KH0698/AK003 - Colored Pendant Sums
Drawings:
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Right Handed Sums with Figure-8-Knots: # Sums = 161, Max # Summands = 24, (Min, Mean, Max) Sum Values = (14, 80, 1000)
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Left Handed Sums with Figure-8-Knots: # Sums = 114, Max # Summands = 22, (Min, Mean, Max) Sum Values = (11, 89, 1000)
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Right Handed Sum Detail: - Click on column name to sort
| # | Color | Sum Schema | Sum Cord | Sum Cord Value | # Summands | Summands |
|---|---|---|---|---|---|---|
| 1 |  | g1p1 : 309W | 309 | 8 | g48p6: 10W + g48p7: 6W + g48p8: 13W + g48p9: 30W + g49p1: 189W + g49p2: 7W + g49p5: 21W + βg49p6: 33W | |
| 2 |  | g1p5 : 77W | 77 | 3 | g28p7: 15W + g28p8: 44W + g28p9: 18W | |
| 3 |  | g1p8 : 30W | 30 | 3 | g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 4 |  | g2p1 : 218W | 218 | 4 | g23p9: 17Wβ + g24p1: 171W + g24p8: 12W + g24p9: 18W | |
| 5 |  | g2p2 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 6 |  | g2p3 : 25W:PB | 25 | 4 | g28p3: 3W:PB + g29p3: 8W:PB + g30p3: 9W:PB + g31p3: 5W:PB | |
| 7 |  | g2p5 : 29W | 29 | 3 | βg26p5: 8W + g26p6: 12W + g26p7: 9W | |
| 8 |  | g2p9 : 47W | 47 | 4 | βg32p6: 15W + g32p7: 6W + g32p8: 13W + g32p9: 13Wβ | |
| 9 |  | g3p1 : 140W | 140 | 5 | βg44p1: 113Wβ + g44p2: 1W + g44p5: 14W + g44p6: 7W + g44p7: 5W | |
| 10 |  | g3p7 : 24W | 24 | 3 | g28p2: 4W + g28p5: 7W + g28p6: 13W | |
| 11 |  | g3p9 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 12 |  | g4p1 : 155W | 155 | 4 | g21p2: 26W + g21p7: 18W + g21p8: 20W + g21p9: 91Wβ½ | |
| 13 |  | g5p1 : 200W | 200 | 3 | g23p9: 17Wβ + g24p1: 171W + g24p8: 12W | |
| 14 |  | g5p4 : 14PB | 14 | 3 | g31p4: 3PBβ + g32p4: 5PB + g33p4: 6PB | |
| 15 |  | g5p6 : 25W | 25 | 3 | g42p7: 3W + g42p8: 9W + g42p9: 13W | |
| 16 |  | g5p7 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 17 |  | g5p9 : 44W | 44 | 3 | β½g14p5: 11W + g14p7: 14W + g14p8: 19W | |
| 18 |  | g6p1 : 219W | 219 | 4 | g33p7: 23W + g33p8: 26W + g33p9: 21W + βg34p1: 149W | |
| 19 |  | g6p5 : 23W | 23 | 3 | g44p7: 5W + g44p8: 6W + g44p9: 12W | |
| 20 |  | g6p8 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 21 |  | g6p9 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 22 |  | g7p1 : 229W | 229 | 3 | β½g54p1: 221W + g54p2: 2W + g54p5: 6W | |
| 23 |  | g7p3 : 27W:PB | 27 | 3 | β½g50p3: 11W:PB + g51p3: 5W:PB + g52p3: 11W:PBβ½ | |
| 24 |  | g7p6 : 22W | 22 | 3 | β½g44p2: 1W + g44p5: 14W + g44p6: 7W | |
| 25 |  | g7p8 : 31W | 31 | 3 | g22p5: 2W + g22p7: 18W + g22p8: 11Wβ½ | |
| 26 |  | g7p9 : 19W | 19 | 3 | g41p6: 10W + g41p7: 3W + g41p8: 6Wβ | |
| 27 |  | g8p1 : 210W | 210 | 4 | βg39p8: 15W + g39p9: 32W + g40p1: 156W + g40p2: 7W | |
| 28 |  | g8p2 : 59W | 59 | 3 | g19p8: 24W + g19p9: 26W + g20p7: 9W | |
| 29 |  | g9p1 : 190W | 190 | 3 | g18p1: 80W + g19p1: 100W + g19p5: 10W | |
| 30 |  | g9p3 : 22W:PB | 22 | 3 | g29p3: 8W:PB + g30p3: 9W:PB + g31p3: 5W:PB | |
| 31 |  | g10p1 : 250W | 250 | 4 | g49p1: 189W + g49p2: 7W + g49p5: 21W + βg49p6: 33W | |
| 32 |  | g10p3 : 20W:PB | 20 | 3 | g28p3: 3W:PB + g29p3: 8W:PB + g30p3: 9W:PB | |
| 33 |  | g10p6 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 34 |  | g10p8 : 57W | 57 | 3 | β½g29p6: 21W + g29p7: 20W + g29p8: 16W | |
| 35 |  | g10p9 : 30W | 30 | 3 | g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 36 |  | g11p1 : 270W | 270 | 4 | g35p1: 235W + g35p2: 23W + g35p5: 6W + g35p6: 6W | |
| 37 |  | g11p2 : 34W | 34 | 3 | g25p5: 10W + g25p6: 8W + g25p7: 16W | |
| 38 |  | g11p3 : 30W:PB | 30 | 3 | g33p3: 10W:PB + g34p3: 10W:PB + g36p3: 10W:PB | |
| 39 |  | g11p5 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 40 |  | g11p6 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 41 |  | g11p9 : 36W | 36 | 3 | βg31p2: 14W + g31p5: 12W + βg31p6: 10W | |
