Welcome Guest [Log In] [Register]

- News Ticker

Donations - Please consider donating to The Ocarina Network to keep us afloat. More detail can be found in this topic. •
The Ocarina Network - Serving the ocarina community since April 27th 2008
Welcome to The Ocarina Network, a place for ocarina enthusiasts from all around the globe!

You're currently viewing The Ocarina Network as a guest.

If you join The Ocarina Network, you'll be able to access member-only sections, and use many member-only features such as customising your profile, sending personal messages, and voting in polls. On top of that we have a great number of music scores and backtracks for you to download.

Registration is simple, fast, and completely free.

Register at The Ocarina Network!

If you're already a member please log into your account to access all of our features:

Username:   Password:
Add Reply
[Tutorial] Making an Ocarina in a Predetermined Key; Yes, math actually comes in handy :3
Topic Started: 2 Dec 2010, 05:58 AM (11,922 Views)
Evil_Intentions
Inline Ocarinist
2 duplicate topics combined.

To use my method, you MUST have your fipple hole size determined. Note: for many reasons this method will work best with a rectangular ocarina

My predetermined fipple hole is 1/2 inches wide X 1/4 inches. Making an area of 1/8. We need to get a DIAMETER from this, even though i am using a square fipple.

so pi*r^2 = 1/8

r = sqrt(1/8) / pi
Diameter = 2(sqrt(1/8)/pi)

so my fipple diameter is about .4 inches. and about is good enough here.

-------------------------------------------------------------------

Now that the diameter is found, we will use an equation to find our desired volume.

V = 1/ (((F/2148.14)^2)/D)

where F is your frequency in hertz (reference) and D is your diameter that you found.

If you plan on making a 10 or less hole ocarina, then your frequency will be the one desired (523.25 for C5)
if you want a 12 hole oc, which means sub holes, then you want to use the note two notes below the tonic of the scale you wish to create. (i want a 12 in C5, so i use A4,440, as my F)

so i plan on making a 10 hole in C. The rest of the tutorial will be based on this.

-----------------------------------------------------------------

so in my case, my equation will look like this:

V = 1/(((523.25/2148.14)^2)/.4)

so let me simplify/work this:

V = 1/(.243583^2/.4)
V = 1/(.059333/.4)
V = 1/1.48331
v = 6.74168

So my volume SHOULD have to be about 6.8 cubic inches. So my chamber will be a rectangle 2in X 4in X 17/20 in


Thats it. I have not had a chance to test my theory yet, and plan to do so this weekend by building my first ocarina to these specs. This technique really only lends itself to rectangular ocarina making because you can cut a rectangular chamber with the proper tools.

Images of my plan thus far. Everything is to finished size exept the holes, but even those can be figured out exactly by using the above method. I will save that for later :D

Spoiler: click to toggle


The finished ocarina will be 2.5 inches wide, 4.75 inches long, and 1.25 inches thick. The inner chamber will be 2 x 4 x 17/20

This is all pretty straight forward algebra. I am a junior in high school and i CAME UP with this using a formula for helmholtz resonance with a given aperture, so i expect you to TRY to understand before posting questions. Tomorow i will be updating this thread with a program that will automatically find the volume for those who are mathematically challenged.

Reminder to readers: again, this has not been tested YET, but will most likely be done this weekend. I post it in the hopes that someone with the materials ready can give it a shot.
note to moderators: this will be posted on both the tutorial, and ocarina making forums to ensure max viewage. Feel free to delete the one you feel doesn't belong in that section.

