Double the "speed", double the frequency?
White noise: sounds exactly the same if you play it back at double the speed
Stack up diminished fifth starting at a low enough fundamental (say 20 Hz). Play back at double speed: sounds exactly the same.
Stack octaves with equal amplitude starting with a low enough fundamental. Play back at twice the speed: sounds exactly the same
Detune the octaves slightly (say multipler of 2.05 starting at 20 Hz). Play back at double the speed: perceived pitch goes DOWN.


You get plenty more when fiddling with the harmonic structure. 
Code example for the last one:

%% make some disharmonic sounds
fs = 44100; % sample rate
q = 2.05; % harmonic multiplier
f0 = 20;  % fundamental
n = 10; % number of harmonics
duration = 2; % length of file at fs
nx = duration*fs;
t = (0:nx-1)'/fs; % time vector
x0 = sin(2*pi*f0*t); % fundamental
f1 = f0;
for i = 2:n  % add harmonics
  f1 = f1*q;
  x0 = x0+sin(2*pi*f1*t);
end

x0 = 0.5.*x0/max(abs(x0)); % normalize
% and play
sound(x0,fs); pause(duration);
sound(x0,2*fs);