"Multiplicity of Pitch"

So, what *is* "multiplicity of pitch"? Terhardt states at:

http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/defpitch.html

<< Present (preferrably monaurally) to a listener two successive sine tones of which one frequency is fixed, the other variable, and have him adjust the variable frequency such that the two tones match in pitch. Do that with many listeners and repeat the experiment until everybody gets sufficiently bored. You will invariably get a one-peaked narrow distribution of matching frequencies around the fixed frequency. When, on the other hand, you replace the fixed sine tone by a complex tone and do the same experiment with a sufficient number of repetitions and listeners, you will get a multi-peaked distribution. If the complex tone is a harmonic complex tone (such as of a musical instrument) the majoritiy of matches will occur at the complex tone's fundamental frequency. However, additional peaks of the distribution will occur at frequencies that may be both harmonic and subharmonic with respect to the complex tone's fundamental frequency. >>

JG: This looks like an argument for the "virtual fundamental" which notes the non-absolute nature of results supporting it. Terhardt states at:

http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/affinity.html

<< The second aspect of tone affinity is sensory affinity. This term denotes the phenomenon that successive harmonic complex tones, i.e., only harmonic complex tones, are more similar to one another when their oscillation frequencies are in a 1:2 or 2:3 relationship, than when they are not. This kind of similarity, i.e., sensory affinity, emerges from the fact that the pitch of any complex tone is multiple (see topic definition of pitch). As a consequence of the multiplicity of pitch, and of the particular intervals that exist between the simultaneous pitches of any single harmonic complex tone, there occurs commonality of pitches when the oscillation frequencies of two successive harmonic complex tones are in a 1:2 or 2:3 ratio. Commonality means that one of the tones has some pitches in common with the other, and this immediately accounts for an enhanced similarity of the tones as compared to other frequency ratios, i.e., for sensory affinity. >>

So what do *you* think Terhardt means by "multiplicity of pitch"?

Curiously, J Gill

--- In tuning@y..., J Gill <JGill99@i...> wrote:
> So, what *is* "multiplicity of pitch"? Terhardt states at:
>
> http://www.mmk.e-technik.tu-
muenchen.de/persons/ter/top/defpitch.html
>
>
> << Present (preferrably monaurally) to a listener two successive
sine tones
> of which one frequency is fixed, the other variable, and have him
adjust
> the variable frequency such that the two tones match in pitch. Do
that with
> many listeners and repeat the experiment until everybody gets
sufficiently
> bored. You will invariably get a one-peaked narrow distribution of
matching
> frequencies around the fixed frequency.

Well, this seems to contradict his whole "affinity works for sine
waves bit". Sorry, can't defend him if I think he contradicts himself!

> When, on the other hand, you
> replace the fixed sine tone by a complex tone and do the same
experiment
> with a sufficient number of repetitions and listeners, you will get
a
> multi-peaked distribution. If the complex tone is a harmonic
complex tone
> (such as of a musical instrument) the majoritiy of matches will
occur at
> the complex tone's fundamental frequency. However, additional peaks
of the
> distribution will occur at frequencies that may be both harmonic
and
> subharmonic with respect to the complex tone's fundamental
frequency. >>

In the latter case, there is absolutely no "coincidence of partials"
going on.

> JG: This looks like an argument for the "virtual fundamental"

Yes.

> which notes
> the non-absolute nature of results supporting it.

Or at least the contradictory way in which Terhardt seems to present
all this stuff.

> Terhardt states at:
>
> http://www.mmk.e-technik.tu-
muenchen.de/persons/ter/top/affinity.html
>
> << The second aspect of tone affinity is sensory affinity. This
term
> denotes the phenomenon that successive harmonic complex tones,
i.e., only
> harmonic complex tones, are more similar to one another when their
> oscillation frequencies are in a 1:2 or 2:3 relationship, than when
they
> are not. This kind of similarity, i.e., sensory affinity, emerges
from the
> fact that the pitch of any complex tone is multiple (see topic
definition
> of pitch). As a consequence of the multiplicity of pitch, and of
the
> particular intervals that exist between the simultaneous pitches of
any
> single harmonic complex tone, there occurs commonality of pitches
when the
> oscillation frequencies of two successive harmonic complex tones
are in a
> 1:2 or 2:3 ratio. Commonality means that one of the tones has some
pitches
> in common with the other, and this immediately accounts for an
enhanced
> similarity of the tones as compared to other frequency ratios,
i.e., for
> sensory affinity. >>
>
> So what do *you* think Terhardt means by "multiplicity of pitch"?

