UR1175/KH0192 - Subsidiary Pendant Sums


Drawings:
Overview Detail View
All Khipus' Ascher Sum FieldmarksRight-Handed XRay
All Subsidiary Pendant Sum RelationshipsLeft-Handed XRay
This Khipu's Fieldmark CatalogSum Overlay
This Khipu's DrawingRight-Handed Sum Detail
Left-Handed Sum Detail

Right Handed Sums:     # Sums = 26,  Max # Summands = 8,   (Min, Mean, Max) Sum Values = (22, 48, 160)
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Note! Duplicate right subsidiary pendant sums exist on one pendant - ['p106s1', 'p110s1', 'p110s3', 'p111s1', 'p116s1', 'p11s1', 'p15s1', 'p1s1', 'p20s1', 'p21s1', 'p26s1', 'p30s1', 'p35s1', 'p36s1', 'p41s1', 'p51s1', 'p56s1', 'p5s1', 'p60s1', 'p65s1', 'p66s1', 'p6s1', 'p70s1', 'p71s1', 'p86s1', 'p91s1']


Left Handed Sums:     # Sums = 8,  Max # Summands = 6,   (Min, Mean, Max) Sum Values = (14, 33, 68)
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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
p1s11, 1, 1 : 160LB1603p81: 10LB + p82: 100YG + p83: 50YB
2
p5s12, 1, 1 : 39W393p44: 22YB:0G + p45: 12W + p46: 5LB
3
p6s12, 2, 1 : 55LB554p145: 2W + p146: 7LB + p147: 40YG + p150: 6W
4
p11s13, 2, 1 : 72LB723p125: 5W + p126: 2LB + p127: 65YG
5
p15s14, 1, 1 : 22W224p152: 6YG + p155: 3W + p156: 10LB + p157: 3YG
6
p20s15, 1, 1 : 24W243p46: 5LB + p49: 6YB:0G + p50: 13W
7
p21s15, 2, 1 : 51LB513p147: 40YG + p150: 6W + p151: 5LB
8
p26s16, 2, 1 : 36LB363p54: 21YB:0G + p55: 5W + p56: 10LB
9
p30s17, 1, 1 : 43W433p169: 34YB + p170: 6W + p171: 3LB
10
p35s18, 1, 1 : 39W393p44: 22YB:0G + p45: 12W + p46: 5LB
11
p36s18, 2, 1 : 62LB626p156: 10LB + p157: 3YG + p160: 3W + p161: 10LB + p162: 16YG + p164: 20YB
12
p41s19, 2, 1 : 26LB264p156: 10LB + p157: 3YG + p160: 3W + p161: 10LB
13
p51s111, 2, 1 : 71LB718p152: 6YG + p155: 3W + p156: 10LB + p157: 3YG + p160: 3W + p161: 10LB + p162: 16YG + p164: 20YB
14
p56s112, 2, 1 : 43LB433p169: 34YB + p170: 6W + p171: 3LB
15
p60s113, 1, 1 : 25W255p152: 6YG + p155: 3W + p156: 10LB + p157: 3YG + p160: 3W
16
p65s114, 1, 1 : 24W244p151: 5LB + p152: 6YG + p155: 3W + p156: 10LB
17
p66s114, 2, 1 : 24LB244p151: 5LB + p152: 6YG + p155: 3W + p156: 10LB
18
p70s115, 1, 1 : 27W275p151: 5LB + p152: 6YG + p155: 3W + p156: 10LB + p157: 3YG
19
p71s115, 2, 1 : 29LB293p160: 3W + p161: 10LB + p162: 16YG
20
p86s118, 2, 1 : 25LB255p152: 6YG + p155: 3W + p156: 10LB + p157: 3YG + p160: 3W
21
p91s119, 2, 1 : 46LB463p161: 10LB + p162: 16YG + p164: 20YB
22
p106s122, 2, 1 : 72LB723p125: 5W + p126: 2LB + p127: 65YG
23
p110s123, 1, 1 : 51W513p147: 40YG + p150: 6W + p151: 5LB
24
p111s123, 2, 1 : 66LB666p145: 2W + p146: 7LB + p147: 40YG + p150: 6W + p151: 5LB + p152: 6YG
25
p110s323, 1, 3 : 46W:KB463p161: 10LB + p162: 16YG + p164: 20YB
26
p116s124, 2, 1 : 68LB688p155: 3W + p156: 10LB + p157: 3YG + p160: 3W + p161: 10LB + p162: 16YG + p164: 20YB + p165: 3W

