UR1140/KH0156 - Indexed Pendant Sum

Drawings:

Overview	Detail View
All Khipus' Ascher Sum Relationships	Right-Handed X-Ray
All Indexed Pendant Sum Relationships	Left-Handed X-Ray
This Khipu's Ascher Sum Relationships	Right-Handed Sum Detail
This Khipu's Drawing	Left-Handed Sum Detail

Right Handed Sums: # Sums = 19, Max # Summands = 6, (Min, Mean, Max) Sum Values = (12, 23, 41)
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Left Handed Sums: # Sums = 21, Max # Summands = 5, (Min, Mean, Max) Sum Values = (11, 29, 75)
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Right Handed Sum Detail: - Click on column name to sort

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p11_{2, 2} : 15_B	15	2	p137: 8_B + p146: 7_B
2	p14_{2, 5} : 22_B	22	2	p41: 12_B + p50: 10_B
3	p16_{2, 7} : 17_B	17	2	p160: 13_B + p169: 4_B
4	p22_{3, 4} : 19_B	19	2	p166: 5_B:BB + p175: 14_B:BB
5	p38_{5, 2} : 32_B	32	5	p101: 6_B + p110: 6_B + p119: 4_B + p128: 8_B + p137: 8_B
6	p40_{5, 4} : 23_B	23	2	p157: 18_B:BB + p166: 5_B:BB
7	p52_{6, 7} : 23_B	23	2	p106: 11_B + p115: 12_B
8	p61_{7, 7} : 14_B:BB	14	2	p142: 3_B + p151: 11_B
9	p65_{8, 2} : 18_B	18	3	p110: 6_B + p119: 4_B + p128: 8_B
10	p67_{8, 4} : 36_B	36	2	p103: 16_B:G + p112: 20_B:G
11	p70_{8, 7} : 17_B:BB	17	2	p160: 13_B + p169: 4_B
12	p74_{9, 2} : 41_B	41	6	p110: 6_B + p119: 4_B + p128: 8_B + p137: 8_B + p146: 7_B + p155: 8_B
13	p83_{10, 2} : 23_B	23	3	p128: 8_B + p137: 8_B + p146: 7_B
14	p84_{10, 3} : 28_B	28	2	p147: 11_B:BB + p156: 17_B:BB
15	p95_{11, 5} : 31_B	31	2	p122: 6_B + p131: 25_B
16	p130_{15, 4} : 19_B:BB	19	2	p166: 5_B:BB + p175: 14_B:BB
17	p143_{16, 8} : 27_B	27	2	p170: 16_B + p179: 11_B
18	p153_{17, 9} : 12_B	12	2	p171: 4_B + p180: 8_B
19	p160_{18, 7} : 13_B	13	2	p169: 4_B + p178: 9_B

