Hi,
The overlapping notes makes the result different when you change the
level of the 7.02 note.
I'm not sure if you ask about differences in perception of the
combined timbre (with the overlapping notes), or differences in the
perception of pitch of a single tone with different amplitude.

If we make the score like this:

i1 0 2 0.1 7.00
i1 2 2 0.1 7.02
i1 4 2 0.5 7.02

Then we have no overlapping notes.
Technically, note 2 and 3 are exactly the same pitch now.

It seems to me you might actually perceive the pitch a little bit
differently with different amplitudes. Interesting. I guess it could
come from resonances (in the room or other parts of the signal chain,
or even in the ear).  Playing a single constant sine wave and
adjusting the level of my amplifier have the same effect, so it seems
the phenomenon is related to something happening after the amp then
(speaker, room, ear, or neural response).



2016-12-04 16:23 GMT-08:00 Joe . :
> 
>
> 
>
> 
>
> 
>
> 0dbfs = 1.0
>
> instr 1
>
> out oscil:a(p4, cpspch(p5))
>
> endin
>
> 
>
> 
>
> i1 0 6 0.1 7.00
>
> i1 2 4 0.1 7.02
>
> i1 4 2 0.5 7.02
>
> 
>
> 
>
>
> To me, the 2nd note sounds lower, almost like a minor 2nd, and the 3rd note
> sounds the way I think it should be. Is this just an audio illusion? Have
> there been studies done on this?
>
>
> Also, I hear a high note even though it's supposed to be outputting a sine
> wave. Is this normal?
>
> /* Joe */
> Csound mailing list Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
> https://github.com/csound/csound/issues Discussions of bugs and features can
> be posted here

Yes, I was asking about the different pitch perception when the first two notes overlap. It has nothing to do with amplitude really, it works the same if they all have the same amplitude. I just wanted to make it more evident. The second and last notes sound distinctly different in pitch to me.

mmm, the relative amplitudes of the simultaneously playing notes will
affect the perception of the combined result,
The phases matter too, meaning that the exact (relative) start time of
each component affects the result.
Try this

i1 0 6 0.1 7.00
i1 2 4 0.1 7.02
i1 4.00 2 0.1 7.02


Then this

i1 0 6 0.1 7.00
i1 2 4 0.1 7.02
i1 4.01 2 0.1 7.02


It is no illusion, just constructive and/or destructive interference
between the waves.
A phase change can change the interference from constructive to
destructive (or vice versa), and an amplitude change of one of the
sources changes their relative influence (constructive or
destructive).


2016-12-04 17:33 GMT-08:00 Joe . :
> Yes, I was asking about the different pitch perception when the first two
> notes overlap. It has nothing to do with amplitude really, it works the same
> if they all have the same amplitude. I just wanted to make it more evident.
> The second and last notes sound distinctly different in pitch to me.
>
>
> On Dec 4, 2016 7:17 PM, "Oeyvind Brandtsegg" 
> wrote:
>>
>> Hi,
>> The overlapping notes makes the result different when you change the
>> level of the 7.02 note.
>> I'm not sure if you ask about differences in perception of the
>> combined timbre (with the overlapping notes), or differences in the
>> perception of pitch of a single tone with different amplitude.
>>
>> If we make the score like this:
>> 
>> i1 0 2 0.1 7.00
>> i1 2 2 0.1 7.02
>> i1 4 2 0.5 7.02
>> 
>> Then we have no overlapping notes.
>> Technically, note 2 and 3 are exactly the same pitch now.
>>
>> It seems to me you might actually perceive the pitch a little bit
>> differently with different amplitudes. Interesting. I guess it could
>> come from resonances (in the room or other parts of the signal chain,
>> or even in the ear).  Playing a single constant sine wave and
>> adjusting the level of my amplifier have the same effect, so it seems
>> the phenomenon is related to something happening after the amp then
>> (speaker, room, ear, or neural response).
>>
>>
>>
>> 2016-12-04 16:23 GMT-08:00 Joe . :
>> > 
>> >
>> > 
>> >
>> > 
>> >
>> > 
>> >
>> > 0dbfs = 1.0
>> >
>> > instr 1
>> >
>> > out oscil:a(p4, cpspch(p5))
>> >
>> > endin
>> >
>> > 
>> >
>> > 
>> >
>> > i1 0 6 0.1 7.00
>> >
>> > i1 2 4 0.1 7.02
>> >
>> > i1 4 2 0.5 7.02
>> >
>> > 
>> >
>> > 
>> >
>> >
>> > To me, the 2nd note sounds lower, almost like a minor 2nd, and the 3rd
>> > note
>> > sounds the way I think it should be. Is this just an audio illusion?
>> > Have
>> > there been studies done on this?
>> >
>> >
>> > Also, I hear a high note even though it's supposed to be outputting a
>> > sine
>> > wave. Is this normal?
>> >
>> > /* Joe */
>> > Csound mailing list Csound@listserv.heanet.ie
>> > https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
>> > https://github.com/csound/csound/issues Discussions of bugs and features
>> > can
>> > be posted here
>>
>>
>>
>> --
>>
>> Oeyvind Brandtsegg
>> Professor of Music Technology
>> NTNU
>> 7491 Trondheim
>> Norway
>> Cell: +47 92 203 205
>>
>> http://www.partikkelaudio.com/
>> http://crossadaptive.hf.ntnu.no
>> http://gdsp.hf.ntnu.no/
>> http://soundcloud.com/brandtsegg
>> http://flyndresang.no/
>> http://soundcloud.com/t-emp
>>
>> Csound mailing list
>> Csound@listserv.heanet.ie
>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
>> Send bugs reports to
>>         https://github.com/csound/csound/issues
>> Discussions of bugs and features can be posted here
>
> Csound mailing list Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
> https://github.com/csound/csound/issues Discussions of bugs and features can
> be posted here

