7L 8s

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7L 8s refers to a Moment of Symmetry scale with 7 large steps and 8 small steps. One especially notable temperament that falls into this MOS pattern is porcupine, of the porcupine family.

Generator octachord g 2g 3g 4g 5g 6g 7g Comments
2\15 1 1 1 1 1 1 1 160 320 480 640 800 960 1120
9\67 4 5 4 5 4 5 4 161.2 322.4 483.6 644.8 806 967.2 1128.4
7\52 3 4 3 4 3 4 3 161.5 323.1 484.6 646.2 807.7 969.2 1130.8
5\37 2 3 2 3 2 3 2 162.2 324.3 486.5 648.6 810.8 973 1135.1 Optimal rank range (L/s=3/2) porcupine
2 pi 2 pi 2 pi 2 162.4 324.8 487.2 649.6 812 974.4 1136.8
13\96 5 8 5 8 5 8 5 162.5 325 487.5 650 812.5 975 1137.5
1 phi 1 phi 1 phi 1 162.6 325.1 487.7 650.2 812.8 975.35 1137.9 Golden porcupine when L/s=phi
8\59 3 5 3 5 3 5 3 162.7 325.4 488.1 650.8 813.6 976.3 1139
1 √3 1 √3 1 √3 1 162.9 325.9 488.7 651.6 814.55 977.5 1140.4
3\22 1 2 1 2 1 2 1 163.6 327.3 490.9 654.5 818.2 981.8 1145.5 Boundary of propriety (generators

smaller than this are proper)

7\51 2 5 2 5 2 5 2 164.7 329.4 494.1 658.8 823.5 988.2 1152.9
1 phi+1 1 phi+1 1 phi+1 1 164.9 329.8 494.75 659.7 824.6 989.5 1154.4
11\80 3 8 3 8 3 8 3 165 330 495 660 825 990 1155
1 e 1 e 1 e 1 165.1 330.2 495.3 660.3 825.4 990.5 1155.6 L/s=e
4\29 1 3 1 3 1 3 1 165.5 331 496.6 662.1 827.6 993.1 1158.6
1 pi 1 pi 1 pi 1 165.7 331.4 497.1 662.85 828.5 994.3 1160 L/s=pi
5\36 1 4 1 4 1 4 1 166.7 333.3 500 666.7 833.3 1000 1166.7
6\43 1 5 1 5 1 5 1 167.4 334.9 502.3 669.8 837.2 1004.65 1172.1
1\7 0 1 0 1 0 1 0 171.4 342.9 514.3 685.7 857.1 1028.6 1200