UR1175/KH0192 - Pendant Pendant Sums

Drawings:

Overview	Detail View
All Khipus' Ascher Sum Fieldmarks	Right-Handed XRay
All Pendant 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 = 58, Max # Summands = 23, (Min, Mean, Max) Sum Values = (11, 86, 445)
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Left Handed Sums: # Sums = 45, Max # Summands = 14, (Min, Mean, Max) Sum Values = (11, 89, 445)
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Right Handed Sum Detail: - Click on column name to sort

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p2_{1, 2} : 160_YG	160	3	p81: 10_LB + p82: 100_YG + p83: 50_BY
2	p6_{2, 2} : 26_LB	26	2	p54: 21_BY:0G + p55: 5_W
3	p10_{3, 1} : 25_W	25	9	p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W
4	p15_{4, 1} : 23_W	23	5	p45: 12_W + p46: 5_LB + p47: 0_YG + p48: 0_BY + p49: 6_BY:0G
5	p17_{4, 3} : 77_YG	77	2	p35: 66_W + p36: 11_LB
6	p20_{5, 1} : 36_W	36	6	p45: 12_W + p46: 5_LB + p47: 0_YG + p48: 0_BY + p49: 6_BY:0G + p50: 13_W
7	p21_{5, 2} : 33_LB	33	2	p65: 30_W + p66: 3_LB
8	p22_{5, 3} : 122_YG	122	2	p43: 100_BY + p44: 22_BY:0G
9	p24_{5, 5} : 50_BY:0G	50	3	p50: 13_W + p51: 10_LB + p52: 27_YG
10	p27_{6, 3} : 82_YG	82	3	p92: 40_YG + p93: 0_BY + p94: 42_BY:0G
11	p28_{6, 4} : 58_BY	58	7	p44: 22_BY:0G + p45: 12_W + p46: 5_LB + p47: 0_YG + p48: 0_BY + p49: 6_BY:0G + p50: 13_W
12	p32_{7, 3} : 79_YG	79	3	p39: 11_BY:0G + p40: 65_W + p41: 3_LB
13	p37_{8, 3} : 129_YG	129	3	p70: 31_W + p71: 5_LB + p72: 93_YG
14	p39_{8, 5} : 11_BY:0G	11	4	p46: 5_LB + p47: 0_YG + p48: 0_BY + p49: 6_BY:0G
15	p42_{9, 3} : 139_YG	139	4	p43: 100_BY + p44: 22_BY:0G + p45: 12_W + p46: 5_LB
16	p44_{9, 5} : 22_BY:0G	22	6	p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG
17	p50_{11, 1} : 13_W	13	2	p85: 3_W + p86: 10_LB
18	p52_{11, 3} : 27_YG	27	7	p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG
19	p54_{11, 5} : 21_BY:0G	21	2	p175: 17_W + p176: 4_LB
20	p57_{12, 3} : 290_YG	290	23	p139: 12_BY:0G + p140: 2_W + p141: 6_LB + p142: 75_YG + p143: 100_BY + p144: 0_BY:0G + p145: 2_W + p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
21	p59_{12, 5} : 55_BY:0G	55	6	p145: 2_W + p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W
22	p60_{13, 1} : 62_W	62	13	p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB + p162: 16_YG
23	p62_{13, 3} : 177_YG	177	5	p72: 93_YG + p73: 50_BY + p74: 20_BY:0G + p75: 3_W + p76: 11_LB
24	p67_{14, 3} : 86_YG	86	3	p97: 30_YG + p98: 10_BY + p99: 46_BY:0G
25	p72_{15, 3} : 93_YG	93	16	p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
26	p76_{16, 2} : 11_LB	11	2	p150: 6_W + p151: 5_LB
27	p77_{16, 3} : 85_YG	85	6	p120: 6_W + p121: 4_LB + p122: 70_YG + p123: 0_LB + p124: 0_BY:0G + p125: 5_W
28	p83_{17, 4} : 50_BY	50	3	p90: 10_W + p91: 0_LB + p92: 40_YG
29	p84_{17, 5} : 20_BY:0G	20	3	p139: 12_BY:0G + p140: 2_W + p141: 6_LB
30	p87_{18, 3} : 120_YG	120	4	p138: 100_BY + p139: 12_BY:0G + p140: 2_W + p141: 6_LB