My question really pertained to the interval between the first two notes sounding quite different than how a major second normally sounds, and not with the third note. The third note in my original does "sound" like you would expect, so I really don't care about it, just the first two.

Hi,
I hear it as C, C+D, and then C+D (the last two containing the same two notes).
Still the relative balance between the two notes makes the last event
sound very different, since we mostly hear the D (the C being
relatively weak in relation to the D).
Because of this, one can perceive an ascending character through the
three events.
As Justin says, the absence of any harmonics can be a bit
disorienting. The register is also relatively low, which makes
perception of the pitch a bit more fuzzy.
Oeyvind


2016-12-04 19:32 GMT-08:00 Joe . :
> Well it wasn't so much that it sounded like a C# as it sounded more like a
> C+C# than a C+D. And don't you "hear" a movement from the first D to the
> second D?
>
> I just wanted to make sure this was audio phenomenon and not a glitch, and
> also, wondered whether or not this has been studied to any degree.
> /* Joe */
>
> On Sun, Dec 4, 2016 at 9:21 PM, Justin Smith  wrote:
>>
>> Why would the fundamental frequencies of c and d together be pitched d? I
>> don't think they sound like c# either, but I wouldn't expect them to sound
>> like a d.
>>
>> One thing that might be going on here is that many of the cues that let us
>> identify intervals are absent without harmonics, and a proper sine wave
>> doesn't have any.
>>
>> On Sun, Dec 4, 2016 at 7:15 PM Joe .  wrote:
>>>
>>> I've attached a wav of what I hear. Is it what you are hearing?
>>>
>>> My original question: Why does it sound like C-C#-D and not C-D-D?
>>>
>>> /* Joe */
>>>
>>> On Sun, Dec 4, 2016 at 9:08 PM, Oeyvind Brandtsegg 
>>> wrote:
>>>>
>>>> Hence my comments about the difference between the second and the third
>>>> event.
>>>>
>>>> btw.  See if the high note disappear if you use oscili or oscil3 instead
>>>> of oscil.
>>>>
>>>> All best
>>>> Oeyvind
>>>>
>>>> 4. des. 2016 6.44 p.m. skrev "Joe ." :
>>>>>
>>>>> My question really pertained to the interval between the first two
>>>>> notes sounding quite different than how a major second normally sounds, and
>>>>> not with the third note. The third note in my original does "sound" like you
>>>>> would expect, so I really don't care about it, just the first two.
>>>>>
>>>>>
>>>>> On Dec 4, 2016 8:19 PM, "Oeyvind Brandtsegg"
>>>>>  wrote:
>>>>>>
>>>>>> mmm, the relative amplitudes of the simultaneously playing notes will
>>>>>> affect the perception of the combined result,
>>>>>> The phases matter too, meaning that the exact (relative) start time of
>>>>>> each component affects the result.
>>>>>> Try this
>>>>>> 
>>>>>> i1 0 6 0.1 7.00
>>>>>> i1 2 4 0.1 7.02
>>>>>> i1 4.00 2 0.1 7.02
>>>>>> 
>>>>>>
>>>>>> Then this
>>>>>> 
>>>>>> i1 0 6 0.1 7.00
>>>>>> i1 2 4 0.1 7.02
>>>>>> i1 4.01 2 0.1 7.02
>>>>>> 
>>>>>>
>>>>>> It is no illusion, just constructive and/or destructive interference
>>>>>> between the waves.
>>>>>> A phase change can change the interference from constructive to
>>>>>> destructive (or vice versa), and an amplitude change of one of the
>>>>>> sources changes their relative influence (constructive or
>>>>>> destructive).
>>>>>>
>>>>>>
>>>>>> 2016-12-04 17:33 GMT-08:00 Joe . :
>>>>>> > Yes, I was asking about the different pitch perception when the
>>>>>> > first two
>>>>>> > notes overlap. It has nothing to do with amplitude really, it works
>>>>>> > the same
>>>>>> > if they all have the same amplitude. I just wanted to make it more
>>>>>> > evident.
>>>>>> > The second and last notes sound distinctly different in pitch to me.
>>>>>> >
>>>>>> >
>>>>>> > On Dec 4, 2016 7:17 PM, "Oeyvind Brandtsegg"
>>>>>> > 
>>>>>> > wrote:
>>>>>> >>
>>>>>> >> Hi,
>>>>>> >> The overlapping notes makes the result different when you change
>>>>>> >> the
>>>>>> >> level of the 7.02 note.
>>>>>> >> I'm not sure if you ask about differences in perception of the
>>>>>> >> combined timbre (with the overlapping notes), or differences in the
>>>>>> >> perception of pitch of a single tone with different amplitude.
>>>>>> >>
>>>>>> >> If we make the score like this:
>>>>>> >> 
>>>>>> >> i1 0 2 0.1 7.00
>>>>>> >> i1 2 2 0.1 7.02
>>>>>> >> i1 4 2 0.5 7.02
>>>>>> >> 
>>>>>> >> Then we have no overlapping notes.
>>>>>> >> Technically, note 2 and 3 are exactly the same pitch now.
>>>>>> >>
