Scala analysis: div28
Dividing 5 into 28 equal parts
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.511 cents 99.511204 2: 199.022 cents 199.022408 3: 298.534 cents 298.533612 4: 398.045 cents 398.044816 5: 497.556 cents 497.556020 6: 597.067 cents 597.067224 7: 696.578 cents 696.578428 8: 796.090 cents 796.089633 9: 895.601 cents 895.600837 10: 995.112 cents 995.112041 11: 1094.623 cents 1094.623245 12: 1194.134 cents 1194.134449 13: 1293.646 cents 1293.645653 14: 1393.157 cents 1393.156857 15: 1492.668 cents 1492.668061 16: 1592.179 cents 1592.179265 17: 1691.690 cents 1691.690469 18: 1791.202 cents 1791.201673 19: 1890.713 cents 1890.712877 20: 1990.224 cents 1990.224081 21: 2089.735 cents 2089.735285 22: 2189.246 cents 2189.246489 23: 2288.758 cents 2288.757694 24: 2388.269 cents 2388.268898 25: 2487.780 cents 2487.780102 26: 2587.291 cents 2587.291306 27: 2686.803 cents 2686.802510 28: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 99.5112 cents 99.5112 1: 99.5112 cents 99.5112 2: 99.5112 cents 99.5112 3: 99.5112 cents 99.5112 4: 99.5112 cents 99.5112 5: 99.5112 cents 99.5112 6: 99.5112 cents 99.5112 7: 99.5112 cents 99.5112 8: 99.5112 cents 99.5112 9: 99.5112 cents 99.5112 10: 99.5112 cents 99.5112 11: 99.5112 cents 99.5112 12: 99.5112 cents 99.5112 13: 99.5112 cents 99.5112 14: 99.5112 cents 99.5112 15: 99.5112 cents 99.5112 16: 99.5112 cents 99.5112 17: 99.5112 cents 99.5112 18: 99.5112 cents 99.5112 19: 99.5112 cents 99.5112 20: 99.5112 cents 99.5112 21: 99.5112 cents 99.5112 22: 99.5112 cents 99.5112 23: 99.5112 cents 99.5112 24: 99.5112 cents 99.5112 25: 99.5112 cents 99.5112 26: 99.5112 cents 99.5112 27: 99.5112 cents 99.5112 28: 99.5112 cents 99.5112
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 28 99.51120 cents 2: 28 199.02241 cents 3: 28 298.53361 cents 4: 28 398.04482 cents 5: 28 497.55602 cents 6: 28 597.06722 cents 7: 28 696.57843 cents 8: 28 796.08963 cents 9: 28 895.60084 cents 10: 28 995.11204 cents 11: 28 1094.62324 cents 12: 28 1194.13445 cents 13: 28 1293.64565 cents 14: 28 1393.15686 cents 15: 28 1492.66806 cents 16: 28 1592.17926 cents 17: 28 1691.69047 cents 18: 28 1791.20167 cents 19: 28 1890.71288 cents 20: 28 1990.22408 cents 21: 28 2089.73528 cents 22: 28 2189.24649 cents 23: 28 2288.75769 cents 24: 28 2388.26890 cents 25: 28 2487.78010 cents 26: 28 2587.29131 cents 27: 28 2686.80251 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0.0 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 99.5 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 199.0 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 298.5 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 398.0 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 497.6 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 597.1 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 696.6 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 796.1 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 895.6 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 995.1 : 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1094.6: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1194.1: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1293.6: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1393.2: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1492.7: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1592.2: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1691.7: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1791.2: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1890.7: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 1990.2: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2089.7: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2189.2: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2288.8: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2388.3: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2487.8: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2587.3: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2686.8: 99.5 199.0 298.5 398.0 497.6 597.1 696.6 796.1 895.6 995.1 1094.6 1194.1 1293.6 1393.2 1492.7 1592.2 1691.7 1791.2 1890.7 1990.2 2089.7 2189.2 2288.8 2388.3 2487.8 2587.3 2686.8 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.5112 .. 99.5112 cents 1/1, 0.0000 cents 99.51120 cents 2: 199.0224 .. 199.0224 cents 1/1, 0.0000 cents 99.51120 cents 3: 298.5336 .. 298.5336 cents 1/1, 0.0000 cents 99.51120 cents 4: 398.0448 .. 398.0448 cents 1/1, 0.0000 cents 99.51120 cents 5: 497.5560 .. 497.5560 cents 1/1, 0.0000 cents 99.51120 cents 6: 597.0672 .. 597.0672 cents 1/1, 0.0000 cents 99.51120 cents 7: 696.5784 .. 