AK003 - 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 = 96, Max # Summands = 9, (Min, Mean, Max) Sum Values = (11, 31, 220)
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Left Handed Sums: # Sums = 77, Max # Summands = 5, (Min, Mean, Max) Sum Values = (11, 33, 535)
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Right Handed Sum Detail: - Click on column name to sort

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p3_{1, 3} : 14_W:PB	14	2	p264: 9_W:PB + p273: 5_W:PB
2	p5_{1, 5} : 67_W	67	4	p293: 17_W + p302: 22_W + p311: 6_W + p320: 22_W
3	p11_{2, 2} : 14_W	14	2	p371: 5_W + p380: 9_W
4	p12_{2, 3} : 25_W:PB	25	4	p246: 3_W:PB + p255: 8_W:PB + p264: 9_W:PB + p273: 5_W:PB
5	p14_{2, 5} : 29_W	29	3	p194: 2_W + p203: 6_W + p212: 21_YB
6	p17_{2, 8} : 16_W	16	2	p197: 11_W + p206: 5_W
7	p18_{2, 9} : 47_W	47	2	p144: 33_W + p153: 14_W
8	p25_{3, 7} : 24_W	24	6	p367: 3_W + p376: 3_W + p385: 4_W + p394: 5_W + p403: 4_W + p412: 5_W
9	p35_{4, 8} : 17_W	17	2	p206: 5_W + p215: 12_W
10	p39_{5, 3} : 24_W:PB	24	2	p427: 12_W:PB + p436: 12_W:KB
11	p40_{5, 4} : 14_PB	14	2	p58: 6_PB + p67: 8_PB
12	p42_{5, 6} : 25_W	25	2	p114: 17_W + p132: 8_W
13	p43_{5, 7} : 14_W	14	2	p232: 9_W + p241: 5_W
14	p44_{5, 8} : 17_W	17	2	p206: 5_W + p215: 12_W
15	p45_{5, 9} : 44_W	44	3	p207: 17_W + p216: 18_W + p225: 9_YB
16	p48_{6, 3} : 14_W:PB	14	2	p264: 9_W:PB + p273: 5_W:PB
17	p50_{6, 5} : 23_W	23	2	p149: 13_W + p167: 10_W
18	p52_{6, 7} : 12_W	12	2	p268: 6_W + p277: 6_W
19	p57_{7, 3} : 27_W:PB	27	2	p336: 15_W:PB + p345: 12_W:PB
20	p62_{7, 8} : 31_W	31	2	p188: 20_W + p197: 11_W
21	p65_{8, 2} : 59_W	59	6	p218: 10_W + p227: 14_W + p236: 8_W + p245: 4_W + p254: 17_W + p263: 6_W
22	p74_{9, 2} : 110_W	110	8	p146: 10_W + p182: 26_W + p191: 21_W + p218: 10_W + p227: 14_W + p236: 8_W + p245: 4_W + p254: 17_W
23	p75_{9, 3} : 22_W:PB	22	2	p120: 12_W:PB + p129: 10_W:PB
24	p79_{9, 7} : 26_W:KB	26	2	p259: 20_W + p268: 6_W
25	p80_{9, 8} : 220_W:KB	220	9	p89: 57_W + p98: 11_W + p107: 21_W + p116: 27_W + p125: 18_W + p134: 12_W + p143: 34_W + p170: 24_W + p179: 16_W
