Scala analysis: iran_diat
Iranian Diatonic from Dariush Anooshfar, Safi-a-ddin Armavi's scale from 125 ET
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 220.800 cents 220.800000 2: 441.600 cents 441.600000 3: 489.600 cents 489.600000 4: 710.400 cents 710.400000 5: 931.200 cents 931.200000 6: 979.200 cents 979.200000 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 220.8000 cents 220.8000 1: 220.8000 cents 220.8000 2: 220.8000 cents 220.8000 3: 48.0000 cents 48.0000 4: 220.8000 cents 220.8000 5: 220.8000 cents 220.8000 6: 48.0000 cents 48.0000 7: 220.8000 cents 220.8000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 48.00000 cents 1: 5 220.80000 cents 2: 4 268.80000 cents 2: 3 441.60000 cents 3: 6 489.60000 cents 3: 1 662.40000 cents 4: 1 537.60000 cents 4: 6 710.40000 cents 5: 3 758.40000 cents 5: 4 931.20000 cents 6: 5 979.20000 cents 6: 2 1152.00000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 220.8 441.6 489.6 710.4 931.2 979.2 1200.0 220.8 : 220.8 268.8 489.6 710.4 758.4 979.2 1200.0 441.6 : 48.0 268.8 489.6 537.6 758.4 979.2 1200.0 489.6 : 220.8 441.6 489.6 710.4 931.2 1152.0 1200.0 710.4 : 220.8 268.8 489.6 710.4 931.2 979.2 1200.0 931.2 : 48.0 268.8 489.6 710.4 758.4 979.2 1200.0 979.2 : 220.8 441.6 662.4 710.4 931.2 1152.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.0000 .. 220.8000 cents 172.80000 cents 48.00000 cents 2: 268.8000 .. 441.6000 cents 172.80000 cents 48.00000 cents 3: 489.6000 .. 662.4000 cents 172.80000 cents 48.00000 cents 4: 537.6000 .. 710.4000 cents 172.80000 cents -124.80000 cents 5: 758.4000 .. 931.2000 cents 172.80000 cents 48.00000 cents 6: 979.2000 .. 1152.0000 cents 172.80000 cents 48.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 48.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 220.80000 cents Average / Smallest step : 3.571429 Largest / Average step : 1.288000 Largest / Smallest step : 4.600000 Median interval of one step : 220.80000 cents, amount: 5 Most common interval of one step : 220.80000 cents, amount: 5 Least squares average step : 173.89714 cents, oct.: 1217.28000 cents Scale is not proper Scale has Myhill's property chromas: 172.80000 cents and 124.80000 cents, ratio: 1.384615 generators: 3 of 489.60000 cents and 4 of 710.40000 cents ET pair of linear temperament : 22&27 Scale is distributional even Scale is a mode of a 125-tone equal temperament with octave 2/1 degrees: 23 46 51 74 97 102 125 generators: 51 and 74 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAABA Step pattern size order : LLSLLSL Interval vector is [ 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 6 0 0 0 0 1 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 48.00000 cents Ratio Whole / Half tone : 4.600000 ( 23/5 ) Scale diversity : 1.150643 Lumma stability : 0.240000 Lumma impropriety factor : 0.104000 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 48.00000 cents Most common intervals : 489.60000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 489.600 979.200 cents Most common triad is 0.0 489.600 710.400 cents, amount: 5 Number of recognisable fifths : 6, average 710.4000 cents Scale contains two identical conjunct tetrachords Formal octave complements present : 5 = 71.4286% Limited inverse transpositions : 1 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 0-1 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 2 0 1 1 1 1 N T3 SD: 49.0794 c. M: 74.0571 c. 9: 1 2 0 2 2 0 2 N T3 S SD: 55.3302 c. M: 89.6000 c. 10: 2 2 0 2 2 0 2 N M DE S SD: 21.4663 c. M:-38.4000 c. 13: 2 3 0 3 2 1 2 N SD: 25.7934 c. M:-36.1846 c. 14: 3 2 1 2 3 0 3 N SD: 24.3956 c. M: 36.3429 c. 15: 3 3 0 3 3 0 3 N M DE S SD: 21.4663 c. M:-38.4000 c. 16: 3 3 0 3 3 1 3 N T3 SD: 23.6057 c. M: 39.6000 c. 17: 3 3 1 3 3 1 3 N M DE S SD: 10.1018 c. M: 18.0706 c. Safi al-Din's maqam `Ussaq 22: 4 4 1 4 4 1 4 N M DE S SD: 2.9272 c. M: 5.2364 c. 27: 5 5 1 5 5 1 5 N M DE S SD: 1.5901 c. M:-2.8444 c. 49: 9 9 2 9 9 2 9 N M DE S SD: 0.4381 c. M: 0.7837 c. 76: 14 14 3 14 14 3 14 N M DE S SD: 0.2825 c. M:-0.5053 c. 125: 23 23 5 23 23 5 23 N M DE S SD: 0.0000 c. M: 0.0000 c. Iranian Diatonic
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: 4.2225 cents 3 x x 4 x 5 x 6 S SD: 15.8655 cents 4 x 5 x 6 x 7:8 S SD: 14.2204 cents 5:6 x 7:8 x 9:10 S SD: 34.5079 cents 6:7 x 8:9:10:11:12 S SD: 16.1435 cents 7:8:9 x 11:12 x 14 SD: 14.6302 cents 8:9:10:11:12 x 14:16 S SD: 14.2691 cents 9:10 x 12:14:15:16:18 S SD: 13.9413 cents 10:11:13 x 15:17:18:20 SD: 11.7563 cents 11:13:14:15:17:19 x 22 SD: 16.3272 cents 12:14:15:16:18 x 21:24 S SD: 12.2807 cents 13:15:17 x 20:22:23:26 SD: 9.1115 cents 14:16:18:19:21:24:25:28 SD: 6.9373 cents 15:17:19:20:23:26 x 30 SD: 8.2582 cents 16:18 x 21:24:27:28:32 S SD: 6.3688 cents 19:22 x 25:29 x 33:38 SD: 9.6290 cents 20:23:26:27:30:34:35:40 SD: 6.1289 cents 21:24:27:28:32:36:37:42 SD: 3.4438 cents 24:27:31:32:36:41:42:48 SD: 3.3639 cents 28:32:36:37:42:48:49:56 SD: 2.7954 cents 37:42:48:49:56:63:65:74 SD: 2.2766 cents 45:51:58:60:68:77:79:90 SD: 1.6756 cents 58:66:75:77:87:99:102:116 SD: 1.6068 cents 59:67:76:78:89:101:104:118 SD: 1.0808 cents 79:90:102:105:119:135:139:158 SD: 0.9922 cents 83:94:107:110:125:142:146:166 SD: 0.9362 cents 104:118:134:138:157:178:183:208 SD: 0.6542 cents 138:157:178:183:208:236:243:276 SD: 0.5236 cents 162:184:209:215:244:277:285:324 SD: 0.4596 cents 183:208:236:243:276:313:322:366 SD: 0.4542 cents 199:226:257:264:300:341:350:398 SD: 0.3552 cents 251:285:324:333:378:430:442:502 SD: 0.2915 cents 272:309:351:361:410:466:479:544 SD: 0.1600 cents 410:466:529:544:618:702:722:820 SD: 0.1524 cents 434:493:560:576:654:743:764:868 SD: 0.1227 cents 581:660:750:771:876:995:1023:1162 SD: 0.1063 cents