>>>>>> >> It seems to me you might actually perceive the pitch a little bit
>>>>>> >> differently with different amplitudes. Interesting. I guess it
>>>>>> >> could
>>>>>> >> come from resonances (in the room or other parts of the signal
>>>>>> >> chain,
>>>>>> >> or even in the ear).  Playing a single constant sine wave and
>>>>>> >> adjusting the level of my amplifier have the same effect, so it
>>>>>> >> seems
>>>>>> >> the phenomenon is related to something happening after the amp then
>>>>>> >> (speaker, room, ear, or neural response).
>>>>>> >>
>>>>>> >>
>>>>>> >>
>>>>>> >> 2016-12-04 16:23 GMT-08:00 Joe . :
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > 0dbfs = 1.0
>>>>>> >> >
>>>>>> >> > instr 1
>>>>>> >> >
>>>>>> >> > out oscil:a(p4, cpspch(p5))
>>>>>> >> >
>>>>>> >> > endin
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > i1 0 6 0.1 7.00
>>>>>> >> >
>>>>>> >> > i1 2 4 0.1 7.02
>>>>>> >> >
>>>>>> >> > i1 4 2 0.5 7.02
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> > 
>>>>>> >> >
>>>>>> >> >
>>>>>> >> > To me, the 2nd note sounds lower, almost like a minor 2nd, and
>>>>>> >> > the 3rd
>>>>>> >> > note
>>>>>> >> > sounds the way I think it should be. Is this just an audio
>>>>>> >> > illusion?
>>>>>> >> > Have
>>>>>> >> > there been studies done on this?
>>>>>> >> >
>>>>>> >> >
>>>>>> >> > Also, I hear a high note even though it's supposed to be
>>>>>> >> > outputting a
>>>>>> >> > sine
>>>>>> >> > wave. Is this normal?
>>>>>> >> >
>>>>>> >> > /* Joe */
>>>>>> >> > Csound mailing list Csound@listserv.heanet.ie
>>>>>> >> > https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports
>>>>>> >> > to
>>>>>> >> > https://github.com/csound/csound/issues Discussions of bugs and
>>>>>> >> > features
>>>>>> >> > can
>>>>>> >> > be posted here
>>>>>> >>
>>>>>> >>
>>>>>> >>
>>>>>> >> --
>>>>>> >>
>>>>>> >> Oeyvind Brandtsegg
>>>>>> >> Professor of Music Technology
>>>>>> >> NTNU
>>>>>> >> 7491 Trondheim
>>>>>> >> Norway
>>>>>> >> Cell: +47 92 203 205
>>>>>> >>
>>>>>> >> http://www.partikkelaudio.com/
>>>>>> >> http://crossadaptive.hf.ntnu.no
>>>>>> >> http://gdsp.hf.ntnu.no/
>>>>>> >> http://soundcloud.com/brandtsegg
>>>>>> >> http://flyndresang.no/
>>>>>> >> http://soundcloud.com/t-emp
>>>>>> >>
>>>>>> >> Csound mailing list
>>>>>> >> Csound@listserv.heanet.ie
>>>>>> >> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
>>>>>> >> Send bugs reports to
>>>>>> >>         https://github.com/csound/csound/issues
>>>>>> >> Discussions of bugs and features can be posted here
>>>>>> >
>>>>>> > Csound mailing list Csound@listserv.heanet.ie
>>>>>> > https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
>>>>>> > https://github.com/csound/csound/issues Discussions of bugs and
>>>>>> > features can
>>>>>> > be posted here
>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>>
>>>>>> Oeyvind Brandtsegg
>>>>>> Professor of Music Technology
>>>>>> NTNU
>>>>>> 7491 Trondheim
>>>>>> Norway
>>>>>> Cell: +47 92 203 205
>>>>>>
>>>>>> http://www.partikkelaudio.com/
>>>>>> http://crossadaptive.hf.ntnu.no
>>>>>> http://gdsp.hf.ntnu.no/
>>>>>> http://soundcloud.com/brandtsegg
>>>>>> http://flyndresang.no/
>>>>>> http://soundcloud.com/t-emp
>>>>>>
>>>>>> Csound mailing list
>>>>>> Csound@listserv.heanet.ie
>>>>>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
>>>>>> Send bugs reports to
>>>>>>         https://github.com/csound/csound/issues
>>>>>> Discussions of bugs and features can be posted here
>>>>>
>>>>> Csound mailing list Csound@listserv.heanet.ie
>>>>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
>>>>> https://github.com/csound/csound/issues Discussions of bugs and features can
>>>>> be posted here
>>>>
>>>> Csound mailing list Csound@listserv.heanet.ie
>>>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
>>>> https://github.com/csound/csound/issues Discussions of bugs and features can
>>>> be posted here
>>>
>>>
>>> Csound mailing list Csound@listserv.heanet.ie
>>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
>>> https://github.com/csound/csound/issues Discussions of bugs and features can
>>> be posted here
>>
>> Csound mailing list Csound@listserv.heanet.ie
>> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
>> https://github.com/csound/csound/issues Discussions of bugs and features can
>> be posted here
>
>
> Csound mailing list Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
> https://github.com/csound/csound/issues Discussions of bugs and features can
> be posted here