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

#	Sum Cord	Sum Cord Value	# Summands	Summands
1	p37_{5, 1} : 34_B	34	3	p1: 3_B + p10: 15_B + p19: 16_B
2	p42_{5, 6} : 25_B	25	2	p15: 7_B + p24: 18_B
3	p74_{9, 2} : 41_B	41	3	p2: 13_B + p11: 15_B + p20: 13_B
4	p80_{9, 8} : 11_B	11	2	p53: 9_B + p62: 2_B
5	p82_{10, 1} : 31_B	31	2	p10: 15_B + p19: 16_B
6	p84_{10, 3} : 28_B	28	2	p3: 8_B + p12: 20_B
7	p89_{10, 8} : 22_B	22	5	p35: 2_B + p44: 7_B + p53: 9_B + p62: 2_B + p71: 2_B
8	p95_{11, 5} : 31_B	31	3	p50: 10_B + p59: 11_B + p68: 10_B
9	p100_{12, 1} : 63_B	63	3	p46: 32_B + p55: 9_B + p64: 22_B
10	p114_{13, 6} : 21_B	21	2	p6: 14_B + p15: 7_B
11	p118_{14, 1} : 34_B	34	3	p1: 3_B + p10: 15_B + p19: 16_B
12	p134_{15, 8} : 21_B	21	4	p26: 3_B + p35: 2_B + p44: 7_B + p53: 9_B
13	p136_{16, 1} : 75_B	75	3	p37: 34_B + p46: 32_B + p55: 9_B
14	p143_{16, 8} : 27_B	27	2	p125: 6_B + p134: 21_B
15	p152_{17, 8} : 12_B	12	3	p26: 3_B + p35: 2_B + p44: 7_B
16	p156_{18, 3} : 17_B:BB	17	2	p111: 11_B:G + p120: 6_B:G
17	p158_{18, 5} : 23_B	23	2	p32: 11_B + p41: 12_B
18	p161_{18, 8} : 37_B	37	4	p62: 2_B + p71: 2_B + p80: 11_B + p89: 22_B
19	p168_{19, 6} : 21_B	21	2	p6: 14_B + p15: 7_B
20	p170_{19, 8} : 16_B	16	2	p44: 7_B + p53: 9_B
21	p179_{20, 8} : 11_B	11	2	p53: 9_B + p62: 2_B

Khipu Notes:

Ashok Khosla Notes:
This khipu has been entered with a strange nonconsecutive numbering scheme, indicating either the clusters are off, or the pendants are misnumbered. Investigation into the databook is warranted.

Ascher Databook Notes:

The khipu is attached to a carved wooden bar.
UR1136 and UR1140 were acquired by the Museum in 1904. The provenance is given as Nasca. For a comparison of them, see UR1136.
UR1140 is discussed by Nordenskiold (see Introduction) .A photograph of it appears in Schmidt, Max, 1929, Kunst und Kultur von Peru, Impropyläen-Verlagzu, Berlin.
The way in which the bar is threaded separates the khipu into 2 parts each containing 10 groups of 9 pendants each

Note: The pendant order on the listing proceeds from one end of the bar to the other, goes around the end, and continues on the other side. However, similar color and number patterns are found in both parts if the pendants are read instead from one end of the bar to the other, and then beginning at the original end on the other side of the bar. We will, therefore, refer to the pendants and groups on side 2 as if following the second scenario. Part 1 is pendants 1--->90 and references to the j^th pendant in the i^th group correspond to pendant 9 (i-1) +j. Part 2 is pendants 180--->91 and references to the j^th pendant in the i^th group correspond to pendant 190-9i-j.

By color, each part is separated into 2 subparts of 6 groups and 4 groups respectively. Each group has the same color pattern: 5 B, 2 mixed, 2 B. In the first 6 groups in part 1, the 2 mixed cords are B:BB/B, and in the last 4 groups they are B:BB. In the first 6 groups in part 2, the 2 mixed cords are B:BB, and in the last 4 groups they are B:G.
Subsidiaries are only on the last pendant in each group in part 1. All are BB.
In all groups in both parts:
1. The last pendant in each group has the maximum value.
2. With the exception of group 10 in part 1, the value on pendant 7 is always great than the value on pendant 8.
Within part 1:
1. For the 6 groups of the first subpart, the sum of the values in the 5th position equals the sum of the values in the 4th position. That is:
  
  \[ \sum\limits_{i=1}^{6} P_{i5} = \sum\limits_{i=1}^{6} P_{i6} \]
2. For the 4 groups of the second subpart, the sum of the values in the first position equals the sum of the values in the second position.
  
  \[ \sum\limits_{i=7}^{10} P_{i1} = \sum\limits_{i=7}^{10} P_{i2} \]
3. Excluding the last pendant in each group, the sum of the values in the first group equals the sum of the values in the corresponding group in the second subpart (group 7).
  
  \[ \sum\limits_{j=1}^{8} P_{1j} = \sum\limits_{j=1}^{8} P_{7j} \]