| 42 |  | g12p1 : 199W | 199 | 4 | g18p1: 80W + g19p1: 100W + g19p5: 10W + g19p6: 9W | |
| 43 |  | g12p3 : 59W:PB | 59 | 5 | β½g24p3: 21W:PB + g25p3: 12W:PB + g26p3: 3W:PB + g27p3: 20W:PB + g28p3: 3W:PB | |
| 44 |  | g12p7 : 35W | 35 | 3 | g16p2: 10W + g16p5: 19W + g16p6: 6W | |
| 45 |  | g12p8 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 46 |  | g12p9 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 47 |  | g13p1 : 200W | 200 | 3 | g23p9: 17Wβ + g24p1: 171W + g24p8: 12W | |
| 48 |  | g13p3 : 42W:PB | 42 | 3 | g56p3: 23W:PB + g57p3: 8W:PB + g58p1: 11W:PBβ½ | |
| 49 |  | g13p5 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 50 |  | g13p7 : 25W | 25 | 3 | g42p7: 3W + g42p8: 9W + g42p9: 13W | |
| 51 |  | g13p8 : 27W | 27 | 3 | βg14p2: 2W + g14p5: 11W + g14p7: 14W | |
| 52 |  | g13p9 : 30W | 30 | 3 | g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 53 |  | g14p1 : 155W | 155 | 4 | g21p2: 26W + g21p7: 18W + g21p8: 20W + g21p9: 91Wβ½ | |
| 54 |  | g14p7 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 55 |  | g14p8 : 19W | 19 | 3 | g41p6: 10W + g41p7: 3W + g41p8: 6Wβ | |
| 56 |  | g14p9 : 53W | 53 | 3 | β½g51p5: 21W + g51p6: 15W + g51p7: 17W | |
| 57 |  | g15p1 : 250W | 250 | 4 | g49p1: 189W + g49p2: 7W + g49p5: 21W + βg49p6: 33W | |
| 58 |  | g15p2 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 59 |  | g15p5 : 30W | 30 | 3 | g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 60 |  | g15p7 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 61 |  | g16p1 : 326W | 326 | 5 | g19p9: 26W + g20p7: 9W + g20p8: 16W + g20p9: 15W + g21p1: 260W | |
| 62 |  | g16p5 : 19W | 19 | 3 | g41p6: 10W + g41p7: 3W + g41p8: 6Wβ | |
| 63 |  | g16p7 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 64 |  | g16p8 : 34W | 34 | 3 | g25p5: 10W + g25p6: 8W + g25p7: 16W | |
| 65 |  | g16p9 : 33W | 33 | 3 | g40p6: 10W + g40p7: 20W + g40p8: 3W | |
| 66 |  | g17p1 : 1000W | 1000 | 24 | βg52p7: 29W + g52p8: 15W + g52p9: 13W + g53p1: 158W + g53p2: 13W + g53p5: 18W + g53p7: 6W + g53p8: 19W + g53p9: 21W + g54p1: 221W + g54p2: 2W + g54p5: 6W + g54p6: 23W + g54p7: 41W + g54p8: 34W + g54p9: 19W + g55p1: 90W + g55p2: 16W + g55p5: 18W + g55p6: 11W + g55p7: 5W + g55p8: 4W + g55p9: 27W + g56p1: 191Wβ½ | |
| 67 |  | g17p9 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 68 |  | g18p1 : 80W | 80 | 4 | g34p2: 22W + g34p5: 23W + g34p6: 22W + g34p7: 13W | |
| 69 |  | g19p1 : 100W | 100 | 5 | βg57p5: 6W + g57p6: 12W + g57p7: 38W + g57p8: 10W + g57p9: 34Wβ | |
| 70 |  | g19p8 : 24W | 24 | 3 | g28p2: 4W + g28p5: 7W + g28p6: 13W | |
| 71 |  | g19p9 : 26W | 26 | 3 | g30p2: 6W + g30p5: 14W + g30p6: 6W | |
| 72 |  | g21p1 : 260W | 260 | 5 | g28p7: 15W + g28p8: 44W + g28p9: 18W + g29p1: 166W + g29p2: 17W | |
| 73 |  | g21p2 : 26W | 26 | 3 | g30p2: 6W + g30p5: 14W + g30p6: 6W | |
| 74 |  | g21p3 : 77W:PB | 77 | 6 | βg39p3: 12W:PB + g40p3: 36W:PB + g41p3: 10W:PB + g42p3: 5W:PB + g43p3: 4W:PB + βg44p3: 10W:PB | |
| 75 |  | g21p4 : 14PB | 14 | 3 | g31p4: 3PBβ + g32p4: 5PB + g33p4: 6PB | |
| 76 |  | g21p7 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 77 |  | g21p8 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 78 |  | g21p9 : 91W | 91 | 4 | β½g29p6: 21W + g29p7: 20W + g29p8: 16W + g29p9: 34W | |
| 79 |  | g22p1 : 272W | 272 | 7 | g28p9: 18W + g29p1: 166W + g29p2: 17W + g29p5: 14W + g29p6: 21W + g29p7: 20W + g29p8: 16W | |
| 80 |  | g22p2 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 81 |  | g22p4 : 15PB | 15 | 3 | g32p4: 5PBβ + g33p4: 6PB + g34p4: 4PB | |
| 82 |  | g22p7 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 83 |  | g22p9 : 30W | 30 | 3 | g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 84 |  | g23p1 : 102W | 102 | 3 | g41p8: 6Wβ + g41p9: 11W + βg42p1: 85W | |
| 85 |  | g24p1 : 171W | 171 | 3 | β½g37p1: 131W + g37p2: 7W + g37p5: 33W | |