26	p89_{10, 8} : 57_W	57	3	p116: 27_W + p125: 18_W + p134: 12_W
27	p92_{11, 2} : 34_W	34	3	p326: 7_W + p335: 16_W + p344: 11_W
28	p95_{11, 5} : 18_W	18	2	p221: 10_W + p230: 8_W
29	p98_{11, 8} : 11_W	11	2	p395: 6_W + p404: 5_W
30	p99_{11, 9} : 36_W	36	2	p306: 8_W + p315: 28_W
31	p102_{12, 3} : 59_W:PB	59	5	p210: 21_W:PB + p219: 12_W:PB + p228: 3_W:PB + p237: 20_W:PB + p246: 3_W:PB
32	p106_{12, 7} : 35_W	35	2	p250: 15_W + p259: 20_W
33	p111_{13, 3} : 42_W:PB	42	2	p408: 22_W:PB + p418: 20_W:PB
34	p113_{13, 5} : 21_W	21	2	p248: 7_W + p257: 14_W
35	p115_{13, 7} : 25_W	25	2	p169: 16_W + p178: 9_W
36	p122_{14, 5} : 12_W	12	2	p167: 10_W + p194: 2_W
37	p124_{14, 7} : 14_W	14	2	p232: 9_W + p241: 5_W
38	p125_{14, 8} : 18_W	18	2	p350: 15_W + p359: 3_W
39	p126_{14, 9} : 53_W	53	3	p469: 13_W + p478: 21_W + p487: 19_W
40	p134_{15, 8} : 12_W	12	2	p404: 5_W + p413: 7_W
41	p140_{16, 5} : 19_W	19	2	p374: 13_W + p383: 6_W
42	p142_{16, 7} : 14_W	14	2	p232: 9_W + p241: 5_W
43	p143_{16, 8} : 34_W	34	2	p468: 15_W + p477: 19_W
44	p169_{19, 7} : 16_W	16	4	p376: 3_W + p385: 4_W + p394: 5_W + p403: 4_W
45	p170_{19, 8} : 24_W	24	3	p350: 15_W + p359: 3_W + p368: 6_W
46	p171_{19, 9} : 26_W	26	2	p279: 13_W + p288: 13_W
47	p179_{20, 8} : 16_W	16	2	p197: 11_W + p206: 5_W
48	p182_{21, 2} : 26_W	26	2	p498: 15_W + p507: 11_W
49	p183_{21, 3} : 77_W:PB	77	5	p408: 22_W:PB + p418: 20_W:PB + p427: 12_W:PB + p436: 12_W:KB + p445: 11_W:PB
50	p184_{21, 4} : 14_PB	14	3	p274: 3_PB + p283: 5_PB + p292: 6_PB
51	p187_{21, 7} : 18_W	18	3	p268: 6_W + p277: 6_W + p286: 6_W
52	p191_{22, 2} : 21_W	21	2	p245: 4_W + p254: 17_W
53	p192_{22, 3} : 33_W:PB	33	2	p210: 21_W:PB + p219: 12_W:PB
54	p193_{22, 4} : 15_PB	15	2	p247: 5_PB + p256: 10_PB
55	p196_{22, 7} : 18_W	18	3	p268: 6_W + p277: 6_W + p286: 6_W
56	p197_{22, 8} : 11_W	11	2	p395: 6_W + p404: 5_W
57	p210_{24, 3} : 21_W:PB	21	3	p273: 5_W:PB + p282: 6_W:PB + p291: 10_W:PB
58	p212_{24, 5} : 21_YB	21	2	p248: 7_W + p257: 14_W
59	p213_{24, 6} : 12_YB	12	2	p393: 7_W + p402: 5_W
60	p214_{24, 7} : 14_YB	14	2	p232: 9_W + p241: 5_W
61	p215_{24, 8} : 12_W	12	2	p404: 5_W + p413: 7_W
