# Arcturus

Arcturus is a no-twos temperament which tempers out the comma 15625/15309. Having an ~5/3 as a generator, this temperament is the application of the Pythagorean principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to tritave composition. However, a heptatonic MOS (2L 5s) will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

## Chords

Arcturus contains the triad 5:7:9 (used in Bohlen-Pierce harmony) and the triad 27:35:45 which divides 5/3 into two nearly-equal parts.

## Tuning spectrum

Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0 cents:

Generator cents

hekts

L s 2g Notes
6\13 877.825

600

146.304

100

0 1755.651

1200

L=1 s=0
43\93 879.399

601.075

143.158

97.8495

20.451

13.9785

1758.797

1202.151

L=7 s=1
37\80 879.654

601.25

142.647

97.5

23.774

16.25

1759.38

1202.5

L=6 s=1
68\147 879.816

601.3605

142.323

97.279

25.877

17.687

1759.632

1202.721

31\67 880.009

601.4925

141.937

97.015

28.387

19.403

1760.081

1202.985

L=5 s=1
87\188 880.16

601.596

141.634

96.8085

30.35

20.745

1760.32

1203.191

56\121 880.243

601.653

141.468

96.694

31.437

21.488

1760.487

1203.306

81\175 880.3335

601.714

141.288

96.571

32.605

22.286

1760.667

1203.429

25\54 880.535

601.852

140.886

96.296

35.221

24.074

1761.069

1203.704

L=4 s=1
94\203 880.708

601.97

140.5385

96.059

37.477

25.616

1761.4165

1203.971

69\149 880.711

602.013

140.413

95.973

38.294

26.1745

1761.542

1204.027

113\244 880.823

602.049

140.308

95.902

38.9745

26.639

1761.647

1204.098

44\95 880.9055

602.105

140.144

95.7895

40.041

27.368

1761.811

1204.2105

L=7 s=2
107\231 880.992

602.1645

139.971

95.671

41.168

28.1385

1761.984

1204.329.

63\136 881.053

602.206

139.85

95.588

41.955

28.6765

1762.105

1204.412

82\177 881.132

602.26

139.692

95.48

42.982

22.034

1762.263

1204.52

19\41 881.394

602.439

139.167

95.122

46.389

31.707

1762.788

1204.878

L=3 s=1
89\192 881.635

602.604

138.684

94.792

49.53

33.854

1763.271

1205.208

70\151 881.701

602.649

138.553

94.702

50.383

25.828

1763.402

1205.298

121\261 881.794

602.682

138.4565

89.655

51.01

34.866

1763.4985

1205.362

51\110 881.8155

602.727

138.324

94.5455

51.8715

35.4545

1763.631

1205.4545

134\289 881.875

602.768

138.204

94.464

52.649

35.986

1763.751

1205.536

83\179 881.912

602.793

138.131

94.413

53.172

36.313

1763.824

1205.586

115\248 881.955

602.823

138.045

94.355

53.684

36.6935

1763.91

1205.645

32\69 882.066

602.899

137.823

94.203

55.129

37.681

1764.132

1205.797

L=5 s=2
109\235 882.183

602.979

137.588

94.043

56.654

38.723

1764.367

1205.957

77\166 882.232

603.012

137.491

93.976

57.288

39.157

1764.464

1206.024

122\263 882.276

603.042

137.404

93.916

57.854

39.544

1764.551

1206.084

45\97 882.35

603.093

137.2545

93.814

58.823

40.206

1764.7005

1203.185

L=7 s=3
103\222 882.439

603.153

137.078

93.694

59.972

40.991

1764.877

1206.306

58\125 882.507

603.2

136.941

93.6

60.863

41.6

1765.014

1206.4

71\153 882.607

603.268

136.742

93.464

62.155

42.484

1765.213

1206.536

13\28 883.0505

603.571

135.854

92.857

67.93

46.429

1766.101

1207.143

L=2 s=1
72\155 883.489

603.871

134.9775

92.258

73.624

50.323

1766.9775

1207.742

59\127 883.585

603.937

134.784

92.126

74.88

51.181

1767.171

1207.574

105\226 883.652

603.982

134.652

92.035

75.742

51.77

1767.303

1207.964

46\99 883.737

604.04

134.482

91.919

76.847

52.525

1767.473

1208.081

L=7 s=4
125\269 883.808

604.089

134.339

91.822

77.775

53.16

1767.616

1208.178

79\170 883.85

604.118

134.256

91.765

78.316

53.529

1767.699

1208.235

112\241 883.896

604.149

134.163

91.701

78.919

53.942

1767.792

1208.299

33\71 884.007

604.225

133.94

91.549

80.364

54.93

1768.0145

1208.451

L=5 s=3
119\256 884.112

604.297

133.731

91.406

81.725

55.859

1768.224

1208.594

86\185 884.152

604.324

133.651

91.351

82.247

56.216

1768.304

1208.649

139\299 884.186

604.348

133.582

91.304

82.694

56.522

1768.373

1208.696

Golden Arcturus is near here
53\114 884.24

604.386

133.4705

91.228

83.419

57.0175

1768.4845

1208.772

126\271 884.303

604.428

133.347

91.144

84.219

57.565

1768.608

1208.856

73\157 884.3485

604.459

133.258

91.083

84.8005

57.962

1768.697

1208.917

5/3-Pythagorean is near here
93\200 884.409

604.5

133.137

91

85.588

58.5

1768.818

1209

20\43 884.63

604.651

132.6945

90.698

88.463

60.465

1769.2605

1209.302

L=3 s=2
87\187 884.867

604.813

132.2215

90.374

91.538

62.567

1769.7335

1209.626

67\144 884.937

604.861

132.08

90.278

92.456

63.194

1769.875

1209.722

114\245 884.991

604.898

131.972

90.204

93.157

52.6735

1769.983

1209.896

47\101 885.068

604.9505

131.819

90.099

94.156

64.356

1770.136

1209.901

L=7 s=5
121\260 885.141

605

131.674

90

95.098

65

1770.281

1210

74\159 885.187

605.031

131.582

89.937

95.696

65.409

1770.373

1210.063

101\217 885.242

605.069

131.4715

89.862

96.4125

65.899

1770.4835

1210.138

27\58 885.393

605.172

131.169

89.655

98.377

67.241

1770.786

1210.345

L=4 s=3
88\189 885.566

605.291

130.822

89.418

100.6325

68.783

1771.133

1210.582

61\131 885.643

605.3435

130.669

89.313

101.631

69.466

1771.286

1210.687

95\204 885.714

605.392

130.526

89.216

102.556

70.098

1771.429

1210.784

34\73 885.842

605.4795

130.271

89.041

104.217

71.233

1771.684

1210.959

L=5 s=4
75\161 886.004

605.59

129.947

88.82

106.3205

72.671

1772.008

1211.18

41\88 886.138

605.682

129.679

88.636

108.065

73.864

1772.276

1211.364

L=6 s=5
48\103 886.348

605.825

129.259

88.3495

110.7935

75.728

1772.696

1211.6505

L=7 s=6
7\15 887.579

606.667

126.797

86.667

1775.158

1213.333

L=1 s=1