source file: mills2.txt Date: Wed, 15 Nov 1995 19:48:06 -0800 Subject: RE: Harry Partch's 43-Tone Scale From: Mmcky@aol.com Speaking of Harry Partch, here is an analysis of his scale: Harry Partch's 43 Tone Scale LCM: 2^11*3^8*5^2*7^2*11^2 43 1971200 160/ 81 42 1935360 64/ 33 41 1900800 40/ 21 40 1871100 15/ 8 Major Seventh 39 1829520 11/ 6 38 1814400 20/ 11 37 1796256 9/ 5 Minor Seventh 36 1774080 16/ 9 Grave Minor Seventh 35 1746360 7/ 4 Harmonic Minor Seventh 34 1710720 12/ 7 33 1683990 27/ 16 Pyth Major Sixth 32 1663200 5/ 3 Major Sixth 31 1632960 18/ 11 30 1596672 8/ 5 Minor Sixth 29 1568160 11/ 7 28 1552320 14/ 9 27 1520640 32/ 21 26 1496880 3/ 2 Perfect Fifth 25 1478400 40/ 27 24 1451520 16/ 11 23 1425600 10/ 7 22 1397088 7/ 5 21 1372140 11/ 8 20 1347192 27/ 20 19 1330560 4/ 3 Perfect Fourth 18 1309770 21/ 16 17 1283040 9/ 7 16 1270080 14/ 11 15 1247400 5/ 4 Major Third 14 1219680 11/ 9 13 1197504 6/ 5 Minor Third 12 1182720 32/ 27 Pyth Minor Third 11 1164240 7/ 6 10 1140480 8/ 7 9 1122660 9/ 8 Major Tone 8 1108800 10/ 9 Minor Tone 7 1097712 11/ 10 6 1088640 12/ 11 5 1064448 16/ 15 Semitone 4 1047816 21/ 20 3 1029105 33/ 32 2 1010394 81/ 80 1 997920 1/ 1 Unison Minimum Chords: 1 60 3: 4: 5 1- 19- 32 2 60 3: 4: 5 2- 20- 33 3 60 3: 4: 5 4- 22- 35 4 60 3: 4: 5 6- 24- 38 5 60 3: 4: 5 9- 26- 40 6 60 3: 4: 5 10- 27- 41 7 60 4: 5: 6 1- 15- 26 8 60 4: 5: 6 5- 19- 30 9 60 4: 5: 6 10- 23- 34 10 60 4: 5: 6 12- 25- 36 11 60 4: 5: 6 13- 26- 37 12 60 10: 12: 15 8- 19- 32 13 60 10: 12: 15 11- 22- 35 14 60 12: 15: 20 4- 18- 35 15 60 12: 15: 20 7- 21- 39 16 60 12: 15: 20 12- 25- 43 17 72 6: 8: 9 6- 24- 31 18 72 6: 8: 9 11- 28- 35 19 72 8: 9: 12 10- 17- 34 20 72 8: 9: 12 14- 21- 39 21 126 6: 7: 9 6- 16- 31 22 126 14: 18: 21 14- 29- 39 23 144 9: 12: 16 3- 21- 39 24 144 9: 12: 16 6- 24- 42 Chord List: LCM's to 280 1 60 3: 4: 5 1- 19- 32 2 60 3: 4: 5 2- 20- 33 3 60 3: 4: 5 4- 22- 35 4 60 3: 4: 5 6- 24- 38 5 60 3: 4: 5 9- 26- 40 6 60 3: 4: 5 10- 27- 41 7 60 4: 5: 6 1- 15- 26 8 60 4: 5: 6 5- 19- 30 9 60 4: 5: 6 10- 23- 34 10 60 4: 5: 6 12- 25- 36 11 60 4: 5: 6 13- 26- 37 12 60 10: 12: 15 1- 13- 26 13 60 10: 12: 15 8- 19- 32 14 60 10: 12: 15 9- 20- 33 15 60 10: 12: 15 11- 22- 35 16 60 10: 12: 15 15- 26- 40 17 60 12: 15: 20 1- 15- 32 18 60 12: 15: 20 4- 18- 35 19 60 12: 15: 20 5- 19- 36 20 60 12: 15: 20 7- 21- 39 21 60 12: 15: 20 10- 23- 41 22 60 12: 15: 20 12- 25- 43 23 72 6: 8: 9 1- 19- 26 24 72 6: 8: 9 6- 24- 31 25 72 6: 8: 9 8- 25- 32 26 72 6: 8: 9 9- 