By "commonality", Terhardt means _not_ coincidences between actual
physically present sine wave components, but rather coincidences
between possible co-existing alternative _pitch interpretations_ of
the sensations present. As Terhardt notes, such pitch interpretations
can often be subharmonics of a fundamental which is accompanied only
by its harmonic overtones -- or even of a sine wave, though he
appears to contradict that here, though not elsewhere.

>
>
> Curiously, J Gill

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., J Gill <JGill99@i...> wrote:

> > So, what *is* "multiplicity of pitch"? Terhardt states at:
> >
> > http://www.mmk.e-technik.tu-
> muenchen.de/persons/ter/top/defpitch.html
> >
> >
> > << Present (preferrably monaurally) to a listener two successive
> sine tones
> > of which one frequency is fixed, the other variable, and have him
> adjust
> > the variable frequency such that the two tones match in pitch. Do
> that with
> > many listeners and repeat the experiment until everybody gets
> sufficiently
> > bored. You will invariably get a one-peaked narrow distribution of
> matching
> > frequencies around the fixed frequency.
>
> Well, this seems to contradict his whole "affinity works for sine
> waves bit". Sorry, can't defend him if I think he contradicts himself!
>
> > When, on the other hand, you
> > replace the fixed sine tone by a complex tone and do the same
> experiment
> > with a sufficient number of repetitions and listeners, you will get
> a
> > multi-peaked distribution. If the complex tone is a harmonic
> complex tone
> > (such as of a musical instrument) the majoritiy of matches will
> occur at
> > the complex tone's fundamental frequency. However, additional peaks
> of the
> > distribution will occur at frequencies that may be both harmonic
> and
> > subharmonic with respect to the complex tone's fundamental
> frequency. >>
>
> In the latter case, there is absolutely no "coincidence of partials"
> going on.

JG: When Terhardt states, "additional peaks of the distribution
will occur at frequencies that may be both harmonic and
subharmonic with respect to the complex tone's fundamental
frequency.", how can you say with assuredness that, "there is"
[absolutely] "no 'coincidence of partials' going on." ???

> > JG: This looks like an argument for the "virtual fundamental"
>
> Yes.
>
> > which notes
> > the non-absolute nature of results supporting it.
>
> Or at least the contradictory way in which Terhardt seems to present
> all this stuff.

JG: How does one then rely upon the outgrowth of such?

> > Terhardt states at:
> >
> > http://www.mmk.e-technik.tu-
> muenchen.de/persons/ter/top/affinity.html
> >
> > << The second aspect of tone affinity is sensory affinity. This
> term
> > denotes the phenomenon that successive harmonic complex tones,
> i.e., only
> > harmonic complex tones, are more similar to one another when their
> > oscillation frequencies are in a 1:2 or 2:3 relationship, than when
> they
> > are not. This kind of similarity, i.e., sensory affinity, emerges
> from the
> > fact that the pitch of any complex tone is multiple (see topic
> definition
> > of pitch). As a consequence of the multiplicity of pitch, and of
> the
> > particular intervals that exist between the simultaneous pitches of
> any
> > single harmonic complex tone, there occurs commonality of pitches
> when the
> > oscillation frequencies of two successive harmonic complex tones
> are in a
> > 1:2 or 2:3 ratio. Commonality means that one of the tones has some
> pitches
> > in common with the other, and this immediately accounts for an
> enhanced
> > similarity of the tones as compared to other frequency ratios,
> i.e., for
> > sensory affinity. >>
> >
> > So what do *you* think Terhardt means by "multiplicity of pitch"?
>
> By "commonality", Terhardt means _not_ coincidences between actual
> physically present sine wave components, but rather coincidences
> between possible co-existing alternative _pitch interpretations_ of
> the sensations present.

