Phase cancellation

Marcel wrote:

> And periodic phase cancelations occur when you add up any sine to any
other sine with
> the single only exception beeing when both sines are in unison (when
they're in unison
> there's no periodic phase cancelation but there can still be phase
cancelation offcourse
> depending on the phases of the sines)

The problem here is that the term "phase cancellation" is very often used in
situations when it's happening at a frequency below our hearing range or
where it's actually static. A proper example of phase cancellation could be
to take a 100Hz sawtooth period at a volume of 100% and subtract a 200Hz
sawtooth period at a volume of 50% froom that. What you get is a 100Hz
square period. And because there's the rule that a sawtooth period, if it's
really clean and sharp, has the second harmonic 2 times softer than the
fundamental frequency, and that the third harmonic is 3 times softer and so
on, then this process simply eliminates every second harmonic, which is
because of phase cancellation. But saying that an ordinary 5/4 contains
phase cancellation seems to me very ... ahum ... courageous, at least.

Petr

Hi Petr,

I agree with what you're saying and I wan't talking about static phase
cancelation.

> But saying that an ordinary 5/4 contains
> phase cancellation seems to me very ... ahum ... courageous, at least.

The for instance 5/4 played by pure sine waves does allways have phase
cancelations.
It has phase shift / cancelations / reversal with the periodicity of the
difference in Hertz of the 2 sines.

This is the phase cancelation I was talking about.
It is the reason you get beating / difference volume tones.

(you may also get static phase cancelation of part of the overtones if the 2
sounds that make 5/4 have harmonic overtones, depending on their phases. but
wasn't talking about that)

Marcel

On Fri, Jan 23, 2009 at 10:37 PM, Petr Pařízek <p.parizek@...> wrote:

> Marcel wrote:
>
> > And periodic phase cancelations occur when you add up any sine to any
> other sine with
> > the single only exception beeing when both sines are in unison (when
> they're in unison
> > there's no periodic phase cancelation but there can still be phase
> cancelation offcourse
> > depending on the phases of the sines)
>
> The problem here is that the term "phase cancellation" is very often used
> in
> situations when it's happening at a frequency below our hearing range or
> where it's actually static. A proper example of phase cancellation could be
> to take a 100Hz sawtooth period at a volume of 100% and subtract a 200Hz
> sawtooth period at a volume of 50% froom that. What you get is a 100Hz
> square period. And because there's the rule that a sawtooth period, if it's
> really clean and sharp, has the second harmonic 2 times softer than the
> fundamental frequency, and that the third harmonic is 3 times softer and so
> on, then this process simply eliminates every second harmonic, which is
> because of phase cancellation. But saying that an ordinary 5/4 contains
> phase cancellation seems to me very ... ahum ... courageous, at least.
>
> Petr
>
>
>
>
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Marcel wrote:

> It has phase shift / cancelations / reversal with the periodicity
> of the difference in Hertz of the 2 sines.

I understand, but I'm really not sure if that was the kind of phase cancellation Carl was talking about because I myself wouldn't call that "phase cancellation". If you mixed two sine waves of 249Hz and 250Hz and played that to me, I would certainly say I could hear phase cancellation because instead of hearing two frequencies of 249Hz and 250Hz, I would rather consider it a 249.5Hz period (i.e. the tone I could hear) which is "amplitude-modulated" with a 0.5Hz period. But if you mixed two sine waves of 200Hz and 250Hz, I would probably not say I can hear any phase cancellation because I would still be waiting for something either slow or "notch-filtered" to come. The thing this that in this case I probably won't hear any 225Hz tone because the fast changes in amplitude make it almost impossible. Instead, I would clearly hear some periodicity of 50Hz.

Petr

> The thing this that in this case I probably won't hear any 225Hz tone
because the fast changes in amplitude make it almost impossible. Instead, I
> would clearly hear some periodicity of 50Hz

Where did you get the 225Hz tone from?
The difference volume tone / beat rate you get from adding a 200Hz tone to a
250Hz tone is 50Hz.
So you right that you'll hear a periodicity / difference volume tone / beat
rate of 50Hz.
The phase cancelations and phase summations repeat at a rate of 50Hz.

