KH0079/AS066 - Colored Pendant Sums


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

Right Handed Sums:     # Sums = 42,  Max # Summands = 10,   (Min, Mean, Max) Sum Values = (12, 44, 300)
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Left Handed Sums:     # Sums = 34,  Max # Summands = 10,   (Min, Mean, Max) Sum Values = (12, 46, 300)
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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
g3p1 : 160W1608g9p1: 16W + g9p2: 15W + g9p3: 24W + g10p1: 9W + g10p2: 72W + g10p3: 9W + g10p4: 9W + g12p1: 6W
2
g3p2 : 101W1017g40p3: 13W + g40p4: 13W + g41p1: 7W + g41p2: 6W + g41p3: 6W + g41p4: 6W + g42p1: 50W
3
g7p1 : 24W243g10p3: 9W + g10p4: 9W + g12p1: 6W
4
g7p2 : 21W214g58p7: 7W + g58p8: 6W + g60p1: 4W + g60p2: 4W
5
g9p1 : 16W164g60p1: 4W + g60p2: 4W + g60p3: 4W + g60p4: 4W
6
g9p3 : 24W243g10p3: 9W + g10p4: 9W + g12p1: 6W
7
g10p2 : 72W729g53p2: 13W + g53p3: 14W + g53p4: 12W + g58p5: 6W + g58p6: 6W + g58p7: 7W + g58p8: 6W + g60p1: 4W + g60p2: 4W
8
g13p1 : 16W164g60p1: 4W + g60p2: 4W + g60p3: 4W + g60p4: 4W
9
g20p1 : 40MB403g43p3: 6MB + g43p4: 6MB + g44p1: 28MB
10
g20p2 : 40MB403g43p3: 6MB + g43p4: 6MB + g44p1: 28MB
11
g20p3 : 40MB403g43p3: 6MB + g43p4: 6MB + g44p1: 28MB
12
g20p4 : 30MB303g25p4: 17MB + g28p1: 6MB + g28p2: 7MB
13
g21p1 : 300W30010g42p1: 50W + g49p1: 31W + g49p2: 31W + g49p3: 32W + g49p4: 18W + g49p5: 31W + g49p6: 31W + g49p7: 32W + g49p8: 31W + g53p1: 13W
14
g22p1 : 40MB403g43p3: 6MB + g43p4: 6MB + g44p1: 28MB
15
g22p2 : 40MB403g43p3: 6MB + g43p4: 6MB + g44p1: 28MB
16
g27p1 : 50W504g35p1: 13W + g35p2: 13W + g35p3: 13W + g35p4: 11W
17
g32p1 : 15MB153g54p1: 5MB + g54p2: 5MB + g54p3: 5MB
18
g32p2 : 15MB153g54p1: 5MB + g54p2: 5MB + g54p3: 5MB
19
g32p3 : 15MB153g54p1: 5MB + g54p2: 5MB + g54p3: 5MB
20
g33p1 : 102W1028g37p1: 13W + g37p2: 12W + g37p3: 13W + g37p4: 12W + g38p1: 13W + g38p2: 13W + g38p3: 13W + g38p4: 13W
21
g34p3 : 12MB123g47p2: 4MB + g47p3: 4MB + g47p4: 4MB
22
g37p2 : 12W123g60p1: 4W + g60p2: 4W + g60p3: 4W
23
g37p4 : 12W123g60p1: 4W + g60p2: 4W + g60p3: 4W
24
g44p1 : 28MB287g47p2: 4MB + g47p3: 4MB + g47p4: 4MB + g47p5: 4MB + g47p6: 4MB + g47p7: 4MB + g47p8: 4MB
25
g44p2 : 28MB287g47p2: 4MB + g47p3: 4MB + g47p4: 4MB + g47p5: 4MB + g47p6: 4MB + g47p7: 4MB + g47p8: 4MB
26
g44p4 : 15MB153g54p1: 5MB + g54p2: 5MB + g54p3: 5MB
27
g45p1 : 200MB2008g56p1: 25MB + g56p2: 25MB + g56p3: 31MB + g56p4: 19MB + g56p5: 25MB + g56p6: 25MB + g56p7: 25MB + g56p8: 25MB
28
g46p1 : 25MB255g54p1: 5MB + g54p2: 5MB + g54p3: 5MB + g54p4: 5MB + g54p5: 5MB
29
g46p2 : 25MB255g54p1: 5MB + g54p2: 5MB + g54p3: 5MB + g54p4: 5MB + g54p5: 5MB
30
g46p3 : 25MB255g54p1: 5MB + g54p2: 5MB + g54p3: 5MB + g54p4: 5MB + g54p5: 5MB
31
g46p4 : 25MB255g54p1: 5MB + g54p2: 5MB + g54p3: 5MB + g54p4: 5MB + g54p5: 5MB
32
g48p1 : 32MB325g51p4: 12MB + g54p1: 5MB + g54p2: 5MB + g54p3: 5MB + g54p4: 5MB
33
g49p1 : 31W314g53p4: 12W + g58p5: 6W + g58p6: 6W + g58p7: 7W
34
g49p2 : 31W314g53p4: 12W + g58p5: 6W + g58p6: 6W + g58p7: 7W
35
g49p3 : 32W323g53p3: 14W + g53p4: 12W + g58p5: 6W
36
g49p4 : 18W184g58p8: 6W + g60p1: 4W + g60p2: 4W + g60p3: 4W
37
g49p5 : 31W314g53p4: 12W + g58p5: 6W + g58p6: 6W + g58p7: 7W
38
g49p6 : 31W314g53p4: 12W + g58p5: 6W + g58p6: 6W + g58p7: 7W
39
g49p7 : 32W323g53p3: 14W + g53p4: 12W + g58p5: 6W
40
g49p8 : 31W314g53p4: 12W + g58p5: 6W + g58p6: 6W + g58p7: 7W
41
g53p3 : 14W143g58p8: 6W + g60p1: 4W + g60p2: 4W
42
g53p4 : 12W123g60p1: 4W + g60p2: 4W + g60p3: 4W

