Another way of getting
a stopped pipe sound from an open pipe is to miter it in the center, so
that the open top is next to the mouth. Try building one like this if
you have never done so, as the result will surprise you. You can
actually get variations of open to stopped pipe sound, depending on
where the top of the pipe is located relative to its mouth. On a
full
length open pipe, they are, of course, located a half wavelength
apart.
This observed phenomenon is due to the fact that
the fundamental
and odd harmonics are radiated in phase from both the mouth as well as
the top, while the even harmonics are 180 degrees out of phase and
cancelled when next to each other. In addition, the pipe's dispersion
pattern will become non directional (omnidirectional), just as in
a
stopped pipe.
In a normal, full length open pipe, the dispersion pattern is
roughly a donut shaped pattern on a plane with the pipe's
axis, in
which the fundamental, along with the even and odd harmonics are
radiated. Only the even harmonics are radiated on the pipe's axis
(a
good reason not to mount open flue pipes horizontally, en chamade
style), as their output and tonal character will be weakened.
I am sure everyone has experienced the fact that the tone of a
pipe organ develops as you move out from under the pipes to a
location
in front of them. This is the reason behind it. Yes, even the deepest
bass notes can be quite directional when the radiating source is a full
half wavelength in size. You will never find this degree of low
frequency directivity from any loudspeaker. The physical size is just
way too small.
>Another way of getting a stopped pipe sound from an open pipe
is to miter it in the center ...
Does your folded pipe method work with string pipes as a trick to
make then sound like reedless krummhorns?
As I recall, very narrow scale pipes don't like being mitered,
especially in as extreme a way as you suggest. But perhaps if it
was
twisted into a rounded rectangle where no miter is sharper than 45
degrees would keep it happy -- though the cost to manufacture could be
high.
> Isn't it the other way?--the fundamental cancels as it is 180 degrees out of phase between the top and the mouth.
Nope. If you visualize the air particles waving back in forth inside the
pipe, at the fundamental the pipe acts like two stopped pipes butted together at
their stopped ends, since the two standing quarter-waves "clap hands" in the
middle of the pipe. Each half radiates a positive pressure wave at the same
time. Same thing holds for the odd harmonics.
Even harmonics have a pressure antinode and flow node in the center, during
one half cycle the pressure in the center "loop" moves either upwards or
downwards, making the upper and lower "half pipes" 180 out of phase.
This implies that if you stand under an organ facade, the front pipes will
sound weak since the fundamental cancels out in your direction (along the pipe's
length) -- someone mentioned that. It also implies that when standing in
front of a small organ, with your ears halfway up the pipe height, the even
harmonics should cancel out the same as when the pipe is bent around on itself.
I guess we don't notice that, thanks to sound reflections and dispersions.
We don't listen to organ pipes in anechoic chambers, though I've been in
churches that sure tried :-( --Mike K.
Pipers,
> Dave: As I recall, very narrow scale pipes don't like
being mitered, especially in as extreme a way as you suggest.
How did you get that? I would rather believe a very narrow pipe could
be less sensitive to mitering than a wide one. At least since the miter
curvature would be less abrupt in relation to width, because of the
wall thickness. Anyway a very minor point I think.
The sound of that note is well-known to be
'odd' or 'harsh' in
comparison to neighboring notes ...
On my recorder I fail to notice any different timbre leaving only the
lowest hole open. On the other hand I don't understand the recorder at
all from another aspect. Mine is very timid in terms of sound volume.
Very contrary to my impression of professionals playing concert pieces.
Is this a matter of a deficient player or a deficient instrument?
> John, on the 'double-folded' open pipe: Isn't it the other
way?--the fundamental
cancels ...
Nice example of how things are screwed up, thinking of them in
different domains. The top and the mouth are anti-phase when you look
at it as a linear line, using a length coordinate x. At one instant
flow is +U (going upwards) at x=0 (the mouth). At the same instant the
flow is anti-phase -U (going downwards) at x=L/2 (the top). But if we
leave the mathematical domain the same thing means that flow is going
inwards, into the pipe at both places. Such that they add rather than
cancel, seen from the outside world.
> Mike: I'd bet a kroner that Johan is already building
a test pipe
Not yet, I am too busy with other things, including grandchildren and
an anemometer, but you will win out later.
From my latest visit a year ago to the Utrecht museum I remember violin
pipes with tuning slots everywhere except one place, namely in the Carl
Frei 'Dubbele Biphone'. Here the pipes are 'permanently' tuned,
alternatingly by carvings or putty fillings at their open ends, not too
elegant to look at. I was told this is for reason of being the most
rational way of production.
Johan
Is this forum really that screwed up, or is it still April Fool's Day
in the rest of the world? I asked, "Isn't it the other way?--the
fundamental cancels as it is 180 degrees out of phase between the top
and the mouth." not because I didn't know, but because I was trying to
be polite. An open pipe, being half a wave lengh long, emits a
fundamental wave 180* out of phase at the mouth and the open end. When
I blow on my flexible pipe and bring the top around to the mouth, the
note goes harmonic and plays the octave. In this state, the pipe is a
full wave length long, and the mouth and top are in phase. The
fundamental cancels, along with the even harmonics, at least here in
Wisconsin. Blocking the interference with a panel brings back the
fundamental. Try it. It could happen in your part of the world, too.
Johan, I think your flow analysis is incorrect. When the U is positive
at the mouth end, the air in compression pushing up on the column is
also being expelled at the mouth, while it is in rarfraction and being
sucked into the top. If the mouth were in the middle of an open tube,
then the two ends would be in phase and would add.
--
John
It is probably the instrument.
My son's Angel soprano recorder has a working length of 275 mm and
a very low cutup of only 3 mm. Due to this fact, it is a very low
pressure instrument of relatively low volume that is easily overblown
at its full length C note. As the holes are opened, the pressure (and
resulting output) can be increased before overblowing occurs. For me,
it is quite difficult to play it without overblowing the instrument at
the lower notes.
If an instrument of the same tuning were
designed with a 6 mm
cutup, the operating pressure could be increased four times (and the
resulting output by 12 dB or 16 times) before overblowing
occured. It
would require more wind to play it (about double the CFM at four
times
the pressure), but easily within the blowing range of any player.
Pipers:
Since I have a pipe that has a flexible miter so I can put the top by
the mouth and move it away, I have observed what happens. At least in
Wisconsin, the sound emitted at the top and the sound emitted from the
mout are 180* out of phase, and the fundamental, as well as the even
harmonics, are cancelled. The pipe overblows, it does not turn into a
stopped pipe. I didn't ask the question because I didn't know that! The
theoretical notions posted recently to the contrary don't apply to me.
There is a possible practical application. Pipes that are too large and
cut up too high to overblow can be forced, not with a nodal hole, but
with a phase cancellation of the fundamental. Since I have naming
rights for such a stop, it is called the Blüflöte from the
German-American word Blü (Big Loud Ügly).
Johan, I think there is a flaw in your flow analysis. For flow at the
mouth to be positive (up the pipe), there has to be high pressure at
the base of the column. That pressure high is also emitted from the
mouth, opposite what is happening at the top. The oscillation of the
jet is a different phenomenon from the emission of the sound wave. --
John
In a message dated 4/5/04 11:05:17 PM Eastern Daylight Time,
j.nolte@att.net
writes:
> For clarification we should be should be sure we are numbering harmonics the same way..
I agree Johan, I've always numbered the harmonics that way.
Some people agree that when they say "overtone" or "partial" instead of
"harmonic", it means that "the Nth parial/overtone" is the "N+1st harmonic) or
(N+1)xfundamental.
Now back to figuring out these twisted pipes ... Mike K.
j.nolte: When the tuning slot is brought near the mouth, the pipe overblows ...
Well, this is disappointing, the pipe overblows instead of hanging on to the
fundamental and canceling out even harmonics.
However, now that I see this, I think it can be explained and could have been
predicted.
We know that if you put two similar pipes of the same pitch very close to
each other and blow both, you get a weak, emasculated tone that's much less than
either pipe alone, let alone the sum of the two. The reason is that the pipes
phase-lock to each other, but in what they perceive as a cooperative way,
with one pipe's mouth blowing out while the other blows in, and vice-versa for
each cycle of the fundamental. That is, both pipes don't try to blow out or in
at the same time.
In this way, the two pipes help each other play -- but from our viewpoint,
much less fundamental sound escapes for our ears to enjoy.
Now given that Nature will have pipes "cooperate" that way, imagine bending
an open pipe's end around towards its mouth. We've already established that at
the fundamental and odd harmonics, the two ends are in phase. But
"cooperation" wants them out of phase, one sucking while the other blows. That's what
the 2nd harmonic (octave) will do, so the pipe overblows to the octave, in the
name of cooperation.
(Cue the old joke about the earthworm falling in love with his/her other end.
They are hermaphroditic, so it might work...)
And I'll bet that even that octave sound is pretty wimpy.
I'm beginning to think that the reason no really new organ stops have been
invented since Praetorious is not our fault, but those damned laws of physics.
There goes the reedless krummhorn. --Mike K.
> 4/5/04 1:53:29 PM rjweis00: The polar patterns of open pipes are quite analogous ...
Yep, on my last posting I almost said something about how my Ham radio
training finally paid off. Been K(N)3JVK, N9NRD, AA9RG, and now AA1UK.
I run a dipole fed at 1/3 its length instead of the middle. Lots of fun
drawing standing wave patterns to figure out why it loads on all bands (well, not
those WARC bands, I mean the real ham bands that vacuum tube gear operates :-)
--Mike K.
> 4/5/04 dave65536: By the way: I thought of a possible explanation for why slots might ...
ISTR hearing that the end-effect length correction of a pipe is something
like the pipe diameter times some function of the wavelength, so for a wide pipe
the effective length of the pipe is different for the higher harmonics than
for the fundamental. Consequently the pipe is "out of tune" with the upper
partials, and they are suppressed for a flutey tone.
In a narrow pipe the end correction is more alike for all harmonics, so the
upper partials can shine.
Now, ISTR a tuning slot creates a leak that makes the pipe look shorter for
the higher harmonics, thus bringing them into tune even for a wider pipe. Or
maybe it's the reverse. But I definitely recall that a slot has more effect on
higher harmonics than low ones -- or the reverse. Been a while since I read
the organ mags in the college library (and most of the theories back then were
ridiculously wrong, anyway :-) --Mike K.
>I'm beginning to think that the reason no really new organ stops have been
>invented since Praetorious is not our fault, but those damned laws of physics.
>There goes the reedless krummhorn. --Mike K.
Hi Mike,
Well, we still haven't disproven your node hole method. And in fact perhaps a wood string made in the form of Richard's pipe might yet work out.
Actually the whole family of skinny strings was unknown in Pretorius' time.
Got more clues on the slot thing today. Apparently longer slots are better and more effective. Not sure how far one can go with that though.
If one is ever able to manage a reedless krummhorn, then the next step would be a reedless vowel pipe. I opened my "world championships of Flue Pipe making" 4 years ago and still no one has submitted an attempt to duplicate the target timbre, http://home.earthlink.net/~dave65536/voice_ah.wav [dead link]
DG
In Physics, the
harmonic number is the same as the multiple of the fundamental
frequency. For ease, if the fundamental frequency is 100 Hz, the second
harmonic would be 200 Hz, the third harmonic 300 Hz, etc.
Pipers: When I wrote: > When the tuning slot is brought near the mouth, the pipe overblows ...
M. Knudsen replied: > Well, this is disappointing, the pipe overblows instead of hanging on ...
Followed by conjecture outside the realm of experience.
Followed by: > And I'll bet that even that octave sound is pretty wimpy.
How much will you bet? I'll give you 10:1 on anything up to $1,000,000.
> I'm beginning to think that the reason no really new organ stops have been invented ...
Or it could be that those guys were as smart as we are after all--
and then they were born first.
Based on the .wav file and my experience, I have concluded that Richard's pipe does
not exhibit the harmonic spectrum of a stopped pipe, and that there is virtually
no cancellation of either the odd or even harmonic series taking place.
To test for interference, a straight control pipe should also be constructed and
voiced in the same way as the folded pipe.
I'll be doing some drawings later to illustrate what happens and why. What happens
is that the first (fundamental) and all successive odd harmonics are cancelled
because at the mouth they are in opposite phase from the open end of the pipe. The
even series is reinforced. Those are the facts. They are not disappointing, they
are interesting, and theory to the contrary is wrong (although the flow at the bottom
of the column is in phase with the flow at the top).
I'll also suggest a few possible pipe constructions to test some theories. Now I
have to discipline myself to finish the Gedeckt that my wife wants to play on Easter.
John
If it is truly the fundamental and odd harmonics
that are being cancelled, how would you explain the fact that exactly
the opposite is true on Robbie's spectrum analysis of my
pipe? The undisputable proof is right there in Robbie's
spectrogram.
The second harmonic is a full 30 dB below the
fundamental (1/1000 the output), along with the fact that the entire
series of even harmonics are all well below the levels
of their previous odd harmonic counterparts. The levels of both the
second and fourth harmonics are even below the level of the fifth
harmonic! This is not the normal signature of any
open pipe. It is certainly not the fundamental and odd
harmonics which appear weak, which would be the case if they
were truly the ones out of phase. I rest my case.
I have built plenty of straight pipes with high cutups during my
four years of independent research and none of them
ever exhibited these characteristics as an open pipe. They always
sounded like open pipes. In developing my toroidal whistles,
I've researched design parameters far beyond anything anyone would
ever
find on a pipe organ. I knew something was different about this
particular pipe when I first blew it about 25 years ago, as I did
not
expect it to sound this way.
My oscilloscope showed a waveform like that of a stopped pipe,
with complete positive and negative symmetry. Normal open pipes just do
not produce waveforms in which the positive and negative halves look
like mirror images of each other (unless only the fundamental is being
produced).
Furthermore, if the fundamental were out of phase from the mouth
and top of a straight open pipe, the main polar radiation of would
be
axial, rather than the lobed donut shaped pattern perpendicular to the
axis actually observed. I further rest my case.
Richard and pipers:
On my pipe it is the fundamental and odd harmonics that are being cancelled. Robbie's analysis is not of my pipe. In your .wav file first you play the fundamental, and then you overblow the pipe. When you overblow it, it overblows to the second (octave), not the third (quint)harmonic. Granted, the second harmonic is weak, and it does not overblow to it cleanly to eliminate the fundamental. If it had the harmonic characteristics of a stopped pipe, it would overblow to the third harmonic, but it does not.
--
John
The reason that my pipe will, in fact, overblow to the second
harmonic is proof that it is indeed of open design.
The other fact that the even harmonics are greatly subdued (the
second harmonic by over 30 dB relative to the fundamental), as clearly
shown in Robbie's spectrogram, is proof that they are out of
phase,
while the fundamental and odd harmonics are not. The even harmonics are
subdued, very much in accordance to those of a stopped pipe (see
Johan's pipe spectra page).
Furthermore, if you put a microphone very close to one of the
openings or separate the two openings with a baffle, the ratio of
even
harmonic energy dramatically increases from either side alone.
Robbie's analysis is that of my pipe. I can't
vouch for what might be happening in yours. I'm looking
forward to
hearing a wav sample of it and having Robbie or Johan likewise subject
it to spectrum analysis. That should give us all a good clue as to what
might be happening. The laws of physics themselves certainly cannot
change.
Hi Pipers,
Indeed, this problem is a good deal more complicated than one might
believe at first sight. Also obvious from the postings by John N. I
cannot quite keep up right now with the current flood of postings.
Here is what my attempt at the double folded pipe is doing:
Original pipe from 4 mm oak parquet slabs. Open, 35 mm square, 720 mm
internal length, minus tuning slot about 35 mm. Flue 0.5 mm, cut up 20
mm, pressure 1.9 kPa (7.5 inWC). Ears plus a slightly curved frein,
reminiscent of Gavioli style, necessary to prevent overblowing. The
cover is 'English' style; the narrowing in the passage of air from foot
to flue is due to an oblique cutting in the cover, while the pipe body
under the cover is flat. - The pipe I sacrificed for this experiment
never was a very good one. I suspect I should perhaps reshape the foot
and cover section into 'German' style.
I cut the pipe in two and made short 90 deg miters. The halves are held
together by a bolt and wingnut, leather gasket strips in between. See
attached photos. 'foldup.jpg' is with the pipe installed as blown on my
organ bass chest, set for 'regular' configuration. 'foldow.jpg' is the
folded configuration. Inspired by what John N mentioned I also tried it
folded, with a 1/4" plywood baffle (about letter paper size) inserted
into the slot between the pipe halves, such that there is no immediate
airway between the mouth and the nearby open 'far' end.
The soundclip '
foldall.mp3' (32 kb, 22 kHz,
mono) is ...- for the three
alternatives, in order straight (with a sideways twitch, =foldup),
folded with baffle, and folded (=foldow). I edited three separate
recordings into one file. I was careful to keep everything exactly the
same in the three recordings, except for changing the pipe
configuration and inserting the baffle in the middle case. The
microphone was front of the pipe, at the level of the bolt, always 0.5
meter from the mouth and from the open end (seeing the baffle on edge).
'foldsp.gif' is spectra of the three sounds, taken in the stable
portions of the long notes.
Results so far make me even more puzzled than before:
1. Listening to the recordings I find the differences in timbre
surprisingly small, though the spectra tell there is some. The
differences appear much more obvious to me when blowing the pipe by
mouth and listening directly. The even harmonics are indeed reduced in
the folded case, according to theory, but not very completely.
2. Why don't they cancel with the baffle in place? With a dipole, i.e.
two close anti-phase point sources, then sound pressure is supposed to
be zero at all places on the equatorial plane of those points. At the
same plane however, there is particle movement perpendicular to it.
Such movement is prevented by the baffle, apparently cancelling the
cancellation.
3. The tonal onset is drastically different in the three cases, only
the straight (foldup) case behaves reasonably well. The folded case
with a baffle has great difficulty to stabilize into decent speech.
So I feel compelled to expand experiments further. One obvious thing is
to rig the pipe outdoors to get a more anechoic environment. Another is
to see whether I can improve onsets by voicing differently between
cases.
-------------
Attached rwt2spc.gif is my spectrum analysis of Richard W:s pipe. Same
result as Robbie's, only a different display format. No doubt a typical
stopped pipe spectrum.
I am happy we agree that harmonic n is n times the fundamental.
'Overtone' I gather is the preferred term speaking of non-harmonic ones
like those from idiophones such as a bell or a xylophone.
Johan
Sorry if I offended anyone with my off-the-cuff theorizing. But things
really are confusing right now. As someone else mentioned, there were two
different sets of results posted. The WAV file definitely backed up the original
idea, that a folded pipe would sound like a stopped pipe, and the posted FFTs
proved it. I think that WAV was form Richard W. But someone else said their test
pipe just overblew, and that's what I theorized about.
Now Johan has gotten results in between, with his reconfigurable miter joint.
None of his MP3 files seem to indicate success in suppressing the even
harmonics, and I agree with him that the speech of the pipe is not good enough for
practical use.
Maybe there are some tricks to doing this so that it works as hoped. Perhaps
it is like Haskell pipes -- theory doesn't quite explain them, and they are
tricky to voice and tune. BTW, Haskell should send me a jug of ketchup to help
me eat my words about "nothing new since Praetorius." Haskell pipes were a
great practical advance. I have a rank of Haskell salicionals here, and a
friend has a rank of them playing in his living room. I tried making one of my
own and got nowhere.
--Mike K.
Johan,
I wonder if the double-mitre is creating an impedence discontunity at the _midpoint_ of the pipe.
This might affect some harmonics more than others.
John Rhodes
(AA7HL)
Vancouver, WA
This whole thing is really turning out to be a learning experience
for all of us, myself included.
When I saw Johan's results last night, I started to seriously question
the part about even order harmonics being out of phase in open pipes.
Can it be that the even hamonic phase cancellation is only occuring in
my design? How can this be?
In my design, the even harmonics are definitely down to the level
normally found in stopped pipes, while in Johan's pipe, this didn't
seen to be the case. One important thing in common with both
of our designs was that the fundamental and odd harmonics were
definitely in phase.
Obviously, no laws of physics are being broken in either
case,
so why the discrepancy? My guess is that my folded pipe uses no corner
reflectors and possibly Johan's does. At least I hope it does. I'm
guessing that folding an open pipe in half such as this produces a
somewhat critical, balance condition, in which otherwise relatively
small design factors take on a heightened importance.
Another suggested it might be due to the use of my high cutup, but
that is not the case, as I increased the pressure accordingly to
compensate for this. All straight pipes I have ever built performed
like straight pipes, regardless of scale or cutup. That is how I
discovered the relationship of scaling and cutup to operating pressure
and output from everything from the softest pipes to the loudest
warning whistles, such as my toroidal designs.
In any case, there would be no selectivity as to
the even harmonics being cancelled in any normal open pipe
design.
For the last 25 years I put this particular pipe aside as a mere
curiousity and believed I knew the answer as to why it exhibited these
characteristics, although I never mentioned it in my actual research.
Robbie's spectrum analysis sure reinforced my feelings about it. My
doubts began when Johan submitted his sample. Now I believe we may
finally be getting close to learning the real truth.
Richard wrote:
This whole thing is really turning out to be a learning experience for all of us, myself included.
I guess that is the point of this forum. I hope the give and take which sometimes on my part can be caustic is understood as being good natured pursuit of knowledge, with maybe a little of arrogance needed to argue a point to the test.
Next I want to learn what is a good program for recording and analyzing sound on my computer. I have a recent Toshiba laptop running windows xp. Yesterday I was going to plug a mike into the side of it a record a sample, but all I have on it is the windows media player, and the basic Real One which freezes up everytime I open it. Freeware, shareware, or something under $100 is what I am looking for.
I might have drawings today, but the essence of my theory is that the jet drive mechanism that creates a pressure high just above the upper lip to create upward flow also creates outward flow through the mouth. Meanwhile, at the other end of the pipe in resonance, the pressure low is causing flow into the top of the pipe. When the outward flow at the mouth (or the vortex shedding, or pressure high, or the voicer magic) is sufficient, the jet is forced outside the pipe and creates a pressure low just above the lip, pulling down on the air column causing outward flow. Meanwhile at the other end, the pressure has gone high, also causing outward flow. The same low pressure pulling down on bottom of the air column is also pulling in through the mouth. In effect, the mouth and the base of the air column are in opposite phase.
--
John
We now all know that
my original open folded test pipe suppressed the production of even
harmonics. I am guessing that the second version with internal
deflectors included may not, since it is providing a straighter path
for the wave to travel. I am also guessing this is more like the
version Johan built.
Possibly the even harmonics are being cancelled by the parallel
(and out of phase?) reflections in the first version of my open
pipe
folded at its half length. This might finally begin to make some sense,
since it is similar to slapback in a room with parallel walls. If the
reflection were out of phase at a particular frequency, it would cause
a null at that frequency.
I'm hoping this proves to be the solution. If this turns out
to
be the case, we now know the reason behind the differences in
performance of such seemingly similar pipes.
Pipers,
Here's a bad recording of my test pipe. It starts with the pipe blowing in the normally upright position, and then I move the top of the slotted pipe down near the mouth. Moving it around after the fundamental cancels strengthens or weakens the dominant second harmonic, and sometimes there is a warbling as the interference is on the edge of the right location for cancelling. The microphone is one that originally came with a computer probably just for voice.
John
Testmitermatic.wav
I certainly hear what
you've been writing about. You mention that the pipe is slotted. Is the
slot covered up, as I could see it causing the problem? Everything
needs to stay airtight. Also, how are you able to move the top around
while the pipe is blowing? If you are using flexible tubing, possibly
the convolutions in it or the narrowing of the diameter at the bend
could be causing the observed problem. These pipes seem to be awfully
sensitive to otherwise seemingly insignificant factors.
As an interesting anecdote, I once had an 8 ft. piece of
1.25" ID
swimming pool pump hose I tried to use as a windline for my homemade
pipe organ. It would sound surprisingly like an elephant trumpeting
whenever enough wind passed through it. I was using the blower
output
of a shop vac. As the flow increased, the convoluted tube would sound
the entire series of harmonics from its open end at about the
same volume level as a car horn! Not very good as a windline,
but maybe
good as a sound effect on a theatre organ. It makes the best elephant
sound effect this side of the real thing!
The pipe has a wire re-inforced section in the middle. Everything there is air tight. The flexible tube does not collapse.
The purpose of making the pipe was to demonstrate that out of phase harmonics are of equal strength and will cancel when the top and mouth are brought together.
As I mentioned in an earlier post, I made a similar pipe an octave higher with just a flexible paper and foil tube. It behaved about the same, but it was more difficult to align the top and mouth to effect cancellation. I cut a slot in the paper tube (just a rectangular hole a little ways down the tube) and that can be directed at the mouth for better results.
There is a very definite pattern of sound radiation from the slot and the mouth, and a very definite map of locations where cancellation occurs. On this approximately 700mm long pipe, cancelation occurs when the slot is right in front of the mouth, and it can be moved up and out at about 30* to about a foot away and still cancel the fundamental. The slot is cut down from the top of the pipe, so there is no leakage.
I do not think of any of the results as problems. The main purpose of the experiment is to demonstrate that it is the fundamental that cancels when the top of the pipe interacts with the mouth.
"No laws of physics were broken in this demonstration." Or were they?
If I do any more recordings, I will try to get a better mike, and keep it to five seconds or less. I noticed the 1.x mb file size after I clicked send.
--
John
Laws of physics can't
be broken. I just haven't been able to figure out the
mechanism that is
causing all of our test pipes to differ so widely in their
characteristics. Yours is different than both Johan's and mine in that
it is the fundamental that is being cancelled. I suppose it is just a
highly unstable design.
Maybe if enough of us experiment with them, we will
learn what that mechanism is.
Pipers,
Think I'm beginning to see the lights! John N sent a recording of his
testmitermatic flexable pipe. Attached is a coarse spectrogram of a
some 4 seconds long excerpt toward the end of it, having relatively
fast alterations beween straight and bent configurations.
It does not at all sound like I believed earlier. No wonder there has
been a lot of confusion.
Right now I believe in the following explanation:
Richard W made a rigid double folded pipe and voiced it optimally for a
steady tone.
John N started from a straight pipe, optimally voiced for that shape,
and found it behaved peculiarly when folded.
I myself made one that could be straight or folded, but nothing in
between. I voiced it such that it was about equally good in both
positions. Was it Mike that said I landed somewhere in between? I think
that is the thing. I now believe my mistake was that this inherently
means that my voicing is equally BAD for both configurations! Does not
bring out the 'full' tonal characteristics of any one of them.
What tells me a story with John's pipe is the warbling. This has little
to do with cancelling of harmonics, I would say it is the driving
mechanism being intermittently thrown out of its proper operation.
The flue jet supposedly is to spend about equally long times inside and
outside the upper lip. It is torn in and out by the FLOW through the
mouth. When the jet is torn inside it hits the resonating air column
and its speed is braked and its kinetic energy is back converted into
static, building up the pipe internal pressure.
My present belief is that the direction of the jet (the voicing) has to
be set differently for the straight and folded pipes. When you put a
second source (the folded top) near the mouth it will disturb the
in/out balance of the flue jet. (Also compare the 'Mitnahme effect',
two nearby slightly detuned pipes that synchronize to each other).
Possibly there remains an argument between John and me about the
pressures at the labium and the top. I am not convinced to have
understood your reasoning altogether here. In particular because you
talk about the PRESSURES at those two points. I want to stress that the
pressures here are relatively low, we are very close to the pressure
nodes for the resonance. Perhaps 120 dB, loud enough, but then still
only 20 Pa. The really high AC pressure of the fundamental is located
inside the middle of the pipe, lengthwise, where it amounts to things
like half the blowing pressure, maybe 500-1000 Pa (2-4 inWC).
Still I am aware of the risk here of being on thin ice. ISTR there was
a dispute some 150 years ago between Helmholtz and Rayleigh whether the
pipe is pressure or flow driven, resolved a century later by Cremer and
Ising. I don't remember any details, but they can be dug up. Anyway,
this is no simple thing to grasp.
Johan
The warbling was caused by moving the flexible end very slightly--less
tha 1/2" from the optimum location for cancelling the fundamental. Move
it a little further, and the fundamental is firm, or move it back and
the fundamental cancels.
By high and low pressures, I am referring to the compressions and rarefractions of the sound wave emitting from the pipe. In the same way, I would say a speaker cone moving into the room is creating high pressure, while the same cone, or another part of it moving away from the room is creating low pressure. More intuitive than rigorously theoretical.
A drawing of my theory (less than 1.7 mb) is attached. The explanation of the drawing is:
The drawing at the left shows acoustic flow up at the mouth
and down at the top of the pipe air column in oscillation for the
fundamental frequency.
The next drawing shows the jet creating high pressure which
causes the upward flow. At the same time in the standing wave,
low pressure at the top causes flow down. At both ends of the
column, the flow is into the column and acoustically in phase
according to accepted theory.
The next drawing adds the mouth opening and shows the flow
coming out of the mouth because of the same jet induced high
pressure. This mechanism reverses the acoustic phase at the
mouth from the phase at the bottom of the air column.
When the high pressure/outward flow forces the jet out of the
pipe, the jet creates a low pressure causing downward flow at
the end of the column, and inward flow at the mouth. The standing
wave high pressure has reversed the flow at the top.
The result, verified experimentally, is that the top of the pipe and the
mouth are in opposite phase for the fundamental, so that when mitered
around to create interference, the fundamental cancels.
--
John
Here is a drawing that shows the range where cancellation is occuring.
At the edges of this range, warbling occurs, and beyond it the
fundamental returns.
The nature of the flexible tube and segment lengths prevents trying the same thing below the mouth. I was able to rotate the slot around the pipe about 1/4 turn before the pipe couldn't be manipulated any further. The range in the drawing can be rotated that far with the same results. The implication for various rigid folded pipes is that the opening--preferrably a slot at the top of the pipe--has to be located very precisely relative to the mouth for this phenomenon to be observed. Perhaps a short flexible tube could be appended to a rigid pipe.
--
John
I believe Johan has found the main answer to the dilemma of
each of our pipes performing differently. Both configurations
require different voicings.
The more I thought about what I heard on John Nolte's sample,
it became
more apparent that this is a case of instability rather than phase
cancellation. The way it warbles and is unstable in frequency as the
top is moved relative to the mouth is the real clue. There would be no
frequency instability if phase cancellation were the only mechanism
going on.
I'm guessing that an open pipe folded in half is probably the
least stable of all possible configurations. Imagine voicing an entire
rank of these! The fact that any of us got it to actually work at all
is somewhat of a feat in itself.
I'm still wondering if Johan's pipe may have used internal
deflectors which might have minimized the even harmonic
cancellation
inherent in mine?
If only the organ builders of centuries past had access to an open
forum such as this, with the type of equipment necessary to verify the
results, such as shared by our members, just think of where we might
all be by now. They had only their ears and their judgement. We have
all the means necessary to verify or debunk a theory (in addition to
our ears and judgement)-and instantly get the word out to others in the
field!
Hi All,
So it seems then that the folded pipe should be expected to cancel its fundamental, because at the moment there is a compression at the mouth at the fundamental, there is a rarefaction at the far end. When they are brought together they cancel. The mouth overpressure pushes out and the other end underpressure sucks in? They should only reinfoce the even harmonics i.e. overblow??
DG
That is what I believe, based on what I am observing.
Dave started us on this thread by asking about slots. For the experiments I am doing, the slot helps a lot so that I can focus the open end on the mouth. It seems to me that when the slot is large enough, probably at least as large as the mouth, most of the coupling of the pipe to the air at the top happens through the slot. When tuning slotted pipes, if the slot is down a ways and does not go all the way to the top of the pipe, shading the top of the pipe has very little effect on the pitch of the pipe, so for efficiency, the tuner shades the slot to hear which way the pitch moves as the pipe is flsattened. On strings, focusing the sound out of a slot in the top may be affecting the timbre by creating just a little cancellation of some of the odd harmonics.
For those of you who want to play with a flexible pipe, I have more pipes in this set that could have no higher purpose. The largest is about 3" in diameter. The smaller pipes--1-1/4" or less are harder to use because the body length is too short to manipulate. Check your local hardware or autoparts store for flexible hoses in the 1-1/2"-3" range and let me know what you need. Your local organ builder or service man will probably also have a supply of old pipes. Don't ask him to break up a good set.
Since lower pitches are better proportioned for these experiments, we are offering a one time sale of 32' open wood pipes with a flexible accordion couplings in your choice of wood and finish for only $12,000 each, fob Milwaukee. Discounts on orders of 10 or more.
Actually, we have made a sawed off sample 16' stopped pipe that can be fitted with a collar for an 8" pvc pipe resonator with a little flex inserted to make the end movable. Ours has an adjustable upper lip, and can be fited with an adjustable flue as well. I'll probably do this before next October's organ builders convention.
--
John
This is not what the FFT analyzer has been showing. In the case of
both Johan's pipe and my pipe the fundamental was in phase at
both ends. The fundamental was by far the
strongest peak in the entire harmonic series. If it were cancelling, it
would then be the weakest.
You can't argue with a spectrum analyzer. I have always put my
primary trust in acoustical means rather than flow means to
analyze
what is really going on in pipes. It hasn't let me down yet. Whenever I
tried a new design, I always had my sound level meter and oscilloscope
handy to make peak level and waveform measurements. I finally got to
the point where I could do it by ear, as I then knew what was going on,
just as a photographer doesn't always need a light meter to get the
best shot.
John Nolte's pipe is another case entirely.
It is not really cancelling the fundamental but rather becoming unstable.
The warbling and frequency instability is proof of this. Johan
attributes this behavior to different voicing requirements for optimum
performance in either the straight or folded configurations. One
size doesn't fit all.
I am still curious, however, as to why Johan's pipe didn't seem to
have the same degree of even harmonic cancellation as mine. Until I
hear differently, I'm attributing this to the fact that my pipe used no
internal deflectors to acoustically straighten the path. I believe it
is the internal reflections between parallel walls of an open
pipe (half wave radiator) folded in half that are cancelling the
even
harmonics in my pipe. I believe these internal reflections of the even
harmonics to be out of phase.
If what David is saying were true, you would also expect the back
wave of a woofer to be out of phase with the front wave in a ported
speaker design, since this is logical. Both measurements and the
ear show that in fact they are additive and in
phase over a given
bandwidth.
Whenever there is a conflict between a long held belief and an
observed fact, you always need to put real world observations and
measurements over simple logic. If we didn't, cosmologists would
still
be using Newtonian physics, which seems to fit well under normal
everyday circumstances. Whenever we push the envelope, there are always
exceptions to the rule.
Hello from upstate New York in the USA,
Although I have some experience in acoustics many years ago, I do not
have the first hand experience with large classical organs that most of
you do. My recent experience is with the pipes of antique barrel
organs - from little bird organs up to small band organs. There were
discussions on another forum some time ago about the effect of using
different materials for making flue pipes. This is the basis for
the following comments. Perhaps there are more details than
necessary here, but it's sort of interesting in general.
There have been proposals for making pipes from everything from glued
up rolls of paper, various types of wood, metal, plastic tubing of
different wall thicknesses and other things. I have duplicated
pipes from basswood (linden), douglas fir, sugar pine, poplar, plywood
(new pipes), other S/P/F, etc.. Usually, there is some discussion and
then the conclusion that the material doesn't really matter that much
as long as the pipe maintains its shape.
I am presently restoring 2 barrel organs made around 1800 in
England. The pipes are monoblock - 19 open/stopped octave pairs
in a single piece. The largest pair is separate from the
others. In one of the organs this large pipe is missing so I have
been trying to prepare myself to make a replacement. But the
interesting thing is this. This pipe is about 16 inches long and
the 2 pipes share the partition down the center. Each pipe is
about 1" wide and 4 inches deep. There is a 90 degree mitre about 3/4
of the way toward the open end. The mitre is made with about
14, 1/4" hand cut dovetails in each of the 3 pieces.
The walls are a little less than 1/4" thick and they are made from
sugar pine. The stopper on the stopped pipe is also sugar pine
about 1/4" thick - no handle at all, just a flat piece pressed into
place. Amazingly, the pipe is still air tight after almost 200
years of weather changes.
Now the interesting part. If you hold the pipe from the ends (as
it is attached to the bottom of the organ) it blows a nice clear C note
and another C an octave higher. So far, so good. However,
if you touch the sides of the pipe while you blow it, the sound almost
disappears. It also changes pitch. There is a difference
depending one how hard you blow it and how hard you touch it, too. So,
I wonder, if the flexible portion of the bent pipe being discussed for
the last few days is made from soft tubing, perhaps the composition of
that section is responsible for some of the differences being noted.
Also, from an earlier discussion, if the amount of energy coming from
the open end is not the same as the amount coming from the mouth, the
cancellation would certainly be effected. Lastly, the exact physical
relationship of the mouth of the pipe and the open end of the pipe and
the placement of the microphone (listener) would have a significant
effect. This would be, not only to the levels, but to the phase
relationships (canceling).
Maybe this, too, would cause the different results.
Regards,
Craig Smith
If someone is interested, I can post some pictures.
>Dave started us on this
thread by asking about slots.
And for my part I would like to return to that topic, seeing how the discussion has wandered off into a swamp with the bent and flexible pipe discussion. My only interest in it is if you can make a reedless clarinet out of it which apparently you can't do.
It is said that a longer slot and a larger amount of regular pipe above the slot contribute most to the effect. I'd rather see the pipes forum experimenting with that than going on this wild goose chase after the bent pipe.
If there are more spare pipes laying around let's study the effect of slotting and set aside the bent pipe issue because even if the claimed effect occurs it is not practical as a real pipe.
DG
Pipers,
Craig Smith: ... Each pipe is about 1" wide and 4
inches deep ... The walls are a little less than 1/4" thick
... However, if you touch the sides of
the pipe while you blow it, the sound almost disappears. It also
changes pitch...
I once joined MMD with a strong statement about the material of the
pipe to be immaterial for its speech.
Due to the unusually large depth and thin wall of this pipe I suspect
we have indeed met an exception here. I wonder: if you stuff the pipe
interior loosely with a rag in order to damp its air resonance, then
you might be able to hear the (4" wide) WALL resonance when you knock
it (play it as a xylophone). My guess this may be close to the pipe
note. If so, it could have an influence on the voicing.
A picture would be nice to see!
Johan
Pipers,
Here today's measurement, to calm Dave down:
Length 450 mm, width 18 mm square, cut up 6 mm, flue 0.6 mm, 2 kPa
blowing. Ears, plus intonation roll from 8 mm plastic hose, see
attached 'slobot.jpg'.
Slot at top end is 57 mm, about 1/8 of the length, plus matching cover,
leater gasketed. The cover was held in place with a clamp. Three
different recordings from 0.5 m distance in attached '
slot2248.mp3' (22 kHz sampling, compressed to
48 kb/s), with spectra in 'slotspc.gif'.
1. First case is with the cover in place, such that the pipe is tight
its full length.
2. Second the cover is slided upwards to leave a hole about 12*18 mm,
about 1/8 of the length from the top, see attached 'slotop.jpg'.
3. Third the cover is removed altogether.
There was no change in voicing between the alternatives, they were
recorded in rapid succession interlaced by adjustment of the top cover.
Cases 2 and 3 are about 2 semitones higher pitch because of shorter
effective length.
Case 1 has a nice regular spectrum. The other two suffer a lot lower
odd harmonics. A particular feature is case 2 where there is a some 60
mm long open tube (including end corrections) attached to the top of
the pipe. This is expected to resonate near 2.8 kHz, and sure, there is
a marked dip in the spectrum at that place.
Johan
Pipers,
Thanks Professor Johan, wow that is quite remarkable. In fact, sound #3 does have a certain 'hornlike' quality, yet even though some even harmonics are weak 2 and 3 don't sound to my ears like a stopped pipe. It's also unclear to me why any even harmonics should get reduced at all!
>A particular feature is case 2 where there is a some 60 mm long open tube ...
This at least is consistent with the description of "hornlike" insofar as an orchestral horn (think flugelhorn) actually has its spectrum drop off quite rapidly above 2 kHz. But! It is #3 that seems more hornlike, not #2 with the 2.8 kHz valley in the spectrum. But perhaps my ear is reacting to the fact that the strongest harmonic in #3 is around 1300Hz, exactly where the formant peak is in e.g. a cornet. ?? puzzling.
Since the 'extra resonator' implicity attached to the top of the pipe in this case is an open one, it should simply transmit its input from one end to the other... or am I not understanding how open-pipe (as opposed to closed-pipe) resonators work??
Now we have another puzzle for the pipes forum to banter back and forth about. On another list it was posted that strings are typically slotted with the slot width about 2/7 the diameter of the pipe and starting about 1 pipe diameter down from the top. Professional pipe voicers claimed that this strengthens the 2nd and 3rd harmonics and is essential to getting the 'real' string tone.
DG
Hi Pipers,
As an aftermath to our recent discussion I spent some time to write a
simulation program (in Borland Delphi
pascal, alas for Win PC only)
that I think is fun to play around with, as well as somewhat
illustrative. It simulates 2-dimensional wave motion in a plane and is
rigged to illustrate the acoustic waves in and around an open pipe. Two
reservations must be told from the beginning: this gives a coarse
qualitative picture, quantitities are not truly represented because of
the 2-D rather 3-D simulation. It represents the acoustics only, not
the aerodynamics. How pressure waves would propagate in an ideal
stationary medium.
For
those math interested, the basic simulation procedure is illustrated in
attached 'pipegrid.gif'. A wave propagation plane is constructed from a
50*100 grid of little masses, length and width indexed with coordinates
i and j. Each mass point can move up/down with an excursion y
(which represents sound pressure at this point) and is connected to its
4 closest neighbors with little springs. The simulation is a 'time
stepping' operation - knowing the current positions y(i,j) of those
5000 masses, you compute what will their new positions be after a short
time interval (tau). This is done in three steps:
1. For each mass, compute what is the force operating on it. This is
computed from position differences to its neighbors, as detail
illustrated in the figure. The formula actually gives a measure of the
local curvature of the field. Results are stored in a 5000 point array
of forces.
2. For each entry in another 5000 point array of velocities, update
from previous velocities v(0) to the new ones by adding accelerations
times time step. The accelerations are known from the forces of the
previous step.
3. In the 5000 point y array, similarly update the old excursions y(0)
with the velocities times time step.
After these 3*5000 operations you know the field one time step later.
The y field is color coded (red positive, green negative) and plotted.
There is an 'automatic gain control' included, such that available
color span is fully used.
There are other tricks involved to take care of the 'boundary
conditions'. One is to 'cut' the grid along two linear paths (omitting
the springs across) to simulate a pipe - no coupling between interior
and exterior. Another is at the outside boundaries of the simulation
area where v(0) is set to zero - this happens to render reasonably
small wave reflection, such as if the area had continued indefinitely
outside.
At i=13,14; j=12 a driving source signal is injected. Either a
'monopole' source forcing both points up and down sinusoidally. Or a
'dipole' where they are forced in anti-phase. The latter would
represent the oscillating jet in a flue pipe.
Then start all over, repeat indefinitely for later time increments.
This renders an animated picture. Speed of animation depends only on
the speed of your computer.
With the left radio buttons you select the excitation frequency to be
around 1, 2, or 3 times the fundamental resonance of the pipe. Observe
that there is no feedback from the wave field to control the source, as
there would be in a real pipe. But you can adjust excitation frequency
some 20% up or down with the scrollbar.
With the checkbox you can select whether to plot a graph of the
'pressure' along the pipe axis. You can also select pipe diameter to be
1 to 3 elements wide, makes some difference to impedance match at its
ends. Selecting 0 removes the pipe altogether.
Clicking inside the display, or the Run/Hold button, holds or resumes
computation. For reasons unknown to me the program cannot be exited
(with the upper right X box) unless it is first halted.
The greatest discrepance against the real world that I note stems from
the simulation being 2-Dimensional rather than 3-D. This means that the
impedance mismatch at the ends of the tube is too small (too good
match) and the apparent Q value of the resonator is rather low. Also
that the amplitude of the proceeding waves outside the pipe are much
too big in relation to the amplitude of the standing wave inside. -
Something could probably be done about this, but I don't think that
would be worthwhile. Because then you would probably see nothing of the
external waves.
Another consequence of the same thing is that the pipe internal
'standing' wave is not altogether standing. It has a rather strong
proceeding component.
Hope you will have nearly as fun as I had!
Johan
Compiled 2009-02-27 JLs