| 86 |  | g24p3 : 21W:PB | 21 | 3 | g31p3: 5W:PB + g32p3: 6W:PB + g33p3: 10W:PB | |
| 87 |  | g24p9 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 88 |  | g25p1 : 117W | 117 | 4 | g54p6: 23Wβ + g54p7: 41W + g54p8: 34W + g54p9: 19W | |
| 89 |  | g26p1 : 208W | 208 | 3 | g27p8: 18W + g27p9: 12W + g28p1: 178W | |
| 90 |  | g26p2 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 91 |  | g27p1 : 178W | 178 | 3 | g40p1: 156W + g40p2: 7W + g40p5: 15W | |
| 92 |  | g27p3 : 20W:PB | 20 | 3 | g28p3: 3W:PB + g29p3: 8W:PB + g30p3: 9W:PB | |
| 93 |  | g27p5 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 94 |  | g27p6 : 23W | 23 | 3 | g44p7: 5W + g44p8: 6W + g44p9: 12W | |
| 95 |  | g27p8 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 96 |  | g28p1 : 178W | 178 | 3 | g40p1: 156W + g40p2: 7W + g40p5: 15W | |
| 97 |  | g28p8 : 44W | 44 | 3 | g34p6: 22W + g34p7: 13W + g34p8: 9W | |
| 98 |  | g28p9 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 99 |  | g29p1 : 166W | 166 | 7 | g43p2: 9W + g43p5: 6W + g43p6: 13W + g43p8: 13W + g43p9: 11W + g44p1: 113W + g44p2: 1Wβ½ | |
| 100 |  | g29p5 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 101 |  | g29p6 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 102 |  | g29p7 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 103 |  | g29p9 : 34W | 34 | 3 | βg32p6: 15W + g32p7: 6W + g32p8: 13W | |
| 104 |  | g30p1 : 148W | 148 | 5 | g42p9: 13W + g43p1: 107W + g43p2: 9W + g43p5: 6W + g43p6: 13W | |
| 105 |  | g30p5 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 106 |  | g30p9 : 42W | 42 | 3 | βg33p2: 5W + g33p5: 17W + g33p6: 20W | |
| 107 |  | g31p2 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 108 |  | g32p1 : 137W | 137 | 3 | g43p8: 13Wβ + g43p9: 11W + βg44p1: 113Wβ | |
| 109 |  | g33p1 : 151W | 151 | 5 | g43p6: 13W + g43p8: 13W + g43p9: 11W + g44p1: 113W + g44p2: 1Wβ½ | |
| 110 |  | g33p6 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 111 |  | g33p7 : 23W | 23 | 3 | g44p7: 5W + g44p8: 6W + g44p9: 12W | |
| 112 |  | g33p8 : 26W | 26 | 3 | g44p5: 14W + g44p6: 7W + g44p7: 5W | |
| 113 |  | g33p9 : 21W | 21 | 3 | g41p5: 8W + g41p6: 10W + g41p7: 3W | |
| 114 |  | g34p1 : 149W | 149 | 6 | g40p6: 10W + g40p7: 20W + g40p8: 3W + g40p9: 14W + g41p1: 89W + g41p2: 13W | |
| 115 |  | g34p2 : 22W | 22 | 3 | β½g44p2: 1W + g44p5: 14W + g44p6: 7W | |
| 116 |  | g34p5 : 23W | 23 | 3 | g44p7: 5W + g44p8: 6W + g44p9: 12W | |
| 117 |  | g34p6 : 22W | 22 | 3 | β½g44p2: 1W + g44p5: 14W + g44p6: 7W | |
| 118 |  | g35p1 : 235W | 235 | 5 | β½g56p1: 191W + g56p2: 16W + g56p5: 6W + g56p6: 8W + g56p7: 14W | |
| 119 |  | g35p2 : 23W | 23 | 3 | g44p7: 5W + g44p8: 6W + g44p9: 12W | |
| 120 |  | g35p7 : 18W | 18 | 3 | g44p6: 7W + g44p7: 5W + g44p8: 6W | |
| 121 |  | g35p9 : 28W | 28 | 3 | g43p2: 9W + g43p5: 6W + g43p6: 13W | |
| 122 |  | g36p1 : 187W | 187 | 9 | g43p2: 9W + g43p5: 6W + g43p6: 13W + g43p8: 13W + g43p9: 11W + g44p1: 113W + g44p2: 1W + g44p5: 14W + g44p6: 7W | |
| 123 |  | g36p5 : 22W | 22 | 3 | β½g44p2: 1W + g44p5: 14W + g44p6: 7W | |
| 124 |  | g36p8 : 21W | 21 | 3 | g41p5: 8W + g41p6: 10W + g41p7: 3W | |
| 125 |  | g36p9 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 126 |  | g37p3 : 19W:PB | 19 | 3 | g41p3: 10W:PB + g42p3: 5W:PB + g43p3: 4W:PB | |
| 127 |  | g37p5 : 33W | 33 | 3 | g40p6: 10W + g40p7: 20W + g40p8: 3W | |
| 128 |  | g37p7 : 19W | 19 | 3 | g41p6: 10W + g41p7: 3W + g41p8: 6Wβ | |
| 129 |  | g37p8 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 130 |  | g37p9 : 37W | 37 | 3 | β½g39p2: 11W + g39p5: 12W + g39p6: 14Wβ | |
| 131 |  | g38p1 : 209W | 209 | 3 | g50p9: 24W + g51p1: 165W + g51p2: 20W | |
| 132 |  | g38p8 : 28W | 28 | 3 | g43p2: 9W + g43p5: 6W + g43p6: 13W | |
| 133 |  | g38p9 : 47W | 47 | 4 | g40p6: 10W + g40p7: 20W + g40p8: 3W + g40p9: 14W | |
