Scala analysis: 705-17
17-note MOS, fifth 705 cents, near-just 13/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 135.000 cents 135.000000 3: 210.000 cents 210.000000 4: 285.000 cents 285.000000 5: 345.000 cents 345.000000 6: 420.000 cents 420.000000 7: 495.000 cents 495.000000 8: 570.000 cents 570.000000 9: 630.000 cents 630.000000 10: 705.000 cents 705.000000 11: 780.000 cents 780.000000 12: 840.000 cents 840.000000 13: 915.000 cents 915.000000 14: 990.000 cents 990.000000 15: 1050.000 cents 1050.000000 16: 1125.000 cents 1125.000000 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 75.0000 cents 75.0000 1: 75.0000 cents 75.0000 2: 60.0000 cents 60.0000 3: 75.0000 cents 75.0000 4: 75.0000 cents 75.0000 5: 60.0000 cents 60.0000 6: 75.0000 cents 75.0000 7: 75.0000 cents 75.0000 8: 75.0000 cents 75.0000 9: 60.0000 cents 60.0000 10: 75.0000 cents 75.0000 11: 75.0000 cents 75.0000 12: 60.0000 cents 60.0000 13: 75.0000 cents 75.0000 14: 75.0000 cents 75.0000 15: 60.0000 cents 60.0000 16: 75.0000 cents 75.0000 17: 75.0000 cents 75.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 60.00000 cents 1: 12 75.00000 cents 2: 10 135.00000 cents 2: 7 150.00000 cents 3: 15 210.00000 cents 3: 2 225.00000 cents 4: 3 270.00000 cents 4: 14 285.00000 cents 5: 8 345.00000 cents 5: 9 360.00000 cents 6: 13 420.00000 cents 6: 4 435.00000 cents 7: 1 480.00000 cents 7: 16 495.00000 cents 8: 6 555.00000 cents 8: 11 570.00000 cents 9: 11 630.00000 cents 9: 6 645.00000 cents 10: 16 705.00000 cents 10: 1 720.00000 cents 11: 4 765.00000 cents 11: 13 780.00000 cents 12: 9 840.00000 cents 12: 8 855.00000 cents 13: 14 915.00000 cents 13: 3 930.00000 cents 14: 2 975.00000 cents 14: 15 990.00000 cents 15: 7 1050.00000 cents 15: 10 1065.00000 cents 16: 12 1125.00000 cents 16: 5 1140.00000 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 8 9 10 11 12 13 14 15 16 17 0.0 : 75.0 135.0 210.0 285.0 345.0 420.0 495.0 570.0 630.0 705.0 780.0 840.0 915.0 990.0 1050.0 1125.0 1200.0 75.0 : 60.0 135.0 210.0 270.0 345.0 420.0 495.0 555.0 630.0 705.0 765.0 840.0 915.0 975.0 1050.0 1125.0 1200.0 135.0 : 75.0 150.0 210.0 285.0 360.0 435.0 495.0 570.0 645.0 705.0 780.0 855.0 915.0 990.0 1065.0 1140.0 1200.0 210.0 : 75.0 135.0 210.0 285.0 360.0 420.0 495.0 570.0 630.0 705.0 780.0 840.0 915.0 990.0 1065.0 1125.0 1200.0 285.0 : 60.0 135.0 210.0 285.0 345.0 420.0 495.0 555.0 630.0 705.0 765.0 840.0 915.0 990.0 1050.0 1125.0 1200.0 345.0 : 75.0 150.0 225.0 285.0 360.0 435.0 495.0 570.0 645.0 705.0 780.0 855.0 930.0 990.0 1065.0 1140.0 1200.0 420.0 : 75.0 150.0 210.0 285.0 360.0 420.0 495.0 570.0 630.0 705.0 780.0 855.0 915.0 990.0 1065.0 1125.0 1200.0 495.0 : 75.0 135.0 210.0 285.0 345.0 420.0 495.0 555.0 630.0 705.0 780.0 840.0 915.0 990.0 1050.0 1125.0 1200.0 570.0 : 60.0 135.0 210.0 270.0 345.0 420.0 480.0 555.0 630.0 705.0 765.0 840.0 915.0 975.0 1050.0 1125.0 1200.0 630.0 : 75.0 150.0 210.0 285.0 360.0 420.0 495.0 570.0 645.0 