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  #1  
Old 08-28-2012, 11:26 PM
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Default calculating standing waves to find fundamental frequency

does anyone know much on this subject? i have a tunebot and want to try tune my drums to their 'perfect' frequency to see what they sound like, ive found out that if you calculate the standing wave of the drum that will give you the fundamental frequency to tune too.

this is what i found:

The standing wave frequency of any drum can be found by the formula

f = V / 2d. V = the velocity of the sound wave which is 1130 ft/sec, where "d" is the dimension in feet and the "f" result found will equal the fundamental frequency.

What relevance is this? The drum inherently will produce a very resonant note regardless of tuning based upon dimensional characteristics but will be extremely strong once heads and everything else allows it to be truly tuned at that frequency. So for a 24" bass drum you can find that 282 hz is the most resonant note for this size drum, which is musically right between a C#4 and D4. Whereas a 22" drum equates to 308 Hz, or musically between a D4 and D#4.

If you apply these principles to a 12" tom, you get 565 Hz or between a D5 to D#5.


the part im unsure with is the 2d, say im tuning my 13x6 snare is it 2 x 13? or 2 x 6? or 2 x 13x6?

also what didn't make sense is that it says for a 22" bass which is what i have, 308hz is the most resonant tone? thats incredibly high as so far we previously tuned to a fundamental of around 80hz, 308hz is way higher than my snare.

if someone could help me understand this that would be great!

thanks if you can help!


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Old 08-29-2012, 12:28 AM
Longfuse Longfuse is offline
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Default Re: calculating standing waves to find fundamental frequency

I have no idea about the accuracy of the formula you have posted. However, taken at face value, the following is the way to calculate the resonant frequency.

Using the example given, 24" bass drum = 2 feet

Therefore the calculation was 1130/2X2 = 282.5 hz

Your 13inch snare = 13/12 ft = 1.08 ft

Therefore f = 1130/(2 X 1.08) = 523 Hz

Again, I'm taking the info you posted at face value. 'f' is NOT the fundamental pitch that your drum is tuned to, which may be much, much lower. 'f' seems to represent the most resonant pitch that your drum can produce. You would not want to tune to that pitch - as you point out, it would be too high.

However, if you think of the resonant pitch as being a harmonic, then it would make sense to tune your drum to: half 'f'; a third of 'f', a quarter of 'f' etc. Basically, the lowest pitch that sounds right and that is divisible by the resonant pitch. The natural harmonics of the skin will then resonate, leaving the fundamental (lower pitch) in tact to provide the bottom end.

That's my guess...
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Old 08-29-2012, 12:28 AM
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Default Re: calculating standing waves to find fundamental frequency

For me, life's too short to try to marry a drums fundamental frequency to specific notes or frequencies. And yes your 12" tom and 22" bass drum are way off.

Dennis
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Old 08-29-2012, 12:48 AM
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Default Re: calculating standing waves to find fundamental frequency

What I don't understand is how such a calculation can be made purely on the size of the drum. Fundamental is also affected by construction, wood species, & other factors. This seems far too simplistic to me. Having conducted numerous tests on different constructions & wood species, I know just how much the fundamental can vary.

TBH, just tune them until they sound right. A good drum will tell you when it's happy.
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Old 08-29-2012, 12:48 AM
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Default Re: calculating standing waves to find fundamental frequency

I think you may be misinterpreting the formula: the resonant frequency of a cylindrical air column is proportionate to its *length*, not to its diameter. So, the fact that they used "d" there is very misleading: to represent depth of the cylinder, not diameter of the cylinder as one might believe. The diameter has a great effect on the Q of the resonant system, but not so much on its fundamental frequency. Which might seem counterintuitive- but life behaves that way... In short, a (perfectly rigid and ideal) 12" deep power tom with 10" heads, a 12" tom with 12" heads, and an old skinny 12" deep marching bass drum with 24" heads would all have exactly the same resonant frequency, if (and only if) you could *ignore the heads*. http://hyperphysics.phy-astr.gsu.edu...opecol.html#c1