696.5784 cents 1/1, 0.0000 cents 99.51120 cents 8: 796.0896 .. 796.0896 cents 1/1, 0.0000 cents 99.51121 cents 9: 895.6008 .. 895.6008 cents 1/1, 0.0000 cents 99.51120 cents 10: 995.1120 .. 995.1120 cents 1/1, 0.0000 cents 99.51120 cents 11: 1094.6232 .. 1094.6232 cents 1/1, 0.0000 cents 99.51120 cents 12: 1194.1344 .. 1194.1344 cents 1/1, 0.0000 cents 99.51120 cents 13: 1293.6457 .. 1293.6457 cents 1/1, 0.0000 cents 99.51120 cents 14: 1393.1569 .. 1393.1569 cents 1/1, 0.0000 cents 99.51120 cents 15: 1492.6681 .. 1492.6681 cents 1/1, 0.0000 cents 99.51120 cents 16: 1592.1793 .. 1592.1793 cents 1/1, 0.0000 cents 99.51120 cents 17: 1691.6905 .. 1691.6905 cents 1/1, 0.0000 cents 99.51120 cents 18: 1791.2017 .. 1791.2017 cents 1/1, 0.0000 cents 99.51120 cents 19: 1890.7129 .. 1890.7129 cents 1/1, 0.0000 cents 99.51120 cents 20: 1990.2241 .. 1990.2241 cents 1/1, 0.0000 cents 99.51120 cents 21: 2089.7353 .. 2089.7353 cents 1/1, 0.0000 cents 99.51120 cents 22: 2189.2465 .. 2189.2465 cents 1/1, 0.0000 cents 99.51120 cents 23: 2288.7577 .. 2288.7577 cents 1/1, 0.0000 cents 99.51120 cents 24: 2388.2689 .. 2388.2689 cents 1/1, 0.0000 cents 99.51120 cents 25: 2487.7801 .. 2487.7801 cents 1/1, 0.0000 cents 99.51120 cents 26: 2587.2913 .. 2587.2913 cents 1/1, 0.0000 cents 99.51120 cents 27: 2686.8025 .. 2686.8025 cents 1/1, 0.0000 cents 99.51120 cents
SHOW DATA
Number of notes : 28 -- Interval properties -- Smallest interval : 99.51120 cents, class 1 Average step (divided formal octave): 99.5112 cents Largest one step interval : 99.51120 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 99.51120 cents, amount: 28 Most common interval of one step : 99.51120 cents, amount: 28 Least squares average step : 99.51120 cents, oct.: 2786.31371 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 99.51120 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.035714 redundancy: 0.964286 Efficiency x scale size : 1.000000 Number of different interval sizes : 27 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 28, average 696.5784 cents Number of recognisable fourths : 28, average 497.5560 cents Scale contains two identical disjunct hexachords Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
28: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 5 match: 4 H SD: 4.3186 cents 2 .. 10 match: 8 H SD: 4.0599 cents 3 .. 15 match: 12 H SD: 6.1703 cents 4 .. 20 match: 16 H SD: 5.0083 cents 5 .. 25 match: 19 S SD: 4.8384 cents 6 .. 30 match: 21 SD: 4.5809 cents 7 .. 35 match: 23 SD: 5.4093 cents 8 .. 40 match: 24 SD: 3.9690 cents 9 .. 45 match: 25 SD: 3.8685 cents 10 .. 50 match: 26 SD: 3.8680 cents 11 .. 55 match: 26 SD: 4.7515 cents 12 .. 60 match: 27 SD: 3.2074 cents 13 .. 65 match: 27 SD: 4.4227 cents 14 .. 70 match: 28 SD: 3.6030 cents 15 .. 75 match: 28 SD: 2.7191 cents 16 .. 80 match: 28 SD: 2.5706 cents 17 .. 85 match: 28 SD: 2.5279 cents 22 .. 110 match: 28 SD: 2.0988 cents 24 .. 120 match: 28 SD: 1.9694 cents 26 .. 130 match: 28 SD: 1.8133 cents 27 .. 135 match: 28 SD: 1.6034 cents 31 .. 155 match: 28 SD: 1.3628 cents 32 .. 160 match: 28 SD: 1.2365 cents 39 .. 195 match: 28 SD: 1.1928 cents 43 .. 215 match: 28 SD: 1.0510 cents 46 .. 230 match: 28 SD: 1.0256 cents 48 .. 240 match: 28 SD: 0.9495 cents 49 .. 245 match: 28 SD: 0.8747 cents 53 .. 265 match: 28 SD: 0.8711 cents 58 .. 290 match: 28 SD: 0.7867 cents 63 .. 315 match: 28 SD: 0.6777 cents 65 .. 325 match: 28 SD: 0.6462 cents 75 .. 375 match: 28 SD: 0.6242 cents 81 .. 405 match: 28 SD: 0.4696 cents 90 .. 450 match: 28 SD: 0.4692 cents 97 .. 485 match: 28 SD: 0.4526 cents 99 .. 495 match: 28 SD: 0.4412 cents 100 .. 500 match: 28 SD: 0.4356 cents 101 .. 505 match: 28 SD: 0.4307 cents 105 .. 525 match: 28 SD: 0.4028 cents 116 .. 580 match: 28 SD: 0.3702 cents 117 .. 585 match: 28 SD: 0.3093 cents 139 .. 695 match: 28 SD: 0.2701 cents 165 .. 825 match: 28 SD: 0.2467 cents 170 .. 850 match: 28 SD: 0.2299 cents 171 .. 855 match: 28 SD: 0.2216 cents 187 .. 935 match: 28 SD: 0.2148 cents 202 .. 1010 match: 28 SD: 0.2117 cents 204 .. 1020 match: 28 SD: 0.1923 cents 236 .. 1180 match: 28 SD: 0.1790 cents 238 .. 1190 match: 28 SD: 0.1765 cents 254 .. 1270 match: 28 SD: 0.1687 cents 255 .. 1275 match: 28 SD: 0.1249 cents 303 .. 1515 match: 28 SD: 0.1238 cents 355 .. 1775 match: 28 SD: 0.1204 cents 367 .. 1835 match: 28 SD: 0.1190 cents 372 .. 1860 match: 28 SD: 0.0989 cents 394 .. 1970 match: 28 SD: 0.0953 cents 403 .. 2015 match: 28 SD: 0.0922 cents 442 .. 2210 match: 28 SD: 0.0844 cents 457 .. 2285 match: 28 SD: 0.0822 cents 510 .. 2550 match: 28 SD: 0.0783 cents 541 .. 2705 match: 28 SD: 0.0676 cents 573 .. 2865 match: 28 SD: 0.0675 cents 592 .. 2960 match: 28 SD: 0.0637 cents