Marcel

On Sat, Jan 24, 2009 at 12:52 AM, Petr Pařízek <p.parizek@...> wrote:

> Marcel wrote:
>
> > It has phase shift / cancelations / reversal with the periodicity
> > of the difference in Hertz of the 2 sines.
>
> I understand, but I'm really not sure if that was the kind of phase
> cancellation Carl was talking about because I myself wouldn't call that
> "phase cancellation". If you mixed two sine waves of 249Hz and 250Hz and
> played that to me, I would certainly say I could hear phase cancellation
> because instead of hearing two frequencies of 249Hz and 250Hz, I would
> rather consider it a 249.5Hz period (i.e. the tone I could hear) which is
> "amplitude-modulated" with a 0.5Hz period. But if you mixed two sine waves
> of 200Hz and 250Hz, I would probably not say I can hear any phase
> cancellation because I would still be waiting for something either slow or
> "notch-filtered" to come. The thing this that in this case I probably won't
> hear any 225Hz tone because the fast changes in amplitude make it almost
> impossible. Instead, I would clearly hear some periodicity of 50Hz.
>
> Petr
>
>
>
>
>
>
>

Marcel wrote:

> Where did you get the 225Hz tone from?

Aha, I thought you were following our discussion on amplitude modulation. So, once again. If you mix pure sines (not only periodic sine waves but also sines of static phases/angles), there's the trigonometric identity which sais that "sin(a+b)+sin(a-b) = sin(a)*cos(b)*2". This means: A) that if you mix two sine waves of 249Hz and 250Hz in equal loudnesses, you'll get exactly the same as if you multiply (i.e. "ring-modulate") a 249.5Hz sine and a 0.5Hz cosine; and B) that if you mix two sines of 200Hz and 250Hz in equal loudnesses, you'll get the same as if you multiply a 225Hz sine and a 25Hz cosine. What I was speaking about there was the fact that if I hear two sine waves of 249Hz and 250Hz together, I don't consider it two tones of different frequencies but rather one tone with changing amplitude because the beat rate is very slow. But if I hear two sine waves of 200Hz and 250Hz together, I really do hear two tones sounding together and think about it as such -- the different situation there is simply the fact that the beat rate (50Hz) is so fast that it makes it virtually impossible to hear the sound as one tone changing in amplitude.

Petr

Aah ok, yes I agree with the amplitude modulation giving thesame result.
But I'm not sure if hearing 2 different tones is purely because of beat
rate.
Lets say the ear will start to hear 2 different frequencies in roughly the
range of 15Hz beat rate.
That would mean that when you play a 35Hz sine and a 50Hz sine you would
start to hear them as different sounds.
And that when you play a 1000Hz sound and a 1015Hz sound you will start
seeing them as different sounds etc, same for 400 + 415Hz.
Is this indeed the pitch resolution curve of the ear when you play pure
sines?

btw the wikipedia page on pitch sais the following:
"A complex tone composed of two sine waves of 1000 and 1200 Hz will have
three pitches. Two spectral pitches at 1000 and 1200 Hz, derived from the
physical frequencies of the pure tones; and one "virtual pitch" at 200 Hz,
derived from the repetition rate of the waveform. "

Marcel

On Sat, Jan 24, 2009 at 10:51 AM, Petr Pařízek <p.parizek@chello.cz> wrote:

> Marcel wrote:
>
> > Where did you get the 225Hz tone from?
>
> Aha, I thought you were following our discussion on amplitude modulation.
> So, once again. If you mix pure sines (not only periodic sine waves but also
> sines of static phases/angles), there's the trigonometric identity which
> sais that "sin(a+b)+sin(a-b) = sin(a)*cos(b)*2". This means: A) that if you
> mix two sine waves of 249Hz and 250Hz in equal loudnesses, you'll get
> exactly the same as if you multiply (i.e. "ring-modulate") a 249.5Hz sine
> and a 0.5Hz cosine; and B) that if you mix two sines of 200Hz and 250Hz in
> equal loudnesses, you'll get the same as if you multiply a 225Hz sine and a
> 25Hz cosine. What I was speaking about there was the fact that if I hear two
> sine waves of 249Hz and 250Hz together, I don't consider it two tones of
> different frequencies but rather one tone with changing amplitude because
> the beat rate is very slow. But if I hear two sine waves of 200Hz and 250Hz
> together, I really do hear two tones sounding together and think about it as
> such -- the different situation there is simply the fact that the beat rate
> (50Hz) is so fast that it makes it virtually impossible to hear the sound as
> one tone changing in amplitude.
>
> Petr
>
>
>
>
>
>
>

Marcel wrote:

> But I'm not sure if hearing 2 different tones is purely because of beat rate.

I don't think so. When I hear 70Hz and 90Hz together, I consider it to be two different tones; and when I hear 15000Hz and 15020Hz, I consider it to be one tone changing in amplitude.