The problem for drums is that the heads are far from negligible in their influence on the column, as is the influence on Q produced by the relationship between length and diameter (which is why pipe organ pipes intended to produce the most pure possible fundamental tone are long and skinny, as well as trombones and sousaphones). As are the shell materials, in terms of mass and rigidity. But particularly heads: they have mass and elasticity, and their influences work in very nonlinear ways to affect the resonance of the whole system. So trying to model anything mathematically without consideration of the head behaviors is going to be pretty much meaningless, I think.
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Old 08-29-2012, 12:52 AM
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Default Re: calculating standing waves to find fundamental frequency

I've always maintained that a drum wants to make one specific note based on the volume of its interior, glad there's a formula for that! Obviously a drum makes various pitches that sound great to our ear or a mic, but technically, mathmatecally, there's one 'perfect' pitch that resonates best. I suppose the octave up or down would also work, assuming you can get a head to tune that far from a given pitch!

Theory and calculations aside, I just tune a drum where it sounds best to me, or the mic, or the audience.

Bermuda
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Old 08-29-2012, 12:54 AM
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Default Re: calculating standing waves to find fundamental frequency

Quote:
Originally Posted by skod View Post
I think you may be misinterpreting the formula: the resonant frequency of a cylindrical air column is proportionate to its *length*, not to its diameter. So, the fact that they used "d" there is very misleading: to represent depth of the cylinder, not diameter of the cylinder as one might believe. The diameter has a great effect on the Q of the resonant system, but not so much on its fundamental frequency. Which might seem counterintuitive- but life behaves that way... In short, a (perfectly rigid and ideal) 12" deep power tom with 10" heads, a 12" tom with 12" heads, and an old skinny 12" deep marching bass drum with 24" heads would all have exactly the same resonant frequency, if (and only if) you could *ignore the heads*. http://hyperphysics.phy-astr.gsu.edu...opecol.html#c1

The problem for drums is that the heads are far from negligible in their influence on the column, as is the influence on Q produced by the relationship between length and diameter (which is why pipe organ pipes intended to produce the most pure possible fundamental tone are long and skinny, as well as trombones and sousaphones). As are the shell materials, in terms of mass and rigidity. But particularly heads: they have mass and elasticity, and their influences work in very nonlinear ways to affect the resonance of the whole system. So trying to model anything mathematically without consideration of the head behaviors is going to be pretty much meaningless, I think.
\

Not to mention the tension on the head (variably) affects the potential energy of the entire system...
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Old 08-29-2012, 12:56 AM
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Default Re: calculating standing waves to find fundamental frequency

Quote:
Originally Posted by keep it simple View Post
What I don't understand is how such a calculation can be made purely on the size of the drum. Fundamental is also affected by construction, wood species, & other factors. This seems far too simplistic to me. Having conducted numerous tests on different constructions & wood species, I know just how much the fundamental can vary.

TBH, just tune them until they sound right. A good drum will tell you when it's happy.
Agreed, not possible. And not as fun.
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Old 08-29-2012, 12:56 AM
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Default Re: calculating standing waves to find fundamental frequency

That being said, it's my personal belief that there are far more important factors to the tone of the drum than how long it resonates for. The tension (potential for resonance), construction and dimensions have far more to do with the sustain of a drum than tuning it to the exact frequency the shell knocks at. Keep it simple pretty much beat me to it.
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Old 08-29-2012, 01:09 AM
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Default Re: calculating standing waves to find fundamental frequency

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Originally Posted by Nickropolis View Post
Agreed, not possible. And not as fun.
What he said! There are reams of articles on the physics of vibration of circular membranes and whatnot, and they are all dry as hell and only suited for the true nerd. And nobody is so much of a nerd as be unable to sleep without crunching together such a model (although I have known and worked with some folks who come close).