| 134 |  | g39p1 : 115W | 115 | 5 | g41p6: 10W + g41p7: 3W + g41p8: 6W + g41p9: 11W + βg42p1: 85W | |
| 135 |  | g39p6 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 136 |  | g39p9 : 32W | 32 | 3 | g40p2: 7W + g40p5: 15W + g40p6: 10W | |
| 137 |  | g40p1 : 156W | 156 | 5 | g43p5: 6W + g43p6: 13W + g43p8: 13W + g43p9: 11W + βg44p1: 113Wβ | |
| 138 |  | g40p3 : 36W:PB | 36 | 3 | βg55p3: 5W:PBβ + g56p3: 23W:PB + βg57p3: 8W:PBβ | |
| 139 |  | g40p7 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 140 |  | g40p9 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 141 |  | g41p1 : 89W | 89 | 3 | g47p6: 43W + g47p7: 34W + g47p8: 12W | |
| 142 |  | g42p1 : 85W | 85 | 5 | β½g51p5: 21W + g51p6: 15W + g51p7: 17W + g51p8: 20W + g51p9: 12W | |
| 143 |  | g43p1 : 107W | 107 | 6 | g50p2: 3Wβ + g50p5: 15W + g50p6: 16W + g50p7: 14W + g50p8: 35W + g50p9: 24W | |
| 144 |  | g44p1 : 113W | 113 | 3 | β½g47p2: 31W + g47p5: 39W + g47p6: 43W | |
| 145 |  | g44p5 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 146 |  | g45p1 : 65W | 65 | 3 | g50p6: 16W + g50p7: 14W + g50p8: 35W | |
| 147 |  | g47p1 : 535W | 535 | 17 | g54p6: 23Wβ + g54p7: 41W + g54p8: 34W + g54p9: 19W + g55p1: 90W + g55p2: 16W + g55p5: 18W + g55p6: 11W + g55p7: 5W + g55p8: 4W + g55p9: 27W + g56p1: 191W + g56p2: 16W + g56p5: 6W + g56p6: 8W + g56p7: 14W + g56p8: 12W | |
| 148 |  | g47p2 : 31W | 31 | 3 | βg54p2: 2Wβ + g54p5: 6W + g54p6: 23Wβ | |
| 149 |  | g47p4 : 35PB | 35 | 4 | g49p4: 8PBβ + g50p4: 14PB + g51p4: 4PB + βg52p4: 9PB | |
| 150 |  | g47p6 : 43W | 43 | 3 | g53p5: 18W + g53p7: 6W + g53p8: 19Wβ | |
| 151 |  | g47p7 : 34W | 34 | 3 | g50p2: 3Wβ + g50p5: 15W + g50p6: 16W | |
| 152 |  | g47p9 : 70W | 70 | 3 | g54p5: 6W + g54p6: 23W + g54p7: 41Wβ½ | |
| 153 |  | g48p1 : 266W | 266 | 6 | g48p7: 6W + g48p8: 13W + g48p9: 30W + g49p1: 189W + g49p2: 7W + g49p5: 21Wβ½ | |
| 154 |  | g48p9 : 30W | 30 | 3 | βg56p2: 16W + g56p5: 6W + g56p6: 8W | |
| 155 |  | g49p1 : 189W | 189 | 3 | g53p1: 158W + g53p2: 13W + g53p5: 18W | |
| 156 |  | g51p2 : 20W | 20 | 3 | β½g55p6: 11W + g55p7: 5W + g55p8: 4W | |
| 157 |  | g51p8 : 20W | 20 | 3 | β½g55p6: 11W + g55p7: 5W + g55p8: 4W | |
| 158 |  | g52p1 : 215W | 215 | 4 | βg52p7: 29W + g52p8: 15W + g52p9: 13W + g53p1: 158W | |
| 159 |  | g52p7 : 29W | 29 | 3 | β½g57p2: 11W + g57p5: 6W + g57p6: 12W | |
| 160 |  | g54p1 : 221W | 221 | 4 | β½g56p1: 191W + g56p2: 16W + g56p5: 6W + g56p6: 8W | |
| 161 |  | g54p8 : 34W | 34 | 3 | βg55p5: 18Wβ + g55p6: 11W + βg55p7: 5W |
Left Handed Sum Detail: - Click on column name to sort
| # | Color | Sum Schema | Sum Cord | Sum Cord Value | # Summands | Summands |
|---|---|---|---|---|---|---|
| 1 |  | g6p1 : 219W | 219 | 4 | g2p9: 47W + g3p1: 140W + g3p5: 8W + g3p7: 24W | |
| 2 |  | g7p1 : 229W | 229 | 5 | g2p9: 47W + g3p1: 140W + g3p5: 8W + g3p7: 24W + g3p8: 10Wβ | |
| 3 |  | g8p1 : 210W | 210 | 4 | g3p7: 24W + g3p8: 10W + g3p9: 21W + βg4p1: 155W | |
| 4 |  | g10p1 : 250W | 250 | 6 | g2p9: 47W + g3p1: 140W + g3p5: 8W + g3p7: 24W + g3p8: 10W + g3p9: 21Wβ½ | |
| 5 |  | g11p1 : 270W | 270 | 3 | g6p8: 20Wβ + g6p9: 21W + βg7p1: 229W | |
| 6 |  | g14p9 : 53W | 53 | 3 | g2p2: 14W + g2p5: 29W + g2p6: 10Wβ | |
| 7 |  | g15p1 : 250W | 250 | 6 | g2p9: 47W + g3p1: 140W + g3p5: 8W + g3p7: 24W + g3p8: 10W + g3p9: 21Wβ½ | |
| 8 |  | g17p1 : 1000W | 1000 | 22 | g12p7: 35Wβ + g12p8: 21W + g12p9: 20W + g13p1: 200W + g13p2: 10W + g13p5: 21W + g13p6: 17W + g13p7: 25W + g13p8: 27W + g13p9: 30W + g14p1: 155W + g14p2: 2W + g14p5: 11W + g14p7: 14W + g14p8: 19W + g14p9: 53W + g15p1: 250W + g15p2: 20W + g15p5: 30W + g15p6: 8W + g15p7: 20W + g15p8: 12W | |
| 9 |  | g17p5 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 10 |  | g18p1 : 80W | 80 | 5 | g2p2: 14W + g2p5: 29W + g2p6: 10W + g2p7: 11W + βg2p8: 16W | |
| 11 |  | g19p1 : 100W | 100 | 4 | g5p6: 25W + g5p7: 14W + g5p8: 17W + g5p9: 44W | |