705.0 780.0 855.0 915.0 990.0 1065.0 1140.0 1200.0 705.0 : 75.0 135.0 210.0 285.0 345.0 420.0 495.0 570.0 630.0 705.0 780.0 840.0 915.0 990.0 1065.0 1125.0 1200.0 780.0 : 60.0 135.0 210.0 270.0 345.0 420.0 495.0 555.0 630.0 705.0 765.0 840.0 915.0 990.0 1050.0 1125.0 1200.0 840.0 : 75.0 150.0 210.0 285.0 360.0 435.0 495.0 570.0 645.0 705.0 780.0 855.0 930.0 990.0 1065.0 1140.0 1200.0 915.0 : 75.0 135.0 210.0 285.0 360.0 420.0 495.0 570.0 630.0 705.0 780.0 855.0 915.0 990.0 1065.0 1125.0 1200.0 990.0 : 60.0 135.0 210.0 285.0 345.0 420.0 495.0 555.0 630.0 705.0 780.0 840.0 915.0 990.0 1050.0 1125.0 1200.0 1050.0: 75.0 150.0 225.0 285.0 360.0 435.0 495.0 570.0 645.0 720.0 780.0 855.0 930.0 990.0 1065.0 1140.0 1200.0 1125.0: 75.0 150.0 210.0 285.0 360.0 420.0 495.0 570.0 645.0 705.0 780.0 855.0 915.0 990.0 1065.0 1125.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 60.0000 .. 75.0000 cents 15.00000 cents 60.00000 cents 2: 135.0000 .. 150.0000 cents 15.00000 cents 60.00000 cents 3: 210.0000 .. 225.0000 cents 15.00000 cents 60.00000 cents 4: 270.0000 .. 285.0000 cents 15.00000 cents 45.00000 cents 5: 345.0000 .. 360.0000 cents 15.00000 cents 60.00000 cents 6: 420.0000 .. 435.0000 cents 15.00000 cents 60.00000 cents 7: 480.0000 .. 495.0000 cents 15.00000 cents 45.00000 cents 8: 555.0000 .. 570.0000 cents 15.00000 cents 60.00000 cents 9: 630.0000 .. 645.0000 cents 15.00000 cents 60.00000 cents 10: 705.0000 .. 720.0000 cents 15.00000 cents 60.00000 cents 11: 765.0000 .. 780.0000 cents 15.00000 cents 45.00000 cents 12: 840.0000 .. 855.0000 cents 15.00000 cents 60.00000 cents 13: 915.0000 .. 930.0000 cents 15.00000 cents 60.00000 cents 14: 975.0000 .. 990.0000 cents 15.00000 cents 45.00000 cents 15: 1050.0000 .. 1065.0000 cents 15.00000 cents 60.00000 cents 16: 1125.0000 .. 1140.0000 cents 15.00000 cents 60.00000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 60.00000 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 75.00000 cents Average / Smallest step : 1.176471 Largest / Average step : 1.062500 Largest / Smallest step : 1.250000 Median interval of one step : 75.00000 cents, amount: 12 Most common interval of one step : 75.00000 cents, amount: 12 Least squares average step : 70.40336 cents, oct.: 1196.85714 cents Scale is strictly proper Scale has Myhill's property chromas: 15.00000 cents and 45.00000 cents, ratio: 3.000000 generators: 7 of 495.00000 cents and 10 of 705.00000 cents Scale is maximally even in 80-tone equal temperament ET pair of linear temperament : 12&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 80-tone equal temperament with octave 2/1 degrees: 5 9 14 19 23 28 33 38 42 47 52 56 61 66 70 75 80 generators: 33 and 47 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABAABAA Step pattern size order : LSLLSLLLSLLSLLSLL Interval vector is [ 0 0 0 5 12 0 0 0 10 7 0 0 0 15 2 0 0 3 14 0 0 0 8 9 0 0 0 13 4 0 0 1 16 0 0 0 6 11 0 0 ] Scale is a Constant Structure, by a