JG: Where is that indicated in Terhardt's web documents
(other than directly below in your quote)?

>As Terhardt notes, such pitch interpretations
> can often be subharmonics of a fundamental which is accompanied >only
> by its harmonic overtones -- or even of a sine wave,

http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/defpitch.html

shows:

<< additional peaks of the distribution will occur at frequencies that [[MAY]] be both harmonic and subharmonic with respect to the complex tone's fundamental frequency.>>

He does not state, "can often be subharmonics", and cites
no examples whatsoever of such (interesting and unusual) data ...

> though he
> appears to contradict that here, though not elsewhere.

JG: Where is "elsewhere"?

Curiously, J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., J Gill <JGill99@i...> wrote:
>
> > > So, what *is* "multiplicity of pitch"? Terhardt states at:
> > >
> > > http://www.mmk.e-technik.tu-
> > muenchen.de/persons/ter/top/defpitch.html
> > >
> > >
> > > << Present (preferrably monaurally) to a listener two
successive
> > sine tones
> > > of which one frequency is fixed, the other variable, and have
him
> > adjust
> > > the variable frequency such that the two tones match in pitch.
Do
> > that with
> > > many listeners and repeat the experiment until everybody gets
> > sufficiently
> > > bored. You will invariably get a one-peaked narrow distribution
of
> > matching
> > > frequencies around the fixed frequency.
> >
> > Well, this seems to contradict his whole "affinity works for sine
> > waves bit". Sorry, can't defend him if I think he contradicts
himself!
> >
> > > When, on the other hand, you
> > > replace the fixed sine tone by a complex tone and do the same
> > experiment
> > > with a sufficient number of repetitions and listeners, you will
get
> > a
> > > multi-peaked distribution. If the complex tone is a harmonic
> > complex tone
> > > (such as of a musical instrument) the majoritiy of matches will
> > occur at
> > > the complex tone's fundamental frequency. However, additional
peaks
> > of the
> > > distribution will occur at frequencies that may be both
harmonic
> > and
> > > subharmonic with respect to the complex tone's fundamental
> > frequency. >>
> >
> > In the latter case, there is absolutely no "coincidence of
partials"
> > going on.
>
> JG: When Terhardt states, "additional peaks of the distribution
> will occur at frequencies that may be both harmonic and
> subharmonic with respect to the complex tone's fundamental
> frequency.", how can you say with assuredness that, "there is"
> [absolutely] "no 'coincidence of partials' going on." ???

Because the _other_ tone is still a sine tone.

the "virtual fundamental"
> >
> > Yes.
> >
> > > which notes
> > > the non-absolute nature of results supporting it.
> >
> > Or at least the contradictory way in which Terhardt seems to
present
> > all this stuff.
>
> JG: How does one then rely upon the outgrowth of such?

I've seen plenty of evidence for multiplicity of pitch in all kinds
of circumstances, including that of a sine wave against a band-passed
noise backgrounds. One statement in Terhardt doesn't bother me when
we've seen him stating the opposite in the context closer to our
concern with "octave equivalence".

>
>
> > > Terhardt states at:
> > >
> > > http://www.mmk.e-technik.tu-
> > muenchen.de/persons/ter/top/affinity.html
> > >
> > > << The second aspect of tone affinity is sensory affinity. This
> > term
> > > denotes the phenomenon that successive harmonic complex tones,
> > i.e., only
> > > harmonic complex tones, are more similar to one another when
their
> > > oscillation frequencies are in a 1:2 or 2:3 relationship, than
when
> > they
> > > are not. This kind of similarity, i.e., sensory affinity,
emerges
> > from the
> > > fact that the pitch of any complex tone is multiple (see topic
> > definition
> > > of pitch). As a consequence of the multiplicity of pitch, and
of
> > the
> > > particular intervals that exist between the simultaneous
pitches of
> > any
> > > single harmonic complex tone, there occurs commonality of
pitches
> > when the
> > > oscillation frequencies of two successive harmonic complex
tones
> > are in a
> > > 1:2 or 2:3 ratio. Commonality means that one of the tones has
some
> > pitches
> > > in common with the other, and this immediately accounts for an
> > enhanced
> > > similarity of the tones as compared to other frequency ratios,
> > i.e., for
> > > sensory affinity. >>
> > >
> > > So what do *you* think Terhardt means by "multiplicity of
pitch"?
> >
> > By "commonality", Terhardt means _not_ coincidences between
actual
> > physically present sine wave components, but rather coincidences
> > between possible co-existing alternative _pitch interpretations_
of
> > the sensations present.
>
> JG: Where is that indicated in Terhardt's web documents
> (other than directly below in your quote)?