31	p89_{18, 5} : 13_BY:0G	13	2	p155: 3_W + p156: 10_LB
32	p92_{19, 3} : 40_YG	40	2	p97: 30_YG + p98: 10_BY
33	p94_{19, 5} : 42_BY:0G	42	7	p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB + p162: 16_YG
34	p97_{20, 3} : 30_YG	30	7	p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB
35	p99_{20, 5} : 46_BY:0G	46	4	p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W
36	p102_{21, 3} : 138_YG	138	4	p177: 60_YG + p178: 50_BY + p179: 18_BY:0G + p180: 10_W
37	p104_{21, 5} : 78_BY:0G	78	3	p178: 50_BY + p179: 18_BY:0G + p180: 10_W
38	p105_{22, 1} : 77_W	77	5	p122: 70_YG + p123: 0_LB + p124: 0_BY:0G + p125: 5_W + p126: 2_LB
39	p106_{22, 2} : 35_LB	35	10	p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
40	p107_{22, 3} : 268_YG	268	21	p140: 2_W + p141: 6_LB + p142: 75_YG + p143: 100_BY + p144: 0_BY:0G + p145: 2_W + p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W
41	p108_{22, 4} : 200_BY	200	10	p121: 4_LB + p122: 70_YG + p123: 0_LB + p124: 0_BY:0G + p125: 5_W + p126: 2_LB + p127: 65_YG + p128: 50_BY + p129: 0_BY:0G + p130: 4_W
42	p111_{23, 2} : 36_LB	36	11	p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W
43	p112_{23, 3} : 445_YG	445	16	p184: 60_BY:0G + p185: 10_W + p186: 12_LB + p187: 58_YG + p188: 0_BY + p189: 60_BY + p190: 8_W + p191: 20_LB + p192: 35_YG + p193: 0_BY + p194: 94_BY:0G + p195: 12_W + p196: 10_LB + p197: 36_YG + p198: 0_BY + p199: 30_BY:0G
44	p113_{23, 4} : 250_BY	250	12	p139: 12_BY:0G + p140: 2_W + p141: 6_LB + p142: 75_YG + p143: 100_BY + p144: 0_BY:0G + p145: 2_W + p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W
45	p114_{23, 5} : 96_BY	96	6	p202: 35_YG + p203: 0_BY + p204: 20_BY:0G + p205: 0_W + p206: 0_LB + p207: 41_YG
46	p115_{24, 1} : 75_W	75	4	p122: 70_YG + p123: 0_LB + p124: 0_BY:0G + p125: 5_W
47	p116_{24, 2} : 66_LB	66	8	p145: 2_W + p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG
48	p118_{24, 4} : 86_BY	86	15	p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
49	p119_{24, 5} : 192_BY:0G	192	7	p122: 70_YG + p123: 0_LB + p124: 0_BY:0G + p125: 5_W + p126: 2_LB + p127: 65_YG + p128: 50_BY
50	p122_{25, 3} : 70_YG	70	10	p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB
51	p127_{26, 3} : 65_YG	65	10	p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB + p162: 16_YG + p163: 0_BY + p164: 20_BY
52	p137_{28, 3} : 80_YG	80	12	p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG
53	p143_{29, 4} : 100_BY	100	3	p218: 50_BY + p219: 0_BY:0G + p220: 50_W
54	p147_{30, 3} : 40_YG	40	11	p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
55	p179_{36, 5} : 18_BY:0G	18	2	p200: 13_W + p201: 5_LB
56	p187_{38, 3} : 58_YG	58	3	p195: 12_W + p196: 10_LB + p197: 36_YG
57	p189_{38, 5} : 60_BY	60	4	p201: 5_LB + p202: 35_YG + p203: 0_BY + p204: 20_BY:0G
58	p194_{39, 5} : 94_BY:0G	94	6	p196: 10_LB + p197: 36_YG + p198: 0_BY + p199: 30_BY:0G + p200: 13_W + p201: 5_LB