el 2016-12-04 a las 21:32 Joe . escribió:

> Well it wasn't so much that it sounded like a C# as it sounded more like
> a C+C# than a C+D. And don't you "hear" a movement from the first D to
> the second D?

yes, there *is* a movement. no, it is *not* a "glitch", and i would say
that yes, the phenomenon has been pretty much studied.

if you translate to frequency, 7.00 and 7.02 are ca. 130.8 and 146.8 Hz.
the difference is 16Hz, well below the critical bandwidth. when you add two
sine waves of the same amplitude and close frequencies f1 and f2, the
result is a pseudo-sine wave whose frequency is the average of the two
frequencies (f1+f2)/2 and has an amplitude modulation or beating at a
frequency that is the difference between the two original frequencies
abs(f2-f1). the resulting average frequency in your case is ca. 138.8,
which is almost exactly 7.01 (C#). the beating frequency is 16Hz, which is
perceived as a roughness in the sound. now, when you increase the
amplitude of one of the sine waves to be five times greater than the
other, the results will be different, obviously. the amplitude modulation
will be minimal and the frequency of the sine wave with greater amplitude
will predominate. and that's what you hear. the phenomenon has to do both
with what happens when you add sinusoids of close frequencies and the
frequency resolution of the basilar membrane. any book on psychoacoustics
should explain the phenomenon of pitch perception in detail. i would say
that the chapter that rash and plomp contributed to the book "the
psychology of music" edited by diana deutsch is still worth reading after
all these years.