Left Handed Sum Detail: - Click on column name to sort
# Color Sum Schema Sum Cord Sum Cord Value # Summands Summands
1
g21p1 : 300W30010g3p2: 101W + g7p1: 24W + g7p2: 21W + g9p1: 16W + g9p2: 15W + g9p3: 24W + g10p1: 9W + g10p2: 72W + g10p3: 9W + g10p4: 9W
2
g25p1 : 13MB133g16p1: 8MB + g19p1: 3MB + g19p2: 2MB
3
g32p1 : 15MB154g16p1: 8MB + g19p1: 3MB + g19p2: 2MB + g19p3: 2MB
4
g32p2 : 15MB154g16p1: 8MB + g19p1: 3MB + g19p2: 2MB + g19p3: 2MB
5
g32p3 : 15MB154g16p1: 8MB + g19p1: 3MB + g19p2: 2MB + g19p3: 2MB
6
g34p1 : 13MB133g16p1: 8MB + g19p1: 3MB + g19p2: 2MB
7
g34p2 : 13MB133g16p1: 8MB + g19p1: 3MB + g19p2: 2MB
8
g34p4 : 13MB133g16p1: 8MB + g19p1: 3MB + g19p2: 2MB
9
g39p1 : 104W1045g10p2: 72W + g10p3: 9W + g10p4: 9W + g12p1: 6W + g12p2: 8W
10
g42p1 : 50W504g35p1: 13W + g35p2: 13W + g35p3: 13W + g35p4: 11W
11
g44p1 : 28MB283g31p3: 7MB + g31p4: 6MB + g32p1: 15MB
12
g44p2 : 28MB283g31p3: 7MB + g31p4: 6MB + g32p1: 15MB
13
g44p4 : 15MB154g16p1: 8MB + g19p1: 3MB + g19p2: 2MB + g19p3: 2MB
14
g46p1 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
15
g46p2 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
16
g46p3 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
17
g46p4 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
18
g48p1 : 32MB323g32p4: 6MB + g34p1: 13MB + g34p2: 13MB
19
g49p3 : 32W324g10p3: 9W + g10p4: 9W + g12p1: 6W + g12p2: 8W
20
g49p4 : 18W183g41p2: 6W + g41p3: 6W + g41p4: 6W
21
g49p7 : 32W324g10p3: 9W + g10p4: 9W + g12p1: 6W + g12p2: 8W
22
g50p1 : 237MB2379g19p1: 3MB + g19p2: 2MB + g19p3: 2MB + g20p1: 40MB + g20p2: 40MB + g20p3: 40MB + g20p4: 30MB + g22p1: 40MB + g22p2: 40MB
23
g51p4 : 12MB123g47p2: 4MB + g47p3: 4MB + g47p4: 4MB
24
g55p1 : 40MB403g43p3: 6MB + g43p4: 6MB + g44p1: 28MB
25
g56p1 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
26
g56p2 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
27
g56p3 : 31MB313g25p3: 8MB + g25p4: 17MB + g28p1: 6MB
28
g56p4 : 19MB193g28p1: 6MB + g28p2: 7MB + g28p3: 6MB
29
g56p5 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
30
g56p6 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
31
g56p7 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
32
g56p8 : 25MB254g28p1: 6MB + g28p2: 7MB + g28p3: 6MB + g28p4: 6MB
33
g57p1 : 200KB2004g14p1: 10KB + g15p1: 30KB + g17p1: 50KB + g24p1: 110KB
34
g61p1 : 32W323g53p3: 14W + g53p4: 12W + g58p5: 6W

