UR1163/KH0180 - Pendant Pendant Sums


Drawings:
Overview Detail View
All Khipus' Ascher Sum FieldmarksRight-Handed XRay
All Pendant Pendant Sum RelationshipsLeft-Handed XRay
This Khipu's Fieldmark CatalogRight-Handed Sum Detail
This Khipu's DrawingLeft-Handed Sum Detail

Right Handed Sums:     # Sums = 1,  Max # Summands = 12,   (Min, Mean, Max) Sum Values = (105, 105, 105)
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Left Handed Sums:     # Sums = 2,  Max # Summands = 5,   (Min, Mean, Max) Sum Values = (13, 14, 15)
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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
p11, 1 : 105B10512p3: 18B + p4: 21BB + p5: 18B + p6: 12BB + p7: 9B + p8: 9BB + p9: 5B + p10: 4BB + p11: 3BB + p12: 2BB + p13: 2B + p14: 2BB

Left Handed Sum Detail: - Click on column name to sort
# Color Sum Schema Sum Cord Sum Cord Value # Summands Summands
1
p154, 1 : 13B135p10: 4BB + p11: 3BB + p12: 2BB + p13: 2B + p14: 2BB
2
p164, 2 : 15B152p14: 2BB + p15: 13B

Khipu Notes:
Ascher Databook Notes:
  1. Construction note: The twisted end of cord 1 is linked through the twisted end of the main cord so that it dangles from the end of the main cord. (See diagram for UR1100.)
  2. This is one of several khipus acquired by the Museum in 1907 with provenance Pachacamac. For others included in this group, see UR1097.
  3. By spacing there are 2 single pendants and then 2 groups of 12 pendants each.
  4. The value of pendant 1 is the sum of the values in Group 1.
  5. With one exception, the colors of the pendants in Group 1 alternate (B, BB, B, BB, etc.) while in Group 2, all pendants are B.
    The sums of the B colored pendants in Group 1, the BB pendants in Group 1, and the B pendants in Group 2 are 52, 53, 54 respectively.
  6. The following regularities are found in Group 1:

    1. Pi = Pi+1        i=(5,10,11)

      Pi = Pi+2        i=(1,10)

    2. Pi = Pi+2 + Pi+3        i=(2,3,5,7,8)  but not i=(1,4,6 9)

    3. Pi * P13-i = 36        i=(1,3,4,5)  but not i=(2,6)

      Of these, the following also hold:
      \[ \frac{P_{i}}{P_{i+1}}=\frac{P_{12-i}}{P_{13-i}}\;\;\;for\;i=(3,4) \]
  7. The following regularities are found in Group 2:

    1. Pi = Pi+1        i=(3,7,9)

      Pi = Pi+2        i=(10)

    2. Pi = Pi+2 + Pi-1        i=(3,7)

    3. Pi * P13-i = 0        i=(1,3,4,5)  but not i=(2,6)
    4. \[ P_{1} = \sum\limits_{i=2}^{6}P_{2i-1}=\sum\limits_{i=2}^{6}P_{2i} \]

  8. Comparing the regularities within each group, the following similarities are found between the groups:

    1. There are 3 consecutive equal pairs and P10= P12
    2. Pi = Pi+2 + Pi+c    i=(3,7)            for Group 1, c=3 while for Group 2, c=1
    3. Pi * P13-i = K        i=(1,3,4,5)      for Group 1, K=36 while for Group 2, K=0.

  9. In every position, the values in Group 1 are greater than or equal to the values in Group 2. For both groups:

    P1 > P2 > P3 ≥ P4 > P5
    P7 ≥ P8 > P9 ≥ P10