UR1175/KH0192 - Indexed Pendant Sums

Drawings:

Overview	Detail View
All Khipus' Ascher Sum Fieldmarks	Right-Handed XRay
All Indexed Pendant Sum Relationships	Left-Handed XRay
This Khipu's Fieldmark Catalog	Right-Handed Sum Detail
This Khipu's Drawing	Left-Handed Sum Detail

Right Handed Sums: # Sums = 34, Max # Summands = 10, (Min, Mean, Max) Sum Values = (11, 62, 290)
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Left Handed Sums: # Sums = 18, Max # Summands = 5, (Min, Mean, Max) Sum Values = (12, 90, 290)
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Right Handed Sum Detail: - Click on column name to sort

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p1_{1, 1} : 26_LB	26	3	p165: 3_W + p170: 6_W + p175: 17_W
2	p2_{1, 2} : 160_YG	160	8	p106: 35_LB + p111: 36_LB + p116: 66_LB + p121: 4_LB + p126: 2_LB + p131: 4_LB + p136: 7_LB + p141: 6_LB
3	p5_{2, 1} : 21_W	21	5	p150: 6_W + p155: 3_W + p160: 3_W + p165: 3_W + p170: 6_W
4	p6_{2, 2} : 26_LB	26	3	p71: 5_LB + p76: 11_LB + p81: 10_LB
5	p10_{3, 1} : 25_W	25	2	p45: 12_W + p50: 13_W
6	p11_{3, 2} : 35_LB	35	3	p191: 20_LB + p196: 10_LB + p201: 5_LB
7	p15_{4, 1} : 23_W	23	2	p170: 6_W + p175: 17_W
8	p16_{4, 2} : 11_LB	11	2	p131: 4_LB + p136: 7_LB
9	p20_{5, 1} : 36_W	36	4	p165: 3_W + p170: 6_W + p175: 17_W + p180: 10_W
10	p21_{5, 2} : 33_LB	33	5	p46: 5_LB + p51: 10_LB + p56: 10_LB + p66: 3_LB + p71: 5_LB
11	p22_{5, 3} : 122_YG	122	3	p182: 29_YG + p187: 58_YG + p192: 35_YG
12	p25_{6, 1} : 12_W	12	3	p150: 6_W + p155: 3_W + p160: 3_W
13	p26_{6, 2} : 12_LB	12	2	p146: 7_LB + p151: 5_LB
14	p30_{7, 1} : 85_W	85	10	p155: 3_W + p160: 3_W + p165: 3_W + p170: 6_W + p175: 17_W + p180: 10_W + p185: 10_W + p190: 8_W + p195: 12_W + p200: 13_W
15	p31_{7, 2} : 11_LB	11	2	p131: 4_LB + p136: 7_LB
16	p35_{8, 1} : 66_W	66	7	p165: 3_W + p170: 6_W + p175: 17_W + p180: 10_W + p185: 10_W + p190: 8_W + p195: 12_W
17	p36_{8, 2} : 11_LB	11	2	p131: 4_LB + p136: 7_LB
18	p37_{8, 3} : 129_YG	129	3	p187: 58_YG + p192: 35_YG + p197: 36_YG
19	p45_{10, 1} : 12_W	12	3	p150: 6_W + p155: 3_W + p160: 3_W
20	p50_{11, 1} : 13_W	13	2	p85: 3_W + p90: 10_W
21	p57_{12, 3} : 290_YG	290	4	p82: 100_YG + p87: 120_YG + p92: 40_YG + p97: 30_YG
22	p59_{12, 5} : 55_YB:0G	55	2	p89: 13_YB:0G + p94: 42_YB:0G
23	p60_{13, 1} : 62_W	62	10	p140: 2_W + p145: 2_W + p150: 6_W + p155: 3_W + p160: 3_W + p165: 3_W + p170: 6_W + p175: 17_W + p180: 10_W + p185: 10_W
24	p70_{15, 1} : 31_W	31	9	p130: 4_W + p135: 2_W + p140: 2_W + p145: 2_W + p150: 6_W + p155: 3_W + p160: 3_W + p165: 3_W + p170: 6_W
25	p72_{15, 3} : 93_YG	93	2	p187: 58_YG + p192: 35_YG
26	p76_{16, 2} : 11_LB	11	2	p131: 4_LB + p136: 7_LB
27	p104_{21, 5} : 78_YB:0G	78	2	p179: 18_YB:0G + p184: 60_YB:0G
28	p106_{22, 2} : 35_LB	35	3	p191: 20_LB + p196: 10_LB + p201: 5_LB
29	p110_{23, 1} : 108_W	108	10	p115: 75_W + p120: 6_W + p125: 5_W + p130: 4_W + p135: 2_W + p140: 2_W + p145: 2_W + p150: 6_W + p155: 3_W + p160: 3_W
30	p113_{23, 4} : 250_YB	250	3	p128: 50_YB + p138: 100_YB + p143: 100_YB
31	p115_{24, 1} : 75_W	75	3	p195: 12_W + p200: 13_W + p210: 50_W
32	p116_{24, 2} : 66_LB	66	7	p171: 3_LB + p176: 4_LB + p181: 12_LB + p186: 12_LB + p191: 20_LB + p196: 10_LB + p201: 5_LB
33	p127_{26, 3} : 65_YG	65	4	p147: 40_YG + p152: 6_YG + p157: 3_YG + p162: 16_YG
34	p169_{34, 5} : 34_YB	34	2	p174: 16_YB:0G + p179: 18_YB:0G