Khipu Notes:
Ascher Databook Notes:
  1. This khipu is associated with KH0070-KH0080. See discussion under KH0070.
  2. From the discoloration of the main cord, and by extrapolation based on the spacing of the complete groups, we hypothesize that this khipu contained 24 groups of 8 pendants.
    Each of the groups had a top cord. Of the original 80 pendants of the first 10 groups, only 35 remain and so the first complete group starts with pendant 36. Of the last 14 groups, no pendants are missing.
  3. Two loose broken cords were associated with this khipu: one, colored DB, had a value of 50; the other, colored AB, had a value of 14.
  4. Both common forms of top cord attachment are present on this khipu. In groups 18, 19, and 21-24, the top cord unites the pendants. In the remaining groups, the top cord is attached to the main cord in the center of the group.
    The first pendant of the 18th group (P92) is a different color than the rest of the group reinforcing the idea that this is a place where a change occurs.
  5. All pendant cords within a group are the same color with the exception of group 18 noted above and groups 16, 20, and 23 in which the first 4 pendants are one color and the last 4 another color.
    In 2 of these groups the top cord is the same color as the first 4 pendants in the group. The third group has the top cord missing so its color is unknown.
  6. Only 6 groups have the top cord the same color as all the pendants in the group. Five of these groups are the only groups for which all pendants in the group have the same value.
  7. The color of the top cords for groups 8-11 (BB, W, DB, W) are repeated for the next 4 groups (12-15).
  8. With the exception of group 19, all groups that have all pendant values and top cord value present show the following relationship:
    \[ \sum\limits_{j=1}^4 P_{ij} = \sum\limits_{j=5}^8 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=13,15,16,17,18,21,22,23,24) \]
    Where one of the three parts of the relationship is unknown due to breakage, the other two still appear:
    \[ \sum\limits_{j=1}^4 P_{ij} = \sum\limits_{j=5}^8 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=12,14,17) \]
    \[ \sum\limits_{j=1}^4 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=9) \]
    \[ \sum\limits_{j=5}^8 P_{ij} = \frac{top\_value}{2}\;\;\;for\;(i=2,10,11) \]

    (Note: Pij is the value of the jth pendant in the ith group.)

  9. As noted in observation 6, five groups have all equal pendant values. The sum value on the top cord must, therefore, be a multiple of 8.
    In some cases where the top value is not a multiple of 8, the pendant values can be viewed as top value/ 8 rounded to the nearest integers.
    This is seen in groups 11,12,16,23 where the sums are 50. The pendant values are 6x6 + 2x7.
    Similarly in group 9, the pendant values can be viewed as rounded to the nearest multiple of 10. That is 150 = 3x40 + 1x30.
  10. Groups 17 and 19 both have the same relationship among the first 4 pendants:
    \[ P_{1} = P_{2} = \frac{x}{4} + 3 \]
    \[ P_{3} = \frac{x}{4} + 4 \]
    \[ P_{4} = \frac{x}{4} - 10 \]
    And as a result:
    \[ P_{1}+P_{2} = \frac{x}{2} + 6,\;\;\;\;\;\;\;P_{3}+P_{4} = \frac{x}{2} - 6\]
    For group 17, where X=100 and for group 19, where X=112.

    Since group 19 is the only group for which P1 + P2 + P3 + P4 ≠ P5 + P6 + P7 + P8, it is interesting to note that also:

    \[ P_{1}+P_{2}+P_{3}+P_{4} = \frac{top\_value}{2}-6\;\;\;where\;\frac{top\_value}{2}\;is\;rounded\;DOWN \]
    \[ P_{5}+P_{6}+P_{7}+P_{8} = \frac{top\_value}{2}+6\;\;\;where\;\frac{top\_value}{2}\;is\;rounded\;UP \]