Arcturus
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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. 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 | L | s | 2g | Notes | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
6\13 | 877.825 | 146.304 | 0.00 | 1755.651 | L=1 s=0 | ||||||
43\93 | 879.399 | 143.158 | 20.451 | 1758.797 | L=7 s=1 | ||||||
37\80 | 879.654 | 142.647 | 23.774 | 1759.38 | L=6 s=1 | ||||||
68\147 | 879.816 | 142.323 | 25.877 | 1759.632 | |||||||
31\67 | 880.009 | 141.937 | 28.387 | 1760.081 | L=5 s=1 | ||||||
87\188 | 880.16 | 141.634 | 30.35 | 1760.32 | |||||||
56\121 | 880.243 | 141.468 | 31.437 | 1760.487 | |||||||
81\175 | 880.3335 | 141.288 | 32.605 | 1760.667 | |||||||
25\54 | 880.535 | 140.886 | 35.221 | 1761.069 | L=4 s=1 | ||||||
94\203 | 880.708 | 140.5385 | 37.477 | 1761.4165 | |||||||
69\149 | 880.711 | 140.413 | 38.294 | 1761.542 | |||||||
113\244 | 880.823 | 140.308 | 38.9745 | 1761.647 | |||||||
44\95 | 880.9055 | 140.144 | 40.041 | 1761.811 | L=7 s=2 | ||||||
107\231 | 880.992 | 139.971 | 41.168 | 1761.984 | |||||||
63\136 | 881.053 | 139.85 | 41.955 | 1762.105 | |||||||
82\177 | 881.132 | 139.692 | 42.982 | 1762.263 | |||||||
19\41 | 881.394 | 139.167 | 46.389 | 1762.788 | L=3 s=1 | ||||||
89\192 | 881.635 | 138.684 | 49.53 | 1763.271 | |||||||
70\151 | 881.701 | 138.553 | 50.383 | 1763.402 | |||||||
121\261 | 881.794 | 138.4565 | 51.01 | 1763.4985 | |||||||
51\110 | 881.8155 | 138.324 | 51.8715 | 1763.631 | |||||||
134\289 | 881.875 | 138.204 | 52.649 | 1763.751 | |||||||
83\179 | 881.912 | 138.131 | 53.172 | 1763.824 | |||||||
115\248 | 881.955 | 138.045 | 53.684 | 1763.91 | |||||||
32\69 | 882.066 | 137.823 | 55.129 | 1764.132 | L=5 s=2 | ||||||
109\235 | 882.183 | 137.588 | 56.654 | 1764.367 | |||||||
77\166 | 882.232 | 137.491 | 57.288 | 1764.464 | |||||||
122\263 | 882.276 | 137.404 | 57.854 | 1764.551 | |||||||
45\97 | 882.35 | 137.2545 | 58.823 | 1764.7005 | L=7 s=3 | ||||||
103\222 | 882.439 | 137.078 | 59.972 | 1764.877 | |||||||
58\125 | 882.507 | 136.941 | 60.863 | 1765.014 | |||||||
71\153 | 882.607 | 136.742 | 62.155 | 1765.213 | |||||||
13\28 | 883.0505 | 135.854 | 67.93 | 1766.101 | L=2 s=1 | ||||||
72\155 | 883.489 | 134.9775 | 73.624 | 1766.9775 | |||||||
59\127 | 883.585 | 134.784 | 74.88 | 1767.171 | |||||||
105\226 | 883.652 | 134.652 | 75.742 | 1767.303 | |||||||
46\99 | 883.737 | 134.482 | 76.847 | 1767.473 | L=7 s=4 | ||||||
125\269 | 883.808 | 134.339 | 77.775 | 1767.616 | |||||||
79\170 | 883.85 | 134.256 | 78.316 | 1767.699 | |||||||
112\241 | 883.896 | 134.163 | 78.919 | 1767.792 | |||||||
33\71 | 884.007 | 133.94 | 80.364 | 1768.0145 | L=5 s=3 | ||||||
119\256 | 884.112 | 133.731 | 81.725 | 1768.224 | |||||||
86\185 | 884.152 | 133.651 | 82.247 | 1768.304 | |||||||
139\299 | 884.186 | 133.582 | 82.694 | 1768.373 | Golden Arcturus is near here | ||||||
53\114 | 884.24 | 133.4705 | 83.419 | 1768.4845 | |||||||
126\271 | 884.303 | 133.347 | 84.219 | 1768.608 | |||||||
73\157 | 884.3485 | 133.258 | 84.8005 | 1768.697 | |||||||
93\200 | 884.409 | 133.137 | 85.588 | 1768.818 | |||||||
20\43 | 884.63 | 132.6945 | 88.463 | 1769.2605 | L=3 s=2 | ||||||
87\187 | 884.867 | 132.2215 | 91.538 | 1769.7335 | |||||||
67\144 | 884.937 | 132.08 | 92.456 | 1769.875 | |||||||
114\245 | 884.991 | 131.972 | 93.157 | 1769.983 | |||||||
47\101 | 885.068 | 131.819 | 94.156 | 1770.136 | L=7 s=5 | ||||||
121\260 | 885.141 | 131.674 | 95.098 | 1770.281 | |||||||
74\159 | 885.187 | 131.582 | 95.696 | 1770.373 | |||||||
101\217 | 885.242 | 131.4715 | 96.4125 | 1770.4835 | |||||||
27\58 | 885.393 | 131.169 | 98.377 | 1770.786 | L=4 s=3 | ||||||
88\189 | 885.566 | 130.822 | 100.6325 | 1771.133 | |||||||
61\131 | 885.643 | 130.669 | 101.631 | 1771.286 | |||||||
95\204 | 885.714 | 130.526 | 102.556 | 1771.429 | |||||||
34\73 | 885.842 | 130.271 | 104.217 | 1771.684 | L=5 s=4 | ||||||
75\161 | 886.004 | 129.947 | 106.3205 | 1772.008 | |||||||
41\88 | 886.138 | 129.679 | 108.065 | 1772.276 | L=6 s=5 | ||||||
48\103 | 886.348 | 129.259 | 110.7935 | 1772.696 | L=7 s=6 | ||||||
7\15 | 887.579 | 126.797 | 1775.158 | L=1 s=1 |