Carnelian’s Blood Taint

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]

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]