source of octave's dominance?

Someone ran this explanation by me. Is it true?:

The coil in the inner ear (cochlea?) is covered with the cilia, each of
which is tuned to a eensy bandwidth of pitch.

Now, there are these long straight nerves running along the coil which
intersect it, and each of those nerves corresponds roughly to a
"pitch-class" (though of course far more finely divided than 12-eq),
intersecting the coil first at one octave of a pitch-class, then the next,
then the next, etc., thus explaining why/how we hear octave equivalence
(and not tritave equivalence).

If the "coil" had a wider "diameter", then the interval of equivalence
would be larger than an octave.

>The coil in the inner ear (cochlea?) is covered with the cilia,
>each of which is tuned to a eensy bandwidth of pitch.

Not each hair cell is tuned, but rather regions on the basilar
membrane (the thing to which the hair cells are attached inside
the cochlea), each containing several hair cells, are so tuned.

>Now, there are these long straight nerves running along the coil
>which intersect it, and each of those nerves corresponds roughly to
>a "pitch-class" (though of course far more finely divided than
>12-eq),

That's the so-called "place theory", which is at best only part of the
picture.

>intersecting the coil first at one octave of a pitch-class, then the
>next, then the next, etc., thus explaining why/how we hear octave
>equivalence (and not tritave equivalence).
>
>If the "coil" had a wider "diameter", then the interval of
>equivalence would be larger than an octave.

This one's new on me. The structure may be that way (I don't know),
but it is not the primary cause of octave equivalence (which occurs
higher up in the brain).

In general, though the ear does a lot of the work of hearing, the
brain does even more. The same is true of the eye/brain and vision.

-Carl

--- In tuning@yahoogroups.com, Chris Bailey <chris@m...> wrote:
>
> Someone ran this explanation by me. Is it true?:
>
> The coil in the inner ear (cochlea?) is covered with the cilia,
each of
> which is tuned to a eensy bandwidth of pitch.

Well, this 'critical bandwidth' is actually about a major second in
the highest registers, becoming somewhat wider in the lower
registers. But it is true that the *centers* of these bandwidths, at
which each of the cochlear receptors are most sensitive, are gradated
far more finely than 12-equal.

> Now, there are these long straight nerves running along the coil
which
> intersect it, and each of those nerves corresponds roughly to a
> "pitch-class" (though of course far more finely divided than 12-
eq),
> intersecting the coil first at one octave of a pitch-class, then
the next,
> then the next, etc., thus explaining why/how we hear octave
equivalence
> (and not tritave equivalence).
>
> If the "coil" had a wider "diameter", then the interval of
equivalence
> would be larger than an octave.

Unfortunately for this explanation, it looks like the cochlea only
winds around three or four times, while we are born with almost ten
octaves of hearing range.

hi Chris and Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > The coil in the inner ear (cochlea?) is covered with
> > the cilia, each of which is tuned to a eensy bandwidth
> > of pitch.
>
> Not each hair cell is tuned, but rather regions on the basilar
> membrane (the thing to which the hair cells are attached inside
> the cochlea), each containing several hair cells, are so tuned.

and as paul pointed out, the total spectrum of bandwidths
is known as the "critical band".

> > Now, there are these long straight nerves running along
> > the coil which intersect it, and each of those nerves
> > corresponds roughly to a "pitch-class" (though of course
> > far more finely divided than 12-eq),
>
> That's the so-called "place theory", which is at best only
> part of the picture.

the other part is the "time theory", which is what i
elaborate on a bit more below ...

> > intersecting the coil first at one octave of a
> > pitch-class, then the next, then the next, etc.,
> > thus explaining why/how we hear octave equivalence
> > (and not tritave equivalence).
> >
> > If the "coil" had a wider "diameter", then the
> > interval of equivalence would be larger than an octave.
>
> This one's new on me. The structure may be that way
> (I don't know), but it is not the primary cause of octave
> equivalence (which occurs higher up in the brain).
>
> In general, though the ear does a lot of the work of
> hearing, the brain does even more. The same is true of
> the eye/brain and vision.

my own theory is that each prime-factor has its own
unique affinity with 1, and thus its own unique "affect".

since 2 is the first prime and the most closely related
to 1, its powers will all retain a very close affinity
with 1 and thus sound very much like it. the "affect"
of 2 is simply the phenomenon known as "8ve-equivalence".

-monz

In a message dated 2004:01:04 12:11:34 AM, ekin@lumma.org quotes & writes:

>>If the "coil" had a wider "diameter", then the interval of
>>equivalence would be larger than an octave.
>
>This one's new on me.