Have you read them all? You'll find it readily.

>
> >As Terhardt notes, such pitch interpretations
> > can often be subharmonics of a fundamental which is accompanied
>only
> > by its harmonic overtones -- or even of a sine wave,
>
> http://www.mmk.e-technik.tu-
muenchen.de/persons/ter/top/defpitch.html
>
> shows:
>
> << additional peaks of the distribution will occur at frequencies
that [[MAY]] be both harmonic and subharmonic with respect to the
complex tone's fundamental frequency.>>
>
> He does not state, "can often be subharmonics", and cites
> no examples whatsoever of such (interesting and unusual) data ...

The data is not unusual at all once you understand virtual pitch.
Read on. http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html

> > though he
> > appears to contradict that here, though not elsewhere.
>
> JG: Where is "elsewhere"?

Such as his claim , which you quoted, that sine waves do
exhibit "affinity".

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > --- In tuning@y..., J Gill <JGill99@i...> wrote:
> >
> > > > So, what *is* "multiplicity of pitch"? Terhardt states at:
> > > >
> > > > http://www.mmk.e-technik.tu-
> > > muenchen.de/persons/ter/top/defpitch.html
> > > >
> > > >
> > > > << Present (preferrably monaurally) to a listener two
> successive
> > > sine tones
> > > > of which one frequency is fixed, the other variable, and have
> him
> > > adjust
> > > > the variable frequency such that the two tones match in pitch.
> Do
> > > that with
> > > > many listeners and repeat the experiment until everybody gets
> > > sufficiently
> > > > bored. You will invariably get a one-peaked narrow distribution
> of
> > > matching
> > > > frequencies around the fixed frequency.
> > >
> > > Well, this seems to contradict his whole "affinity works for sine
> > > waves bit". Sorry, can't defend him if I think he contradicts
> himself!
> > >
> > > > When, on the other hand, you
> > > > replace the fixed sine tone by a complex tone and do the same
> > > experiment
> > > > with a sufficient number of repetitions and listeners, you will
> get
> > > a
> > > > multi-peaked distribution. If the complex tone is a harmonic
> > > complex tone
> > > > (such as of a musical instrument) the majoritiy of matches will
> > > occur at
> > > > the complex tone's fundamental frequency. However, additional
> peaks
> > > of the
> > > > distribution will occur at frequencies that may be both
> harmonic
> > > and
> > > > subharmonic with respect to the complex tone's fundamental
> > > frequency. >>
> > >
> > > In the latter case, there is absolutely no "coincidence of
> partials"
> > > going on.
> >
> > JG: When Terhardt states, "additional peaks of the distribution
> > will occur at frequencies that may be both harmonic and
> > subharmonic with respect to the complex tone's fundamental
> > frequency.", how can you say with assuredness that, "there is"
> > [absolutely] "no 'coincidence of partials' going on." ???
>
> Because the _other_ tone is still a sine tone.

JG: Yes, I see what you are saying here.
>
> the "virtual fundamental"
> > >
> > > Yes.
> > >
> > > > which notes
> > > > the non-absolute nature of results supporting it.
> > >
> > > Or at least the contradictory way in which Terhardt seems to
> present
> > > all this stuff.
> >
> > JG: How does one then rely upon the outgrowth of such?
>
> I've seen plenty of evidence for multiplicity of pitch in all kinds
> of circumstances, including that of a sine wave against a band-
> passed
> noise backgrounds. One statement in Terhardt doesn't bother me when
> we've seen him stating the opposite in the context closer to our
> concern with "octave equivalence".

