First -- definitely up.
Second -- if you ignore very silent (pictured gray) and high frequency (3.5k+) thing -- up too.
Third -- definitely up.
Fourth -- again, if you ignore very silent (pictured gray) and high frequency (3.5k+) thing -- down.
If you don't ignore silent high-frequency components you get "up down up up".
Other options seem completely illegitimate
>Other options seem completely illegitimate
From your point of view.
Well, yes, one can pick any of those frequencies to be the base pitch and you won't be quite wrong
I looked it up on wikipedia
those are shepard tones and they are filtered, the farther away from a certain frequency the quieter the tone
the sinusoidal tones are base frequency times a power of two, f_b*2^n
the higher tones clearly are filtered. you can see traces of them. in the tritone paradox they are shifted by half an octave and if there are enough sinusoidal tones so that the upper and lower ones are filtered out anyway it literally does not matter whether you shift it half an octave up or down because the result will be the same
so its not about whether they are shifted up or down but where they are in relation to the filter. if a tone would get filtered half an octave higher, it will sound like 'down' and if not it would sound like 'up'
for a precise answer you would have to integrate the amplitude over all frequencies
Yes, which is exactly the point. Ambiguity.
no matter how i listen to it i can't hear anything other than up, up, up, down
Alright, I'm back. Here is a spectrogram of the audio, better than 's spectrogram. As you can see, the first tone pair cheats by moving up, but adds another frequency below it (which is quieter). Technically, based on harmonic content, it moves down, but because of the lack of odd harmonics, you cannot make out a base frequency using the missing fundamental phenomenon. Utter BS. If you look just at the frequency content, the pattern is Ambiguous, Down, Up, Up. is correct.
Alternatively, if you just look at the loudest harmonics, you can see that the pattern is Up, Up, Up, Down. Thus, this "paradox" depends on which frequencies the listener hears the strongest, and explains my most anons hear this pattern.
I'm going to make an example that uses the entire human frequency range. Keep posted, anons.
Descend > Descend > Ascend >Ascend
is the point that 3 tones are played at once, then another three tones such that the average tone is the same; and then our brains picks out which ones are "important" and causes us to hear an ascending or descending scale?
okay interesting, thanks
have you read my new post
i see ( ) answers my question in ( ).
I guess "three-tone" is just origin terminology.