An intermittent step: more periodicity buzz examples

I wanted to repeat the experiment with a perfect impulse train rather
than the random-amplitude version I posted before, so I did. This
time, the waveform isn't just a "harmonic timbre," but an actual chord
- it's 1:2:3:4:5:6:7:... with sines, all played at equal volume. I am,
as you all know, of the hypothesis that the "buzzing" heard in this
waveform/chord is an advanced, evolved version of the periodicity buzz
heard in 5:6:7. Carl is skeptical, which is a zero-entropy statement.
:) But before I can satisfy Carl's request to hear my experiment
repeated with smaller chords (like 5:6:7), I have to go through this
stage anyway, for signal processing reasons, so it's useful to post
the results here.

This will, in the future, be useful because of magic signal processing
stuff that will make this easy to evaluate for random chords. There
are six waveforms this time:

1) A periodic perfect impulse train
2) A periodic linear chirp (not symmetric)
3) A periodic logarithmic chirp (not symmetric)
4) Three random phase versions - periodic noise

Here's the graph of how everything looks:

http://www.mikebattagliamusic.com/music/sflattestgraph.png

This time, since it was a pain in the ass for all involved to make so
many separate wave files, I combined all of the examples for each
frequency into one wave file. You get 1 second of the impulse train,
then one second of the chirp, then one second of the other chirp, etc.
Here you go:

http://www.mikebattagliamusic.com/music/441sflattestwaves.wav
http://www.mikebattagliamusic.com/music/220.5sflattestwaves.wav
http://www.mikebattagliamusic.com/music/110.25sflattestwaves.wav
http://www.mikebattagliamusic.com/music/55.125sflattestwaves.wav
http://www.mikebattagliamusic.com/music/27.5625sflattestwaves.wav

Note how there is almost no audible difference between the impulse
train and the chirps at 441 Hz, but by the time you get down to
27.5625 there's a HUGE difference.

Anyway, if you understood my explanation of the "impulse train buzz" =
"periodicity buzz" phenomenon, you'll find this interesting. If not,
then hold tight for the next wave of examples, which will be applied
to chords.

-Mike

On Wed, Jan 12, 2011 at 3:03 AM, Mike Battaglia <battaglia01@...> wrote:

One quick correction - I made an error in rendering these that causes
each one to only have harmonics up to 50. For the 441 Hz example, this
is okay, because 50 harmonics brings you to 441 * 50 = 22050, which is
the highest frequency that CD quality audio can represent anyway. So
each one of these is a

1:2:3:4:5:6:...:45:46:47:48:49:50

chord. This is pretty interesting, because I think the effect is
actually more striking than with the version in which the harmonics go
all the way up the range of hearing.

I want to bring special attention to this one:

> http://www.mikebattagliamusic.com/music/55.125sflattestwaves.wav

I find the results are most apparent here. Listen to the impulse train
one, and you'll hear the rapid-fire "clicking" on top that I believe
is related to periodicity buzz. When the chirp rolls around, it's
pretty clear that there's something different going on. But when you
get to the noise, you hear this for what it is - it's somehow noise,
but somehow in such a way that triggers the VF mechanism.

Keep in mind that this chord is 1:2:3:4:5:6:...:45:46:47:48:49:50,
with all sines, and the only thing different between any of these
examples is the starting phase of each sine. Phase can make quite a
difference!

For those who are interested in hearing the "full human range of
hearing" version, in which all harmonics are present for every
waveform right up until we can't hear them anymore, here you go:

http://www.mikebattagliamusic.com/music/441sflattestwavesfull.wav
http://www.mikebattagliamusic.com/music/220.5sflattestwavesfull.wav
http://www.mikebattagliamusic.com/music/110.25sflattestwavesfull.wav
http://www.mikebattagliamusic.com/music/55.125sflattestwavesfull.wav
http://www.mikebattagliamusic.com/music/27.5625sflattestwavesfull.wav

-Mike