But we all already have the most ideal tuning device ever created: the one that came up with equal temperament, the various tunings for stringed instruments, and most astonishingly the exquisite tuning of the very complex body resonances of a violin: the Mark 1 earbone. Most of us even have a spare, in fact! Just takes some practice to use...
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Old 08-29-2012, 01:15 AM
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Default Re: calculating standing waves to find fundamental frequency

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Originally Posted by skod View Post
What he said! There are reams of articles on the physics of vibration of circular membranes and whatnot, and they are all dry as hell and only suited for the true nerd. And nobody is so much of a nerd as be unable to sleep without crunching together such a model (although I have known and worked with some folks who come close).
.
You clearly haven't met my Grandad. The Research Physicist for the BBC! This is exactly the kind of thing he worked with for the best part of forty years...
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Old 08-30-2012, 03:52 AM
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Default Re: calculating standing waves to find fundamental frequency

Quote:
Originally Posted by bermuda View Post
I've always maintained that a drum wants to make one specific note based on the volume of its interior, glad there's a formula for that! Obviously a drum makes various pitches that sound great to our ear or a mic, but technically, mathmatecally, there's one 'perfect' pitch that resonates best. I suppose the octave up or down would also work, assuming you can get a head to tune that far from a given pitch!

Theory and calculations aside, I just tune a drum where it sounds best to me, or the mic, or the audience.

Bermuda
thats exactly what im after! finding that one perfect tone of the drum to see what it sounds like, i have the mapex saturn limited edition exotic 6 piece, 22 bass, 10 12 14 16 toms, i know these toms can produce an awesome sound as ive heard it by luck from tuning (couldn't keep it at that pitch as i was tuning to certain notes of a key signature at the time) just wanna find out if there is a way to find this 'perfect' pitch without spending hours trying lots of different tuning! lol
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Old 08-30-2012, 03:58 AM
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Default Re: calculating standing waves to find fundamental frequency

thanks for all your replies, i thought it would be way harder to work out than the simple calculation i found! i think it was from a book called the drum tuning bible or something?

starting to spend a lot more time tuning my kit and was wondering does anyone have any particular methods they like to use on a new kit to find the sweet spot of a drum? or is it purely trial&error?
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Old 08-30-2012, 04:05 AM
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Default Re: calculating standing waves to find fundamental frequency

Quote:
Originally Posted by skod View Post
I think you may be misinterpreting the formula: the resonant frequency of a cylindrical air column is proportionate to its *length*, not to its diameter. So, the fact that they used "d" there is very misleading: to represent depth of the cylinder, not diameter of the cylinder as one might believe. The diameter has a great effect on the Q of the resonant system, but not so much on its fundamental frequency. Which might seem counterintuitive- but life behaves that way... In short, a (perfectly rigid and ideal) 12" deep power tom with 10" heads, a 12" tom with 12" heads, and an old skinny 12" deep marching bass drum with 24" heads would all have exactly the same resonant frequency, if (and only if) you could *ignore the heads*. http://hyperphysics.phy-astr.gsu.edu...opecol.html#c1

The problem for drums is that the heads are far from negligible in their influence on the column, as is the influence on Q produced by the relationship between length and diameter (which is why pipe organ pipes intended to produce the most pure possible fundamental tone are long and skinny, as well as trombones and sousaphones). As are the shell materials, in terms of mass and rigidity. But particularly heads: they have mass and elasticity, and their influences work in very nonlinear ways to affect the resonance of the whole system. So trying to model anything mathematically without consideration of the head behaviors is going to be pretty much meaningless, I think.
ah i see, that makes more sense now, i did try this formula on my snare and it wasn't too bad (we did it a octave lower than the frequency given) but it wasn't impressive enough, the tune bot is amazing though for tuning, works perfect every time
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Old 11-06-2012, 06:22 PM
Dazzathedrummer Dazzathedrummer is offline
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Default Re: calculating standing waves to find fundamental frequency

I've just bought a Tune bot so i've been scanning the net for opinions on tuning.

regarding the fundamental/most resonant frequency, the most useful thing that I heard was to simply tap on the side of the drum and figure out what the main note is.
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Old 12-14-2013, 04:25 PM
SmoothOperator SmoothOperator is offline
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Default Re: calculating standing waves to find fundamental frequency

My suspission is that the two headed tom behaves more like a Helmholtz resonator than a vibrating column of air, since the wave length of the fundamental is so much longer than the drum.

