And now for something new: fundamental tracker screws up for tones 3 units apart?

For reference, all files in this post can be found at
/tuning/files/MikeBattaglia/diff3test.zip.

Petr posted this question somewhere in the old GCD thread: what do you hear
when you listen to a complex tone with a harmonic content of 2:5:8:11:14:...
that is, a tone which starts on 2 and increases by units of 3 recursively?
Check the results out for yourself in 2-5-8 test.wav.

First is a 440 Hz sine played for reference. Next we have 2:5:8:11:14:etc
with the partials at unity gain. And after that we have 2:5:8:11:14 with the
partials at a 1/N rolloff, similar to a sawtooth or a square wave.

You should right away notice that the perceived fundamental of the latter
two examples is NOT 440 Hz. Rather, you hear it as the 880 Hz "2" tone, even
in the case where the partials are all at unity gain. I'm pretty surprised
by this, as you don't even hear a hint of the 440 Hz tone in the second two.
This is strange enough, but the next example is even stranger: Check out the
5-8-11 tone and notice that 880 Hz is still what jumps out at you.

Also check out the 4-7-10 test: I hear it as an sort of ambiguous "1-2"
mixture that flip flops between the two of them.

Attached for each test is a set of pictures showing the first six partials
of each test and two periods, with a 440 Hz impulse train overlaid, so you
can confirm for yourself that the period is 1/440 second.

It might be that this phenomenon is somewhat frequency-dependent: when I
tried the test again at 220 Hz, I could hear a faint 220 Hz tone on the
bottom. Either way though, the 2-5-8-11 example jumped right out at me as
being a "2", and it wasn't unless I really listened hard that I could hear a
faint "1" somewhere down there. This never seems to happen for tones that
are 2 units apart, like 3:5:7:9:etc, where the 1 jumps out at you bright and
clear. It was also much easier to hear the actual "1" for the examples in
which the harmonics were at unity gain.

This might imply that the process by which a virtual fundamental is placed
and the process by which the tones are "grouped" or "fused" together into a
timbre are two separate things. It might also be related to the process by
which a minor chord is heard as having a root different from the "1" of
10:12:15. Hence, a faint virtual pitch on the bottom is produced, but you
then gravitate toward hearing the much louder "2" as the fundamental. The
tendency we have towards confusing octaves might aid in this somewhat.

Thoughts?

-Mike

It seems that the zip file format I used was giving some of you a hard time
with the WAV files, so I used the older zip 2.0 format instead.

-Mike

On Wed, Aug 19, 2009 at 1:27 PM, Mike Battaglia <battaglia01@...>wrote:

> For reference, all files in this post can be found at
> /tuning/files/MikeBattaglia/diff3test.zip.
>
> Petr posted this question somewhere in the old GCD thread: what do you hear
> when you listen to a complex tone with a harmonic content of 2:5:8:11:14:...
> that is, a tone which starts on 2 and increases by units of 3 recursively?
> Check the results out for yourself in 2-5-8 test.wav.
>
> First is a 440 Hz sine played for reference. Next we have 2:5:8:11:14:etc
> with the partials at unity gain. And after that we have 2:5:8:11:14 with the
> partials at a 1/N rolloff, similar to a sawtooth or a square wave.
>
> You should right away notice that the perceived fundamental of the latter
> two examples is NOT 440 Hz. Rather, you hear it as the 880 Hz "2" tone, even
> in the case where the partials are all at unity gain. I'm pretty surprised
> by this, as you don't even hear a hint of the 440 Hz tone in the second two.
> This is strange enough, but the next example is even stranger: Check out the
> 5-8-11 tone and notice that 880 Hz is still what jumps out at you.
>
> Also check out the 4-7-10 test: I hear it as an sort of ambiguous "1-2"
> mixture that flip flops between the two of them.
>
> Attached for each test is a set of pictures showing the first six partials
> of each test and two periods, with a 440 Hz impulse train overlaid, so you
> can confirm for yourself that the period is 1/440 second.
>
> It might be that this phenomenon is somewhat frequency-dependent: when I
> tried the test again at 220 Hz, I could hear a faint 220 Hz tone on the
> bottom. Either way though, the 2-5-8-11 example jumped right out at me as
> being a "2", and it wasn't unless I really listened hard that I could hear a
> faint "1" somewhere down there. This never seems to happen for tones that
> are 2 units apart, like 3:5:7:9:etc, where the 1 jumps out at you bright and
> clear. It was also much easier to hear the actual "1" for the examples in
> which the harmonics were at unity gain.
>
> This might imply that the process by which a virtual fundamental is placed
> and the process by which the tones are "grouped" or "fused" together into a
> timbre are two separate things. It might also be related to the process by
> which a minor chord is heard as having a root different from the "1" of
> 10:12:15. Hence, a faint virtual pitch on the bottom is produced, but you
> then gravitate toward hearing the much louder "2" as the fundamental. The
> tendency we have towards confusing octaves might aid in this somewhat.
>
> Thoughts?
>
> -Mike