Scala analysis: apol
synmav3 in apollo {100/99, 225/224} temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 207.252 cents 207.252202 2: 381.117 cents 381.116799 3: 496.374 cents 496.373899 4: 703.626 cents 703.626101 5: 877.491 cents 877.490697 6: 992.748 cents 992.747798 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 207.2522 cents 207.2522 1: 207.2522 cents 207.2522 2: 173.8646 cents 173.8646 3: 115.2571 cents 115.2571 4: 207.2522 cents 207.2522 5: 173.8646 cents 173.8646 6: 115.2571 cents 115.2571 7: 207.2522 cents 207.2522
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 115.25710 cents 1: 2 173.86460 cents 1: 3 207.25220 cents 2: 2 289.12170 cents 2: 2 322.50930 cents 2: 2 381.11680 cents 2: 1 414.50440 cents 3: 5 496.37390 cents 3: 1 529.76150 cents 3: 1 588.36900 cents 4: 1 611.63100 cents 4: 1 670.23850 cents 4: 5 703.62610 cents 5: 1 785.49560 cents 5: 2 818.88320 cents 5: 2 877.49070 cents 5: 2 910.87830 cents 6: 3 992.74780 cents 6: 2 1026.13540 cents 6: 2 1084.74290 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 207.3 381.1 496.4 703.6 877.5 992.7 1200.0 207.3 : 173.9 289.1 496.4 670.2 785.5 992.7 1200.0 381.1 : 115.3 322.5 496.4 611.6 818.9 1026.1 1200.0 496.4 : 207.3 381.1 496.4 703.6 910.9 1084.7 1200.0 703.6 : 173.9 289.1 496.4 703.6 877.5 992.7 1200.0 877.5 : 115.3 322.5 529.8 703.6 818.9 1026.1 1200.0 992.7 : 207.3 414.5 588.4 703.6 910.9 1084.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 115.2571 .. 207.2522 cents 91.99510 cents 115.25710 cents 2: 289.1217 .. 414.5044 cents 125.38271 cents 81.86950 cents 3: 496.3739 .. 588.3690 cents 91.99510 cents 81.86950 cents 4: 611.6310 .. 703.6261 cents 91.99510 cents 23.26200 cents 5: 785.4956 .. 910.8783 cents 125.38271 cents 81.86950 cents 6: 992.7478 .. 1084.7429 cents 91.99510 cents 81.86950 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 115.25710 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 207.25220 cents Average / Smallest step : 1.487358 Largest / Average step : 1.208971 Largest / Smallest step : 1.798173 Median interval of one step : 173.86460 cents, amount: 2 Most common interval of one step : 207.25220 cents, amount: 3 Least squares average step : 171.55037 cents, oct.: 1200.85261 cents Scale is strictly proper Step pattern alph. order: ABCABCA Step pattern size order : LMSLMSL Scale is a Constant Structure, by a margin of 23.26200 cents Scale diversity : 1.463679 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.484378 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 23.26200 cents Most common intervals : 496.37390 cents & inv., amount: 5 Most common triad is 0.0 496.374 703.626 cents, amount: 3 Number of recognisable fifths : 5, average 703.6261 cents Scale contains two identical conjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 5 = 71.4286% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 26.9554 c. M: 38.2597 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 25.4461 c. M: 37.4907 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 11.9208 c. M:-22.5093 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 19: 3 3 2 3 3 2 3 SP M ME S SD: 10.9548 c. M: 17.7785 c. Nineteen-tone Mixolydian 22: 4 3 2 4 3 2 4 P SD: 6.7805 c. M:-10.9296 c. Murchhana Suddhasadja, Raga Harikambhoji, Palaiyazh 29: 5 4 3 5 4 3 5 SP SD: 4.6096 c. M: 8.7030 c. 34: 6 5 3 6 5 3 6 P SD: 4.2295 c. M:-7.1185 c. 41: 7 6 4 7 6 4 7 SP SD: 1.4540 c. M:-2.3742 c. 63: 11 9 6 11 9 6 11 SP SD: 1.4451 c. M:-2.2716 c. 75: 13 11 7 13 11 7 13 SP SD: 1.5122 c. M:-2.8832 c. 104: 18 15 10 18 15 10 18 SP SD: 0.3640 c. M: 0.5676 c. 145: 25 21 14 25 21 14 25 SP SD: 0.2831 c. M: 0.4271 c. 249: 43 36 24 43 36 24 43 SP SD: 0.2079 c. M: 0.3939 c. 324: 56 47 31 56 47 31 56 SP SD: 0.1984 c. M:-0.3647 c. 365: 63 53 35 63 53 35 63 SP SD: 0.1717 c. M:-0.3175 c. 428: 74 62 41 74 62 41 74 SP SD: 0.1554 c. M: 0.2244 c. 469: 81 68 45 81 68 45 81 SP SD: 0.0645 c. M:-0.1212 c. 573: 99 83 55 99 83 55 99 SP SD: 0.0483 c. M:-0.0776 c. 718: 124 104 69 124 104 69 124 SP SD: 0.0305 c. M: 0.0583 c. 1187: 205 172 114 205 172 114 205 SP SD: 0.0086 c. M:-0.0156 c. 1905: 329 276 183 329 276 183 329 SP SD: 0.0083 c. M: 0.0144 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: 0.8356 cents 3 x x 4 x 5 x 6 S SD: 2.3561 cents 4 x 5 x 6 x 7:8 S SD: 6.1342 cents 5 x 6:7 x 8:9:10 S SD: 25.6088 cents 6:7 x 8:9:10:11:12 S SD: 13.7562 cents 7:8:9 x 11:12 x 14 SD: 22.6276 cents 8:9:10:11:12:13:14:16 S SD: 10.0999 cents 12:14:15:16:18:20:21:24 S SD: 9.2653 cents 14:16:17:19:21:23:25:28 SD: 9.1370 cents 15:17:19:20:23:25:27:30 SD: 7.6546 cents 16:18:20:21:24:27:28:32 S SD: 6.5048 cents 18:20:22:24:27:30:32:36 S SD: 6.0906 cents 21:24:26:28:32:35:37:42 SD: 5.6333 cents 23:26:29:31:35:38:41:46 SD: 5.5713 cents 24:27:30:32:36:40:43:48 SD: 2.7615 cents 32:36:40:43:48:53:57:64 SD: 2.6005 cents 40:45:50:53:60:66:71:80 SD: 2.1975 cents 48:54:60:64:72:80:85:96 SD: 1.4479 cents 70:79:87:93:105:116:124:140 SD: 1.1748 cents 85:96:106:113:128:141:151:170 SD: 1.0768 cents 88:99:110:117:132:146:156:176 SD: 1.0605 cents 93:105:116:124:140:154:165:186 SD: 1.0339 cents 94:106:117:125:141:156:167:188 SD: 0.6675 cents 102:115:127:136:153:169:181:204 SD: 0.6319 cents 118:133:147:157:177:196:209:236 SD: 0.6025 cents 142:160:177:189:213:236:252:284 SD: 0.4338 cents 150:169:187:200:225:249:266:300 SD: 0.3915 cents 235:265:293:313:353:390:417:470 SD: 0.2056 cents 353:398:440:470:530:586:626:706 SD: 0.1930 cents 377:425:470:502:566:626:669:754 SD: 0.1455 cents 479:540:597:638:719:795:850:958 SD: 0.1008 cents