Hello CaptainBlack,
thank you for your answer. However, this is exactly where I have problems. I already expanded my formula an tried to get the Epsilons out. But all the resulting squares make it hard to find a result. I put this whole thing into MATLAB:
Code:
clear;clc;
% a : The true values for the frats
% ar: (1) The true values for the ratios (2) tratios distorted by +0.5 (3)
% the ratios distorted by -0.5 (4/5) crossed ratios (6/7) alternating
% ratios
% ar_maxmin : the extreme values of the ratios
% avg : the average of the ratios with respect to the calculation done for
% ar
% rerror : the deviation of the ratios to the 12th squareroot of 2
a = zeros(3,13);
for i = 1:13
a(1,i) = 600*(2^(-1/12))^(i-1);
a(2,i) = a(1,i) + 0.5;
a(3,i) = a(1,i) - 0.5;
end
ar = zeros(6,12);
for i = 1:12
ar(1,i) = a(2,i)/a(2,i+1);
ar(2,i) = a(3,i)/a(3,i+1);
ar(3,i) = a(2,i)/a(3,i+1);
ar(4,i) = a(3,i)/a(2,i+1);
ar(5,i) = a(2 + mod(i,2),i)/a(2 + mod(i+1,2),i+1);
ar(6,i) = a(2 + mod(i+1,2),i)/a(2 + mod(i,2),i+1);
end
ar_maxmin = [max(ar,[],2) min(ar,[],2) max(ar,[],2)-min(ar,[],2)];
avg = mean(ar,2)
rerror = abs([2^(1/12); 2^(1/12); 2^(1/12); 2^(1/12); 2^(1/12); 2^(1/12)] - avg);
clear i;
what gives me approximatly the same results that i need. However, I see no way of solving that by pure theory. I also tried to approximate the result by getting rid of some of the terms and deriving a higher number to find an upper bound of the error but I solved that the error would not be higher then 6000 mm (surprise...!) what does not really lead me anywhere. Could you therefore be a little more spesific? Im not lazy, promised, I just cannot see what you mean. Thank you!