| 12 |  | g21p1 : 260W | 260 | 3 | β½g7p8: 31W + g7p9: 19W + g8p1: 210W | |
| 13 |  | g21p4 : 14PB | 14 | 4 | β½g12p4: 1PB + g13p4: 4PB + g14p4: 2PB + g15p4: 7PB | |
| 14 |  | g21p9 : 91W | 91 | 5 | g19p7: 16W + g19p8: 24W + g19p9: 26W + g20p7: 9W + g20p8: 16W | |
| 15 |  | g22p1 : 272W | 272 | 4 | g1p7: 10W + g1p8: 30W + g2p1: 218W + g2p2: 14W | |
| 16 |  | g22p4 : 15PB | 15 | 3 | g9p4: 4PB + g11p4: 10PB + g12p4: 1PBβ½ | |
| 17 |  | g24p1 : 171W | 171 | 6 | β½g22p8: 11W + g22p9: 30W + g23p1: 102W + g23p5: 6W + g23p8: 5W + g23p9: 17Wβ | |
| 18 |  | g25p1 : 117W | 117 | 3 | g1p5: 77W + g1p7: 10W + g1p8: 30W | |
| 19 |  | g26p1 : 208W | 208 | 3 | g8p9: 7W + g9p1: 190W + g9p2: 11Wβ½ | |
| 20 |  | g27p1 : 178W | 178 | 6 | g25p1: 117W + g25p2: 10W + g25p5: 10W + g25p6: 8W + g25p7: 16W + g25p8: 17W | |
| 21 |  | g28p1 : 178W | 178 | 6 | g25p1: 117W + g25p2: 10W + g25p5: 10W + g25p6: 8W + g25p7: 16W + g25p8: 17W | |
| 22 |  | g28p6 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 23 |  | g28p8 : 44W | 44 | 3 | β½g14p5: 11W + g14p7: 14W + g14p8: 19W | |
| 24 |  | g29p9 : 34W | 34 | 3 | g25p5: 10W + g25p6: 8W + g25p7: 16W | |
| 25 |  | g30p9 : 42W | 42 | 3 | g3p5: 8W + g3p7: 24W + g3p8: 10Wβ | |
| 26 |  | g31p9 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 27 |  | g32p1 : 137W | 137 | 3 | g25p1: 117W + g25p2: 10W + g25p5: 10W | |
| 28 |  | g32p2 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 29 |  | g32p8 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 30 |  | g32p9 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 31 |  | g33p8 : 26W | 26 | 3 | g30p2: 6W + g30p5: 14W + g30p6: 6W | |
| 32 |  | g33p9 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 33 |  | g34p1 : 149W | 149 | 4 | β½g22p8: 11W + g22p9: 30W + g23p1: 102W + g23p5: 6W | |
| 34 |  | g34p7 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 35 |  | g35p1 : 235W | 235 | 3 | g5p1: 200W + g5p2: 10W + g5p6: 25W | |
| 36 |  | g35p7 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 37 |  | g35p9 : 28W | 28 | 3 | g23p5: 6W + g23p8: 5W + g23p9: 17Wβ | |
| 38 |  | g36p1 : 187W | 187 | 3 | β½g3p9: 21W + g4p1: 155W + g4p5: 11Wβ½ | |
| 39 |  | g36p6 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 40 |  | g36p8 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 41 |  | g37p9 : 37W | 37 | 3 | g2p6: 10Wβ + g2p7: 11W + βg2p8: 16W | |
| 42 |  | g38p1 : 209W | 209 | 5 | g30p9: 42Wβ + g31p1: 131W + g31p2: 14W + g31p5: 12W + βg31p6: 10W | |
| 43 |  | g38p8 : 28W | 28 | 3 | g23p5: 6W + g23p8: 5W + g23p9: 17Wβ | |
| 44 |  | g38p9 : 47W | 47 | 4 | βg32p6: 15W + g32p7: 6W + g32p8: 13W + g32p9: 13Wβ | |
| 45 |  | g39p1 : 115W | 115 | 5 | g37p5: 33W + g37p6: 6W + g37p7: 19W + g37p8: 20W + g37p9: 37W | |
| 46 |  | g39p9 : 32W | 32 | 3 | β½g32p5: 11W + g32p6: 15W + g32p7: 6W | |
| 47 |  | g40p3 : 36W:PB | 36 | 3 | β½g24p3: 21W:PB + g25p3: 12W:PB + g26p3: 3W:PBβ | |
| 48 |  | g41p1 : 89W | 89 | 5 | g34p2: 22W + g34p5: 23W + g34p6: 22W + g34p7: 13W + g34p8: 9W | |
| 49 |  | g41p2 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 50 |  | g42p1 : 85W | 85 | 3 | g38p7: 10W + g38p8: 28W + g38p9: 47W | |
| 51 |  | g42p5 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 52 |  | g42p9 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 53 |  | g43p1 : 107W | 107 | 3 | g17p5: 13W + g17p9: 14W + g18p1: 80W | |
| 54 |  | g43p6 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 55 |  | g43p8 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 56 |  | g44p1 : 113W | 113 | 3 | g23p1: 102W + g23p5: 6W + g23p8: 5W | |
| 57 |  | g45p1 : 65W | 65 | 3 | g8p2: 59W + g8p5: 1W + g8p8: 5W | |
| 58 |  | g46p1 : 179W | 179 | 4 | β½g36p8: 21W + g36p9: 20W + g37p1: 131W + βg37p2: 7W | |
| 59 |  | g46p3 : 22W:PB | 22 | 3 | g29p3: 8W:PB + g30p3: 9W:PB + g31p3: 5W:PB | |