Questions, just ask :D :whistle:
Here is the program i promised. Makes the math quite a bit easier 8-D
Attached to this post:
Attachments: FreqCalc.zip (129.6 KB)
Edited by speckles, 4 Dec 2010, 05:45 AM.
Offline Profile Quote Post Goto Top
 
dwent
Member Avatar
Transverse Ocarinist x 3
that is genius. :clap: and a quick written command line program to do the hard work for those allergic to numbers.
questions about that program... units of measurement are irrelevant correct? i enter aperture in metric, i get volume in metric.
second, when it asks for the speed of air... have you determined any average or standard values that can be input here? i didnt see any mention of this in the above post, so i wasn't sure what number is relevant.
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Its c++ not command line 8-D

And as long as all units are constant. Inches/second for speed of sound, INches for aperture diameter, Inches cubed for volume then it will all work.

Speed of sound is 343.2 m/s:

13560 in/s
34300.2 cm/s
343000.2 mm/s

Those are the most common measurements

speed of air/sound(dont remember what i have in the program) gets divided my 2*pi, so in my above post i am using inches. 13560/(2*pi) is about 2158.14
Edited by Evil_Intentions, 3 Dec 2010, 11:12 PM.
Offline Profile Quote Post Goto Top
 
Sherb
Member Avatar
Nyanyanyanyanya

Thanks for this~!

even though I don't understand half of it, I'm sure many people will find this helpful.

I'm gonna move this to ocarina making, and pin it up there.
Maybe it will stop the 9000+ threads we get on this topic.
Offline Profile Quote Post Goto Top
 
speckles
Member Avatar
I’ve been hypnotized

From your images, I'm assuming you are using wood. (nice graphics, BTW) This could be built from clay, using clay slabs, but clay shrinkage would need to be factored in, or did I miss that? Clay typically shrinks from 5 - 10% depending on the type used
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
@sherb No problem :D i remember seeing someone say "You cant just MAKE an ocarina in the key you want. You have to try many times to perfect it" i thought to myself "challenge accepted.

I finished gouging out the centers of my two halves. I will be doing the voicing tomorrow. If my first ocarina EVER plays a C the first try, i will be amazed. :jumpy:

I would again like to remind readers that this is not FULLY proven yet. I say fully, because i made a few ocarinas out of paper using my methods, and all were within a semitone from the predicted key. Tomorrow will be the confirmation.


@speckles I have never worked with clay ever, and this is my first ocarina, so i am definitely not the one to ask

Offline Profile Quote Post Goto Top
 
Sigurthr
Member Avatar
Flutist and Ham Radio Operator. Talarđu Íslenska?

Remember that for the pitch to be exact you may need to add in to calculations about air tempurature/density.

The volume of air inside correlates to the pitch by way of the density of the air, if it is not factored in you may have a different pitch in the product. (it all depends on your math and your particular formulas, I'm a theoretical guy not a numbers guy so I can't check to see if you've incorporated it or not)

A440 = X volume @ Y temperature, not just A440 = X.
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Sigurthr
4 Dec 2010, 07:33 AM
Remember that for the pitch to be exact you may need to add in to calculations about air tempurature/density.

The volume of air inside correlates to the pitch by way of the density of the air, if it is not factored in you may have a different pitch in the product. (it all depends on your math and your particular formulas, I'm a theoretical guy not a numbers guy so I can't check to see if you've incorporated it or not)

A440 = X volume @ Y temperature, not just A440 = X.
Ah, but temperature/density is already factored in.


EDIT: my bad. One can't really factor in temperature, but normal air density is factored in already.
Edited by Evil_Intentions, 4 Dec 2010, 07:43 AM.
Offline Profile Quote Post Goto Top
 
Goudy Stout


I admire the fact that you worked all this out and made a program. You have helped many people greatly.

The only problem is that there is much more to ocarina making than just the key it is in. Your first ocarina will probably not have a good timbre or range (it will get airy by the higher notes). All this can be measured, but its the experience that can give you a good timbre as you know what to look for. If you're making proper wooden, clay or any material ocarinas, experience will generally be better than mathematics, also, by the time you can get a good range and timbre out of your ocarinas, you should be able to guess well the size of a certain key and get within a semitone of it (the ocarinas pitch is very unstable, a semitone out should still be able to play in the desired key if made properly).