62	p223_{25, 7} : 16_W	16	4	p376: 3_W + p385: 4_W + p394: 5_W + p403: 4_W
63	p227_{26, 2} : 14_W	14	2	p371: 5_W + p380: 9_W
64	p231_{26, 6} : 12_W	12	2	p393: 7_W + p402: 5_W
65	p235_{27, 1} : 178_W	178	2	p388: 113_W + p397: 65_W
66	p238_{27, 4} : 12_PB	12	2	p301: 4_PB + p310: 8_PB
67	p240_{27, 6} : 23_W	23	3	p393: 7_W + p402: 5_W + p411: 11_W
68	p242_{27, 8} : 19_W	19	2	p269: 17_W + p278: 2_W
69	p244_{28, 1} : 178_W	178	2	p388: 113_W + p397: 65_W
70	p250_{28, 7} : 15_W	15	4	p367: 3_W + p376: 3_W + p385: 4_W + p394: 5_W
71	p260_{29, 8} : 16_W	16	2	p495: 4_W + p504: 12_W
72	p261_{29, 9} : 34_W	34	2	p288: 13_W + p297: 21_W
73	p270_{30, 9} : 42_W	42	2	p442: 18_W + p451: 24_W
74	p272_{31, 2} : 14_W	14	2	p371: 5_W + p380: 9_W
75	p275_{31, 5} : 12_W	12	2	p501: 6_W + p510: 6_W
76	p295_{33, 7} : 23_W	23	2	p358: 20_W + p367: 3_W
77	p296_{33, 8} : 26_W	26	3	p495: 4_W + p504: 12_W + p513: 10_W
78	p304_{34, 7} : 13_W	13	3	p385: 4_W + p394: 5_W + p403: 4_W
79	p308_{35, 2} : 23_W	23	2	p326: 7_W + p335: 16_W
80	p313_{35, 7} : 18_W	18	4	p385: 4_W + p394: 5_W + p403: 4_W + p412: 5_W
81	p314_{35, 8} : 11_W	11	2	p395: 6_W + p404: 5_W
82	p327_{37, 3} : 19_W:PB	19	3	p363: 10_W:PB + p372: 5_W:PB + p381: 4_W:PB
83	p329_{37, 5} : 33_W	33	3	p374: 13_W + p383: 6_W + p392: 14_W
84	p331_{37, 7} : 19_W	19	2	p494: 5_W + p503: 14_W
85	p336_{38, 3} : 15_W:PB	15	2	p363: 10_W:PB + p372: 5_W:PB
86	p341_{38, 8} : 28_W	28	3	p368: 6_W + p377: 9_W + p386: 13_W
87	p342_{38, 9} : 47_W	47	4	p369: 11_W + p378: 13_W + p387: 11_W + p396: 12_W
88	p347_{39, 5} : 12_W	12	2	p501: 6_W + p510: 6_W
89	p350_{39, 8} : 15_W	15	2	p368: 6_W + p377: 9_W
90	p354_{40, 3} : 36_W:PB	36	3	p490: 5_W:PB + p499: 23_W:PB + p508: 8_W:PB
91	p408_{46, 3} : 22_W:PB	22	2	p463: 11_W:PB + p481: 11_W:PB
92	p417_{47, 2} : 31_W	31	2	p489: 16_W + p498: 15_W
93	p419_{47, 4} : 35_PB	35	4	p437: 8_PB + p446: 14_PB + p455: 4_PB + p464: 9_PB
94	p421_{47, 6} : 43_W	43	2	p430: 10_W + p439: 33_W
95	p429_{48, 5} : 64_W	64	4	p438: 21_W + p447: 15_W + p456: 21_W + p465: 7_W
96	p450_{50, 8} : 35_W	35	2	p459: 20_W + p468: 15_W