| 60 |  | g46p5 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 61 |  | g46p10 : 22W | 22 | 3 | β½g44p2: 1W + g44p5: 14W + g44p6: 7W | |
| 62 |  | g47p1 : 535W | 535 | 12 | βg34p1: 149W + g34p2: 22W + g34p5: 23W + g34p6: 22W + g34p7: 13W + g34p8: 9W + g34p9: 9W + g35p1: 235W + g35p2: 23W + g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 63 |  | g47p2 : 31W | 31 | 3 | g22p5: 2W + g22p7: 18W + g22p8: 11Wβ½ | |
| 64 |  | g47p3 : 20W:PB | 20 | 3 | g28p3: 3W:PB + g29p3: 8W:PB + g30p3: 9W:PB | |
| 65 |  | g47p4 : 35PB | 35 | 4 | g20p4: 4PB + g21p4: 14PB + g22p4: 15PB + g23p4: 2PB | |
| 66 |  | g47p5 : 39W | 39 | 3 | g16p5: 19W + g16p6: 6W + g16p7: 14W | |
| 67 |  | g47p6 : 43W | 43 | 3 | g38p6: 5W + g38p7: 10W + g38p8: 28W | |
| 68 |  | g47p7 : 34W | 34 | 3 | g25p5: 10W + g25p6: 8W + g25p7: 16W | |
| 69 |  | g47p9 : 70W | 70 | 3 | βg29p7: 20W + g29p8: 16W + g29p9: 34W | |
| 70 |  | g48p1 : 266W | 266 | 3 | g37p8: 20W + g37p9: 37W + g38p1: 209W | |
| 71 |  | g48p5 : 74W | 74 | 3 | β½g2p7: 11W + g2p8: 16W + g2p9: 47W | |
| 72 |  | g48p8 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 73 |  | g48p9 : 30W | 30 | 3 | g35p5: 6W + g35p6: 6W + g35p7: 18Wβ | |
| 74 |  | g49p1 : 189W | 189 | 3 | g28p1: 178W + g28p2: 4W + g28p5: 7W | |
| 75 |  | g49p5 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 76 |  | g49p6 : 33W | 33 | 3 | g40p6: 10W + g40p7: 20W + g40p8: 3W | |
| 77 |  | g49p7 : 33W | 33 | 3 | g40p6: 10W + g40p7: 20W + g40p8: 3W | |
| 78 |  | g49p9 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 79 |  | g50p1 : 116W | 116 | 3 | g40p9: 14W + g41p1: 89W + g41p2: 13W | |
| 80 |  | g50p4 : 14PB | 14 | 3 | g31p4: 3PBβ + g32p4: 5PB + g33p4: 6PB | |
| 81 |  | g50p7 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 82 |  | g50p8 : 35W | 35 | 3 | g16p2: 10W + g16p5: 19W + g16p6: 6W | |
| 83 |  | g50p9 : 24W | 24 | 3 | g28p2: 4W + g28p5: 7W + g28p6: 13W | |
| 84 |  | g51p1 : 165W | 165 | 4 | g31p8: 2W + g31p9: 13W + g32p1: 137W + g32p2: 13W | |
| 85 |  | g51p2 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 86 |  | g51p5 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 87 |  | g51p8 : 20W | 20 | 3 | g41p7: 3W + g41p8: 6W + g41p9: 11Wβ½ | |
| 88 |  | g52p1 : 215W | 215 | 4 | g28p9: 18W + g29p1: 166W + g29p2: 17W + g29p5: 14Wβ | |
| 89 |  | g52p2 : 51W | 51 | 3 | g19p9: 26W + g20p7: 9W + g20p8: 16W | |
| 90 |  | g52p6 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 91 |  | g52p7 : 29W | 29 | 3 | βg26p5: 8W + g26p6: 12W + g26p7: 9W | |
| 92 |  | g52p9 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 93 |  | g53p1 : 158W | 158 | 3 | βg36p9: 20Wβ + g37p1: 131W + βg37p2: 7W | |
| 94 |  | g53p2 : 13W | 13 | 3 | β½g8p5: 1W + g8p8: 5W + g8p9: 7W | |
| 95 |  | g53p4 : 13PB | 13 | 3 | g13p4: 4PBβ + g14p4: 2PB + g15p4: 7PB | |
| 96 |  | g53p5 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 97 |  | g53p8 : 19W | 19 | 3 | g41p6: 10W + g41p7: 3W + g41p8: 6Wβ | |
| 98 |  | g53p9 : 21W | 21 | 3 | g31p7: 6W + g31p8: 2W + g31p9: 13W | |
| 99 |  | g54p1 : 221W | 221 | 4 | g51p1: 165W + g51p2: 20W + g51p5: 21W + βg51p6: 15W | |
| 100 |  | g54p6 : 23W | 23 | 3 | g44p7: 5W + g44p8: 6W + g44p9: 12W | |
| 101 |  | g54p7 : 41W | 41 | 3 | β½g22p2: 21W + g22p5: 2W + g22p7: 18Wβ | |
| 102 |  | g54p8 : 34W | 34 | 3 | g25p5: 10W + g25p6: 8W + g25p7: 16W | |
| 103 |  | g54p9 : 19W | 19 | 3 | g41p6: 10W + g41p7: 3W + g41p8: 6Wβ | |
| 104 |  | g55p1 : 90W | 90 | 3 | g48p5: 74W + g48p6: 10W + g48p7: 6W | |
| 105 |  | g55p5 : 18W | 18 | 3 | βg31p6: 10W + g31p7: 6W + g31p8: 2W | |
| 106 |  | g55p9 : 27W | 27 | 3 | βg14p2: 2W + g14p5: 11W + g14p7: 14W | |
| 107 |  | g56p1 : 191W | 191 | 4 | βg36p9: 20Wβ + g37p1: 131W + g37p2: 7W + g37p5: 33W | |
| 108 |  | g56p4 : 29PB | 29 | 5 | g7p4: 6PBβ + g8p4: 8PB + g9p4: 4PB + g11p4: 10PB + g12p4: 1PBβ½ | |
| 109 |  | g56p7 : 14W | 14 | 3 | g45p2: 4W + g45p5: 5W + g45p6: 5W | |