margin of 45.00000 cents Ratio Whole / Half tone : 2.800000 ( 14/5 ) Scale diversity : 1.130650 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.800000 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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 : 15.00000 cents Most common intervals : 495.00000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 495.000 990.000 cents Most common triad is 0.0 495.000 705.000 cents, amount: 15 Number of recognisable fifths : 17, average 705.8824 cents Number of appreciable fifths : 16, average 705.0000 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 13 = 76.4706% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.6690 c. M:-8.8235 c. 46: 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 SP M ME S SD: 3.4510 c. M: 6.5217 c. 63: 4 3 4 4 3 4 4 4 3 4 4 3 4 4 3 4 4 SP M ME S SD: 1.2599 c. M: 2.3810 c. 80: 5 4 5 5 4 5 5 5 4 5 5 4 5 5 4 5 5 SP M ME S SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.5225 cents 3 .. 6 match: 3 H SD: 10.2641 cents 4 .. 8 match: 4 H SD: 9.9762 cents 5 .. 10 match: 5 H SD: 9.9448 cents 6 .. 12 match: 6 H SD: 5.9780 cents 7 .. 14 match: 7 H SD: 5.7822 cents 8 .. 16 match: 8 H SD: 7.2111 cents 9 .. 18 match: 9 H SD: 5.6631 cents 10 .. 20 match: 10 H SD: 6.8966 cents 11 .. 22 match: 11 H SD: 5.5982 cents 12 .. 24 match: 12 H SD: 5.1742 cents 13 .. 26 match: 13 H SD: 5.3397 cents 14 .. 28 match: 14 H SD: 4.4128 cents 15 .. 30 match: 14 SD: 6.2433 cents 16 .. 32 match: 15 SD: 4.5110 cents 17 .. 34 match: 15 SD: 5.2797 cents 18 .. 36 match: 16 SD: 3.5641 cents 19 .. 38 match: 16 SD: 4.9685 cents 20 .. 40 match: 16 SD: 5.2200 cents 21 .. 42 match: 17 SD: 3.7227 cents 22 .. 44 match: 17 SD: 3.1676 cents 23 .. 46 match: 17 SD: 2.6181 cents 36 .. 72 match: 17 SD: 2.2647 cents 37 .. 74 match: 17 SD: 2.1744 cents 39 .. 78 match: 17 SD: 1.8847 cents 40 .. 80 match: 17 SD: 1.7808 cents 46 .. 92 match: 17 SD: 1.4343 cents 60 .. 120 match: 17 SD: 1.4187 cents 61 .. 122 match: 17 SD: 1.2153 cents 62 .. 124 match: 17 SD: 1.0941 cents 69 .. 138 match: 17 SD: 1.0365 cents 72 .. 144 match: 17 SD: 0.8457 cents 85 .. 170 match: 17 SD: 0.8078 cents 91 .. 182 match: 17 SD: 0.8054 cents 95 .. 190 match: 17 SD: 0.7188 cents 109 .. 218 match: 17 SD: 0.6071 cents 123 .. 246 match: 17 SD: 0.5617 cents 135 .. 270 match: 17 SD: 0.5410 cents 139 .. 278 match: 17 SD: 0.3965 cents 185 .. 370 match: 17 SD: 0.3360 cents 200 .. 400 match: 17 SD: 0.3083 cents 223 .. 446 match: 17 SD: 0.2148 cents 318 .. 636 match: 17 SD: 0.2132 cents 336 .. 672 match: 17 SD: 0.2115 cents 341 .. 682 match: 17 SD: 0.2096 cents 342 .. 684 match: 17 SD: 0.2072 cents 357 .. 714 match: 17 SD: 0.1871 cents 362 .. 724 match: 17 SD: 0.1857 cents 380 .. 760 match: 17 SD: 0.1598 cents 408 .. 816 match: 17 SD: 0.1275 cents 481 .. 962 match: 17 SD: 0.1257 cents 495 .. 990 match: 17 SD: 0.1185 cents 520 .. 1040 match: 17 SD: 0.1143 cents 543 .. 1086 match: 17 SD: 0.0904 cents