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

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p79_{9, 7} : 26_W:KB	26	2	p43: 14_W + p52: 12_W
2	p106_{12, 7} : 35_W	35	2	p16: 11_W + p25: 24_W
3	p111_{13, 3} : 42_W:PB	42	2	p75: 22_W:PB + p84: 20_W:PB
4	p113_{13, 5} : 21_W	21	3	p59: 11_W + p68: 1_W + p77: 9_W:KB
5	p116_{13, 8} : 27_W	27	2	p26: 10_W + p35: 17_W
6	p140_{16, 5} : 19_W	19	2	p23: 8_W + p32: 11_W
7	p143_{16, 8} : 34_W	34	2	p35: 17_W + p44: 17_W
8	p184_{21, 4} : 14_PB	14	2	p58: 6_PB + p67: 8_PB
9	p191_{22, 2} : 21_W	21	3	p101: 9_W + p110: 10_W + p119: 2_W
10	p193_{22, 4} : 15_PB	15	3	p76: 4_PB + p94: 10_PB + p103: 1_PB
11	p212_{24, 5} : 21_YB	21	3	p59: 11_W + p68: 1_W + p77: 9_W:KB
12	p224_{25, 8} : 17_W	17	2	p206: 5_W + p215: 12_W
13	p238_{27, 4} : 12_PB	12	2	p13: 7_PB + p22: 5_PB
14	p240_{27, 6} : 23_W	23	3	p132: 8_W + p141: 6_W + p168: 9_W
15	p251_{28, 8} : 44_W	44	3	p26: 10_W + p35: 17_W + p44: 17_W
16	p258_{29, 6} : 21_W	21	2	p168: 9_W + p213: 12_YB
17	p260_{29, 8} : 16_W	16	2	p197: 11_W + p206: 5_W
18	p269_{30, 8} : 17_W	17	2	p206: 5_W + p215: 12_W
19	p270_{30, 9} : 42_W	42	2	p234: 30_YB + p243: 12_W
20	p285_{32, 6} : 14_W	14	2	p132: 8_W + p141: 6_W
21	p296_{33, 8} : 26_W	26	2	p17: 16_W + p26: 10_W
22	p299_{34, 2} : 22_W	22	2	p119: 2_W + p128: 20_W
23	p308_{35, 2} : 23_W	23	2	p254: 17_W + p263: 6_W
24	p313_{35, 7} : 18_W	18	3	p268: 6_W + p277: 6_W + p286: 6_W
25	p329_{37, 5} : 33_W	33	2	p113: 21_W + p122: 12_W
26	p336_{38, 3} : 15_W:PB	15	2	p219: 12_W:PB + p228: 3_W:PB
27	p341_{38, 8} : 28_W	28	3	p197: 11_W + p206: 5_W + p215: 12_W
28	p342_{38, 9} : 47_W	47	2	p144: 33_W + p153: 14_W
29	p348_{39, 6} : 14_W	14	2	p132: 8_W + p141: 6_W
30	p350_{39, 8} : 15_W	15	2	p278: 2_W + p287: 13_W
31	p354_{40, 3} : 36_W:PB	36	3	p210: 21_W:PB + p219: 12_W:PB + p228: 3_W:PB
32	p375_{42, 6} : 15_W	15	2	p141: 6_W + p168: 9_W
33	p408_{46, 3} : 22_W:PB	22	2	p120: 12_W:PB + p129: 10_W:PB
34	p410_{46, 5} : 18_W	18	2	p221: 10_W + p230: 8_W
35	p411_{46, 6} : 11_W	11	2	p330: 6_W + p339: 5_W
36	p416_{47, 1} : 535_W	535	3	p289: 151_W + p298: 149_W + p307: 235_W
37	p417_{47, 2} : 31_W	31	2	p191: 21_W + p218: 10_W