Likewise. A lot of non-octave musics out there in the world have
everything from "compressed" and "stretched" octaves to far out intervals with nuthin'
remotely close to an octave... and still sounds "good" (or fun ;) ... even
those weird-ass Guadacanal (sp?) minor2nd "stack" and "array" scales, which are
supposedly dissonant by old, "trad" Middle Path (Euro-species) theories... so,
go figger...
and the oodles of differin' Australian Aborigine digeridoo scales/modes,
though more minimalistic and dronal than LaMonte Young, practically defy
conventional analysis - "Eastern" or "Western"... (if I could wrap my head around just
a few of these, I'd be oh so frikkin' happy and hyper... just one alone would
make me quite satisfied... er, for awhile at least...)

> The structure may be that way (I don't know),
>but it is not the primary cause of octave equivalence (which occurs
>higher up in the brain).

::recallin' some Brian McLaren articles John Chalmers referred me to::
Hmm, mayhaps it _is_ more a brainie-matter of socio-biological and
socio-cultural/-political/-etc. nature/nurture deal...than simple biophys and
generalized bioacoustics...

>In general, though the ear does a lot of the work of hearing, the
>brain does even more. The same is true of the eye/brain and vision.

If the human brain was any simpler than it is, it would be way too far
complex for us to even ponder pondering it ;) intriguin' paradox that...
And I won't even dare get too too far and deep into panentheistic* ideas
of the Ever-Evolving Mind of the Cosmos...

* not to be totally confused with _pantheism_ (i.e., the certain Hindu
concepts of the Atman Nature of Brahma).
In a very tight nutshell, _Panentheism_ = everything in "God", "God" in
everything and "God" being the sum of it all and transcending all, the entire
cosmic process is "God" & "God" works like an improvising multimedia artist
attempting to win order and beauty out of opportunity. The entire process moving
along undetermined lines, "God" is thus also "the Great Companion - the
Fellow-Sufferer Who Understands, our Greatest Ally in the Cosmic Chaos Process"...

-|-|--|---|-----|--------|-------------|---------------------|
Hanuman Zhang, heeding the Call(ing) to Divine Chaos & Creation

_NADA BRAHMA_ < Sanskrit > "sound = Godhead"

"You breathe redemption, motive, power, You're elemental, super-collider

yeah tenn0!, You are air and earth, fire and ocean, You are Word, You are

tenn0 tenn0!" --- mortal - "tenn0"

_LILA_ < Sanskrit >
1. the universe is what happens when God wants to play -
Divine Play - the play of the Divine in its Cosmic Dance, whimsy - like a
child playing alone God the Cosmic Dancer - whose routine is all creatures and
all worlds - the Cosmos flows - a world from the tireless unending resistless
stream of God's energy that _is_ Lila
2. joyous exercise of spontaneity involved in the art of creation this is
Lila

>Do I contradict myself?
>Very well then, I contradict myself.
>I am large, I contain multitudes.
> --Walt Whitman, _Leaves of Grass_

"...divine chaos ...rumors of chaos have been known to enhance the mature
religious vision.... for the godhead manifests no more of its reality than
the limited grammar of each person's imagination and conceptual system can
handle. A second advantage is suggested by William James in _Varieties of Religious
Experience_. James affirms the possibilty of many gods, mostly because he
takes seriously his multiverse theory of personal monads, each one of us
experiencing a unique religious revelation. An orderly monistic and monotheistic
system, he fears, might succumb to a craving for logical coherence, and trim away
some of the mystery, rich indeterminancy, and tragic ambiguity in a complete
numinous experience. For some temperaments, the ambivalent gentleness and
savagery of fate can be imagined effectively in a godhead split into personified
attributes, sometimes at war, sometimes in shifting alliance." - Vernon Ruland,
_Eight Sacred Horizons: The Religious Imagination East and West_