Left Handed Sum Detail: - Click on column name to sort

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p57_{12, 3} : 290_YG	290	3	p27: 82_YG + p32: 79_YG + p37: 129_YG
2	p94_{19, 5} : 42_YB:0G	42	3	p29: 9_YB:0G + p39: 11_YB:0G + p44: 22_YB:0G
3	p105_{22, 1} : 77_W	77	2	p40: 65_W + p45: 12_W
4	p107_{22, 3} : 268_YG	268	2	p37: 129_YG + p42: 139_YG
5	p109_{22, 5} : 136_YB	136	5	p54: 21_YB:0G + p59: 55_YB:0G + p64: 20_YB:0G + p69: 20_YB:0G + p74: 20_YB:0G
6	p111_{23, 2} : 36_LB	36	4	p71: 5_LB + p76: 11_LB + p81: 10_LB + p86: 10_LB
7	p113_{23, 4} : 250_YB	250	3	p53: 100_YB + p58: 100_YB + p68: 50_YB
8	p114_{23, 5} : 96_YB	96	3	p54: 21_YB:0G + p59: 55_YB:0G + p64: 20_YB:0G
9	p116_{24, 2} : 66_LB	66	4	p76: 11_LB + p81: 10_LB + p86: 10_LB + p106: 35_LB
10	p175_{36, 1} : 17_W	17	3	p80: 4_W + p85: 3_W + p90: 10_W
11	p181_{37, 2} : 12_LB	12	2	p146: 7_LB + p151: 5_LB
12	p186_{38, 2} : 12_LB	12	2	p146: 7_LB + p151: 5_LB
13	p194_{39, 5} : 94_YB:0G	94	3	p174: 16_YB:0G + p179: 18_YB:0G + p184: 60_YB:0G
14	p195_{40, 1} : 12_W	12	3	p150: 6_W + p155: 3_W + p160: 3_W
15	p200_{41, 1} : 13_W	13	2	p85: 3_W + p90: 10_W
16	p209_{42, 5} : 49_YB:0G	49	3	p44: 22_YB:0G + p49: 6_YB:0G + p54: 21_YB:0G
17	p217_{44, 3} : 140_YG	140	5	p142: 75_YG + p147: 40_YG + p152: 6_YG + p157: 3_YG + p162: 16_YG
18	p221_{45, 2} : 12_LB	12	2	p146: 7_LB + p151: 5_LB

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: P₂₁₁ = P₃₄₁ + P_3,10,1 + P_3,13,1 + P_3,16,1 + P_3,19,1 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.

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