Petr

Ok then we seem to agree again on that atleast :)
What I'm meaning is that audio rate beating seems audible to me and that
this is unrelated to the distinction of 2 pitches.
What I ment before was not that we percieve beating only when we hear 2
pitches as one pitch.

But you say now that in the case of 70Hz and 90Hz together you're not
hearing the 20Hz beating / periodicity of the wave?

Marcel

On Sat, Jan 24, 2009 at 8:16 PM, Petr Pařízek <p.parizek@...> wrote:

> Marcel wrote:
>
> > But I'm not sure if hearing 2 different tones is purely because of beat
> rate.
>
> I don't think so. When I hear 70Hz and 90Hz together, I consider it to be
> two different tones; and when I hear 15000Hz and 15020Hz, I consider it to
> be one tone changing in amplitude.
>
> Petr
>
>
>
>
>
>
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> But I'm not sure if hearing 2 different tones is purely
> because of beat rate.

As well you shouldn't be, since it's not true! :)
It's not because of beat rates at all.

> Lets say the ear will start to hear 2 different frequencies
> in roughly the range of 15Hz beat rate.
> That would mean that when you play a 35Hz sine and a 50Hz
> sine you would start to hear them as different sounds.

The sounds become separate when their regions of excitation
become far enough apart on the basilar membrane. This
occurs at about 1/2CB (critical band). The critical band
is log-wider in the bass than it is in the treble. When
its center frequency is above 500Hz, it's about the width
of a whole tone. Below 500Hz, its width is fixed at about
100Hz. 35Hz and 50Hz both fall in the 100Hz-wide CB
centered on 43Hz, and in fact they are only 15Hz apart,
which is much less than 1/2CB. So one will hear a single
beating tone at 43Hz in this case.

> And that when you play a 1000Hz sound and a 1015Hz sound
> you will start seeing them as different sounds etc,

Not yet. The CB centered at 1008 Hz is about 126Hz wide.
Separate tones should start to emerge in the case of
1000Hz and 1063Hz. But these figures are approximate,
and will depend on the volume of the stimuli as well as
other factors.

-Carl

Ok thank you, very interesting.I don't know enough about this area.

Is it then so that this holds for pure sine waves, and that for overtone
rich sounds you start hearing different pitches for tones much closer
together because their overtones are seperated more in hertz?

And that this all has a different working mechanism than for single sines
played shortly one after the other with small pitch differences? (so no
harmony)
I've read that for single sounds the human hearing has a sensitivity of
about 1 cent.

Marcel

On Sun, Jan 25, 2009 at 1:11 AM, Carl Lumma <carl@...> wrote:

> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Marcel de
> Velde <m.develde@...> wrote:
>
> > But I'm not sure if hearing 2 different tones is purely
> > because of beat rate.
>
> As well you shouldn't be, since it's not true! :)
> It's not because of beat rates at all.
>
> > Lets say the ear will start to hear 2 different frequencies
> > in roughly the range of 15Hz beat rate.
> > That would mean that when you play a 35Hz sine and a 50Hz
> > sine you would start to hear them as different sounds.
>
> The sounds become separate when their regions of excitation
> become far enough apart on the basilar membrane. This
> occurs at about 1/2CB (critical band). The critical band
> is log-wider in the bass than it is in the treble. When
> its center frequency is above 500Hz, it's about the width
> of a whole tone. Below 500Hz, its width is fixed at about
> 100Hz. 35Hz and 50Hz both fall in the 100Hz-wide CB
> centered on 43Hz, and in fact they are only 15Hz apart,
> which is much less than 1/2CB. So one will hear a single
> beating tone at 43Hz in this case.
>
> > And that when you play a 1000Hz sound and a 1015Hz sound
> > you will start seeing them as different sounds etc,
>
> Not yet. The CB centered at 1008 Hz is about 126Hz wide.
> Separate tones should start to emerge in the case of
> 1000Hz and 1063Hz. But these figures are approximate,
> and will depend on the volume of the stimuli as well as
> other factors.
>
> -Carl
>
>
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Ok thank you, very interesting.I don't know enough about this
> area.
>
> Is it then so that this holds for pure sine waves, and that for
> overtone rich sounds you start hearing different pitches for
> tones much closer together because their overtones are seperated
> more in hertz?

I'm not sure how that'd work.

> And that this all has a different working mechanism than for
> single sines played shortly one after the other with small
> pitch differences? (so no harmony) I've read that for single
> sounds the human hearing has a sensitivity of about 1 cent.

The "melodic JND" is usually given between 3-6 cents,
depending how it's measured. But yes.

-Carl