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Chris and Carl,
>
>
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...>
wrote:
>
> > > The coil in the inner ear (cochlea?) is covered with
> > > the cilia, each of which is tuned to a eensy bandwidth
> > > of pitch.
> >
> > Not each hair cell is tuned, but rather regions on the basilar
> > membrane (the thing to which the hair cells are attached
inside
> > the cochlea), each containing several hair cells, are so
tuned.
>
>
> and as paul pointed out, the total spectrum of bandwidths
> is known as the "critical band".
>
>
> > > Now, there are these long straight nerves running along
> > > the coil which intersect it, and each of those nerves
> > > corresponds roughly to a "pitch-class" (though of course
> > > far more finely divided than 12-eq),
> >
> > That's the so-called "place theory", which is at best only
> > part of the picture.
>
>
>
> the other part is the "time theory", which is what i
> elaborate on a bit more below ...
>
>
>
> > > intersecting the coil first at one octave of a
> > > pitch-class, then the next, then the next, etc.,
> > > thus explaining why/how we hear octave equivalence
> > > (and not tritave equivalence).
> > >
> > > If the "coil" had a wider "diameter", then the
> > > interval of equivalence would be larger than an octave.
> >
> > This one's new on me. The structure may be that way
> > (I don't know), but it is not the primary cause of octave
> > equivalence (which occurs higher up in the brain).
> >
> > In general, though the ear does a lot of the work of
> > hearing, the brain does even more. The same is true of
> > the eye/brain and vision.
>
>
>
> my own theory is that each prime-factor has its own
> unique affinity with 1, and thus its own unique "affect".
>
> since 2 is the first prime and the most closely related
> to 1, its powers will all retain a very close affinity
> with 1 and thus sound very much like it. the "affect"
> of 2 is simply the phenomenon known as "8ve-equivalence".
>
>
>
> -monz

What's wrong with Helmholtz's explanation of the octave being
that all of the harmonics of a note are included in the octave
down and no new partials are included in the octave higher?
This of course implies that octaves and twelfths behave
similarly, but this can be explained by the octave being a much
stronger harmonic in most timbres and by the larger frequency
jump. Also, to my ear twelfths do actually have *almost* the
same effect as octaves when considered in isolated
comparisons.

To elaborate further, having first identified the octave as either
introducing nothing new (higher) or including all (lower) of the
same harmonics (obviously give a little room for timbre issues),
then there is another difference between twelfth and octave.
Going from the first not tor a higher twelfth we can then lower an
octave which includes all the harmonics of the note of the twelfth,
yet does NOT contain all the harmonics of the original note,
therefore the relation of the twelfth to the fifth is stronger, but in
another sense somewhat equal, to the relationship of twelfth to
the original note. But the octave is clearly related primarily to the
original note. Hence when moving by octaves alone no real
change in the form of the harmonic spectrum will occur, but once
twelfths are introduced, they harmonically include already the
relationship of octaves and then are less clearly related and
farther in frequency distance.

Sorry I know this was not worded or explained as clearly as
should be. This is the gist of my impression of Helmholtz. What
is wrong with this as a complete explanation of the significance
of the octave?

-Aaron Wolf

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> What's wrong with Helmholtz's explanation of the octave being
> that all of the harmonics of a note are included in the octave
> down and no new partials are included in the octave higher?
> This of course implies that octaves and twelfths behave
> similarly, but this can be explained by the octave being a much
> stronger harmonic in most timbres and by the larger frequency
> jump.

So what you're left with here is not much of an _explanation_ at all -
- rather a "moral" justification, and a pretty weak one at that. For
example, how would you explain that, after a certain amount of
stretching of the partials, one fails to hear equivalence at the 2nd?
As well as the slightly stretched octave-equivalence of sine waves,
which have no partials? We've come a little bit further in the time
since Helmholtz, and I think his writings are really only important
for historical grounding at this point (not for science), though
certainly these puzzles are still far from being solved.

> Hence when moving by octaves alone no real
> change in the form of the harmonic spectrum will occur, but once
> twelfths are introduced, they harmonically include already the
> relationship of octaves and then are less clearly related and
> farther in frequency distance.

But Pierce and others were explicitly considering spectra (such as
all time-symmetrical ones) where even harmonics are completely
absent. The series of partials for such timbres goes root, twelfth,
major seventeenth, etc. So for such sounds, your argument would seem
to imply tritave- (tweltfh-)equivalence, not octave-equivalence. But
I don't hear things that way.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> --- In tuning@yahoogroups.com, "backfromthesilo"
> <backfromthesilo@y...> wrote:
>
> > What's wrong with Helmholtz's explanation of the octave
being
> > that all of the harmonics of a note are included in the octave
> > down and no new partials are included in the octave higher?
> > This of course implies that octaves and twelfths behave
> > similarly, but this can be explained by the octave being a
much
> > stronger harmonic in most timbres and by the larger
frequency
> > jump.
>
> So what you're left with here is not much of an _explanation_ at
all -
> - rather a "moral" justification, and a pretty weak one at that. For
> example, how would you explain that, after a certain amount of
> stretching of the partials, one fails to hear equivalence at the
2nd?
> As well as the slightly stretched octave-equivalence of sine
waves,
> which have no partials? We've come a little bit further in the
time
> since Helmholtz, and I think his writings are really only
important
> for historical grounding at this point (not for science), though
> certainly these puzzles are still far from being solved.
>
> > Hence when moving by octaves alone no real
> > change in the form of the harmonic spectrum will occur, but
once
> > twelfths are introduced, they harmonically include already the
> > relationship of octaves and then are less clearly related and
> > farther in frequency distance.
>
> But Pierce and others were explicitly considering spectra (such
as
> all time-symmetrical ones) where even harmonics are
completely
> absent. The series of partials for such timbres goes root,
twelfth,
> major seventeenth, etc. So for such sounds, your argument
would seem
> to imply tritave- (tweltfh-)equivalence, not octave-equivalence.
But
> I don't hear things that way.