| 110 |  | g56p9 : 27W | 27 | 3 | βg14p2: 2W + g14p5: 11W + g14p7: 14W | |
| 111 |  | g57p1 : 329W | 329 | 6 | g5p2: 10W + g5p6: 25W + g5p7: 14W + g5p8: 17W + g5p9: 44W + g6p1: 219W | |
| 112 |  | g57p4 : 11PB | 11 | 4 | g23p4: 2PB + g24p4: 3PB + g25p4: 5PB + g26p4: 1PBβ½ | |
| 113 |  | g57p7 : 38W | 38 | 3 | β½g4p5: 11W + g4p8: 17W + g4p9: 10W | |
| 114 |  | g57p9 : 34W | 34 | 3 | g25p5: 10W + g25p6: 8W + g25p7: 16W |
Khipu Notes:
Fieldguide Notes:
Author's Notes
This khipu was part of the Maiman collection, a set of khipus gathered from deaccesioning of the Haifa museum as well as other sources. Another khipu in the collection is referenced in Bat-ami Artzi's article The Secret of the Knot: Khipu No. 936 from the Maiman Collection. The collection is also described in the book Weaving for the Afterlife - Peruvian Textiles from the Maiman Collection Volume 1 - Pages 335-336, by Krzysztof Makowski, Alfredo Rosenzweig, Maria Jesus JimΓ©nez Diaz.
The khipu is mounted on canvas. Backwards! It is in good condition, and the regularity and tightness of the knots indicate a master khipu-kamayoq. It consists almost entirely of 9 pendant cord seriated groups in a W, W, W:PB, PB, W, W, W, W, W order. Numerous sums are evident, as are knot-twists in both S and Z directions.
Primary Cord Notes
The primary cord has numerous blue (or white) wrappings around the cord between cord groups. There are blue (or white) wrappings at:
Image has been assembled from a series of smaller images. Some alignment errors may occur.
The khipu is described in the book Weaving the Afterlife:
Cat. 281
Big khipu (khipu) of "canutos"
Period: Late Horizon; (1450-1550 CE)
Style: Inca, Inca Imperial Period or Huari-Tiahuanaco
Location: Highlands
Dimensions: 115 x 165 cm.
Inv. 925|
Yarns:
Main Cord: Camelid fiber Z25, blue-greenish, red, brown, yellow; Cotton S2Z and Z25 white (wrapping elements)
Cords: Camelid fiber Z3S black-brownish; Camelid fiber Z25, white, dark purple, yellow, white, red, rose, green; Camelid fiber Z orange; Cotton Z blue (wrapping elements) The main cord is of cross-knit loop stitch on a foundation.
khipu is a device for the registry of information in numerical form. It consists of a primary horizontal cord to which a variable number of vertical cords are attached, and the numbers were introduced by knots. A single knot is up to nine loops to give the value: nine. The absence of knots in the denoted position indicates zero. The units were at the farther or lower end of the string, the higher multiples of tens, hundreds or thousands were placed on the upper part.
CaΓ±uto - translates literally as a part of a cane from knot to knot (definition from the Diccionario de la Real Academia de la Lengua EspaΓ±ola). A short tube, not very long nor thick. The canuto on the khipu is a tube formed by wrapping together several cords with colorful yarns, at the beginning of the cords, near the main cord. In this khipu, there are thirty-five canutos or groupings: twenty-seven groupings of four strings, six of three strings and two of two strings. The total number of cords is 130. The maximum length of the knotted strings is 120 cm. and the shortest is 52 cm. The part of the main cord with attached knotted strings is only 25 cm. long. This main cord has extensions on both sides but only up to 40 cm. are preserved. There are three main levels of composite knots, but up to four levels. The coding in three colors of the canuto is repeated in two-three adjoining canutos. In addition, there is coding in two colors at the lower end of each individual string, differing from the canuto. The seriation is four with some exceptions.
This khipu was one of a group of three, found together. There are similar khipus in the Poli Collection and "Banco Central de la Reserva" (two colors).
