Carnelian’s Blood Taint

detail from House Suth family tree
detail from House Suth family tree

quoting from The Masters:

‘Zero, zero . . . three, ah . . . ‘ Vennel was reading out his father’s blood-taint, ‘fifteen, ah . . . nineteen, another fifteen . . . ten . . . two, no, three, now two, a final ten.’
‘Is that what is inscribed on Lord Suth’s ring?’ asked Aurum.
‘Exactly,’ said Jaspar.
Carnelian felt the fingers lift away. He waited, grimacing. Vennel’s hand was there again, to the left of his spine.
‘Zero, zero, zero, two, one . . . three . . . nineteen, ah . . . nine, sixteen, ah . . . seventeen and a final . . . ten.’
The eleven fractions of his mother’s taint.

Thus Suth’s blood-taint is: 0, 0, 3, 15, 19, 15, 10, 3, 2, 10 which can also be written 249/219 [that is, 249 divided by 2 to the power of 19) = 0.0004749 [as a decimal fraction].

Carnelian’s mother’s blood-taint is: 0, 0, 0, 2, 1, 3, 19, 9, 16, 17, 10 which can also be written 27/221 = 0.0000129 [as a decimal fraction]

Carnelian’s blood taint

thus Carnelian’s blood-taint = 0.5*(0.0004749 + 0.0000129) = 0.0002439

or calculating it precisely = (249/219 + 27/221)/2 = 1023/222

which produces a blood-taint in Quyan fractions of: 0, 0, 1, 19, 0, 9, 14, 16, 9, 13, 15 = [0/20 + 0/400 + 1/8000 + 19/160000 etc]