I obviously addressed the issue of tritave equivalence and I even
think that if you have the right timbre and don't listen to any
octaves for a while tritave equivalence almost makes sense to
my ear. On the other hand, octaves may be equivalent but they
certainly don't really sound the same. The feeling of a note in
different octaves is far from something to disregard.

I know Helmholtz is old but for purely harmonic timbres what he
said is far from blatantly wrong. Your statement is just so
extremely dismissive. If the modern theory is so clear then why
isn't there some modern book that just difinitively replaces
Helmholtz. I don't mean to imply that there aren't complicated
exceptions and timbre issues that Helmholtz didn't consider, but
what grounds to you have to dismiss any of his claims on this
issue?

Furthermore, I think harmonically that twelfths and octaves are
VERY similar in harmonic timbres. I think the biggest reason to
hear them differently is because we already have a developed
melodic sense that identifies octave-equivalent scale degrees
and it is hard to separate that (meaning our melodic MEMORY)
from the harmonic feeling of the two tones.

Aaron

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> On the other hand, octaves may be equivalent but they
> certainly don't really sound the same. The feeling of a note in
> different octaves is far from something to disregard.

Absolutely. The sense in which the word "equivalence" makes sense has
to do with a putative "chroma" concept -- or not. See the SpecMus
archives for more on this.

> I know Helmholtz is old but for purely harmonic timbres what he
> said is far from blatantly wrong. Your statement is just so
> extremely dismissive.

I didn't think so -- I mentioned the historical importance, which is
extremely relevant for the kinds of conversations we have on this
list.

> If the modern theory is so clear

That's not what I said at all!

> then why
> isn't there some modern book that just difinitively replaces
> Helmholtz.

Because such a book would be way too large. Helmholtz's book is not
used in modern classes on acoustics or psychoacoustics. I would
recommend beginning with Juan Roederer's _Introduction to the Physics
and Psychophysics of Music_ and following the references from there
as they lead you into areas that interest you more. Nevertheless,
Helmholtz was one of the giants of the field and I meant in no way to
disparage his achievement.

> I don't mean to imply that there aren't complicated
> exceptions and timbre issues that Helmholtz didn't consider, but
> what grounds to you have to dismiss any of his claims on this
> issue?

Again, he points out some properties which are *suggestive*, but that
doesn't amount to an *explanation* in my book. Helmholtz was
completely unaware of many aspects of hearing, for example the
virtual pitch phenomenon, and was mistaken in many areas, for example
the location of the production of combinational tones.

> Furthermore, I think harmonically that twelfths and octaves are
> VERY similar in harmonic timbres. I think the biggest reason to
> hear them differently is because we already have a developed
> melodic sense that identifies octave-equivalent scale degrees
> and it is hard to separate that (meaning our melodic MEMORY)
> from the harmonic feeling of the two tones.

You may be right and I won't close my mind on this issue. I don't
know of any culture which names its pitches in a repeating scale of
twelfths or stretched twelfths or shrunk twelfths, and the music I've
heard that uses such scales fails to engender a new kind of chroma
that wraps at the twelfth in my ear. But it may yet happen . . .