JG: So, these anomalies are isolated "noiselets" in a larger
body of thought (other than Terhardt's) which serves to
define the basis of your understanding of a term "multiplicity
pf pitch"? Or are you decribing research "findings" which
could be construed to comport with Terhardt's ideas?
>
> >
> >
> > > > Terhardt states at:
> > > >
> > > > http://www.mmk.e-technik.tu-
> > > muenchen.de/persons/ter/top/affinity.html
> > > >
> > > > << The second aspect of tone affinity is sensory affinity. This
> > > term
> > > > denotes the phenomenon that successive harmonic complex tones,
> > > i.e., only
> > > > harmonic complex tones, are more similar to one another when
> their
> > > > oscillation frequencies are in a 1:2 or 2:3 relationship, than
> when
> > > they
> > > > are not. This kind of similarity, i.e., sensory affinity,
> emerges
> > > from the
> > > > fact that the pitch of any complex tone is multiple (see topic
> > > definition
> > > > of pitch). As a consequence of the multiplicity of pitch, and
> of
> > > the
> > > > particular intervals that exist between the simultaneous
> pitches of
> > > any
> > > > single harmonic complex tone, there occurs commonality of
> pitches
> > > when the
> > > > oscillation frequencies of two successive harmonic complex
> tones
> > > are in a
> > > > 1:2 or 2:3 ratio. Commonality means that one of the tones has
> some
> > > pitches
> > > > in common with the other, and this immediately accounts for an
> > > enhanced
> > > > similarity of the tones as compared to other frequency ratios,
> > > i.e., for
> > > > sensory affinity. >>
> > > >
> > > > So what do *you* think Terhardt means by "multiplicity of
> pitch"?
> > >
> > > By "commonality", Terhardt means _not_ coincidences between
> actual
> > > physically present sine wave components, but rather coincidences
> > > between possible co-existing alternative _pitch interpretations_
> of
> > > the sensations present.
> >
> > JG: Where is that indicated in Terhardt's web documents
> > (other than directly below in your quote)?
>
> Have you read them all? You'll find it readily.

JG: I've read a number of them. How about citing some
examples of where you find these references on his webpages?
>
> >
> > >As Terhardt notes, such pitch interpretations
> > > can often be subharmonics of a fundamental which is accompanied
> >only
> > > by its harmonic overtones -- or even of a sine wave,
> >
> > http://www.mmk.e-technik.tu-
> muenchen.de/persons/ter/top/defpitch.html
> >
> > shows:
> >
> > << additional peaks of the distribution will occur at frequencies
> that [[MAY]] be both harmonic and subharmonic with respect to the
> complex tone's fundamental frequency.>>
> >
> > He does not state, "can often be subharmonics", and cites
> > no examples whatsoever of such (interesting and unusual) data ...
>
> The data is not unusual at all once you understand virtual pitch.
> Read on. http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html

JG: I have, and while it is interesting, I am not inclined
to necessarily view it through that perspective (exclusively).
There may be indications that it sometimes occurs, but there
seem to be plenty of examples where such a proposed concept
*breaks down*. Therefore, I wonder what level of prominence
it can rightly take in considering comprehensive as well as
complicated examples of the spectral diversity of sound ...
In the domain of simple models of complex (fundamental plus
harmonics) tones in combination, it may well carry some weight.

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> > I've seen plenty of evidence for multiplicity of pitch in all
kinds
> > of circumstances, including that of a sine wave against a band-
> > passed
> > noise backgrounds. One statement in Terhardt doesn't bother me
when
> > we've seen him stating the opposite in the context closer to our
> > concern with "octave equivalence".
>
> JG: So, these anomalies are isolated "noiselets" in a larger
> body of thought (other than Terhardt's) which serves to
> define the basis of your understanding of a term "multiplicity
> pf pitch"?