38	p419_{47, 4} : 35_PB	35	4	p175: 4_PB + p184: 14_PB + p193: 15_PB + p202: 2_PB
39	p420_{47, 5} : 39_W	39	2	p293: 17_W + p302: 22_W
40	p421_{47, 6} : 43_W	43	3	p222: 8_W + p231: 12_W + p240: 23_W
41	p422_{47, 7} : 34_W	34	2	p124: 14_W + p133: 20_W
42	p423_{47, 8} : 12_W	12	2	p404: 5_W + p413: 7_W
43	p428_{48, 4} : 12_PB	12	2	p13: 7_PB + p22: 5_PB
44	p429_{48, 5} : 64_W	64	5	p338: 16_W + p347: 12_W + p356: 15_W + p365: 8_W + p374: 13_W
45	p434_{49, 1} : 178_W	178	2	p388: 113_W + p397: 65_W
46	p438_{49, 5} : 21_W	21	2	p248: 7_W + p257: 14_W
47	p445_{50, 3} : 11_W:PB	11	2	p246: 3_W:PB + p255: 8_W:PB
48	p446_{50, 4} : 14_PB	14	2	p58: 6_PB + p67: 8_PB
49	p448_{50, 6} : 16_W	16	2	p267: 6_W + p276: 10_W
50	p449_{50, 7} : 14_W	14	2	p232: 9_W + p241: 5_W
51	p450_{50, 8} : 35_W	35	2	p296: 26_W + p305: 9_W
52	p451_{50, 9} : 24_W	24	2	p369: 11_W + p378: 13_W
53	p456_{51, 5} : 21_W	21	2	p248: 7_W + p257: 14_W
54	p457_{51, 6} : 14_W	14	2	p132: 8_W + p141: 6_W
55	p462_{52, 2} : 51_W	51	4	p317: 17_W + p326: 7_W + p335: 16_W + p344: 11_W
56	p463_{52, 3} : 11_W:PB	11	2	p246: 3_W:PB + p255: 8_W:PB
57	p466_{52, 6} : 21_W	21	2	p168: 9_W + p213: 12_YB
58	p467_{52, 7} : 29_W	29	2	p286: 6_W + p295: 23_W
59	p468_{52, 8} : 15_W	15	2	p278: 2_W + p287: 13_W
60	p474_{53, 5} : 18_W	18	2	p221: 10_W + p230: 8_W
61	p477_{53, 8} : 19_W	19	2	p269: 17_W + p278: 2_W
62	p481_{54, 3} : 11_W:PB	11	2	p246: 3_W:PB + p255: 8_W:PB
63	p484_{54, 6} : 23_W	23	3	p132: 8_W + p141: 6_W + p168: 9_W
64	p485_{54, 7} : 41_W	41	3	p250: 15_W + p259: 20_W + p268: 6_W
65	p486_{54, 8} : 34_W	34	2	p35: 17_W + p44: 17_W
66	p492_{55, 5} : 18_W	18	2	p221: 10_W + p230: 8_W
67	p493_{55, 6} : 11_W	11	2	p330: 6_W + p339: 5_W
68	p496_{55, 9} : 27_W	27	2	p216: 18_W + p225: 9_YB
69	p498_{56, 2} : 15_W	15	2	p471: 13_W + p480: 2_W
70	p499_{56, 3} : 23_W:PB	23	2	p228: 3_W:PB + p237: 20_W:PB
71	p500_{56, 4} : 29_PB	29	2	p184: 14_PB + p193: 15_PB
72	p503_{56, 7} : 14_W	14	2	p232: 9_W + p241: 5_W
73	p504_{56, 8} : 12_W	12	2	p404: 5_W + p413: 7_W
74	p505_{56, 9} : 27_W	27	2	p216: 18_W + p225: 9_YB
75	p511_{57, 6} : 12_W	12	2	p393: 7_W + p402: 5_W
76	p512_{57, 7} : 38_W	38	2	p25: 24_W + p43: 14_W
77	p514_{57, 9} : 34_W	34	2	p288: 13_W + p297: 21_W

