Cajon sounds like a tom

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attek

Cajon sounds like a tom

Post by attek » 2013-11-15 9:41 PM

Looking for some thoughts...
I've started making a few snare cajons out of a need for some percussion when sitting around with friends playing acoustic guitar.
The first one i did turned out awesome..it was easy, thrown together and sounds the way i like....snappy snare and sort of a dead thumpy bass. Box was made with 1/2 inch oak ply & 1/8 birch for the tapa..bass hole in the back is 4 inch, tapa is glued on the bottom and sides to about 3/4 the way up then 1 screw on each side and 2 across the top... Its sounds awesome.
Now the next 2 i have been having issues with.
For the second i used the same wood but used a bit different dimensions (still roughly 12 x 18), screwed the tapa all the way around, used 1/8 birch for the back as well this time with a lower positioned 5 inch hole.
The third i went to the 9 mm baltic birch for the box and back and 1/8 again for the front, a 4 1/2 Center position hole in the back and glued 3/4 up the side with 4 screws like the first.
the problem i am having is that they sound like tight toms and nothing like my first one. if you tap the front (with out muffling) i get a bouncy tone or a sound something like "dune"..if u know what i mean.
Just wondering if any one has any thoughts as this isn't the tone im going for.
Thanks

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casey
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Re: Cajon sounds like a tom

Post by casey » 2013-11-26 3:07 PM

I think i know the tom sound you're describing. I don't care for it either, though i could see how some would like it. I have heard it in a few "fancy" cajons made by stringed-instrument luthiers who make a cajon one day... they seem to think of it like a real drum head that needs to sing, where I (and apparently you) want more of the snare snap kind of sound. I also associate the "doon" tom sound with more traditional cajons (at least the snareless ones): real drums, basically, not kick/snare simluations. :-)

Interesting to hear of the greatly different sounds you're getting from very similar designs.

The big question is: what's the snare setup you're using? Assuming you're using something in the first one that you like, that's the huge factor and something that generally needs tons of tweaking to get to sound a certain way (and maybe you just got lucky on the first one.)

If you're not using any kind of snare on the inside, then you're saying that the first one has a snare-like sound just by virtue of how the tapa sounds... I take it the 1/8 birch plywood tapas are all the exact same wood on all three cajons?

I doubt the sides or hole size are causing this (unless some freak thing is happening where the hole size perfectly tunes the resonant cavity to the tapa frequency, but i think it's unlikely... you could test by partially obstructing the hole with your foot or a piece of plywood while playing to see if it makes a difference.) My instinct would call 9mm "too thin" for the box, but I haven't actually tried it. I wouldn't go less than 1/2". Regardless, i would expect thinner walls to make the cajon less resonant/ringing.

I haven't experimented with different tapas (on the todo list!) but my understanding from reading up on it is that the contact of the tapa to the box/frame is important. Assuming the tapa sits on an internal frame at the front (and not just the walls of the cajon), then take note of how flush (or portruding slightly) the frame is compared to the edge of the walls... the tapa can rest on the frame entirely, on both, or, if the frame is too shallow, only the walls. Might be relevant. I.e. if you are using a power sander and tilt a little while working, you might be messing up the tapa contact against the frame. I am surprised to hear of the big differences you're hearing given the gluing... you'd think that'd take care of most of these little issues to some extent.

Similarly, exactly how the unattached top corners of the tapa lie against the box could be important... The overall air-seal of the box is relevant to the sustain of the tapa tone. If cajons #2 and #3 have a better seal there (or the various edges where the walls meet), it could be contributing? Maybe you could put some tiny shims of paper in the corners near where the glue ends to cause the corners to lift off like .5mm or so and see if it changes anything. (makes them snap more, too, which is neat.)

How do the sizes of the tapas compare, exactly? That could matter...

The grain orientation of the tapa likely matters... is that the same on all three? Assuming it's 3-ply, 2 of the three plies usually have parallel grain, so the wood flexes more along one axis, and the cajon isn't square, so it becomes relevant. (My rough understanding is that "aircraft" plywood has layers that are only 45-degrees off, so it's easier to shape.)

If you don't have a snare setup, you could consider adding one... I mention that because adding a snare can effectively remove any "tom" tone... in fact, the tom tone is probably a good sign: if it's ringing it means it holds on to its energy for a while and can use that to drive the snare well.

My favorite (not yet on the site) uses heavy-gauge aluminum electrical wire -- the thick stuff that feeds electrical panels... basically like one of the thicker of the four sub-cables in this picture:

http://upload.wikimedia.org/wikipedia/c ... l_wire.jpg

I cut a drum snare in half, screw it to a little flat piece of wood, and attach the wire with a short length of plumber's hanging tape to the same piece of wood. Then i attach the other end of the wire to the inside wall of the cajon with another piece plumber's tape. Simple to make, easy to position, sturdy, etc.

Do let the forum know whatever you discover in your experiments! It's an interesting problem.

Ben

Re: Cajon sounds like a tom

Post by Ben » 2013-11-26 5:43 PM

If you make a cajon that has too much tone then you are making it too good! You can dampen the resonance (to a thud). Some players use their foot to dampen the tone. You could use a 1/4" tapa instead (much less ring). Or you can muffle the tapa inside by taping some felt, tissue paper or cloth to the front and bottom from behind, like you would a kick drum. You may be able to adjust it by changing the tightness of the screws. Or get really fancy and make an adjustable damper for the center/rear of the tapa, like they make adjustable snares. Obviously, stuffing a towel in there will really kill it.

The port acts somewhat like a Helmholz resonator...and with the typical volume/dimensions, the tuning is around 100Hz. You can lower that by using some 4" PVC as a port tube, but that will only work if you have the hole on a thicker side panel.

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Re: Cajon sounds like a tom

Post by casey » 2013-11-26 9:06 PM

Ben wrote:The port acts somewhat like a Helmholz resonator...and with the typical volume/dimensions, the tuning is around 100Hz. You can lower that by using some 4" PVC as a port tube, but that will only work if you have the hole on a thicker side panel.
Do you have a source or math on that 100Hz? I ask because i was looking in to the helmoltz frequency of the cajon a while back and doing tests and so forth, and it's an interesting subject. This is part of my "some day i'll post this" post, but: my (highly non-expert) impression was that the normal helmholtz equation was not applicable because the lack of "port" changes the math dramatically.

Following http://www.phys.unsw.edu.au/jw/Helmholtz.html and treating the cajon hole like a guitar sound hole, i came up with 87Hz for my cajon (which is bigger than most, so that lines up with your 100Hz). And my resonance testing showed 70-90Hz, so that lined up with my calcs...

The tuning of the port hole didn't matter on my cajon at all, at first, but once i improved the seal of my door, it acted like you would expect: if i stick my foot in the hole while playing, the kick drops in pitch.

-c

Ben

Re: Cajon sounds like a tom

Post by Ben » 2013-11-27 5:46 PM

I base that on the formula used to determine the vent length of a ported loudspeaker.
http://www.mobileinformationlabs.com/Ho ... th%201.htm

Using volume 1.3L, frequency 92Hz and port diameter 4", you get 0.125", the typical 1/8" back. If you put the port on a 1/2" thick side, you get a bit lower: 85Hz. The longer the port, the lower you go. So, if you install some 4" PVC pipe in the 1/2" side like we usually do to make speakers, you can get to 50Hz with a 7" port. Even deeper if the port is narrower. But how much sound (response, SPL) will you get out of the port tuned that low?

http://34iac.acoustics.sk/proceedings/Kicak.pdf

Here he measures the response of the Cajon. The response of the tapa itself 11"x19" peaks around 130Hz. If you tune the port to 50Hz, you aren't getting much out of it since the tapa itself doesn't really vibrate much that low! It's like putting a tiny woofer in a big box with a long port. It's not going to sound like a subwoofer. Better to match the tuning of the port to the resonance of the woofer. 100Hz is plenty low for most ears. But it would be fun to experiment. Another suggestion for the initial poster would be to block the port and he'll lose the boom.

Ben

Re: Cajon sounds like a tom

Post by Ben » 2013-11-27 5:56 PM

"...normal helmholtz equation was not applicable because the lack of "port" changes the math dramatically."

Surprisingly, thanks to the considerable volume of the box, the 1/8" to 1/2" port length (just the thickness of the box) is plenty long enough to get to 100Hz.

Same is true of a guitar sound hole by the way. You get a Helmholtz resonator effect. The big difference between such a short port on a guitar or cajon compared to a vented speaker box is that you also get a lot of direct sound of much higher frequency, which you want. With a long port, more of that is lost.

"...if i stick my foot in the hole while playing, the kick drops in pitch." I think that makes for a classy cajon virtuoso stunt while playing! I have a hard enough time damping the tapa with my foot as I've seen some do.

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Re: Cajon sounds like a tom

Post by casey » 2013-11-27 7:43 PM

Thanks!
Ben wrote:I base that on the formula used to determine the vent length of a ported loudspeaker.
http://www.mobileinformationlabs.com/Ho ... th%201.htm

Using volume 1.3L, frequency 92Hz and port diameter 4", you get 0.125", the typical 1/8" back. If you put the port on a 1/2" thick side, you get a bit lower: 85Hz. The longer the port, the lower you go. So, if you install some 4" PVC pipe in the 1/2" side like we usually do to make speakers, you can get to 50Hz with a 7" port. Even deeper if the port is narrower. But how much sound (response, SPL) will you get out of the port tuned that low?
A few thoughts --

- there are some instructions on the 'net that use a 1/4" or thinner back, but most (including Ocana, who inspired this site) say to use 1/2" or thicker, which is my philosophy as well. An 1/8" back is like a second tapa. Might be cool, and will likely lower the resonance of the instrument, which might be desired, but my guess is that it will make the sound weaker overall. Have you seen an 1/8th-inch back as typical?

- When I put the dimensions of my cajon into that calculator at 92 Hz, I get a thickness of .6 inches, which is very close to my actual .5 inches. But if I put in 80Hz (right in the middle of the measured resonance of my cajon), it yields 2.26 inches (even 87Hz yields 1.6 inches), implying to me that maybe the model is not so accurate? I wouldn't be surprised if the forumla they use assumes a port of some significant length and the real-world accuracy drops off as the port goes to zero? The guitar-resonance section of the Helmholtz link I gave above, which describes the complications of calculating Helmholtz for volumes without a neck/port shows how it derives a forumla for a guitar of:

f = 74 * sqrt(r/V)

For my cajon that's: 74*sqrt(.079375/.056716) = 87.5 Hz ... which lines up nicely with the general-wash-of-70-90-with-a-peak-closer-to-90 Hz that I measured.
http://34iac.acoustics.sk/proceedings/Kicak.pdf

Here he measures the response of the Cajon. The response of the tapa itself 11"x19" peaks around 130Hz. If you tune the port to 50Hz, you aren't getting much out of it since the tapa itself doesn't really vibrate much that low! It's like putting a tiny woofer in a big box with a long port. It's not going to sound like a subwoofer. Better to match the tuning of the port to the resonance of the woofer. 100Hz is plenty low for most ears. But it would be fun to experiment. Another suggestion for the initial poster would be to block the port and he'll lose the boom.
- For me, and, I suspect, many players, the resonance of the tapa itself isn't all that relevant: we just use a flexible piece of something there to kick the air spring in to action. So whether it resonates with the air volume may not be too important, as it's rarely allowed to vibrate when I play it anyway. The OP could even intentionally tune the air volume away from the tapa in order to minimize the ring. I do wonder how the resonance might affect the sound of the instrument when I'm hitting the snare, though (i.e. when i'm playing the tapa but not dampening it at the same time.) But the snares themselves do a lot of damping; in other words, there is no tom-like ring to my tapa at all.

- with the snares off, my tapa seems to have a resonance of more like 50 or 60Hz, but my cajon is significantly larger than the one they tested, and who knows what manufacturing differences in the plywood are in play, etc.
Same is true of a guitar sound hole by the way. You get a Helmholtz resonator effect.
Yeah, no doubt; but the link I posted above cconvinced me that while the effect is the same, the equation needs to be specialized to estimate the frequency, since the normal equation assumes certain ballpark boundaries on the ratio of volume/diameter/port-length/etc that the guitar/cajon doesn't exhibit.
The big difference between such a short port on a guitar or cajon compared to a vented speaker box is that you also get a lot of direct sound of much higher frequency, which you want. With a long port, more of that is lost.
Ah, nice point. I may actually like that -- most of my high frequency is coming directly off my tapa, so thudding down the kick sound might be cool. It is an intresting issue, though: as you say, 100 Hz is pretty bassy. I like the sound of my foot in the hole, which takes it down probably to 60 or so: awesomely deep, but also kinda weird and not always appropriate for the song somehow... feels like a rookie mistake to me: I start playing a drum or the bass and the first thing I want is the loudest, punchiest, deepest, darkest sound i can get, but then you start listening to your favorite music and realize that sometimes their bass has almost nothing below 80Hz or the kick drum sounds like a tom, etc. And gradually my mixes start coming back into sanity in the low end. So, even though we can port our cajons to get a 45Hz kick, do we really want to? :-) It would be neat to have an adjustable feature, though; I considered a simple sliding piece of plywood to cover the hole in varying amounts. Might still do that.
"...if i stick my foot in the hole while playing, the kick drops in pitch." I think that makes for a classy cajon virtuoso stunt while playing! I have a hard enough time damping the tapa with my foot as I've seen some do.
...my hole is on the side, which makes this a lot easier to do. :-)

Guest

Re: Cajon sounds like a tom

Post by Guest » 2013-11-28 11:10 PM

I'm building one now for maximum resonance, with an 1/8" tapa front and back, so I can play the back without snare. I suspect this will be louder than a thicker back, since the back will resonate along with the tapa, granted there are cancellations at some frequencies when you do this. I anticipate and hope for a lot of "doon" sound that I can treat, starting with damping the rear tapa, then the port. But our band plays pretty loud for acoustic and I believe in the old saw that what sounds ringy or boomy when we practice solo drums contributes to overall volume in a live setting while the extraneous resonances are covered up...recording is a different story.

"But if I put in 80Hz (right in the middle of the measured resonance of my cajon), it yields 2.26 inches (even 87Hz yields 1.6 inches), implying to me that maybe the model is not so accurate?"

Not sure I follow. The port dimensions are not altering, much, the fundamental resonance of the tapa, they are determining the resonance of the ported system: the air volume and port that are amplifying the sound from the tapa. (Actually the ported system does affect the tapa resonance itself slightly.) With your larger tapa, I expect that a longer and/or narrower port would make the bass louder and deeper. But tuned to 100Hz it's still in the range, since an 80Hz tapa is still putting out plenty of 100Hz energy. It should be said that the tapa and the hole are putting out a wide frequency range of sounds...otherwise we would hear a sine wave...we are just focusing on the deep fundamental and trying to amplify that. The peak of response down low. There is also the issue that if you tune the ported box too far away from the fundamental resonance of the tapa, you increase what's called 'group delay', which means phase issues and that can sound ringy and boomy.

"I wouldn't be surprised if the forumla they use assumes a port of some significant length and the real-world accuracy drops off as the port goes to zero?"

There are error factors, but the calculations are theoretically sound, even those that yield negative port lengths! The main reason the port length isn't critical is that the volume is so large and we aren't trying to tune it very low. A typical speaker might be half this volume and we try to tune the port to 50Hz...much trickier.

"For me, and, I suspect, many players, the resonance of the tapa itself isn't all that relevant..."

Wait, the tapa is the only driver here. It vibrating is the sole root cause of all the sound from the cajon, whether you tap it in the middle for boom or rap the corner with your knuckles. With a hole, the tapa sets into resonance the volume of air in the box and port. The response component of the ported reflex system is the difference between the total response of the cajon with the hole and the total response with the hole completely covered...more bass around 100Hz.

"...takes it down probably to 60 or so: awesomely deep, but also kinda weird and not always appropriate for the song somehow"

I think this is the issue with the OP. He's stumbled on a highly resonant tuned system, and it's too boomy. I'm reminded of the legend of the Beatles engineer who put towels on Ringo's drums, inadvertently starting a fad in making expensive drums played by professionals sound like cardboard boxes! There is a balance.

I should mention that while I'm an experienced speaker builder and carpenter and have played a few cajons, this is my first cajon build, so my knowledge is only theoretical so far, while you've made them! I look forward to posting my results to your site.

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Re: Cajon sounds like a tom

Post by casey » 2013-11-29 4:48 AM

Guest wrote:I'm building one now for maximum resonance, with an 1/8" tapa front and back, so I can play the back without snare. I suspect this will be louder than a thicker back, since the back will resonate along with the tapa, granted there are cancellations at some frequencies when you do this.
It sounds like what you're going for is a longer ringing of the tapa tone... I too can see this happening with the double tapa thing (though i'm not sure -- i wonder if the cancellation you mention might foil that plan), but I suspect the deep sub-80 Hz "kick" sound will be a little weaker and shorter (and lower in pitch) with a double tapa. Excited to hear what your results are like.
"But if I put in 80Hz (right in the middle of the measured resonance of my cajon), it yields 2.26 inches (even 87Hz yields 1.6 inches), implying to me that maybe the model is not so accurate?"

Not sure I follow. The port dimensions are not altering, much, the fundamental resonance of the tapa, they are determining the resonance of the ported system
Yeah - with all the various frequencies I gave (except where explicitly describing the tapa) I was talking about the air spring / cavity resonance, not the tapa resonance. When I play my tapa, I hit it with the full weight of my flat hand, and my hand stays there: that is to say, the tapa doesn't vibrate at all -- not even once cycle -- it's fully damped. It's used as a driver of the air spring of the box, but not like a vibrating membrane drum. This is how many/most of the players I've seen play their cajons (or their tapas are so dead that the resonance is moot anyway). I have seen some more traditional players in afro-cuban ensembles play it more like a drum head, where the ringing tapa is part of the sound. It's surely more "proper" and correct to do so, but I'm using the cajon as a kick/snare simulation, really, so I have slightly different design goals. My suspicion is that the 1/8th-inch plywood is more ringy at the more traditional smaller sizes as well, but i don't have direct experience with that.

E.g. this dude plays the "kick" version at 3:39, and the more traditional "doon" sound at 1:09: http://www.youtube.com/watch?v=ngGcNeKpZjE

I was guessing that the OP was looking for a sound more like this guy at 4:51: http://www.youtube.com/watch?v=dpReSnkGrTU
...whose cajon seems to have a naturally dead kick sound.
"I wouldn't be surprised if the forumla they use assumes a port of some significant length and the real-world accuracy drops off as the port goes to zero?"

There are error factors, but the calculations are theoretically sound, even those that yield negative port lengths! The main reason the port length isn't critical is that the volume is so large and we aren't trying to tune it very low. A typical speaker might be half this volume and we try to tune the port to 50Hz...much trickier.
My point is that the helmholtz equation is an approximation of a complex system that makes certain simplifications; as the operating parameters get near the edge of the envelope that the equation is designed for, it gets shaky.

Classic Helmholtz visualizes the air in the neck of the port as a mass weighing on the spring of the air in the cavity. The formula:

f = (v/2pi) * sqrt(A/V*L)

...where v is speed of sound, A is area of the port, V is the volume of the cavity, and L is the length of the port. We can see that as L goes to zero, the resonant frequency of this idealized cavity goes to infinity, which is obviously not the case! Put another way, the aerodynamics of air in a tube are totally different than air through an opening in a membrane, and with port length going to zero we're crossing into that territory. I conclude from this that classic Helmholtz is not appropriate for short port lengths. This same kind of formula is in evidence at the link you sent: it's solving for L, but you can see that as the desired resonant frequency gets close to a certain limit the change in port length becomes vanishingly minute.

From the link I posted above: "the air in the body of a guitar acts almost like a Helmholtz oscillator. This case is complicated [...] because the air 'in' the sound hole of the guitar has a geometry that is less easily visualised than that in the neck of a bottle."

This is why they use a variation on Helmholtz that they describe, because you can't visualize the 2mm-thick top of the guitar as a very short port, the equation just doesn't hold up well at that extreme.

For my cajon (with a "port" length of 1/2 inches), classic helmholtz says the frequency of the cavity is 282 Hz (this is all in meters):

(340/(2*pi))*sqrt((pi*(.079375^2))/(.508*.3429*.3302*.0127)) = 281.677

...which is clearly not the reality. But with a port just 0.5 inches longer (1 inch) that drops to 200 Hz -- a 81 Hz difference if I use 1 inch plywood instead of 1/2 inch? -- not likely. Using 1/4-inch would supposedly take the resonance to almost 400 Hz. 2 inches drops it to 140 Hz. A bit more credible, but I'm still not sure I trust that equation until the port is 5 or so inches long, if it's even accurate then. I assume the equation on the site you linked to probably uses some reflex-port equation variant that is more accurate at short port lengths (since people aren't building speakers with 4-foot long ports typically) and for speaker sizes/shapes, but it still demonstrates this same basic pattern of hypersensitivty toward the extremes.

The equation from my link, which is tailored for measuring guitar cavity resonance, which IMO is a closer model than a bass reflex port system, yields 87.5 Hz, which is right around what I measured in my cajon. I don't know what version they're using on this reflex-cabinet calculator: http://www.lautsprechershop.de/index_hi ... ltz_en.htm
...but that link gives me 89.7 Hz with a 1/2 inch port and 90 Hz with a 0-inch port, which lines up well, and shows that they're using something besides regular helmholtz.

For me the upshot is: build it so you can change it later. :-) Even if we had the perfect equation, there are plenty of uncertainties that we're going to need to adjust for.
"...takes it down probably to 60 or so: awesomely deep, but also kinda weird and not always appropriate for the song somehow"

I think this is the issue with the OP. He's stumbled on a highly resonant tuned system, and it's too boomy.
Yeah, agreed. I assumed the OP was hearing more "doon" resonance in general from the tapa when they were expecting more of a dead-thud kick sound. If we haven't scared the OP away, maybe they will let us know what they are looking for. :-)
I look forward to posting my results to your site.
Please do!

Ben

Re: Cajon sounds like a tom

Post by Ben » 2013-11-30 5:10 PM

" When I play my tapa, I hit it with the full weight of my flat hand, and my hand stays there"

I agree that is the classic slappy bass sound and the tapa is damped a lot that that way, but it still sets into resonance the rest of the box as well as the air and the port. That hard mid slap also contrasts with the much higher pitched corner tapping, when you get more snare.

" the tapa doesn't vibrate at all -- not even once cycle -- it's fully damped."

Then the result would be complete silence! We could argue about this a lot! The dead hand slapped tapa surely is vibrating, just less and at a higher pitch now that your hand is there.

About the resonance of these panels: the thinner, lighter panel resonates more and at a lower pitch than the thicker, heavier one. If we made the whole thing out of 5mm ply, it would be very ringy and have a lot of tone, but we wouldn't be able to sit on it. Wecould mount it on a stand and play the faces like tympani. Out of 13mm ply it has not enough tone, so the thin front is the perfect compromise. I haven't found a lot of difference with the thin back of mine, when I stick a thicker block on it, but the benefit is I can use that as a snare-free tapa.

"http://www.youtube.com/watch?v=dpReSnkGrTU
...whose cajon seems to have a naturally dead kick sound."

That cajon has way too mich snare sound, in my opninion. The cajon on the first link there sounds much better.

"For my cajon (with a "port" length of 1/2 inches), classic helmholtz says the frequency of the cavity is 282 Hz (this is all in meters):

(340/(2*pi))*sqrt((pi*(.079375^2))/(.508*.3429*.3302*.0127)) = 281.677"

Sounds much too high, like a smaller box. I would check that. One needs to be careful with units: cubic inches, liters or cubic feet, and inches, radius or dimatere, when we plug in. I trust the calculations, but I use online calculators since they all agree. Yes, the frequency rises abruptly when you go from tiny lengths to considerable ones. But you may not hear much difference when you actually experiment with lengths that size. The calculations are telling you only the central frequency, within the range that the port is amplifying. Not how much sound you will hear at that frequency. I was getting a great big fuity sound when I tried out my cajon hitting just the rear tapa glued in and the front open. I might glue in the front too. I like to completely finish a project and leave changes for the next iteration!

Speaking of which, I can't find any plywood thinner than 5mm in the Home Despot, and it sounds plenty resonant enough and looks good. My local wood guy may have more thicknesses in baltic birch, but he's almost blind and likes to cut everying himself!

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Re: Cajon sounds like a tom

Post by casey » 2013-12-01 4:26 AM

" the tapa doesn't vibrate at all -- not even once cycle -- it's fully damped."

Then the result would be complete silence! We could argue about this a lot! The dead hand slapped tapa surely is vibrating, just less and at a higher pitch now that your hand is there.
The result would not be silence, it would be the sound of the air spring oscillating in the cavity. If you slap your hand on the opening of a big ceramic jug, it makes a sustained tone from the bouncing air spring, the frequency of which is exactly what the Helmholtz equation is designed to predict, despite the fact that the walls of the container are totally still (well, still enough to make this point). I'm not saying the tapa doesn't move, I'm saying it doesn't complete a cycle: it experiences incursion, and back to rest, but doesn't come into excursion. It just makes a wavefront that bounces around in the box.

I could see the tapa being relevant if the hand/tapa coupling acted as a higher-mass, more-slowly-oscillating system. Meaning, maybe the intial hit (and intial incursion of the tapa) is the main instigation of the air spring movement, but then the hand/tapa bounces a couple more times (at a much lower frequency than the tapa's natural resonance) before stopping completely, and maybe that interferes (constructive or destructively depending on the phase/frequency relationship to the cavity resonance.) But that feels like somewhat of a stretch. I'd be surprised if the resonance of the air chamber was anything but the hugely dominant player in the tone (of a damped, flat-hand kick sound. Obviously the many other tones are a different story.) This is, after all, why the pitch lowers when you narrow the hole: it's not that the tapa is vibrating more slowly for some reason, it's that the air spring now resonates more deeply.
"For my cajon (with a "port" length of 1/2 inches), classic helmholtz says the frequency of the cavity is 282 Hz (this is all in meters):

(340/(2*pi))*sqrt((pi*(.079375^2))/(.508*.3429*.3302*.0127)) = 281.677"

Sounds much too high, like a smaller box. I would check that. One needs to be careful with units: cubic inches, liters or cubic feet, and inches, radius or dimatere, when we plug in.
Agreed, it's important to double-check. The fact that it's much too high is my point, though: the equation doesn't work for short port lengths, and yields values that, in this case, are way out of reasonable range.

Online helmholtz calculators give me the same result: 281Hz. As long as I'm not making a unit error, that's what helmholtz predicts for a 20x13x13.5 cajon with a 1/2" "port" and a 6.25"-diameter hole. It's obviously wrong, which is part of my argument that Helmholtz doesn't work for short port lengths.

That's:

340 m/s
3.125 inches radius = .079375 meters
20 inches = .508 meters
13.5 inches = .3429 meters
13 inches = .3302 meters
0.5 inches = .0127 meters

...no unit error that I see.

Consider this paper: http://www.itwm.fraunhofer.de/fileadmin ... icht10.pdf

They restate the issue of short port length, and raise another issue, which is the ratio of hole size to cavity volume, which may be another reason that Helmholtz won't accurately apply to cajons. They give the example of a guitar, which has a similar hole-to-volume ratio, as not working with classic Helmhotz:
The lowest resonant frequency of a cavity resonator is usually approximated by the classical Helmholtz formula. However, if the opening is rather large and the front wall is narrow this formula is no longer valid. ... The opening of the resonator may be a long duct, as in case of a bottle, or just a hole in a narrow wall, as in case of guitars. ... Things become more involved with guitar–like resonators, the subject of this paper. In particular, if the radius of the aperture is not so much smaller than the diameter of the cavity the classical Helmholtz formula yields wrong estimates of the lowest resonant frequency. Even for cavities with moderate aspect ratio there may occur errors of more than 10%.
Yes, the frequency rises abruptly when you go from tiny lengths to considerable ones.
Maybe you said that backwards accidentally; the frequency rises to infinity when you go to zero port length: that alone proves that Helmholtz doesn't work for short port lengths. If I made my cajon of rigid 1mm-thick titantium (pretend it's rigid, even though it would flex in reality), Helmholtz says the resonant frequency would be >1000Hz, which is very obviously wrong, by more than an order of magnitude. If I use 2mm titanium instead, it drops to 700 Hz: a supposed difference of 300 Hz in the resonant frequency because of a 1mm change in the thickness of the wall? Not likely. The Helmholtz equation is assuming a mass of air in a neck acting like a weight on a spring: this simplified visualization does not apply aerodynamically when you talk about short port lengths. If port length is zero, there is no "mass" on the "spring", so the resonant frequency goes to infinity. And as the port length goes towards zero, the model of it being a mass on a spring falls apart because the aerodynamics are totally different. Which is why the UNSW article I linked states that Helmholtz does not apply to guitar bodies, and by my extension, cajons.

Consider also this image, which is a graph of Helmholtz-predicted frequency of my cajon as the port length goes from 0 (far left) to six inches (far right):

Image

...pretty easy to see that as the thickness gets down low the numbers start to get crazy high (indeed, to infinity).
I like to completely finish a project and leave changes for the next iteration!
I hear that. I'm more of a "tinker endlessly with the first project" kind of guy. :-)
Speaking of which, I can't find any plywood thinner than 5mm in the Home Despot, and it sounds plenty resonant enough and looks good. My local wood guy may have more thicknesses in baltic birch, but he's almost blind and likes to cut everying himself!
I got mine from a local plywood place. I was kinda shocked how floppy the 1/8inch (~3mm) was when I cut the tapa, but once it was mounted it made sense. And by now you know my philosophy about the tapa :-) so I'm sure 5mm will work fine. I got a piece of plexiglass I'm interested to try out... I feel like since tapas are pretty easy to make, there's no reason not to try a variety (not that i've done so... it's on the to-do list...)

-c

Guest

Re: Cajon sounds like a tom

Post by Guest » 2013-12-02 3:41 AM

When I checked out the 1/4" wood I held the 4x8 pieces loosely and tapped them. 1/4" luan ply was the best sounding. The more ply was quieter and the masonite was terrible. I am happy with the cheap plywood. The grain on it really pops with danish wood oil.

Sorry, typo: the freq. goes down as vent length increases...quite right! But...we're not doing the same calculation or maybe even discussing the same theory. The practical limits for the vent tuning of your box with a 6.25" diameter are: 101Hz, with a 1mm long vent down to 60Hz, with a 9" vent, since you have to leave space between the inside vent opening and the wall inside.

I get a 95Hz vent tuning with your 1.75 ft3 box (internal), with the vent 6.25" long and 0.5" diameter. From several online vented box calculators.

http://www.calculatoredge.com/new/ventlength.htm#factor
http://www.mobileinformationlabs.com/Ho ... th%201.htm

Where's your equation from? The equations I'm using include an end correction factor which may be taking into account the effect you're talking about with very short lengths. They are certainly based on the theories of Helmholtz but they may have been tweaked thru years of speaker building theory (Thiele-Small). They calculate the resonant F of a system of air driven by a woofer(tapa) in an otherwise closed volume connected to a vent to the outside. I've used them countless times, and they do work in practice. I used to do them by hand with my Casio but the online cloud-based number crunchers are the same. That second one lists the equation.

You can still hear all kinds of frequencies up to 1000Hz, thru the vent, but they are not the Helmholz resonator effect, which is all this is calculating. I can hear the snares thru the vent, but that doesn't mean it's tuned to that high a frequency.

Another important effect is that sitting on this thing stops the majority of the box mass from quietly dissipating the tapa vibrations. Sitting on it allows the tapa to resonate.

Anyway, we are agreed that the vent adds a lot to the volume of this thing. Another application of speaker theory is that proximity of the cajon, especially the port, to room boundaries will reinforce the bass. And a matter of inches can mean a lot. Put it within 8" a corner with the vent pointing at a wall and play it hard and someone sitting in the opposite corner of a small restaurant should hear quite a pounding!

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Re: Cajon sounds like a tom

Post by casey » 2013-12-02 9:03 AM

Guest wrote:I am happy with the cheap plywood. The grain on it really pops with danish wood oil.
Yeah, maybe i'm not enough of a wood snob, but i'm in to plywood too. :-)
But...we're not doing the same calculation or maybe even discussing the same theory. The practical limits for the vent tuning of your box with a 6.25" diameter are: 101Hz, with a 1mm long vent down to 60Hz, with a 9" vent, since you have to leave space between the inside vent opening and the wall inside.

I get a 95Hz vent tuning with your 1.75 ft3 box (internal), with the vent 6.25" long and 0.5" diameter. From several online vented box calculators.
My box's main resonance is <90 Hz, but the volume is 2.03 ft3, not 1.75, so that may explain the discrepancy there.

I now see the crux of our mutual confusion: a terminology issue; I'm talking about the classic Helmholtz equation and you're talking about generic Helmholtz resonance and Helmholtz-based calculators for bass cabinets (which are not classic Helmholtz). I was skeptical of the first calculator you posted because I (incorrectly) suspected it of leaning on classic Helmholtz too much and it didn't line up with my cajon's resonance. Regardless, it's not too far from the results I've derived elsewhere, just slightly higher than I believe is accurate (but nothing as bad as classic Helmholtz.) When I saw that page I took their "port" to be the same as the "port" in classic Helmholtz, when in fact they are using a different equation.
Where's your equation from?
Hermann von Helmholtz. :-)

Wikipedia has the Helmholtz equation: https://en.wikipedia.org/wiki/Helmholtz_resonance
It is reproduced again at the link I posted above: http://www.phys.unsw.edu.au/jw/Helmholtz.html

And any classic Helmholtz calculator online will give you the same results.
The equations I'm using include an end correction factor which may be taking into account the effect you're talking about with very short lengths. They are certainly based on the theories of Helmholtz but they may have been tweaked thru years of speaker building theory (Thiele-Small). They calculate the resonant F of a system of air driven by a woofer(tapa) in an otherwise closed volume connected to a vent to the outside. I've used them countless times, and they do work in practice.
The first link you provided lists the equation, which is very different from the Helmholtz equation (it is perhaps derived from or inspired by it, but does not resemble it). I do agree that formulas for bass cabinets and ports and such can be applicable to a cajon. As I mentioned above, this one: http://www.lautsprechershop.de/index_hi ... ltz_en.htm
...lines up pretty nicely with the test results of my cajon (it gives 89.7 Hz for my cajon).

My point is to let people know that plugging a cajon's dimensions into classic Helmholtz is not going to work. Generic Helmholtz resonance is happening, of course. And one must be careful about the calculator chosen.
You can still hear all kinds of frequencies up to 1000Hz, thru the vent, but they are not the Helmholz resonator effect, which is all this is calculating.
Yes, the 1000Hz was the "classic Helmholtz" equation result, which I presented as obviously wrong. The "true Helmholtz" resonance is obviously much lower. Right around, oh, say, 87 Hz. :-) or 90, depending on the calculator you use. I favor the UNSW "guitar" calculator because it assumes a thin wall and no port, where the bass reflex calculators might be less inaccurate at that extreme (though they obviously aren't far off, since the difference from the "guitar" calculator is only a few Hz.) If I was going to add a tube port to my cajon, I'd use one of those bass reflex calculators for sure. With no port, I trust the "guitar" calculator more (especially because it agrees with my real-world tests.)

I suspect that another possible explanation for the minor discrepancy between bass reflex calculators and my cajon could be that they don't take into effect a floppy tapa lowering the overall air spring resonant frequency a few Hz.
Another important effect is that sitting on this thing stops the majority of the box mass from quietly dissipating the tapa vibrations. Sitting on it allows the tapa to resonate.
The cajon as detailed on this site, I would maintain, isn't much of a tapa vibrator. My tapa, at least, exhibits no difference when the box is sat upon.
Another application of speaker theory is that proximity of the cajon, especially the port, to room boundaries will reinforce the bass. And a matter of inches can mean a lot. Put it within 8" a corner with the vent pointing at a wall and play it hard and someone sitting in the opposite corner of a small restaurant should hear quite a pounding!
Yeah that's a wild effect. My hole is on the side, and I somewhat regret it, because when I play with others I always want to turn sideways or have to sit at other awkward angles to get the hole pointed at a wall or corner. It'd be much easier if it were in the back. Live and learn.

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Re: Cajon sounds like a tom

Post by Guest » 2013-12-02 4:12 PM

"I suspect that another possible explanation for the minor discrepancy between bass reflex calculators and my cajon..."
In practice, even a sophisticated computer designed system based on a complex model is not perfect since the real world is so detailed, so serious builders measure the impedance of the driver (what the tapa is actually doing in the box) and adjust the stuffing and vent accordingly. With a cajon it's not too hard to tell what direct tone the tapa is making and checking that that main low tone coincides roughly with the tone from the port when open. That makes for maximum resonance and total output. The sound from my tapa seems about one whole tone higher than the port resonance. So, if I widened the port a smidgen I could maybe get them to coincide, but I won't bother.

"...could be that they don't take into effect a floppy tapa lowering the overall air spring resonant frequency a few Hz."
The calculations are optimized for a very floppy woofer. The exact nature of the vibrations of the tapa which (assuming you are only hitting the tapa) I maintain are the source of all the sound from the cajon, both direct, transmitted through the other walls and via the volume of air and port, do not affect the target bass tuning frequency of the vent/volume system. We choose to design the vented system to coincide with the tapa. We're talking about two interconnected systems that can be treated separately, because: The taba vibrating does not change the volume of air in the box enough to matter, since it only moves maybe a millimeter back and forth. And the volume of box/vent does not alter the resonance of the tapa that much.

The vent calculations are only predicting what frequency will be focused by a vent of a certain dimension when excited by a box of air of a certain volume. In speakers, there are different, more complex models to predict the resonant frequency of the driver in a box of a certain volume.

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casey
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Re: Cajon sounds like a tom

Post by casey » 2013-12-03 3:07 AM

You've convinced me on one point: that the tapa is much more relevant to the bass kick sound than I thought. Did some tests on mine and it's definitely not just the air spring. Glad to clear that up, thanks.
"...could be that they don't take into effect a floppy tapa lowering the overall air spring resonant frequency a few Hz."

The calculations are optimized for a very floppy woofer.
Yeah, I'm not hip to the dynamics of woofer cabinets, so maybe it is basically equivalent, as you theorize. Of course the same issue crops up in my "guitar" calculator, which does not account for any floppiness at all, so even if I'm right it's not a unique deficiency of the bass port calculators. I was just throwing out ideas that might explain the discrepancy (which probably doesn't even need to be explained, given the closeness of the results.)
[The tapa vibrations] do not affect the target bass tuning frequency of the vent/volume system. We choose to design the vented system to coincide with the tapa. We're talking about two interconnected systems that can be treated separately, because: The taba vibrating does not change the volume of air in the box enough to matter, since it only moves maybe a millimeter back and forth. And the volume of box/vent does not alter the resonance of the tapa that much.
The presence of a tapa lowers the overall resonance not because it changes the volume of air but because it loosens the air spring. (in terms of the calculators you posted, my point is moot if they compensate adequately for floppiness; I just mention it for the sake of the visualization.) At that UNSW link, they discuss the identical phenomena in guitar bodies: "the swelling of the body is important. This makes the 'spring' of the air rather softer, and so lowers the frequency. The purely Helmholtz resonance can be investigated by keeping the body volume constant. When measuring this, a common practice is to bury the guitar in sand, to impede the swelling or 'breathing' of the body. However, guitars are not usually played in this situation. So the Helmholtz calculation will give an overestimate of the frequency of resonance for a real, flexible body." In this way, the tapa will lower the pitch of the resonant frequency of the combined system (and that's why I predicted that your double-tapa cajon would be deeper in tone.)

I'm not saying that the tapa vibration and air spring vibration are mandatorily consonant and completely coupled, just that they play into each other in significant ways, as opposed to blending inertly into each other. In my testing, I could watch the frequency response of my cajon's cavity change (a lot) as I gradually increased the pressure of my hand of the tapa.

You mentioned the option of trying to match the tapa resonance and cavity resonance: i was hoping to try that some day as well. I think it'll be easier on a cajon the size of mine since the tapa resonance is lower (there being less of a gap between tapa and body resonances to bridge). I had also considered adding a mass to the inside center of the tapa to lower its fundamental mode. This discussion has me more eager to try that stuff...

To sum up, it sounds like you're visualizing the sound of the cajon as sourced from the tapa vibrations, and the port resonance independently emphasizing frequencies from that. I'm visualizing the tapa as being coupled with the air mass to a significant degree, so that the tapa/air-spring system finds a balance that depends both on the tapa resonance and the cavity resonance. Before, i thought the damped kick sound was exempt from this coupling and only dependent on the cavity resonance (because the tapa was so restrained in that case), but i no longer hold that opinion.

Ben

Re: Cajon sounds like a tom

Post by Ben » 2013-12-06 4:16 PM

It is convenient when designing for total sound to separate the tapa's direct radiation from the resonance of the body/air spring/port, but I agree the true situation is very complex. The port definitely contributes a lot of sound.

Next, I'm thinking of a table-top cajon with port and two resonant sides. These sound good, a bit more like bongos. Of course, you lose your seat and wear out your knees:

http://www.schlagwerk.com/products/cajo ... /cajonito/
http://www.schlagwerk.com/products/cajo ... -comparsa/

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Re: Cajon sounds like a tom

Post by casey » 2016-10-28 4:55 AM

Ben wrote:Next, I'm thinking of a table-top cajon with port and two resonant sides.
I'm psyched to turn a tall speaker cabinet into a marimbula...

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