"Noiselets" perhaps, though I suspect the key is some linguistic
distinction Terhardt makes but we are not yet observing.

> Or are you decribing research "findings" which
> could be construed to comport with Terhardt's ideas?

That too. Just look at T's references to articles by others, or start
with another source, like the best textbook, Donald E. Hall's
_Musical Acoustics_, or Juan Roederer's _Introduction to the Physics
and Psychophysics of Music_.

> > > > > Terhardt states at:
> > > > >
> > > > > http://www.mmk.e-technik.tu-
> > > > muenchen.de/persons/ter/top/affinity.html
> > > > >
> > > > > << The second aspect of tone affinity is sensory affinity.
This
> > > > term
> > > > > denotes the phenomenon that successive harmonic complex
tones,
> > > > i.e., only
> > > > > harmonic complex tones, are more similar to one another
when
> > their
> > > > > oscillation frequencies are in a 1:2 or 2:3 relationship,
than
> > when
> > > > they
> > > > > are not. This kind of similarity, i.e., sensory affinity,
> > emerges
> > > > from the
> > > > > fact that the pitch of any complex tone is multiple (see
topic
> > > > definition
> > > > > of pitch). As a consequence of the multiplicity of pitch,
and
> > of
> > > > the
> > > > > particular intervals that exist between the simultaneous
> > pitches of
> > > > any
> > > > > single harmonic complex tone, there occurs commonality of
> > pitches
> > > > when the
> > > > > oscillation frequencies of two successive harmonic complex
> > tones
> > > > are in a
> > > > > 1:2 or 2:3 ratio. Commonality means that one of the tones
has
> > some
> > > > pitches
> > > > > in common with the other, and this immediately accounts for
an
> > > > enhanced
> > > > > similarity of the tones as compared to other frequency
ratios,
> > > > i.e., for
> > > > > sensory affinity. >>
> > > > >
> > > > > So what do *you* think Terhardt means by "multiplicity of
> > pitch"?
> > > >
> > > > By "commonality", Terhardt means _not_ coincidences between
> > actual
> > > > physically present sine wave components, but rather
coincidences
> > > > between possible co-existing alternative _pitch
interpretations_
> > of
> > > > the sensations present.
> > >
> > > JG: Where is that indicated in Terhardt's web documents
> > > (other than directly below in your quote)?
> >
> > Have you read them all? You'll find it readily.
>
> JG: I've read a number of them. How about citing some
> examples of where you find these references on his webpages?

Does the "virtual pitch" page begin to make it clear? He doesn't even
refer to spectral components as "pitches" -- to him, they are
different, separated entities, differing by more than a mere
philosophical distinction between "reality" and "sensation" --
so "multiplicity of pitch" clearly does not refer to a multiplicity
of spectral components.

> > The data is not unusual at all once you understand virtual pitch.
> > Read on. http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html
>
> JG: I have, and while it is interesting, I am not inclined
> to necessarily view it through that perspective (exclusively).
> There may be indications that it sometimes occurs, but there
> seem to be plenty of examples where such a proposed concept
> *breaks down*.