I am very excited to see the result of this ocarina though, and i hope that you make it well enough to get a good tone out of it :)
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Goudy Stout
5 Dec 2010, 06:09 AM
I admire the fact that you worked all this out and made a program. You have helped many people greatly.

The only problem is that there is much more to ocarina making than just the key it is in. Your first ocarina will probably not have a good timbre or range (it will get airy by the higher notes). All this can be measured, but its the experience that can give you a good timbre as you know what to look for. If you're making proper wooden, clay or any material ocarinas, experience will generally be better than mathematics, also, by the time you can get a good range and timbre out of your ocarinas, you should be able to guess well the size of a certain key and get within a semitone of it (the ocarinas pitch is very unstable, a semitone out should still be able to play in the desired key if made properly).

I am very excited to see the result of this ocarina though, and i hope that you make it well enough to get a good tone out of it :)
You seak truth my friend. My first attempt failed. I gouged out the middle of each hlaf, made voicing etc...etc..and no tone, not a sound. I have a backup that is made of 6, 1/4inch walls. I will see how that turns out.
Offline Profile Quote Post Goto Top
 
Dullahan
Member Avatar
Don't you just love soundwalking?

Post pictures of your attempt. That way we may give you hints on what's wrong! :)
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Dullahan
6 Dec 2010, 03:45 AM
Post pictures of your attempt. That way we may give you hints on what's wrong! :)
Thats kind, but my oc is pretty screwed up. I had to hand gouge everything. I followed the guide on making a wooden ocarina, but i made it out of two rectangular blocks. I think i just need to make a better wedge, but i may just wait till my grandpa gets a router again.

I really wish someone who knew what they were doing could just make a quick rectangular oc with a body cavity of 2in x 4in x 7/8 in and a fipple hole of .4 inches just to see what it plays. Should only be an hours work(not including glue drying) for an experienced person.


I'm still relying on that "wall" method, as this little gouging foray didn't end so well. But i am optimistic, seeing as i have made 6 paper ocarinas of varying shapes (tetrahedrons, cubes, rectangles, icosohedrons) that all play within a note of what was predicted...and they're made of PAPER
Offline Profile Quote Post Goto Top
 
tytoalba
Member Avatar
Inline Ocarinist x 2

Evil_Intentions
6 Dec 2010, 04:54 AM

I really wish someone who knew what they were doing could just make a quick rectangular oc with a body cavity of 2in x 4in x 7/8 in and a fipple hole of .4 inches just to see what it plays. Should only be an hours work(not including glue drying) for an experienced person.


I'm still relying on that "wall" method, as this little gouging foray didn't end so well. But i am optimistic, seeing as i have made 6 paper ocarinas of varying shapes (tetrahedrons, cubes, rectangles, icosohedrons) that all play within a note of what was predicted...and they're made of PAPER
Try doubling the length of windway and maintain a thickness of at least 0.4 cm holes.
Offline Profile Quote Post Goto Top
 
spoonyspork
Member Avatar
L'il Tooter
What if you got an ocarina kit from Hind (HERE), measured everything, reversed the math, built it, and see what you get and if the results are expected? :)

Also, looking at your sketchup model, you might be better to get some pre-cut crafting block slabs (can be found for cheap at crafting stores and such)... that would make you having minimum cutting (just the curve around the edge and maybe trimming down the voicing - I think it could easily be cut to build the whole voicing rather than carving it out. I will try and sketch up what I'm talking about when I get home later. I might try experimenting with it myself in fact, despite my saying I'd never attempt woodcraft :D
Edited by spoonyspork, 6 Dec 2010, 04:56 PM.
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
I thank everyone's interest in this, but i know you all want some form of proof, so i have attached a net i made. It is a cube who's side lengths are 2.12515 inches long, and has a .5x.5 inch fipple. Giving it a calculated pitch of 523.248 hertz. Built properly, and blown with the correct amount of air, you will get within half a semitone of a c. :thumbsup:

Some may notice that the mouthpiece is the same as another paper ocarina floating around. So you can find the instructions for the mouthpiece on another site if it isn't blatantly obvious enough.

