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**
UR1175/KH0192 - Subsidiary Pendant Sum
**

**Drawings:**

**Right Handed Sums:**

*# Sums*= 26,

*Max # Summands*= 8,

*(Min, Mean, Max) Sum Values*= (22, 48, 160)

*Click on Image to View Larger*

*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)

*Click on Image to View Larger*

**Right Handed Sum Detail:**-

*Click on column name to sort*

# | Color | Sum Schema | Sum Cord | Sum Cord Value | # Summands | Summands |
---|---|---|---|---|---|---|

1 | p1s1_{1, 1, 1} : 160_{LB} | 160 | 3 | p81: 10_{LB} + p82: 100_{YG} + p83: 50_{YB} | ||

2 | p5s1_{2, 1, 1} : 39_{W} | 39 | 3 | p44: 22_{YB:0G} + p45: 12_{W} + p46: 5_{LB} | ||

3 | p6s1_{2, 2, 1} : 55_{LB} | 55 | 4 | p145: 2_{W} + p146: 7_{LB} + p147: 40_{YG} + p150: 6_{W} | ||

4 | p11s1_{3, 2, 1} : 72_{LB} | 72 | 3 | p125: 5_{W} + p126: 2_{LB} + p127: 65_{YG} | ||

5 | p15s1_{4, 1, 1} : 22_{W} | 22 | 4 | p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} + p157: 3_{YG} | ||

6 | p20s1_{5, 1, 1} : 24_{W} | 24 | 3 | p46: 5_{LB} + p49: 6_{YB:0G} + p50: 13_{W} | ||

7 | p21s1_{5, 2, 1} : 51_{LB} | 51 | 3 | p147: 40_{YG} + p150: 6_{W} + p151: 5_{LB} | ||

8 | p26s1_{6, 2, 1} : 36_{LB} | 36 | 3 | p54: 21_{YB:0G} + p55: 5_{W} + p56: 10_{LB} | ||

9 | p30s1_{7, 1, 1} : 43_{W} | 43 | 3 | p169: 34_{YB} + p170: 6_{W} + p171: 3_{LB} | ||

10 | p35s1_{8, 1, 1} : 39_{W} | 39 | 3 | p44: 22_{YB:0G} + p45: 12_{W} + p46: 5_{LB} | ||

11 | p36s1_{8, 2, 1} : 62_{LB} | 62 | 6 | p156: 10_{LB} + p157: 3_{YG} + p160: 3_{W} + p161: 10_{LB} + p162: 16_{YG} + p164: 20_{YB} | ||

12 | p41s1_{9, 2, 1} : 26_{LB} | 26 | 4 | p156: 10_{LB} + p157: 3_{YG} + p160: 3_{W} + p161: 10_{LB} | ||

13 | p51s1_{11, 2, 1} : 71_{LB} | 71 | 8 | p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} + p157: 3_{YG} + p160: 3_{W} + p161: 10_{LB} + p162: 16_{YG} + p164: 20_{YB} | ||

14 | p56s1_{12, 2, 1} : 43_{LB} | 43 | 3 | p169: 34_{YB} + p170: 6_{W} + p171: 3_{LB} | ||

15 | p60s1_{13, 1, 1} : 25_{W} | 25 | 5 | p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} + p157: 3_{YG} + p160: 3_{W} | ||

16 | p65s1_{14, 1, 1} : 24_{W} | 24 | 4 | p151: 5_{LB} + p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} | ||

17 | p66s1_{14, 2, 1} : 24_{LB} | 24 | 4 | p151: 5_{LB} + p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} | ||

18 | p70s1_{15, 1, 1} : 27_{W} | 27 | 5 | p151: 5_{LB} + p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} + p157: 3_{YG} | ||

19 | p71s1_{15, 2, 1} : 29_{LB} | 29 | 3 | p160: 3_{W} + p161: 10_{LB} + p162: 16_{YG} | ||

20 | p86s1_{18, 2, 1} : 25_{LB} | 25 | 5 | p152: 6_{YG} + p155: 3_{W} + p156: 10_{LB} + p157: 3_{YG} + p160: 3_{W} | ||