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el 2016-12-05 a las 01:30 luis jure escribió:

> i would say that the chapter that rash and plomp contributed to the book
> "the psychology of music" edited by diana deutsch is still worth reading
> after all these years.

in fact, i should have just copied the relevant paragraphs (in the second
edition of the book, it's chapter 4, page 103):


We consider first the case of two simultaneous simple tones. Several
conditions can be distinguished, depending on frequency difference (Figure
7). If the two primary tones have equal frequencies, they fuse into one
tone, in which the intensity depends on the phase relation between the
two tones. If the tones differ somewhat in frequency, the result is a
signal with periodic amplitude and frequency variations with a rate equal
to the frequency difference. The frequency variations are only slight and
are not considered here. The amplitude variations, however, can be
considerable and result in a fluctuating intensity and perceived loudness.
These loudness fluctuations are called beats, if they can be discerned
individually by the ear, which occurs if their rate is less than about
20 Hz (Terhardt, 1968a, 1968b, 1974b; Zwicker, 1952). A stimulus equal to
the sum of two simple tones with equal amplitudes and frequencies f and g:

p(t) = sin 2pift + sin 2pigt,

can be described as:

p(t) = (2cos 2pi 1/2 [g-f]t) x (sin 2pi 1/2 [f + g]t)

This is a signal with a frequency that is the average of the original
primary frequencies and an amplitude that fluctuates slowly with a beat
frequency of g - f Hz (Figure 8). Amplitude variation is less strong if
the two primary tones have different amplitudes.

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I think it is important to distinguish between what you see and what
you hear here. The reference nicely explains the mathematical
behaviour, and this coincides with what we can *see* if we look at the
waveform. We see a sine wave of frequency (131+147)/2 = 139 Hz
modulated by a 16Hz sine. But we do hear two tones 7.00 and 7.02 (at
least I do, no doubt, after this nice discussion I tested and tested
again, and I am positive). However, if I diminish the difference to
just one semitone, I do hear the intermediate frequency as described.
With a score like this:
i1 0 4 0.1 7.00
i1 2 2 0.1 7.01
i1 4 2 0.1 7.01
... then I hear the described middle note (between C and C# in this
example), so I put a clean C# as event number 3 in the score, to hear
the stepwise motion from C to C# with the middle intermediate step
produced by the mechanism described in the reference. But the original
example of 7.00+7.02 is clearly two pitches to my ears.

2016-12-04 20:42 GMT-08:00 luis jure :
> el 2016-12-05 a las 01:30 luis jure escribió:
>
>> i would say that the chapter that rash and plomp contributed to the book
>> "the psychology of music" edited by diana deutsch is still worth reading
>> after all these years.
>
> in fact, i should have just copied the relevant paragraphs (in the second
> edition of the book, it's chapter 4, page 103):
>
>
> We consider first the case of two simultaneous simple tones. Several
> conditions can be distinguished, depending on frequency difference (Figure
> 7). If the two primary tones have equal frequencies, they fuse into one
> tone, in which the intensity depends on the phase relation between the
> two tones. If the tones differ somewhat in frequency, the result is a
> signal with periodic amplitude and frequency variations with a rate equal
> to the frequency difference. The frequency variations are only slight and
> are not considered here. The amplitude variations, however, can be
> considerable and result in a fluctuating intensity and perceived loudness.
> These loudness fluctuations are called beats, if they can be discerned
> individually by the ear, which occurs if their rate is less than about
> 20 Hz (Terhardt, 1968a, 1968b, 1974b; Zwicker, 1952). A stimulus equal to
> the sum of two simple tones with equal amplitudes and frequencies f and g:
>
> p(t) = sin 2pift + sin 2pigt,
>
> can be described as:
>
> p(t) = (2cos 2pi 1/2 [g-f]t) x (sin 2pi 1/2 [f + g]t)
>
> This is a signal with a frequency that is the average of the original
> primary frequencies and an amplitude that fluctuates slowly with a beat
> frequency of g - f Hz (Figure 8). Amplitude variation is less strong if
> the two primary tones have different amplitudes.
>
> Csound mailing list
> Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
> Send bugs reports to
>         https://github.com/csound/csound/issues
> Discussions of bugs and features can be posted here



-- 

Oeyvind Brandtsegg
Professor of Music Technology
NTNU
7491 Trondheim
Norway
Cell: +47 92 203 205

http://www.partikkelaudio.com/
http://crossadaptive.hf.ntnu.no
http://gdsp.hf.ntnu.no/
http://soundcloud.com/brandtsegg
http://flyndresang.no/
http://soundcloud.com/t-emp

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It is clearly two pitches, and not the usual color of a major second, at all.