TIPS:
Best to use an xacto knife to cut the fipple.this is about precision.
Use cardstock or a heavy paper.
score lines before folding.
if using tape, tape inside AND out.
DO NOT RESIZE THE IMAGE. Save to your comp and print out AS IS.


Im off to work on my second wood model. Hopefully it works BRB


....and YES the side lengths are actually 2.12515 inches. i love being a nerd :D

My official name for these paper tests are "geocs" if you wish for another shape (icosohedron, tetrahedron) or another key, please tell me. The more tests the better :fly:
Attached to this post:
Attachments: cCube.png (259.6 KB)
Edited by Evil_Intentions, 6 Dec 2010, 10:01 PM.
Offline Profile Quote Post Goto Top
 
Goudy Stout


If you can make it out of separate sheets, it might work better. I made a wooden ocarina early last year out of 6 'walls' of wood, they were around .7 cm thick and i worked the aperture by chisel, and it turned out pretty good, got a little airy towards the top of the range.

Spoiler: click to toggle


The things that you could think about when making the ocarina could be the thinkness of the walls, shape of the actual body of the ocarina (try to make it larger at the aperture area than at the finger hole area), gradient of the ramp, shape of the labium/edge (rounder, shape, flat, some suggestions for different timbres) and shape of the aperture (song hole/voicing/voice hole, whatever you want to call it). Try to change its shape to more of a rectangle shape, or even better, an oval, circle or arc. Im sure you know this, but for anyone else, make sure that it has the same area as the square as it will affect the pitch if it is different :)

As said before, if you upload a picture of the finished product, quite a few people here would be able to help you fix it. All you need to do is ask ;)
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Goudy Stout
7 Dec 2010, 04:26 AM
If you can make it out of separate sheets, it might work better. I made a wooden ocarina early last year out of 6 'walls' of wood, they were around .7 cm thick and i worked the aperture by chisel, and it turned out pretty good, got a little airy towards the top of the range.

Spoiler: click to toggle


The things that you could think about when making the ocarina could be the thinkness of the walls, shape of the actual body of the ocarina (try to make it larger at the aperture area than at the finger hole area), gradient of the ramp, shape of the labium/edge (rounder, shape, flat, some suggestions for different timbres) and shape of the aperture (song hole/voicing/voice hole, whatever you want to call it). Try to change its shape to more of a rectangle shape, or even better, an oval, circle or arc. Im sure you know this, but for anyone else, make sure that it has the same area as the square as it will affect the pitch if it is different :)

As said before, if you upload a picture of the finished product, quite a few people here would be able to help you fix it. All you need to do is ask ;)
I fear it is too late for my lil gouged oc, but my "wall" oc has 4 walls glued(need a bigger clam for the other 2 :mad:) and if i hold the other 2 walls tightly and blow, it is mostly air, but you can almost "feel" the not. If you get what im saying. Like it is more than jst air, but so close to becoming a tone. I fear my problem lies with the fact that my windway is only 1/4 inches long. I will upload ics tomorrow probably.
Offline Profile Quote Post Goto Top
 
Goudy Stout


I dont think the problem is the windway length. Xuns are almost like an ocarina in the fact that they have apertures, but they are different because the xun does not have a windway. I once made an ocarina with a cm long windway (which i then added a mouthpiece to, was my 5th ocarina :/ ) and it still produced a tone.