26- 33 27 72 6: 8: 9 10- 27- 34 28 72 6: 8: 9 11- 28- 35 29 72 6: 8: 9 13- 30- 37 30 72 6: 8: 9 15- 32- 40 31 72 8: 9: 12 1- 9- 26 32 72 8: 9: 12 5- 13- 30 33 72 8: 9: 12 8- 15- 32 34 72 8: 9: 12 10- 17- 34 35 72 8: 9: 12 11- 18- 35 36 72 8: 9: 12 12- 19- 36 37 72 8: 9: 12 13- 20- 37 38 72 8: 9: 12 14- 21- 39 39 84 4: 6: 7 1- 26- 35 40 84 12: 14: 21 1- 11- 35 41 90 5: 6: 9 1- 13- 37 42 90 6: 9: 10 1- 26- 32 43 90 6: 9: 10 5- 30- 36 44 90 6: 9: 10 6- 31- 38 45 90 6: 9: 10 9- 33- 40 46 90 6: 9: 10 10- 34- 41 47 90 6: 9: 10 12- 36- 43 48 90 9: 10: 15 1- 8- 32 49 90 9: 10: 15 2- 9- 33 50 90 9: 10: 15 4- 11- 35 51 90 9: 10: 15 5- 12- 36 52 90 9: 10: 15 7- 14- 39 53 90 9: 10: 15 9- 15- 40 54 90 10: 15: 18 1- 26- 37 55 120 5: 6: 8 1- 13- 30 56 120 5: 6: 8 8- 19- 36 57 120 5: 6: 8 9- 20- 37 58 120 8: 12: 15 1- 26- 40 59 120 8: 10: 15 1- 15- 40 60 120 15: 20: 24 1- 19- 30 61 120 15: 20: 24 8- 25- 36 62 120 15: 20: 24 9- 26- 37 63 126 6: 7: 9 1- 11- 26 64 126 6: 7: 9 6- 16- 31 65 126 6: 7: 9 9- 18- 33 66 126 6: 7: 9 10- 19- 34 67 126 6: 7: 9 13- 22- 37 68 126 14: 18: 21 1- 17- 26 69 126 14: 18: 21 8- 23- 32 70 126 14: 18: 21 11- 26- 35 71 126 14: 18: 21 12- 27- 36 72 126 14: 18: 21 14- 29- 39 73 140 4: 5: 7 1- 15- 35 74 140 20: 28: 35 1- 22- 35 75 144 9: 12: 16 1- 19- 36 76 144 9: 12: 16 2- 20- 37 77 144 9: 12: 16 3- 21- 39 78 144 9: 12: 16 6- 24- 42 79 144 9: 12: 16 8- 25- 43 80 168 6: 7: 8 1- 11- 19 81 168 6: 7: 8 6- 16- 24 82 168 6: 7: 8 9- 18- 26 83 168 6: 7: 8 10- 19- 27 84 168 6: 7: 8 13- 22- 30 85 168 6: 7: 8 17- 26- 34 86 168 6: 7: 8 19- 28- 36 87 168 6: 7: 8 23- 32- 41 88 168 7: 8: 12 1- 10- 34 89 168 7: 8: 12 4- 13- 37 90 168 14: 21: 24 1- 26- 34 91 168 14: 21: 24 8- 32- 41 92 168 21: 24: 28 1- 10- 19 93 168 21: 24: 28 4- 13- 22 94 168 21: 24: 28 9- 17- 26 95 168 21: 24: 28 11- 19- 28 96 168 21: 24: 28 15- 23- 32 97 168 21: 24: 28 18- 26- 35 98 168 21: 24: 28 19- 27- 36 99 168 21: 24: 28 21- 29- 39 100 180 9: 10: 12 1- 8- 19 101 180 9: 10: 12 2- 9- 20 102 180 9: 10: 12 4- 11- 22 103 180 9: 10: 12 9- 15- 26 104 180 9: 10: 12 13- 19- 30 105 180 9: 10: 12 17- 23- 34 106 180 9: 10: 12 19- 25- 36 107 180 9: 10: 12 20- 26- 37 108 180 15: 18: 20 1- 13- 19 109 180 15: 18: 20 8- 19- 25 110 180 15: 18: 20 9- 20- 26 111 180 15: 18: 20 11- 22- 28 112 180 15: 18: 20 15- 26- 32 113 180 15: 18: 20 19- 30- 36 114 180 15: 18: 20 23- 34- 41 115 180 15: 18: 20 25- 36- 43 116 198 6: 9: 11 1- 26- 39 117 198 18: 22: 33 1- 14- 39 118 210 5: 6: 7 1- 13- 22 119 