This page shows the epimoric12.scl tuning and a tempered approximation in the O3 tuning. Scala files are also available on the web. The frequency ratios of this 12-note JI tuning could be expressed as follows: 144 156 162 168 176 192 208 216 234 243 252 264 288 1/1 13/12 9/8 7/6 11/9 4/3 13/9 3/2 13/8 27/16 7/4 11/6 2/1 Margo Schulter September 14, 2010 ! epimoric12.scl ! 12-note tuning with all superparticular steps (2-3-7-9-11-13 JI) 12 ! 13/12 9/8 7/6 11/9 4/3 13/9 3/2 13/8 27/16 7/4 11/6 2/1 | 12-note tuning with all superparticular steps (2-3-7-9-11-13 JI) 0: 1/1 0.000 unison, perfect prime 1: 13/12 138.573 tridecimal 2/3-tone 2: 9/8 203.910 major whole tone 3: 7/6 266.871 septimal minor third 4: 11/9 347.408 undecimal neutral third 5: 4/3 498.045 perfect fourth 6: 13/9 636.618 tridecimal diminished fifth 7: 3/2 701.955 perfect fifth 8: 13/8 840.528 tridecimal neutral sixth 9: 27/16 905.865 Pythagorean major sixth 10: 7/4 968.826 harmonic seventh 11: 11/6 1049.363 21/4-tone, undecimal neutral seventh 12: 2/1 1200.000 octave ! O3-epimoric12_A.scl ! Tempered version of epimoric12.scl (factors of 2-3-7-9-11-13) 12 ! 138.28126 207.42188 264.84376 345.70313 495.70313 633.98438 703.12500 841.40625 910.54688 967.96876 1048.82813 2/1 | 12-note tuning with all superparticular steps (2-3-7-9-11-13 JI) 1/1 : 13/12 9/8 7/6 11/9 4/3 13/9 3/2 13/8 27/16 7/4 11/6 2/1 13/12: 27/26 14/13 44/39 16/13 4/3 18/13 3/2 81/52 21/13 22/13 24/13 2/1 9/8 : 28/27 88/81 32/27 104/81 4/3 13/9 3/2 14/9 44/27 16/9 52/27 2/1 7/6 : 22/21 8/7 26/21 9/7 39/28 81/56 3/2 11/7 12/7 13/7 27/14 2/1 11/9 : 12/11 13/11 27/22 117/88 243/176 63/44 3/2 18/11 39/22 81/44 21/11 2/1 4/3 : 13/12 9/8 39/32 81/64 21/16 11/8 3/2 13/8 27/16 7/4 11/6 2/1 13/9 : 27/26 9/8 243/208 63/52 33/26 18/13 3/2 81/52 21/13 22/13 24/13 2/1 3/2 : 13/12 9/8 7/6 11/9 4/3 13/9 3/2 14/9 44/27 16/9 52/27 2/1 13/8 : 27/26 14/13 44/39 16/13 4/3 18/13 56/39 176/117 64/39 16/9 24/13 2/1 27/16: 28/27 88/81 32/27 104/81 4/3 112/81 352/243 128/81 416/243 16/9 52/27 2/1 7/4 : 22/21 8/7 26/21 9/7 4/3 88/63 32/21 104/63 12/7 13/7 27/14 2/1 11/6 : 12/11 13/11 27/22 14/11 4/3 16/11 52/33 18/11 39/22 81/44 21/11 2/1 2/1 | 12-note tuning with all superparticular steps (2-3-7-9-11-13 JI) 0.0 : 138.6 203.9 266.9 347.4 498.0 636.6 702.0 840.5 905.9 968.8 1049.4 1200.0 138.6 : 65.3 128.3 208.8 359.5 498.0 563.4 702.0 767.3 830.3 910.8 1061.4 1200.0 203.9 : 63.0 143.5 294.1 432.7 498.0 636.6 702.0 764.9 845.5 996.1 1134.7 1200.0 266.9 : 80.5 231.2 369.7 435.1 573.7 639.0 702.0 782.5 933.1 1071.7 1137.0 1200.0 347.4 : 150.6 289.2 354.5 493.1 558.5 621.4 702.0 852.6 991.2 1056.5 1119.5 1200.0 498.0 : 138.6 203.9 342.5 407.8 470.8 551.3 702.0 840.5 905.9 968.8 1049.4 1200.0 636.6 : 65.3 203.9 269.2 332.2 412.7 563.4 702.0 767.3 830.3 910.8 1061.4 1200.0 702.0 : 138.6 203.9 266.9 347.4 498.0 636.6 702.0 764.9 845.5 996.1 1134.7 1200.0 840.5 : 65.3 128.3 208.8 359.5 498.0 563.4 626.3 706.9 857.5 996.1 1061.4 1200.0 905.9 : 63.0 143.5 294.1 432.7 498.0 561.0 641.5 792.2 930.8 996.1 1134.7 1200.0 968.8 : 80.5 231.2 369.7 435.1 498.0 578.6 729.2 867.8 933.1 1071.7 1137.0 1200.0 1049.4: 150.6 289.2 354.5 417.5 498.0 648.7 787.3 852.6 991.2 1056.5 1119.5 1200.0 1200.0 | Tempered version of epimoric12.scl (factors of 2-3-7-9-11-13) 1/1 : 138.3 207.4 264.8 345.7 495.7 634.0 703.1 841.4 910.5 968.0 1048.8 2/1 138.3 : 69.1 126.6 207.4 357.4 495.7 564.8 703.1 772.3 829.7 910.5 1061.7 2/1 207.4 : 57.4 138.3 288.3 426.6 495.7 634.0 703.1 760.5 841.4 992.6 1130.9 2/1 264.8 : 80.9 230.9 369.1 438.3 576.6 645.7 703.1 784.0 935.2 1073.4 1142.6 2/1 345.7 : 150.0 288.3 357.4 495.7 564.8 622.3 703.1 854.3 992.6 1061.7 1119.1 2/1 495.7 : 138.3 207.4 345.7 414.8 472.3 553.1 704.3 842.6 911.7 969.1 1050.0 2/1 634.0 : 69.1 207.4 276.6 334.0 414.8 566.0 704.3 773.4 830.9 911.7 1061.7 2/1 703.1 : 138.3 207.4 264.8 345.7 496.9 635.2 704.3 761.7 842.6 992.6 1130.9 2/1 841.4 : 69.1 126.6 207.4 358.6 496.9 566.0 623.4 704.3 854.3 992.6 1061.7 2/1 910.5 : 57.4 138.3 289.5 427.7 496.9 554.3 635.2 785.2 923.4 992.6 1130.9 2/1 968.0 : 80.9 232.0 370.3 439.5 496.9 577.7 727.7 866.0 935.2 1073.4 1142.6 2/1 1048.8: 151.2 289.5 358.6 416.0 496.9 646.9 785.2 854.3 992.6 1061.7 1119.1 2/1 2/1