Left Handed Sum Detail: - Click on column name to sort
# Color Sum Schema Sum Cord Sum Cord Value # Summands Summands
1
p65s114, 1, 1 : 24W243p46: 5LB + p49: 6YB:0G + p50: 13W
2
p66s114, 2, 1 : 24LB243p46: 5LB + p49: 6YB:0G + p50: 13W
3
p71s115, 2, 1 : 29LB293p49: 6YB:0G + p50: 13W + p51: 10LB
4
p91s119, 2, 1 : 46LB465p45: 12W + p46: 5LB + p49: 6YB:0G + p50: 13W + p51: 10LB
5
p110s323, 1, 3 : 46W:KB465p45: 12W + p46: 5LB + p49: 6YB:0G + p50: 13W + p51: 10LB
6
p116s124, 2, 1 : 68LB686p44: 22YB:0G + p45: 12W + p46: 5LB + p49: 6YB:0G + p50: 13W + p51: 10LB
7
p176s136, 2, 1 : 14LB143p151: 5LB + p152: 6YG + p155: 3W
8
p216s144, 2, 1 : 14LB143p151: 5LB + p152: 6YG + p155: 3W

Khipu Notes:
Ascher Databook Notes:
  1. This is one of several khipus acquired by the Museum in 1907 with provenance Pachacamac. For a list of them, see UR1097.
  2. By spacing, the khipu is separated into 45 groups of 5 pendants each. There is a larger space after every 3rd group and a still larger space between the 21st and 22nd groups and the 24th and 25th groups. Thus, the khipu is in 3 parts: part 1 is 7 sets of 3 groups each; part 2 is 1 set of 3 groups; and part 3 is 7 sets of 3 groups.
  3. All groups in part 1 have the same color pattern: W (with a W subsidiary); LB (with an LB subsidiary); YG; YB; YB: 0G. Groups in parts 2 and 3 have the same pattern for the first 3 pendant positions and then vary in one or both of the last 2 positions. Calling the colors in the part 1 pattern C1-C5, the color patterns are summarized in Table 1.

    TABLE 1

    Part 1 (groups 1-21)C1C2C3C4C5
    Part 2 (groups 1-3)C1C2C3C4C4
    Part 3 (groups 1-5)C1C2C3C2C5
    Part 3 (groups 6-8)C1C2C3C2C4
    Part 3 (groups 9-21)C1C2C3C4C4


    In all groups, there is at least one subsidiary on pendants 1 and 2 (a W and an LB respectively) and no subsidiaries on the other positions. Additional subsidiaries on the first 2 positions are, with one exception, KB:W or LB-W.
  4. In parts 1 and 3, many values are repeated in the same position in consecutive groups or in the same position 2 groups later. The former can be represented as:,

    Pij= Pi+1,j and the latter as Pij = Pi+2,j

    In part 1, these hold in 20 and 12 places respectively; in part 2 in no places; and in part 3 in 27 and 18 places.

  5. The values in part 2 are related to the sums of values in part 3. Position by position, values in group 1 of part 2 are related to the sums of values in the first groups in each of the 7 sets in part 3; group 2 values are related to sums of values in the second groups of each of the sets; and group 3 values to the sums of values of the third group. That is:
    \[ P_{2ij}= \sum\limits_{k=0}^{6} P_{3,3k+i,j}\;\;\;for\;j=(1,2,...5),\;\; i=(1,2,3) \]
    This represents 15 sums and 105 values being summed. Of the 15 values in part 2, 8 are exactly these sums (or off by 1 in 1 digit); 5 are exact sums of only some of the 7 pendants:

    Example: P211 = P341 + P3,10,1 + P3,13,1 + P3,16,1 + P3,19,1 thus omitting P311 and P371

    and 2 are less than the sums but cannot be associated with a specific subset of the 7 pendants. (Note that the main cord is broken and so there could have been another part prior to part 1 that summed its values.