210 5: 6: 7 8- 19- 28 120 210 5: 6: 7 15- 26- 35 121 210 6: 7: 10 1- 11- 32 122 210 6: 7: 10 6- 16- 38 123 210 6: 7: 10 9- 18- 40 124 210 6: 7: 10 10- 19- 41 125 210 10: 14: 15 1- 22- 26 126 210 10: 14: 15 8- 28- 32 127 210 10: 14: 15 10- 30- 34 128 210 10: 14: 15 15- 35- 40 129 210 14: 15: 21 5- 10- 30 130 210 14: 15: 21 11- 15- 35 131 210 14: 15: 21 13- 17- 37 132 210 21: 30: 35 1- 23- 32 133 210 21: 30: 35 4- 26- 35 134 210 21: 30: 35 5- 27- 36 135 210 21: 30: 35 7- 29- 39 136 210 30: 35: 42 1- 11- 22 137 210 30: 35: 42 10- 19- 30 138 210 30: 35: 42 17- 26- 37 139 240 10: 15: 16 1- 26- 30 140 240 10: 15: 16 8- 32- 36 141 240 10: 15: 16 9- 33- 37 142 240 12: 15: 16 1- 15- 19 143 240 12: 15: 16 4- 18- 22 144 240 12: 15: 16 10- 23- 27 145 240 12: 15: 16 13- 26- 30 146 240 12: 15: 16 19- 32- 36 147 240 12: 15: 16 20- 33- 37 148 240 12: 15: 16 24- 38- 42 149 240 15: 16: 20 1- 5- 19 150 240 15: 16: 24 1- 5- 30 151 240 15: 16: 20 3- 7- 21 152 240 15: 16: 24 8- 12- 36 153 240 15: 16: 20 8- 12- 25 154 240 15: 16: 24 9- 13- 37 155 240 15: 16: 20 9- 13- 26 156 240 15: 16: 20 15- 19- 32 157 240 15: 16: 20 18- 22- 35 158 240 15: 16: 20 23- 27- 41 159 252 7: 9: 12 1- 17- 34 160 252 7: 9: 12 4- 20- 37 161 252 7: 9: 12 8- 23- 41 162 252 9: 12: 14 1- 19- 28 163 252 9: 12: 14 9- 26- 35 164 252 9: 12: 14 10- 27- 36 165 252 18: 21: 28 1- 11- 28 166 252 18: 21: 28 9- 18- 35 167 252 18: 21: 28 10- 19- 36 168 252 21: 28: 36 1- 19- 34 169 252 21: 28: 36 4- 22- 37 170 252 21: 28: 36 8- 25- 41 171 264 6: 8: 11 1- 19- 39 172 264 8: 11: 12 1- 21- 26 173 264 8: 11: 12 6- 26- 31 174 264 8: 11: 12 10- 29- 34 175 264 22: 24: 33 1- 6- 26 176 264 22: 24: 33 11- 16- 35 177 264 22: 24: 33 14- 19- 39 178 264 24: 33: 44 1- 21- 39 179 280 5: 7: 8 1- 22- 30 180 280 5: 7: 8 8- 28- 36 181 280 7: 8: 10 1- 10- 23 182 280 7: 8: 10 4- 13- 26 183 280 7: 8: 10 11- 19- 32 184 280 7: 8: 10 16- 24- 38 185 280 7: 8: 10 18- 26- 40 186 280 7: 8: 10 19- 27- 41 187 280 28: 35: 40 1- 15- 23 188 280 28: 35: 40 4- 18- 26 189 280 28: 35: 40 5- 19- 27 190 280 28: 35: 40 7- 21- 29 191 280 28: 35: 40 13- 26- 34 192 280 28: 35: 40 19- 32- 41 193 280 35: 40: 56 1- 10- 30 194 280 35: 40: 56 9- 17- 37 Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 16 Nov 1995 08:27 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA24449; Wed, 15 Nov 1995 22:27:36 -0800 Date: Wed, 15 Nov 1995 22:27:36 -0800 Message-Id: <951116062522_71670.2576_HHB31-3@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu