bandwidth vs interval

...can someone remind me...(I read it hear once...)...how small of an
interval is it at which, to the ear, it becomes (something like)
bandwidth noise, and not two pitches? Was it a minor third, or a
major second? thanks

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> ...can someone remind me...(I read it hear once...)...
> how small of an interval is it at which, to the ear, it
> becomes (something like) bandwidth noise, and not two
> pitches? Was it a minor third, or a major second? thanks

it's called the "critical band"

http://tonalsoft.com/enc/critical-band.htm

you can see the most frequently reproduced graph
of it here:

http://www.avatar.com.au/courses/PPofM/psychohearing/psycho6.html

the width of the critical band varies with frequency,
being narrowest in the couple of 8ves above and
below middle-C, approximately a minor-3rd thru most
of the audible range. it gets wider at the low extremes
of the audible range.

-monz

Hi Monz,

on 7/30/04 11:18 AM, monz <monz@tonalsoft.com> wrote:

> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
>> ...can someone remind me...(I read it hear once...)...
>> how small of an interval is it at which, to the ear, it
>> becomes (something like) bandwidth noise, and not two
>> pitches? Was it a minor third, or a major second? thanks
>
> it's called the "critical band"
>
> http://tonalsoft.com/enc/critical-band.htm

Based on reading the first section of the page above (the part written by
Paul) the "critical band" is the interval where rougness begins, and the
point of fusing is indicated as being less than this, but not defined. So
from this, "critical band" would not be the answer to traktus5's question.

Looking at the graph below then suggests that the answer is the "limit of
frequency discrimination" which lies between a half-tone and a whole tone
for most of the audible range. It sure didn't seem right that pitches fuse
when closer than a minor third, though I suppose I probably haven't checked
this with "pure tones" (presumably meaning sine tones).

But reading the text in the "[from Joe Monzo]" section *does* seem to
indicate that the "critical band" is where fusing starts.

So I'm not quite sure about it all, but as I read it there is a discrepancy
between the text in the two sections.

Also, note that the "[from Joe Monzo]" section does not mention pure tones,
which might make it incorrect if taken out of the context of this page.

Just a few thoughts, in case the page can be clarified in some way.

***

Also, I can't help but bring up my email from last year (which inspired no
replies at that time) in connection with this, although here I am clearly
not talking about sine tones:

on 11/29/03 9:47 PM, Kurt Bigler <kkb@breathsense.com> wrote:

> on 11/29/03 4:33 AM, monz <monz@attglobal.net> wrote:
>
>> i mainly got encouraged to do this because many of my
>> students have joined the school bands and so now play
>> clarinet, sax, or oboe in addition to piano.
>>
>> ... and of course, i've been encouraging *them* to play
>> these instruments, since it's a window into microtonality
>> which the piano doesn't easily provide!
>
> I just discovered that in the lowest notes on my piano I can simulate
> quarter-tones by playing two adjacent notes simultaneously. Unfortunately
> this only seems to work well up through the lowest F key. That is it only
> works on the lowest 9 notes on the piano (yielding 17 quqrtertones). Above
> that the intermediate note doesn't seem to be heard, but rather the upper note
> seems to dominate the pitch.
>
> Interesting to "note", anyway. I'm curious whether the cross-over point
> (where this stops working) varies on different pianos, or if it is a rather
> fixed limit. Anyone interested in trying this and reporting back?

Also, I should clarify that I was talking about simulating *melodic* quarter
tones here. I was not playing with harmonic intervals in any way.

-Kurt

From: "Kurt Bigler" <kkb@b>

> > I just discovered that in the lowest notes on my piano I can simulate
> > quarter-tones by playing two adjacent notes simultaneously.
Unfortunately
> > this only seems to work well up through the lowest F key. That is it
only
> > works on the lowest 9 notes on the piano (yielding 17 quqrtertones).
Above
> > that the intermediate note doesn't seem to be heard, but rather the
upper note
> > seems to dominate the pitch.
> >
> > Interesting to "note", anyway. I'm curious whether the cross-over point
> > (where this stops working) varies on different pianos, or if it is a
rather
> > fixed limit. Anyone interested in trying this and reporting back?

Well, I never had this experience with the piano but it can be shown quite
clearly on sounds with less overtones. Anyway, a few years ago, when working
with digitized sound, I was studiing such things like "ring modulation" in
great detail (I mean the effect of multipliing two signals by each other)
and I think I could give an interesting point for you here which may more or
less explain the matter you spoke about.
If you have a chance to find some detailed papers about acoustics or some
good software for working with it, you may find out that mixing two sine
waves of frequencies of X and Y (if Y is lower) is just the same as
multiplying a sine wave of "(X+Y)/2" with a cosine wave of "(X-Y)/2". You
can also take it from the other side and say that multipliing a sine wave of
X with a cosine wave of Y is the same as mixing two sine waves whose
frequencies are "X+Y" and "X-Y". This explains why you heard quartertones
while playing two tones a semitone apart. I don't know if you have a
possibility to take sine waves through some distortion effect, but I can
highly recommend experimenting with this. Overdriving a single sine wave
results in something which sounds a bit like a square wave. But suppose you
mix two sine waves of 100Hz and 120Hz both at the same volume. When you pass
this through an overdriving effect, you'll get a feeling that you can hear
110Hz with very quick tremolo. In fact, 110Hz is the frequency between the
two that you mixed and the tremolo is the difference of 20Hz. If you,
instead of mixing two sines of 100Hz and 120Hz, multiply a 110Hz sine with a
10Hz cosine, you get just the same.
Hope this helps.
Petr

on 8/4/04 12:52 PM, Petr Parízek <p.parizek@tiscali.cz> wrote:

> From: "Kurt Bigler" <kkb@b>
>>> I just discovered that in the lowest notes on my piano I can simulate
>>> quarter-tones by playing two adjacent notes simultaneously. Unfortunately
>>> this only seems to work well up through the lowest F key. That is it
>>> only works on the lowest 9 notes on the piano (yielding 17 quqrtertones).
>>> Above that the intermediate note doesn't seem to be heard, but rather the
>>> upper note seems to dominate the pitch.
>>>
>>> Interesting to "note", anyway. I'm curious whether the cross-over point
>>> (where this stops working) varies on different pianos, or if it is a
>>> rather fixed limit. Anyone interested in trying this and reporting back?
>
> Well, I never had this experience with the piano but it can be shown quite
> clearly on sounds with less overtones. Anyway, a few years ago, when working
> with digitized sound, I was studiing such things like "ring modulation" in
> great detail (I mean the effect of multipliing two signals by each other)
> and I think I could give an interesting point for you here which may more or
> less explain the matter you spoke about.
> If you have a chance to find some detailed papers about acoustics
...
> Hope this helps.
> Petr

Thanks. The theory I've actually got, and also the experience with
synthesis in analog or simulated analog modes, tho I appreciate that you
wrote so much!

The thing I'm most interested in here is more the actual practical results
on acoustic instruments (perhaps even beyond the piano), and also how this
relates to the graph on monz's webpage. In fact the practical results are
so limited as to be probably of little (musical) value, but nonetheless I
was curious whether other people on their pianos had tried similar things
and whether it works over the same range. Also curious that outside the
"sweet" range the perceived pitch for me seems to be the *higher* of the two
pitches.

Thanks,
Kurt

From: "Kurt Bigler" <kkb@b>

> The thing I'm most interested in here is more the actual practical results
> > on acoustic instruments (perhaps even beyond the piano), and also how
this
> relates to the graph on monz's webpage. In fact the practical results are
> so limited as to be probably of little (musical) value, but nonetheless I
> was curious whether other people on their pianos had tried similar things
> and whether it works over the same range. Also curious that outside the
> "sweet" range the perceived pitch for me seems to be the *higher* of the
two
> pitches.

I don't know how much you know about the east African "ilimba" but it's a
very interesting instrument which may also possess some of the sonic
qualities you're interested in. Most often I saw describing the ilimba as a
"thumb piano". The hole used for sound amplification is usually covered with
a very soft membrane (somewhere on the web I found that this can be made,
for example, from spider cocoon fibres) and this makes the tones sound very
much like if they were overdriven electronically, though they aren't. It's
amazing, professional musicians use external amplifiers and effect units to
achieve such a thing, and somewhere in East Africa, they get it without any
amplifiers or pickups. Moreover, they play mostly otonal music which sounds
really sweet through this "acoustic overdrive". For example, Hukwe Zawose
from Tanzania, who is my favorite ilimba player, almost always used a scale
of ratios 6:7:8:9:10:12. The intervals between consecutive tones in this
scale have mostly the same difference tone between them (i.e. the relative
frequency of 1) so it sounds really wonderful if this is distorted.
Petr