Scala analysis: diaopt7
7-limit optimized diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 192.227 cents 192.227000 2: 384.454 cents 384.454000 3: 501.764 cents 501.764000 4: 697.175 cents 697.175000 5: 887.279 cents 887.279000 6: 1082.690 cents 1082.690000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 117.3100 cents 117.3100 1: 192.2270 cents 192.2270 2: 192.2270 cents 192.2270 3: 117.3100 cents 117.3100 4: 195.4110 cents 195.4110 5: 190.1040 cents 190.1040 6: 195.4110 cents 195.4110 7: 117.3100 cents 117.3100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 117.31000 cents 1: 1 190.10400 cents 1: 2 192.22700 cents 1: 2 195.41100 cents 2: 2 309.53700 cents 2: 2 312.72100 cents 2: 1 384.45400 cents 2: 2 385.51500 cents 3: 2 501.76400 cents 3: 2 502.82500 cents 3: 2 504.94800 cents 3: 1 580.92600 cents 4: 1 619.07400 cents 4: 2 695.05200 cents 4: 2 697.17500 cents 4: 2 698.23600 cents 5: 2 814.48500 cents 5: 1 815.54600 cents 5: 2 887.27900 cents 5: 2 890.46300 cents 6: 2 1004.58900 cents 6: 2 1007.77300 cents 6: 1 1009.89600 cents 6: 2 1082.69000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 192.2 384.5 501.8 697.2 887.3 1082.7 1200.0 192.2 : 192.2 309.5 504.9 695.1 890.5 1007.8 1200.0 384.5 : 117.3 312.7 502.8 698.2 815.5 1007.8 1200.0 501.8 : 195.4 385.5 580.9 698.2 890.5 1082.7 1200.0 697.2 : 190.1 385.5 502.8 695.1 887.3 1004.6 1200.0 887.3 : 195.4 312.7 504.9 697.2 814.5 1009.9 1200.0 1082.7: 117.3 309.5 501.8 619.1 814.5 1004.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 117.3100 .. 195.4110 cents 78.10100 cents 117.31000 cents 2: 309.5370 .. 385.5150 cents 75.97800 cents 114.12600 cents 3: 501.7640 .. 580.9260 cents 79.16200 cents 116.24900 cents 4: 619.0740 .. 698.2360 cents 79.16200 cents 38.14800 cents 5: 814.4850 .. 890.4630 cents 75.97800 cents 116.24900 cents 6: 1004.5890 .. 1082.6900 cents 78.10100 cents 114.12600 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 117.31000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 195.41100 cents Average / Smallest step : 1.461330 Largest / Average step : 1.139897 Largest / Smallest step : 1.665766 Median interval of one step : 192.22700 cents, amount: 2 Least squares average step : 175.62616 cents, oct.: 1229.38310 cents Scale is strictly proper Step pattern alph. order: AABCDCB Step pattern size order : CCADBDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 38.14800 cents Scale diversity : 1.300861 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.611265 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.06100 cents Number of recognisable fifths : 6, average 696.8210 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.9715 c. M: 54.1186 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 29.5622 c. M:-47.7730 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 10.5197 c. M:-17.3100 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 19: 3 3 2 3 3 3 2 SP M ME S SD: 4.5765 c. M: 9.0058 c. Nineteen-tone Major, Ionian 31: 5 5 3 5 5 5 3 SP M DE S SD: 1.7601 c. M:-3.0436 c. Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian 50: 8 8 5 8 8 8 5 SP M DE S SD: 1.4340 c. M: 2.6900 c. Fifty tone Major 81: 13 13 8 13 13 13 8 SP M DE S SD: 1.1499 c. M:-1.9397 c. 112: 18 18 11 18 18 18 11 SP M DE S SD: 1.2033 c. M:-2.0067 c. 131: 21 21 13 21 21 21 13 SP M DE S SD: 1.1986 c. M:-2.0528 c. 143: 23 23 14 23 23 23 14 SP M DE S SD: 1.2819 c. M:-2.2315 c. 181: 29 29 18 29 29 29 18 SP M DE S SD: 1.2466 c. M:-2.1034 c. 184: 29 30 18 30 29 30 18 SP T3 SD: 1.2189 c. M: 3.0966 c. 193: 31 31 19 31 31 31 19 SP M DE S SD: 1.1666 c. M:-1.8629 c. 196: 31 32 19 32 31 32 19 SP T3 SD: 1.1578 c. M: 2.4311 c. 206: 33 33 20 34 32 34 20 SP S SD: 1.0763 c. M:-1.8541 c. 215: 34 35 21 35 34 35 21 SP T3 SD: 1.0064 c. M: 2.4596 c. 225: 36 36 22 37 35 37 22 SP S SD: 0.9602 c. M: 1.9457 c. 237: 38 38 23 39 37 39 23 SP S SD: 0.8464 c. M:-1.5592 c. 256: 41 41 25 42 40 42 25 SP S SD: 0.7027 c. M: 1.3415 c. 268: 43 43 26 44 42 44 26 SP S SD: 0.7204 c. M:-1.3325 c. 287: 46 46 28 47 45 47 28 SP S SD: 0.5398 c. M:-1.0828 c. 306: 49 49 30 50 48 50 30 SP S SD: 0.5255 c. M: 1.0045 c. 318: 51 51 31 52 50 52 31 SP S SD: 0.4622 c. M:-0.9382 c. 337: 54 54 33 55 53 55 33 SP S SD: 0.3987 c. M:-0.7478 c. 349: 56 56 34 57 55 57 34 SP S SD: 0.4544 c. M:-0.8193 c. 368: 59 59 36 60 58 60 36 SP S SD: 0.3459 c. M:-0.6511 c. 387: 62 62 38 63 61 63 38 SP S SD: 0.3866 c. M:-0.5616 c. 399: 64 64 39 65 63 65 39 SP S SD: 0.3572 c. M:-0.5694 c. 418: 67 67 41 68 66 68 41 SP S SD: 0.3474 c. M:-0.6283 c. 430: 69 69 42 70 68 70 42 SP S SD: 0.4053 c. M:-0.6623 c. 449: 72 72 44 73 71 73 44 SP S SD: 0.3574 c. M:-0.6859 c. 625: 100 100 61 102 99 102 61 SP S SD: 0.3406 c. M: 0.6440 c. 637: 102 102 62 104 101 104 62 SP S SD: 0.3293 c. M: 0.6651 c. 644: 103 103 63 105 102 105 63 SP S SD: 0.3618 c. M: 0.6031 c. 656: 105 105 64 107 104 107 64 SP S SD: 0.2746 c. M: 0.5445 c. 675: 108 108 66 110 107 110 66 SP S SD: 0.2812 c. M: 0.4540 c. 687: 110 110 67 112 109 112 67 SP S SD: 0.2328 c. M: 0.4540 c. 706: 113 113 69 115 112 115 69 SP S SD: 0.2183 c. M: 0.3476 c. 737: 118 118 72 120 117 120 72 SP S SD: 0.1791 c. M: 0.2958 c. 756: 121 121 74 123 120 123 74 SP S SD: 0.2105 c. M: 0.3496 c. 768: 123 123 75 125 122 125 75 SP S SD: 0.1700 c. M: 0.3000 c. 993: 159 159 97 162 157 162 97 SP S SD: 0.1647 c. M: 0.2699 c. 1012: 162 162 99 165 160 165 99 SP S SD: 0.1831 c. M: 0.3225 c. 1024: 164 164 100 167 162 167 100 SP S SD: 0.1198 c. M: 0.2015 c. 1043: 167 167 102 170 165 170 102 SP S SD: 0.1259 c. M: 0.2224 c. 1055: 169 169 103 172 167 172 103 SP S SD: 0.0913 c. M:-0.1536 c. 1074: 172 172 105 175 170 175 105 SP S SD: 0.0726 c. M: 0.1282 c. 1105: 177 177 108 180 175 180 108 SP S SD: 0.0267 c. M: 0.0445 c. 2241: 359 359 219 365 355 365 219 SP S SD: 0.0200 c. M:-0.0409 c. 2260: 362 362 221 368 358 368 221 SP S SD: 0.0203 c. M: 0.0351 c. 2291: 367 367 224 373 363 373 224 SP S SD: 0.0150 c. M:-0.0256 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 2.3900 cents 3 x x 4 x 5 x 6 S SD: 1.5762 cents 4 x 5 x 6:7 x 8 S SD: 20.4270 cents 5 x 6:7 x 8:9:10 S SD: 28.9196 cents 6:7 x 8:9:10:11:12 S SD: 13.6703 cents 7:8:9 x 10:12:13:14 S SD: 18.7478 cents 8:9:10:11:12:13:15:16 SD: 9.9337 cents 12:13:15:16:18:20:22:24 SD: 9.0781 cents 15:17:19:20:22:25:28:30 SD: 7.0048 cents 16:18:20:21:24:27:30:32 S SD: 5.5316 cents 24:27:30:32:36:40:45:48 S SD: 2.1009 cents 36:40:45:48:54:60:67:72 SD: 2.0120 cents 51:57:64:68:76:85:95:102 SD: 1.8821 cents 60:67:75:80:90:100:112:120 SD: 1.0559 cents 69:77:86:92:103:115:129:138 SD: 1.0204 cents 93:104:116:124:139:155:174:186 SD: 0.8213 cents 101:113:126:135:151:169:189:202 SD: 0.7590 cents 113:126:141:151:169:189:211:226 SD: 0.7566 cents 121:135:151:162:181:202:226:242 SD: 0.6570 cents 137:153:171:183:205:229:256:274 SD: 0.3702 cents 145:162:181:194:217:242:271:290 SD: 0.3588 cents 161:180:201:215:241:269:301:322 SD: 0.3373 cents 214:239:267:286:320:357:400:428 SD: 0.3200 cents 238:266:297:318:356:397:445:476 SD: 0.2822 cents 282:315:352:377:422:471:527:564 SD: 0.2306 cents 306:342:382:409:458:511:572:612 SD: 0.1947 cents 357:399:446:477:534:596:667:714 SD: 0.1594 cents 375:419:468:501:561:626:701:750 SD: 0.1489 cents 494:552:617:660:739:825:923:988 SD: 0.1326 cents 502:561:627:671:751:838:938:1004 SD: 0.1295 cents 563:629:703:752:842:940:1052:1126 SD: 0.1284 cents 571:638:713:763:854:953:1067:1142 SD: 0.0947 cents