Arellano (1999) describes this type of khipus "with canutos". See also Radicati di Primegio (1990). Bonavia (1993) classifies a similar khipu as "Huari? 500/600-900 CE". However, we are convinced that Cat. 281 is typical Inca (1450-1530 CE). The much older Huari khipus (600-900 CE) are different in construction or in many other aspects (Conklin, 1990).
With reference to the color wrapping of the cords, Conklin (1990) states that this technique began in Chavin times. The 'wrapping of warps' system was continued in the Middle Horizon: "the study of the Khipus de Canuto show clear evidence that the khipus must have had a long period of development and were not an Inca invention". He notes further, "it is possible that the mathematics of the Inca system developed from the art and ritual of previous times. The decimal system propitiated the use of a plurality of bases. Perhaps the information on the Middle Horizon Khipus had a bigger relation to the rituals than with astronomy."
Recently, Shady (see Mann, 2005) found rudimentary devices resembling khipus (pendant strings twisted around small sticks) at the ancient ceremonial center of Caral (2500-1600 BCE). If this is confirmed, it would be among the oldest textile manifestations in Peru and one of the earliest recording systems in the world. For a list of references on khipus, see our Note # 382.
Author's Notes
This khipu was part of the Maiman collection, a set of khipus gathered from deaccesioning of the Haifa museum as well as other sources. Another khipu in the collection is referenced in Bat-ami Artzi's article The Secret of the Knot: Khipu No. 936 from the Maiman Collection. The collection is also described in the book Weaving for the Afterlife - Peruvian Textiles from the Maiman Collection Volume 1 - Pages 335-336, by Krzysztof Makowski, Alfredo Rosenzweig, Maria Jesus JimΓ©nez Diaz.
The khipu is mounted on canvas. Backwards! It is in good condition, and the regularity and tightness of the knots indicate a master khipu-kamayoq. It consists almost entirely of 9 pendant cord seriated groups in a W, W, W:PB, PB, W, W, W, W, W order. Numerous sums are evident, as are knot-twists in both S and Z directions.
Primary Cord Notes
The primary cord has numerous blue (or white) wrappings around the cord between cord groups. There are blue (or white) wrappings at:
- wrapping from 42.5 - 45
- wrapping from 67.5 - 68.9
- wrapping (white) from 85.9-86.9
- wrapping from 102.5-103.3
- wrapping from 127.0 - 128.5
- 96.1 cm - Repair
- 116.0 cm - break/mend in primary cord
Image has been assembled from a series of smaller images. Some alignment errors may occur.
The khipu is described in the book Weaving the Afterlife:
Cat. 281
Big khipu (khipu) of "canutos"
Period: Late Horizon; (1450-1550 CE)
Style: Inca, Inca Imperial Period or Huari-Tiahuanaco
Location: Highlands
Dimensions: 115 x 165 cm.
Inv. 925|
Yarns:
Main Cord: Camelid fiber Z25, blue-greenish, red, brown, yellow; Cotton S2Z and Z25 white (wrapping elements)
Cords: Camelid fiber Z3S black-brownish; Camelid fiber Z25, white, dark purple, yellow, white, red, rose, green; Camelid fiber Z orange; Cotton Z blue (wrapping elements) The main cord is of cross-knit loop stitch on a foundation.
khipu is a device for the registry of information in numerical form. It consists of a primary horizontal cord to which a variable number of vertical cords are attached, and the numbers were introduced by knots. A single knot is up to nine loops to give the value: nine. The absence of knots in the denoted position indicates zero. The units were at the farther or lower end of the string, the higher multiples of tens, hundreds or thousands were placed on the upper part.
CaΓ±uto - translates literally as a part of a cane from knot to knot (definition from the Diccionario de la Real Academia de la Lengua EspaΓ±ola). A short tube, not very long nor thick. The canuto on the khipu is a tube formed by wrapping together several cords with colorful yarns, at the beginning of the cords, near the main cord. In this khipu, there are thirty-five canutos or groupings: twenty-seven groupings of four strings, six of three strings and two of two strings. The total number of cords is 130. The maximum length of the knotted strings is 120 cm. and the shortest is 52 cm. The part of the main cord with attached knotted strings is only 25 cm. long. This main cord has extensions on both sides but only up to 40 cm. are preserved. There are three main levels of composite knots, but up to four levels. The coding in three colors of the canuto is repeated in two-three adjoining canutos. In addition, there is coding in two colors at the lower end of each individual string, differing from the canuto. The seriation is four with some exceptions.
This khipu was one of a group of three, found together. There are similar khipus in the Poli Collection and "Banco Central de la Reserva" (two colors).
Arellano (1999) describes this type of khipus "with canutos". See also Radicati di Primegio (1990). Bonavia (1993) classifies a similar khipu as "Huari? 500/600-900 CE". However, we are convinced that Cat. 281 is typical Inca (1450-1530 CE). The much older Huari khipus (600-900 CE) are different in construction or in many other aspects (Conklin, 1990).
With reference to the color wrapping of the cords, Conklin (1990) states that this technique began in Chavin times. The 'wrapping of warps' system was continued in the Middle Horizon: "the study of the Khipus de Canuto show clear evidence that the khipus must have had a long period of development and were not an Inca invention". He notes further, "it is possible that the mathematics of the Inca system developed from the art and ritual of previous times. The decimal system propitiated the use of a plurality of bases. Perhaps the information on the Middle Horizon Khipus had a bigger relation to the rituals than with astronomy."
Recently, Shady (see Mann, 2005) found rudimentary devices resembling khipus (pendant strings twisted around small sticks) at the ancient ceremonial center of Caral (2500-1600 BCE). If this is confirmed, it would be among the oldest textile manifestations in Peru and one of the earliest recording systems in the world. For a list of references on khipus, see our Note # 382.