21 | p91s1_{19, 2, 1} : 46_{LB} | 46 | 3 | p161: 10_{LB} + p162: 16_{YG} + p164: 20_{YB} | ||

22 | p106s1_{22, 2, 1} : 72_{LB} | 72 | 3 | p125: 5_{W} + p126: 2_{LB} + p127: 65_{YG} | ||

23 | p110s1_{23, 1, 1} : 51_{W} | 51 | 3 | p147: 40_{YG} + p150: 6_{W} + p151: 5_{LB} | ||

24 | p111s1_{23, 2, 1} : 66_{LB} | 66 | 6 | p145: 2_{W} + p146: 7_{LB} + p147: 40_{YG} + p150: 6_{W} + p151: 5_{LB} + p152: 6_{YG} | ||

25 | p110s3_{23, 1, 3} : 46_{W:KB} | 46 | 3 | p161: 10_{LB} + p162: 16_{YG} + p164: 20_{YB} | ||

26 | p116s1_{24, 2, 1} : 68_{LB} | 68 | 8 | p155: 3_{W} + p156: 10_{LB} + p157: 3_{YG} + p160: 3_{W} + p161: 10_{LB} + p162: 16_{YG} + p164: 20_{YB} + p165: 3_{W} |

**Left Handed Sum Detail:**-

*Click on column name to sort*

# | Color | Sum Schema | Sum Cord | Sum Cord Value | # Summands | Summands |
---|---|---|---|---|---|---|

1 | p65s1_{14, 1, 1} : 24_{W} | 24 | 3 | p46: 5_{LB} + p49: 6_{YB:0G} + p50: 13_{W} | ||

2 | p66s1_{14, 2, 1} : 24_{LB} | 24 | 3 | p46: 5_{LB} + p49: 6_{YB:0G} + p50: 13_{W} | ||

3 | p71s1_{15, 2, 1} : 29_{LB} | 29 | 3 | p49: 6_{YB:0G} + p50: 13_{W} + p51: 10_{LB} | ||

4 | p91s1_{19, 2, 1} : 46_{LB} | 46 | 5 | p45: 12_{W} + p46: 5_{LB} + p49: 6_{YB:0G} + p50: 13_{W} + p51: 10_{LB} | ||

5 | p110s3_{23, 1, 3} : 46_{W:KB} | 46 | 5 | p45: 12_{W} + p46: 5_{LB} + p49: 6_{YB:0G} + p50: 13_{W} + p51: 10_{LB} | ||

6 | p116s1_{24, 2, 1} : 68_{LB} | 68 | 6 | p44: 22_{YB:0G} + p45: 12_{W} + p46: 5_{LB} + p49: 6_{YB:0G} + p50: 13_{W} + p51: 10_{LB} | ||

7 | p176s1_{36, 2, 1} : 14_{LB} | 14 | 3 | p151: 5_{LB} + p152: 6_{YG} + p155: 3_{W} | ||

8 | p216s1_{44, 2, 1} : 14_{LB} | 14 | 3 | p151: 5_{LB} + p152: 6_{YG} + p155: 3_{W} |

**Khipu Notes:**

**Ascher Databook Notes:**

- This is one of several khipus acquired by the Museum in 1907 with provenance Pachacamac. For a list of them, see UR1097.
- 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.
- 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) C1 C2 C3 C4 C5 Part 2 (groups 1-3) C1 C2 C3 C4 C4 Part 3 (groups 1-5) C1 C2 C3 C2 C5 Part 3 (groups 6-8) C1 C2 C3 C2 C4 Part 3 (groups 9-21) C1 C2 C3 C4 C4

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.

- 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:,

P_{ij}= P_{i+1,j}and the latter as P_{ij}= P_{i+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.

- 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: P_{211}= P_{341}+ P_{3,10,1}+ P_{3,13,1}+ P_{3,16,1}+ P_{3,19,1}thus omitting P_{311}and P_{371}

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.