

973.6455

665.494

127\336 45 37 45 718.893

491.369

1437.787

982.738

254.726

174.107

973.619

665.476

48\127 17 14 17 718.849

491.339

1437.698

982.677

254.592

174.016

973.441

665.354

17\45 6 5 6 718.516

491.111

1437.032

982.222

253.549

173.333

972.11

664.444

20\53 7 6 7 717.719

490.566

1435.438

981.132

251.202

171.698

968.9205

662.264

4g=21/4 near here
23\61 8 7 8 717.131

490.164

1434.261

980.328

249.437

170.492

966.567

660.656

49\130 17 15 17 716.891

490

1433.7815

980

248.717

170

965.608

660

4g=quarter-comma meantone 21/4 near here

6g=12 near here

26\69 9 8 9 716.679

489.855

1433.357

979.71

248.081

169.565

964.76

659.42

29\77 10 9 10 716.321

489.61

1432.641

979.221

247.007

168.831

963.328

658.442

32\85 11 10 11 716.03

489.412

1432.06

978.8235

246.135

168.235

962.1655

657.647

35\93 12 11 12 715.7895

489.247

1431.579

978.495

245.4135

167.742

961.203

656.989

38/101 13 12 13 715.587

489.109

1431.174

978.218

244.806

167.327

960.393

656.436

2g=16\7 near here
3\8 1 1 1 713.233

487.5

1426.466

975

237.744

162.5

950.9775

650