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> --- In tuning@yahoogroups.com, "backfromthesilo"
> <backfromthesilo@y...> wrote:
>
> > On the other hand, octaves may be equivalent but they
> > certainly don't really sound the same. The feeling of a note in
> > different octaves is far from something to disregard.
>
> Absolutely. The sense in which the word "equivalence" makes
sense has
> to do with a putative "chroma" concept -- or not. See the
SpecMus
> archives for more on this.
>
> > I know Helmholtz is old but for purely harmonic timbres what
he
> > said is far from blatantly wrong. Your statement is just so
> > extremely dismissive.
>
> I didn't think so -- I mentioned the historical importance, which
is
> extremely relevant for the kinds of conversations we have on
this
> list.
>
> > If the modern theory is so clear
>
> That's not what I said at all!
>
> > then why
> > isn't there some modern book that just difinitively replaces
> > Helmholtz.
>
> Because such a book would be way too large. Helmholtz's
book is not
> used in modern classes on acoustics or psychoacoustics. I
would
> recommend beginning with Juan Roederer's _Introduction to
the Physics
> and Psychophysics of Music_ and following the references
from there
> as they lead you into areas that interest you more.
Nevertheless,
> Helmholtz was one of the giants of the field and I meant in no
way to
> disparage his achievement.
>
> > I don't mean to imply that there aren't complicated
> > exceptions and timbre issues that Helmholtz didn't consider,
but
> > what grounds to you have to dismiss any of his claims on
this
> > issue?
>
> Again, he points out some properties which are *suggestive*,
but that
> doesn't amount to an *explanation* in my book. Helmholtz was
> completely unaware of many aspects of hearing, for example
the
> virtual pitch phenomenon, and was mistaken in many areas,
for example
> the location of the production of combinational tones.
>
> > Furthermore, I think harmonically that twelfths and octaves
are
> > VERY similar in harmonic timbres. I think the biggest reason
to
> > hear them differently is because we already have a
developed
> > melodic sense that identifies octave-equivalent scale
degrees
> > and it is hard to separate that (meaning our melodic
MEMORY)
> > from the harmonic feeling of the two tones.
>
> You may be right and I won't close my mind on this issue. I
don't
> know of any culture which names its pitches in a repeating
scale of
> twelfths or stretched twelfths or shrunk twelfths, and the music
I've
> heard that uses such scales fails to engender a new kind of
chroma
> that wraps at the twelfth in my ear. But it may yet happen . . .

Thanks for the book recommendation. As I will certainly read
some newer book on acoustics, it is nice to have a
recommendation as to where to start. Everyone seems to
mention the Benade book, but it is not exactly *new* and I've
heard some criticism. I trust you in your recommendation.
There's a scathing review at Amazon.com though of the
Roederer that made me wary. Also the Benade has a medium
review from 2000 containing the claim:
"there is no really top notch acoustics book with modern
research available at this time."
Do you agree with that? It seems there's nothing quite right out
there, just a lot of stuff with mixed good and bad info and
historical interest...

In relation to that, I'm nearly finished with On The Sensation and
I'm wishing there was some kind of at least list if not explanation
that said generally what is still accepted and what to disregard
from Helmholtz/Ellis. Is there?

Thanks!

Aaron Wolf

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> There's a scathing review at Amazon.com though of the
> Roederer that made me wary.

Who wrote the review and what did they say?

> Also the Benade has a medium
> review from 2000 containing the claim:
> "there is no really top notch acoustics book with modern
> research available at this time."
> Do you agree with that?

Probably, though I've been out of the libraries for years now.

> It seems there's nothing quite right out
> there, just a lot of stuff with mixed good and bad info and
> historical interest...

Maybe you'll be the one to write that book. My suggestion is to read
every book and article referenced by Roederer, every book and article
referenced by those, and so on, all with a critical mind for possible
inconsistencies. Eventually, you'll have a pretty good view of the
landscape.

> In relation to that, I'm nearly finished with On The Sensation and
> I'm wishing there was some kind of at least list if not explanation
> that said generally what is still accepted and what to disregard
> from Helmholtz/Ellis. Is there?

Hmm . . . if someone gave me a grant, I'd find it delicious to try to
do this, also for other books like Partch's. But I think, as you read
more, you'll get a sense of what's outdated, what's controversial
(even Ellis totally disagrees with Helmholtz on some points, as
you'll soon see), and what's solid.

In a message dated 2004:01:06 03:50:47 AM, paul@stretch-music.com writes:

>> It seems there's nothing quite right out
>> there, just a lot of stuff with mixed good and bad info and
>> historical interest...
>
>Maybe you'll be the one to write that book. My suggestion is to read
>every book and article referenced by Roederer, every book and article
>referenced by those, and so on, all with a critical mind for possible
>inconsistencies. Eventually, you'll have a pretty good view of the
>landscape.

Or just go visit Karlheinz Essl's website & links for a few days... or
the acoustics and music research webring... (I don't have the URLs at hand)

-|-|--|---|-----|--------|-------------|---------------------|
Hanuman Zhang, heeding the Call(ing) to Divine Chaos & Creation

_NADA BRAHMA_ < Sanskrit > "sound = Godhead"

_LILA_ < Sanskrit >
1. the universe is what happens when God wants to play -
Divine Play - the play of the Divine in its Cosmic Dance, whimsy - like a
child playing alone God the Cosmic Dancer - whose routine is all creatures and
all worlds - the Cosmos flows - a world from the tireless unending resistless
stream of God's energy that _is_ Lila
2. joyous exercise of spontaneity involved in the art of creation this is
Lila