If the ocarina is making NO sound at all, the windway might not be aligned with the labium/edge properly, the edge is too thick or the aperture is too large/not the right shape. Im not sure what the problem is right now, but if you take some pictures it would be much easier for me to help you :)
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Well, it is just about done, and guess what...IIT WORKS. I had to make an adjustment to the fipple due to the volume being a bit larger than expected. It is now at a flat C, and the last 2 walls are being glues. The fipple cleanup sanding should bring it up to a perfect C, then it's time for holes :D

What should i do? a 10 hole, or a 6 hole?
Offline Profile Quote Post Goto Top
 
Goudy Stout


Evil_Intentions
7 Dec 2010, 10:53 PM
What should i do? a 10 hole, or a 6 hole?
Keep in mind that 10 hole is linear fingering and 6 hole is combination fingering. Linear is probably the best to tune as all the notes are accurate if tuned properly, combination fingering isn't possible to precisely tune because getting one note perfectly in tune will affect another notes tuning (this is explained very simply :) but in short, you will not get the whole scale in tune because of that reason).

I am glad that it works and its great to have another wooden ocarina maker on this forum (there seems to be a LOT more wooden makers than clay makers now, im both :B ).
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
I just finished gluing the last two sides on a new soprano G ocarina. The tone is much more pure, and airstream can be varied greatly while maintaining a tone, something my previous attempt did not :shakefist: . I believe i shall make this a 4 hole, as not to jinx myself
Offline Profile Quote Post Goto Top
 
Goudy Stout


Evil_Intentions
10 Dec 2010, 03:02 AM
I believe i shall make this a 4 hole, as not to jinx myself
Remember that linear fingering is probably harder to get (almost perfectly) in tune and that linear fingering is easier to tune with as the holes can be tuned right to the cent. In my opinion, tuning a 4 hole is harder than tuning a 7 - 13 hole.
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Goudy Stout
10 Dec 2010, 08:05 AM
Evil_Intentions
10 Dec 2010, 03:02 AM
I believe i shall make this a 4 hole, as not to jinx myself
Remember that linear fingering is probably harder to get (almost perfectly) in tune and that linear fingering is easier to tune with as the holes can be tuned right to the cent. In my opinion, tuning a 4 hole is harder than tuning a 7 - 13 hole.
This ocarina is 1x2 on the top. i dont think i can fit more than 4 holes :p
Offline Profile Quote Post Goto Top
 
Goudy Stout


Quote:
 
This ocarina is 1x2 on the top. i dont think i can fit more than 4 holes :p
Then you should most likely do a 4 hole :) (I first thought 1 x 2 cm, because i live in australia, but then realised that it was in inches!)
Offline Profile Quote Post Goto Top
 
crumpy
Member Avatar
very very crumpy
So is there any news on how successful this is?

I have to admit my first thought, upon noticing that pretty much any amateurish handmade ocarina on the net is based on guess work or trial and error to get the initial tone, was that there must be a fairly easy way to work out the theoretical volume needed in order to get the right frequency.

with this information you could easily make an ocarina in any key providing you have the knowledge/capability to make the rest of it work.

have you managed to successfully prove this formula?
Edited by crumpy, 27 Feb 2011, 08:00 AM.
Offline Profile Quote Post Goto Top
 
Ryguy27
Member Avatar
Ryguy27
yay for math!!! :fly:
Offline Profile Quote Post Goto Top
 
Evil_Intentions
Inline Ocarinist
Sorry it's been so long since I've been around here. With summer break in a week, I will probably start experimenting more. To answer a previous question, the proof is a bit up in this thread. I posted a "geoc", or paper ocarina, tuned to C. I have also made 2 wooden ocarinas, both of which play within half a semitone of their intended note. So yes, I believe this works. I also realized I never posted pictures. I have since destroyed my C ocarina by accident, but I found my little soprano G earlier which reminded me about all this. It's in some rough shape though, and I had to rechisle the fipple to get it to play.

Video proof: http://www.youtube.com/watch?v=nztevSPenyM

Posted Image


Edited by Evil_Intentions, 19 May 2011, 01:58 AM.
Offline Profile Quote Post Goto Top
 
bowwing333
Member Avatar
Was Lost but now am Found
Wow thank you!
Offline Profile Quote Post Goto Top
 
Robert Hickman
Member Avatar
Ocarina maker

It would be interesting if someone can figure out how to make this work for non-rectangular ocarinas.

Offline Profile Quote Post Goto Top
 
SuperBobKing
Member Avatar
Quadruple Ocarinist
You just have to be able to calculate the interior volume of the abnormal shape. The best way I can think of is to when the ocarina is still in halves to pour in a liquid and measure the volume of the liquid, or the measure out a block of clay that is the right volume and mold it into the shape of the internal chamber. Although it may be better to try and use that milk plastic to mold the shape because unless you fire it the clay would stick to the ocarina and would shrink during firing, but I guess you could make a mold of the piece of clay that is the internal shape and then use that mold to make another out of plaster.
Offline Profile Quote Post Goto Top
 
maria
Inline Ocarinist x 4
Can someone tell me what the original formula was that was used to calculate the frequency of the ocarina? Numbers were plugged in, but what is the formula? Thanks!
Offline Profile Quote Post Goto Top
 
SuperBobKing
Member Avatar
Quadruple Ocarinist
Evil_Intentions
2 Dec 2010, 05:58 AM
V = 1/ (((F/2148.14)^2)/D)

where F is your frequency in hertz (reference) and D is your diameter that you found.

If you plan on making a 10 or less hole ocarina, then your frequency will be the one desired (523.25 for C5)
if you want a 12 hole oc, which means sub holes, then you want to use the note two notes below the tonic of the scale you wish to create. (i want a 12 in C5, so i use A4,440, as my F)
That was taken directly from the original post, because it did contain the original formula.

Offline Profile Quote Post Goto Top
 
Ocarina moon
Member Avatar
Beginner
How do I make a tenor g submarine style ocarina?
I am also going to need help making an alto g dragon tooth as well
Also a Zelda style ocarina too
The dragon tooth and Zelda style are for my buddies
Edited by Ocarina moon, 16 Sep 2012, 04:27 PM.
Offline Profile Quote Post Goto Top
 
shihomaru
Newbie
This is really cool, My girlfriend said she would be trying to make an ocarina for me in her ceramics class next semester so this guide was a great thing for me to send her to help. Thank you so much! I just have one question, how do you know how big to scale it for which tuning if it's not a common shape?
Offline Profile Quote Post Goto Top
 
Mr. giggums
Beginner
I have been trying to understand how the formula works but from what I have found elsewhere the correct formula should be:
Posted Image
where V = volume (in^3), A = area of fipple (in^2), L = length of windpipe (in), and F = frequency (Hz)

compared to the formula posted above:
Posted Image
where D = diameter (in) and the rest are the same as above

The difference is that A/L got simplified into D but that doesn't make sense. Also when I tried to plug in reasonable numbers the formula's answers vastly differ.
Edited by Mr. giggums, 28 Apr 2013, 11:08 PM.
Offline Profile Quote Post Goto Top
 
Seashell
Beginner
Mr. giggums
5 Apr 2013, 04:14 AM
I have been trying to understand how the formula works but from what I have found elsewhere the correct formula should be:
Posted Image
where V = volume (in^3), A = area of fipple (in^2), L = length of windpipe (in), and F = frequency (Hz)

compared to the formula posted above:
Posted Image
where D = diameter (in) and the rest are the same as above

The difference is that A/L got simplified into D but that doesn't make sense. Also when I tried to plug in reasonable numbers the formula's answers vastly differ.
Hello, all! I'm new around here, so please excuse any faux pas in this post.

No doubt about it: there's a crying need for a formula to aid ocarina designers. Cut-and-try is time consuming and wastes materials. And I agree that any empirical formula needs some sort of theoretical justification. Otherwise, we can't be sure when it will apply and when it won't, since all formulas for musical instruments make asumptions and have limitations.

I've been looking into how to calculate the resonant frequence of an actual ocarina for some time, reading all the relevant physics papers I can find on-line (about a dozen). I'm afraid the news is not good.

Physicists don't often study actual ocarinas, they study Helmholtz resonators and "ideal" ocarinas instead. I have not been able to find a single
paper that tested its conclusions against a real ocarina (musical instrument). (However, I have ordered a book that is said to contain a formula for an actual ocarina. I'll post about it after the book arrives).

Unfortuantely, there are big differences between a Helmholtz reonator and an ocarina, and between an ideal ocarina and a real one. Sure, ocarinas are *similar in principle* to a Helmholtz resonator, but there are important differences:

1) An HR is a passive device: you don't blow into, you listen through it. That's how Hermannn von Helmholtz used them: to identify frequencies -- he put the tiny hole in the bottom against his ear, then listened to whatever sound he was interested in. But as soon as you blow into the neck of an HR-like cavity -- say a Coke bottle-- you change the effective length and/or area of the neck. Moreover, your blowing adds energy to the oscillation, tending to raise its frequency (given that the resonant peak of an HR isn't all that sharp -- see below).

2) In addition to the fipple aperture which is always open, an ocarina usually has finger holes. This raises an entirely new problem: an HR with more than one neck! I've found comments that this is "analgous" to parallel impedences (or resistances) in electronics circuits, but not an actual formular. For this post, I'll stick to an ocarina with no finger holes or all the finger holes closed (bass note).

3) Moreover, an ocraina fipple opening isn't like a Coke bottle or HR neck: typically, it's wider than it is deep.. I found in a single paper an empirically-derived constant which is supposed to estimate the effective length for a typical ocarina fipple:

L = 2 * (8 * radius) / (3 * pi)
= 16 * radius / (3 * pi)
= (16/(3 * pi)) * radius
=

Unfortuantely, the authors (T. Kobayashi, et. al.) do not provide a citation, so the source is unknown and the odd form goes unexplained. Also, notice that it disregards the actual length (shell thickness)--apparently because it is small compared to the diameter, it can (for the fipple hole only!) be disregarded. Subsituting the above for L in the frquency formula gives:

F = (c / (2 * pi)) * sqrt( Area / ((16 * Radius) / (3 * pi)) )
= (c / (2 * pi)) * sqrt( (Area * 3 * pi) / (16 * Radius) )
since Area = pi * Radius^2:
= (c / (2 * pi)) * sqrt( (pi * Radius * Radius * 3 * pi) / (16 * Radius) )
= (c / (2 * pi)) * sqrt( (3/16) * pi^2 * Radius )
= (c / (2 * pi)) * sqrt( 1.85 * Radius )

and indeed, this last is the formula the paper uses. However, they only test it against a computer simulation of an ideal ocarina (in 3
dimensions).. Here is a link to the paper:
https://arxiv.org/pdf/0911.3567.pdf

Based on some fooling around I did, it appears that the exact construction of the fipple opening is crucial in determining the frequency of the instruments all-finger-holes-closed note with reasonable accuracy. Since the fipple is open all the time, it is a factor in determining all the pitch of all the instrument's notes.

Most of the published research on Helmholtz resonators has to do with uising them for sound damping (e.g., in a forced air duct) or flow optimization (e..g, in the intake manifold of an internal combustion engine. For these purposes, frequency does not have to be at all exact. Simple formulas derived from the Helmholtz resonator model work great.

But the ear is sensitive to very small changes in frequency--especially in a musical context, especially in ensemble playing. 440 Hz is a concert A (A4). 450 Hz will attract the laser-like eyes of the orchestra conductor: "You, yes, *you* in the second violins: you're sharp!".

Most people (including most orchestra conductors) can't hear absolute pitch: any pitch in the vocal range can serve as a proxy for A4, say 500 Hz. But as soon as you add a second instrument, you get the same problem: if I play 500 Hz and you play 550 Hz, it sounds like...beat tones.

The pitch of a real ocarina....well let's just say its not as that of a tuning fork. Hand identical ocarinas to five different players and ask them each to play with all finger holes closed, and you're quitely likely to get a range of almost one tone. One thing the ocarina does have in common with the Helmholtz resonator is that--as mentioned above--the resonant frquency peak isn't very sharp (unlike an air column instrument such as a recorder). So players continually use air pressure (and embrochure, if it's a xun) to adjust the pitch. Flutes and reed players make similar adjustments with embrochure: but withing a much narrower range. No matter how hard you blow into a recorder, it won't go as sharp as an ocarina (though it might jump into its second register).

So to really test a formula against a real ocarina, you need a compressor with a very accurate pressure regulator--not something you can buy at the hardware store. Designing valid experiments is harder than it seems.

Back to theory: the resonant frquency of a Helmholtz Resonator proportional to: sqrt( Area_of_hole / Volume * Length).
To get answer in absolute pitch (Hz), a constant must be introduced:

F = Constant * sqrt( Area_of_hole / Volume * Length).
where:
constant = Speed_of_sound / (2 * pi)

This formula is dervived from a more fundemental one in terms of the mass of the gas in the neck. If you think of an ocarina as a weight
suspended by a spring, then the volume inside is the spring (it compresses) and the mass of air in the neck is the weight (it resists motion).
But not only the air inside of the neck moves, so does a little air on each end. This "end effect" must be taken into consideration:

F = Constant * sqrt( Area_of_hole / Volume * Effective_Length).
where:
Constant = Speed_of_sound / (2 * Pi)
Effective_Length = Length + (End_effect_constant * diameter_of_hole)

A different paper gives 0.3 as a typical value for end effect. So:
Effective_Length = Length + (0.3 * diameter_of_hole )
and
F = Constant * sqrt( Area_of_hole / Volume * (Length + (0.3 * Diameter_of_hole))

Putting it all together, for a Helmholtz Resonator (not an ocarina!):
F = ( Speed_of_sound / (2 * Pi) ) * sqrt( Area_of_hole / (Volume * (Length + (0.3 * Diameter_of_hole)) )

The speed of sound depends on the temperature of the air. The effect of changes in barometric pressure is neglibible. Speed of sound must be expressed in whatever unit-of-measure you are using: if the dimensions are to be given in inches, then speed of sound should be in inches-per-second; if dimensions are in centimeters, the speed should be in centimeters-per-second. Frequency will always be in Hertz (cyles per second).

Alas, this formula does *not* work for an ocarina. Anything you find on the Net that is based on the Helmhotlz Resonator formula should not be used--it won't work for an ocarina. It might be get the frequency to within a few tones, but that's not accurate enough. It's on the righ track though.

Once you add an open finger hole, the there is an entirely different model: the Helmholtz resonator having two necks--which requires a different formula.

BTW, one reason to care about theory is that understanding it better may suggest ways to build better ocarinas. Modern instruments (such as the Boehme system flute, pedal harp and pianoforte) came about only musicians began to see the limitations of folk instruments as a problem, and makers began to ask "how can we fix this?".

Edit: fixed calculations of fipple effective length
Edited by Seashell, 3 Jun 2018, 05:01 AM.
Offline Profile Quote Post Goto Top
 
Ocypode
Double Ocarinist
Seashell
3 Jun 2018, 12:43 AM
Mr. giggums
5 Apr 2013, 04:14 AM

Physicists don't often study actual ocarinas


I bet that would make a nice scientific article. Especially so since there is already an article about ocarina, so a second could build upon it:
https://arxiv.org/pdf/0911.3567

It has already been mentioned here.
Offline Profile Quote Post Goto Top
 
1 user reading this topic (1 Guest and 0 Anonymous)
« Previous Topic · Ocarina Making · Next Topic »
Add Reply



Find us on TwitterFacebook | Read the FAQ