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

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p12_{3, 3} : 77_YG	77	3	p4: 30_BY:0G + p5: 21_W + p6: 26_LB
2	p22_{5, 3} : 122_YG	122	3	p5: 21_W + p6: 26_LB + p7: 75_YG
3	p57_{12, 3} : 290_YG	290	3	p2: 160_YG + p3: 100_BY + p4: 30_BY:0G
4	p60_{13, 1} : 62_W	62	2	p24: 50_BY:0G + p25: 12_W
5	p62_{13, 3} : 177_YG	177	6	p49: 6_BY:0G + p50: 13_W + p51: 10_LB + p52: 27_YG + p53: 100_BY + p54: 21_BY:0G
6	p68_{14, 4} : 50_BY	50	2	p64: 20_BY:0G + p65: 30_W
7	p76_{16, 2} : 11_LB	11	4	p46: 5_LB + p47: 0_YG + p48: 0_BY + p49: 6_BY:0G
8	p87_{18, 3} : 120_YG	120	5	p76: 11_LB + p77: 85_YG + p78: 0_BY + p79: 20_BY:0G + p80: 4_W
9	p99_{20, 5} : 46_BY:0G	46	7	p45: 12_W + p46: 5_LB + p47: 0_YG + p48: 0_BY + p49: 6_BY:0G + p50: 13_W + p51: 10_LB
10	p105_{22, 1} : 77_W	77	2	p35: 66_W + p36: 11_LB
11	p107_{22, 3} : 268_YG	268	13	p85: 3_W + p86: 10_LB + p87: 120_YG + p88: 0_BY + p89: 13_BY:0G + p90: 10_W + p91: 0_LB + p92: 40_YG + p93: 0_BY + p94: 42_BY:0G + p95: 0_W + p96: 0_LB + p97: 30_YG
12	p109_{22, 5} : 136_BY	136	2	p67: 86_YG + p68: 50_BY
13	p111_{23, 2} : 36_LB	36	2	p70: 31_W + p71: 5_LB
14	p112_{23, 3} : 445_YG	445	14	p77: 85_YG + p78: 0_BY + p79: 20_BY:0G + p80: 4_W + p81: 10_LB + p82: 100_YG + p83: 50_BY + p84: 20_BY:0G + p85: 3_W + p86: 10_LB + p87: 120_YG + p88: 0_BY + p89: 13_BY:0G + p90: 10_W
15	p114_{23, 5} : 96_BY	96	2	p76: 11_LB + p77: 85_YG
16	p117_{24, 3} : 335_YG	335	7	p67: 86_YG + p68: 50_BY + p69: 20_BY:0G + p70: 31_W + p71: 5_LB + p72: 93_YG + p73: 50_BY
17	p118_{24, 4} : 86_BY	86	3	p97: 30_YG + p98: 10_BY + p99: 46_BY:0G
18	p119_{24, 5} : 192_BY:0G	192	5	p67: 86_YG + p68: 50_BY + p69: 20_BY:0G + p70: 31_W + p71: 5_LB
19	p122_{25, 3} : 70_YG	70	2	p83: 50_BY + p84: 20_BY:0G
20	p128_{26, 4} : 50_BY	50	3	p90: 10_W + p91: 0_LB + p92: 40_YG
21	p137_{28, 3} : 80_YG	80	3	p120: 6_W + p121: 4_LB + p122: 70_YG
22	p142_{29, 3} : 75_YG	75	4	p122: 70_YG + p123: 0_LB + p124: 0_BY:0G + p125: 5_W
23	p147_{30, 3} : 40_YG	40	2	p97: 30_YG + p98: 10_BY
24	p162_{33, 3} : 16_YG	16	5	p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
25	p164_{33, 5} : 20_BY	20	6	p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W
26	p167_{34, 3} : 30_YG	30	10	p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W
27	p169_{34, 5} : 34_BY	34	3	p79: 20_BY:0G + p80: 4_W + p81: 10_LB
28	p172_{35, 3} : 54_YG	54	3	p128: 50_BY + p129: 0_BY:0G + p130: 4_W
29	p175_{36, 1} : 17_W	17	3	p150: 6_W + p151: 5_LB + p152: 6_YG
30	p177_{36, 3} : 60_YG	60	9	p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB + p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W
31	p182_{37, 3} : 29_YG	29	3	p160: 3_W + p161: 10_LB + p162: 16_YG
32	p187_{38, 3} : 58_YG	58	6	p146: 7_LB + p147: 40_YG + p148: 0_LB + p149: 0_BY + p150: 6_W + p151: 5_LB
33	p192_{39, 3} : 35_YG	35	10	p152: 6_YG + p153: 0_LB + p154: 0_BY + p155: 3_W + p156: 10_LB + p157: 3_YG + p158: 0_BY + p159: 0_BY:0G + p160: 3_W + p161: 10_LB
34	p194_{39, 5} : 94_BY:0G	94	2	p29: 9_BY:0G + p30: 85_W
35	p197_{40, 3} : 36_YG	36	3	p162: 16_YG + p163: 0_BY + p164: 20_BY
36	p200_{41, 1} : 13_W	13	2	p160: 3_W + p161: 10_LB
37	p207_{42, 3} : 41_YG	41	2	p181: 12_LB + p182: 29_YG
38	p209_{42, 5} : 49_BY:0G	49	5	p161: 10_LB + p162: 16_YG + p163: 0_BY + p164: 20_BY + p165: 3_W
39	p211_{43, 2} : 40_LB	40	2	p201: 5_LB + p202: 35_YG
40	p212_{43, 3} : 15_YG	15	2	p55: 5_W + p56: 10_LB
41	p215_{44, 1} : 70_W	70	2	p186: 12_LB + p187: 58_YG
42	p217_{44, 3} : 140_YG	140	4	p207: 41_YG + p208: 0_BY + p209: 49_BY:0G + p210: 50_W
43	p222_{45, 3} : 125_YG	125	5	p212: 15_YG + p213: 0_BY + p214: 0_BY:0G + p215: 70_W + p216: 40_LB
44	p223_{45, 4} : 90_BY	90	2	p210: 50_W + p211: 40_LB
45	p224_{45, 5} : 11_BY:0G	11	2	p151: 5_LB + p152: 6_YG

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