Khipu Notes:

Fieldguide Notes:

Author's Notes
This khipu was part of the Maiman collection, a set of khipus gathered from deaccesioning of the Haifa museum as well as other sources. Another khipu in the collection is referenced in Bat-ami Artzi's article The Secret of the Knot: Khipu No. 936 from the Maiman Collection.
The collection is also described in the book Weaving for the Afterlife - Peruvian Textiles from the Maiman Collection Volume 1 - Pages 335-336, by Krzysztof Makowski, Alfredo Rosenzweig, Maria Jesus Jiménez Diaz.

The khipu is mounted on canvas. Backwards! It is in good condition, and the regularity and tightness of the knots indicate a master khipu-kamayoq. It consists almost entirely of 9 pendant cord seriated groups in a W, W, W:PB, PB, W, W, W, W, W order. Numerous sums are evident, as are knot-twists in both S and Z directions.

Primary Cord Notes
The primary cord has numerous blue (or white) wrappings around the cord between cord groups. There are blue (or white) wrappings at:

wrapping from 42.5 - 45
wrapping from 67.5 - 68.9
wrapping (white) from 85.9-86.9
wrapping from 102.5-103.3
wrapping from 127.0 - 128.5

Additionally, there are breaks and mends in the primary cord at:

96.1 cm - Repair
116.0 cm - break/mend in primary cord

Image has been assembled from a series of smaller images. Some alignment errors may occur.

The khipu is described in the book Weaving the Afterlife:
Cat. 281
Big khipu (khipu) of "canutos"
Period: Late Horizon; (1450-1550 CE)
Style: Inca, Inca Imperial Period or Huari-Tiahuanaco
Location: Highlands
Dimensions: 115 x 165 cm.
Inv. 925|
Yarns:
Main Cord: Camelid fiber Z25, blue-greenish, red, brown, yellow; Cotton S2Z and Z25 white (wrapping elements)
Cords: Camelid fiber Z3S black-brownish; Camelid fiber Z25, white, dark purple, yellow, white, red, rose, green; Camelid fiber Z orange; Cotton Z blue (wrapping elements) The main cord is of cross-knit loop stitch on a foundation.

khipu is a device for the registry of information in numerical form. It consists of a primary horizontal cord to which a variable number of vertical cords are attached, and the numbers were introduced by knots. A single knot is up to nine loops to give the value: nine. The absence of knots in the denoted position indicates zero. The units were at the farther or lower end of the string, the higher multiples of tens, hundreds or thousands were placed on the upper part.

Cañuto - translates literally as a part of a cane from knot to knot (definition from the Diccionario de la Real Academia de la Lengua Española). A short tube, not very long nor thick. The canuto on the khipu is a tube formed by wrapping together several cords with colorful yarns, at the beginning of the cords, near the main cord. In this khipu, there are thirty-five canutos or groupings: twenty-seven groupings of four strings, six of three strings and two of two strings. The total number of cords is 130. The maximum length of the knotted strings is 120 cm. and the shortest is 52 cm. The part of the main cord with attached knotted strings is only 25 cm. long. This main cord has extensions on both sides but only up to 40 cm. are preserved. There are three main levels of composite knots, but up to four levels. The coding in three colors of the canuto is repeated in two-three adjoining canutos. In addition, there is coding in two colors at the lower end of each individual string, differing from the canuto. The seriation is four with some exceptions.
This khipu was one of a group of three, found together. There are similar khipus in the Poli Collection and "Banco Central de la Reserva" (two colors).
Arellano (1999) describes this type of khipus "with canutos". See also Radicati di Primegio (1990). Bonavia (1993) classifies a similar khipu as "Huari? 500/600-900 CE". However, we are convinced that Cat. 281 is typical Inca (1450-1530 CE). The much older Huari khipus (600-900 CE) are different in construction or in many other aspects (Conklin, 1990).
With reference to the color wrapping of the cords, Conklin (1990) states that this technique began in Chavin times. The 'wrapping of warps' system was continued in the Middle Horizon: "the study of the Khipus de Canuto show clear evidence that the khipus must have had a long period of development and were not an Inca invention". He notes further, "it is possible that the mathematics of the Inca system developed from the art and ritual of previous times. The decimal system propitiated the use of a plurality of bases. Perhaps the information on the Middle Horizon Khipus had a bigger relation to the rituals than with astronomy."
Recently, Shady (see Mann, 2005) found rudimentary devices resembling khipus (pendant strings twisted around small sticks) at the ancient ceremonial center of Caral (2500-1600 BCE). If this is confirmed, it would be among the oldest textile manifestations in Peru and one of the earliest recording systems in the world. For a list of references on khipus, see our Note # 382.