Such as?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
>
> > > I've seen plenty of evidence for multiplicity of pitch in all
> kinds
> > > of circumstances, including that of a sine wave against a band-
> > > passed
> > > noise backgrounds. One statement in Terhardt doesn't bother me
> when
> > > we've seen him stating the opposite in the context closer to our
> > > concern with "octave equivalence".
> >
> > JG: So, these anomalies are isolated "noiselets" in a larger
> > body of thought (other than Terhardt's) which serves to
> > define the basis of your understanding of a term "multiplicity
> > pf pitch"?
>
> "Noiselets" perhaps, though I suspect the key is some linguistic
> distinction Terhardt makes but we are not yet observing.
>
> > Or are you decribing research "findings" which
> > could be construed to comport with Terhardt's ideas?
>
> That too. Just look at T's references to articles by others, or start
> with another source, like the best textbook, Donald E. Hall's
> _Musical Acoustics_, or Juan Roederer's _Introduction to the Physics
> and Psychophysics of Music_.
>
> > > > > > Terhardt states at:
> > > > > >
> > > > > > http://www.mmk.e-technik.tu-
> > > > > muenchen.de/persons/ter/top/affinity.html
> > > > > >
> > > > > > << The second aspect of tone affinity is sensory affinity.
> This
> > > > > term
> > > > > > denotes the phenomenon that successive harmonic complex
> tones,
> > > > > i.e., only
> > > > > > harmonic complex tones, are more similar to one another
> when
> > > their
> > > > > > oscillation frequencies are in a 1:2 or 2:3 relationship,
> than
> > > when
> > > > > they
> > > > > > are not. This kind of similarity, i.e., sensory affinity,
> > > emerges
> > > > > from the
> > > > > > fact that the pitch of any complex tone is multiple (see
> topic
> > > > > definition
> > > > > > of pitch). As a consequence of the multiplicity of pitch,
> and
> > > of
> > > > > the
> > > > > > particular intervals that exist between the simultaneous
> > > pitches of
> > > > > any
> > > > > > single harmonic complex tone, there occurs commonality of
> > > pitches
> > > > > when the
> > > > > > oscillation frequencies of two successive harmonic complex
> > > tones
> > > > > are in a
> > > > > > 1:2 or 2:3 ratio. Commonality means that one of the tones
> has
> > > some
> > > > > pitches
> > > > > > in common with the other, and this immediately accounts for
> an
> > > > > enhanced
> > > > > > similarity of the tones as compared to other frequency
> ratios,
> > > > > i.e., for
> > > > > > sensory affinity. >>
> > > > > >
> > > > > > So what do *you* think Terhardt means by "multiplicity of
> > > pitch"?
> > > > >
> > > > > By "commonality", Terhardt means _not_ coincidences between
> > > actual
> > > > > physically present sine wave components, but rather
> coincidences
> > > > > between possible co-existing alternative _pitch
> interpretations_
> > > of
> > > > > the sensations present.

JG: This gets too "airy" for me. I often wonder how you derive
some of these things out of Terhardt. I guess that it's just
too removed from tangible elements, in favor of conceptual
propositions which seem farther and farther from verifiability.

> > > > JG: Where is that indicated in Terhardt's web documents
> > > > (other than directly below in your quote)?
> > >
> > > Have you read them all? You'll find it readily.
> >
> > JG: I've read a number of them. How about citing some
> > examples of where you find these references on his webpages?
>
> Does the "virtual pitch" page begin to make it clear? He doesn't >even
> refer to spectral components as "pitches" -- to him, they are
> different, separated entities, differing by more than a mere
> philosophical distinction between "reality" and "sensation" --
> so "multiplicity of pitch" clearly does not refer to a multiplicity
> of spectral components.

JG: I dunno. Must be "over my head" ...
>
> > > The data is not unusual at all once you understand virtual pitch.
> > > Read on. http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html
> >
> > JG: I have, and while it is interesting, I am not inclined
> > to necessarily view it through that perspective (exclusively).
> > There may be indications that it sometimes occurs, but there
> > seem to be plenty of examples where such a proposed concept
> > *breaks down*.
>
> Such as?

JG: When conditions are not (conveniently) "harmonic" and
simplified in terms of spectral complexity. These concepts
may not earn the "universality" to which some ascribe them.

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> > > > > > By "commonality", Terhardt means _not_ coincidences
between
> > > > actual
> > > > > > physically present sine wave components, but rather
> > coincidences
> > > > > > between possible co-existing alternative _pitch
> > interpretations_
> > > > of
> > > > > > the sensations present.
>
> JG: This gets too "airy" for me. I often wonder how you derive
> some of these things out of Terhardt.

It's all in there, very clearly.

> I guess that it's just
> too removed from tangible elements, in favor of conceptual
> propositions which seem farther and farther from verifiability.

Not at all. This is very straighforward psychophysics.

