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:
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Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}
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| Generator(edt) | Cents | Step ratio | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | ||||||||
| 7\13 | 1024.130 | 877.825 | 1:1 | 1.000 | Equalized 11L 2s⟨3/1⟩ | ||||||
| 48\89 | 1025.773 | 876.182 | 7:6 | 1.167 | |||||||
| 41\76 | 1026.055 | 875.900 | 6:5 | 1.200 | |||||||
| 75\139 | 1026.235 | 875.720 | 11:9 | 1.222 | |||||||
| 34\63 | 1026.452 | 875.503 | 5:4 | 1.250 | |||||||
| 95\176 | 1026.623 | 875.332 | 14:11 | 1.273 | |||||||
| 61\113 | 1026.719 | 875.236 | 9:7 | 1.286 | |||||||
| 88\163 | 1026.822 | 875.133 | 13:10 | 1.300 | |||||||
| 27\50 | 1027.056 | 874.899 | 4:3 | 1.333 | Supersoft 11L 2s⟨3/1⟩ | ||||||
| 101\187 | 1027.259 | 874.696 | 15:11 | 1.364 | |||||||
| 74\137 | 1027.333 | 874.622 | 11:8 | 1.375 | |||||||
| 121\224 | 1027.395 | 874.560 | 18:13 | 1.385 | |||||||
| 47\87 | 1027.493 | 874.462 | 7:5 | 1.400 | |||||||
| 114\211 | 1027.597 | 874.358 | 17:12 | 1.417 | |||||||
| 67\124 | 1027.669 | 874.286 | 10:7 | 1.429 | |||||||
| 87\161 | 1027.765 | 874.190 | 13:9 | 1.444 | |||||||
| 20\37 | 1028.084 | 873.871 | 3:2 | 1.500 | Soft 11L 2s⟨3/1⟩ | ||||||
| 93\172 | 1028.383 | 873.572 | 14:9 | 1.556 | |||||||
| 73\135 | 1028.465 | 873.490 | 11:7 | 1.571 | |||||||
| 126\233 | 1028.525 | 873.430 | 19:12 | 1.583 | |||||||
| 53\98 | 1028.608 | 873.347 | 8:5 | 1.600 | |||||||
| 139\257 | 1028.684 | 873.271 | 21:13 | 1.615 | |||||||
| 86\159 | 1028.730 | 873.225 | 13:8 | 1.625 | |||||||
| 119\220 | 1028.785 | 873.170 | 18:11 | 1.636 | |||||||
| 33\61 | 1028.926 | 873.029 | 5:3 | 1.667 | Semisoft 11L 2s⟨3/1⟩ | ||||||
| 112\207 | 1029.077 | 872.878 | 17:10 | 1.700 | |||||||
| 79\146 | 1029.140 | 872.815 | 12:7 | 1.714 | |||||||
| 125\231 | 1029.196 | 872.759 | 19:11 | 1.727 | |||||||
| 46\85 | 1029.293 | 872.662 | 7:4 | 1.750 | |||||||
| 105\194 | 1029.409 | 872.546 | 16:9 | 1.778 | |||||||
| 59\109 | 1029.499 | 872.456 | 9:5 | 1.800 | |||||||
| 72\133 | 1029.630 | 872.325 | 11:6 | 1.833 | |||||||
| 13\24 | 1030.226 | 871.729 | 2:1 | 2.000 | Basic 11L 2s⟨3/1⟩ Scales with tunings softer than this are proper | ||||||
| 71\131 | 1030.831 | 871.124 | 11:5 | 2.200 | |||||||
| 58\107 | 1030.966 | 870.989 | 9:4 | 2.250 | |||||||
| 103\190 | 1031.060 | 870.895 | 16:7 | 2.286 | |||||||
| 45\83 | 1031.180 | 870.775 | 7:3 | 2.333 | |||||||
| 122\225 | 1031.282 | 870.673 | 19:8 | 2.375 | |||||||
| 77\142 | 1031.342 | 870.613 | 12:5 | 2.400 | |||||||
| 109\201 | 1031.408 | 870.547 | 17:7 | 2.429 | |||||||
| 32\59 | 1031.569 | 870.386 | 5:2 | 2.500 | Semihard 11L 2s⟨3/1⟩ | ||||||
| 115\212 | 1031.721 | 870.234 | 18:7 | 2.571 | |||||||
| 83\153 | 1031.780 | 870.175 | 13:5 | 2.600 | |||||||
| 134\247 | 1031.830 | 870.125 | 21:8 | 2.625 | |||||||
| 51\94 | 1031.912 | 870.043 | 8:3 | 2.667 | |||||||
| 121\223 | 1032.002 | 869.953 | 19:7 | 2.714 | |||||||
| 70\129 | 1032.069 | 869.886 | 11:4 | 2.750 | |||||||
| 89\164 | 1032.159 | 869.796 | 14:5 | 2.800 | |||||||
| 19\35 | 1032.490 | 869.465 | 3:1 | 3.000 | Hard 11L 2s⟨3/1⟩ | ||||||
| 82\151 | 1032.850 | 869.105 | 13:4 | 3.250 | |||||||
| 63\116 | 1032.958 | 868.997 | 10:3 | 3.333 | |||||||
| 107\197 | 1033.042 | 868.913 | 17:5 | 3.400 | |||||||
| 44\81 | 1033.161 | 868.794 | 7:2 | 3.500 | |||||||
| 113\208 | 1033.274 | 868.681 | 18:5 | 3.600 | |||||||
| 69\127 | 1033.346 | 868.609 | 11:3 | 3.667 | |||||||
| 94\173 | 1033.432 | 868.523 | 15:4 | 3.750 | |||||||
| 25\46 | 1033.671 | 868.284 | 4:1 | 4.000 | Superhard 11L 2s⟨3/1⟩ | ||||||
| 81\149 | 1033.949 | 868.006 | 13:3 | 4.333 | |||||||
| 56\103 | 1034.073 | 867.882 | 9:2 | 4.500 | |||||||
| 87\160 | 1034.188 | 867.767 | 14:3 | 4.667 | |||||||
| 31\57 | 1034.397 | 867.558 | 5:1 | 5.000 | |||||||
| 68\125 | 1034.664 | 867.291 | 11:2 | 5.500 | |||||||
| 37\68 | 1034.887 | 867.068 | 6:1 | 6.000 | |||||||
| 43\79 | 1035.241 | 866.714 | 7:1 | 7.000 | |||||||
| 6\11 | 1037.430 | 864.525 | 1:0 | → ∞ | Collapsed 11L 2s⟨3/1⟩ | ||||||