The Tritone Paradox

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.

Like I said, it's contextual. The brain fills in the missing harmonics for some and not for others.

It's analagous to the picture of the cube where the front face looks different to different people and you can switch between them.

i hear down down down up

Image is my setup. Used additive harmonics to generate octaves. I couldn't get a true logarithmic volume/pitch scale, so I made the equalizer approximate it. The second file and spectrogram has no EQ on it, so volume warning.

www.mediafire.com/download/hawfdusu47s1fwd/TritoneFakerdox.mp3

mediafire.com/download/a42ns5pqtfvpj79/TritoneFakerdox_noEQ.mp3

If one were to modify their auditory cortex by deliberate training (e.g: musical instrument), I wonder if that would mutate the sequence they had originally heard.

Or rather, the perception of such.

What you hear is determined by the frequencies you hear the most.

People used to high pitches will hear the first and second go up.

People used to lower pitches will hear the first and second go down.

If you use different speakers, it can sound different too.

Or just run the sound through filters to change it.

So in the case of the OP, would him hearing it as up > down > up > down be considered as overall relatively pitch-neutral?

All ascending, but the last one is ambiguous.

Got different results playing on different speakers at different volumes. I am a violist and have good ear, can usally play what i hear

it catches the attention of one of my dogs completely, he starts to sniff and inclinate his head every time i play it

That's fair. At some point, the average person is unable to discern frequencies too close together so they only hear the loudest. That would be the baseline, I guess.
tonometric.com/adaptivepitch/