> > > > > JG: Where is that indicated in Terhardt's web documents
> > > > > (other than directly below in your quote)?
> > > >
> > > > Have you read them all? You'll find it readily.
> > >
> > > JG: I've read a number of them. How about citing some
> > > examples of where you find these references on his webpages?
> >
> > Does the "virtual pitch" page begin to make it clear? He doesn't
>even
> > refer to spectral components as "pitches" -- to him, they are
> > different, separated entities, differing by more than a mere
> > philosophical distinction between "reality" and "sensation" --
> > so "multiplicity of pitch" clearly does not refer to a
multiplicity
> > of spectral components.
>
> JG: I dunno. Must be "over my head" ...

It shouldn't be. Try reading the stuff again, and try some other
sources too -- Terhardt's language may start to make more sense if
you have a greater familiarity with the psychoacoustic literature.
This ain't no pie in the sky!

> > > > The data is not unusual at all once you understand virtual
pitch.
> > > > Read on.
http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html
> > >
> > > JG: I have, and while it is interesting, I am not inclined
> > > to necessarily view it through that perspective (exclusively).
> > > There may be indications that it sometimes occurs, but there
> > > seem to be plenty of examples where such a proposed concept
> > > *breaks down*.
> >
> > Such as?
>
> JG: When conditions are not (conveniently) "harmonic"

Nothing breaks down there.

> and
> simplified in terms of spectral complexity.

Are you still thinking in terms of a long-term Fourier transform of a
signal? This is clearly not how we hear.

> These concepts
> may not earn the "universality" to which some ascribe them.

???

Jeremy, have you read

http://www.mmk.ei.tum.de/persons/ter/top/specpitch.html

carefully? How about

http://www.mmk.ei.tum.de/persons/ter/top/strikenote.html

?

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> JG: This gets too "airy" for me. I often wonder how you derive
> some of these things out of Terhardt.

Now that I think about it, all this Terhardt stuff was confusing to
me at first too, and I often misintepreted various words and phrases.
However, going over all the material repeatedly, eventually the whole
picture "clicked into place" in an unambiguous way. "Pitch" for
Terhardt does not mean "spectral component". This is very important
for understanding what he's saying.

This article in particular:

http://www.mmk.ei.tum.de/persons/ter/top/strikenote.html

should help you understand what Terhardt means by "multiple pitches".
He does _not_ mean "multiple spectral components", as hopefully will
be clear.

I found a better paragraph on the Terhardt website for explaining
what he meant by "multiplicity of pitch", which both J. Gill and Bob
Wendell misinterpreted as referring to overtones:

from http://www.mmk.ei.tum.de/persons/ter/top/virtualp.html

'For example, when three Fourier components with the frequencies 600,
800, and 1000 Hz are heard, the auditory system is wise enough to
know that "in real life nothing is just what it appears to be". That
is, not only the spectral pitches corresponding to 600, 800, and 1000
Hz are apprehended, but it is supposed that these components are
likely to be harmonics of a complex tone the lower harmonics of which
have been attenuated or even removed by linear distortion of the
sound path. So it is advisable to look out for the fundamental pitch
of that prospective complex tone. This is done by assuming
subharmonic virtual pitches of each of the spectral pitches to be
candidates of the unknown fundamental pitch. In terms of frequency,
those subharmonics are simply obtained by dividing every component
frequency by each of the integer numbers 1, 2, 3, and so on, until
about 12. Then the test of subharmonic match comes into play.
Obviously, in the above example, a first "full match" is obtained at
the fundamental frequency 200 Hz, as this is the 3rd subharmonic of
600 Hz, the fourth subharmonic of 800 Hz, and the fifth subharmonic
of 1000 Hz. By definition, such a match amplifies the relative
prominence which is assigned to any of the virtual-pitch candidates,
such that the above "full match" will yield a well pronounced virtual
pitch at 200 Hz. However, another "full match" is obtained at 100 Hz,
and since this also is an oscillation frequency that frequently
occurs in real life, it is considered as an alternative virtual pitch
that competes in prominence with the former one. This is how both
multiplicity of virtual pitch, and pitch-commonality (see topics tone
affinity, octave equivalence) of harmonic complex tones come about.'