If this were true, then the tom would essentially behave as a three spring system: top head, bottom head, air volume. If we assume the port area is equal to the port length, then the frequency of the air behaving as a spring would be.

F=(v/(2*pi*sqrt(V))

Where v is the speed of sound and V is the volume of the drum.

http://en.wikipedia.org/wiki/Helmholtz_resonance

You could add other springs to the system, shells etc. If the two heads were tuned identically, and were of the same composition, it would be essentially a two spring system.
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Old 12-15-2013, 02:48 AM
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Default Re: calculating standing waves to find fundamental frequency

You don't tune a drum. You tension it.
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Old 12-15-2013, 03:33 AM
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Default Re: calculating standing waves to find fundamental frequency

Quote:
Originally Posted by Dunnett View Post
You don't tune a drum. You tension it.
Ronn....are you saying this cause you are

(a)joking around
(b)employing hyper vigilance in using appropriate nomenclature
or
(c)because you are implying that the drum already has a fundamental tone or "tuning" based on its physical size/quarter wavelength relationship....and you tension the heads to support that

curious...
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Old 12-15-2013, 03:42 AM
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Default Re: calculating standing waves to find fundamental frequency

I know a drummer who plays with so many different types of gigging bands that he really
doesn't bother to tune his drums because he would have to retune for a different gig. I could
never do that but he does and almost no one ever wants to "sit in" on his gigs. He's the
only drummer I ever knew that does that.
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Old 12-15-2013, 03:46 AM
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Default Re: calculating standing waves to find fundamental frequency

I have always used one of these two depending on the winter/spring solstace.
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Old 12-15-2013, 03:53 AM
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Default Re: calculating standing waves to find fundamental frequency

I would look at circular membrane vibrations and nodes. There is a ton of math on that.
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Old 12-15-2013, 04:09 AM
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Default Re: calculating standing waves to find fundamental frequency

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Originally Posted by GRUNTERSDAD View Post
I have always used one of these two depending on the winter/spring solstace.
Sure, but if the Framistan is not calibrated with the 7th Fetzer Valve, neither is valid...seasonal events notwithstanding.
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  #23  
Old 12-15-2013, 04:31 AM
wildbill wildbill is offline
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Default Re: calculating standing waves to find fundamental frequency

I've heard of standing waves in reference to acoustically treating rooms.

It's when a wave bounces off a wall and reinforces the same frequency wave on its way back.
EDIT: these standing waves are undesirable, and can be eliminated through non-parallel walls,
rounding of corners and edges, sound absorbing panels, and other means. /Edit.
I suppose it could also be applied to the interior surfaces of drums.

That's different than a fundamental frequency though.


I like Gruntersdad's winter/spring solstice tuning method better though.

.

Last edited by wildbill; 12-15-2013 at 03:54 PM.
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Old 12-15-2013, 09:10 AM
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Default Re: calculating standing waves to find fundamental frequency

Quote:
Originally Posted by Dunnett View Post
You don't tune a drum. You tension it.
Quote:
Originally Posted by shemp View Post
Ronn....are you saying this cause you are

(a)joking around
(b)employing hyper vigilance in using appropriate nomenclature
or
(c)because you are implying that the drum already has a fundamental tone or "tuning" based on its physical size/quarter wavelength relationship....and you tension the heads to support that

curious...
Of course, I can't speak for Ronn, but I feel the same when I "tune" a drum. I'm tensioning the heads such that the instrument delivers according to it's design/construction. I select a drum based on what I want it to give, pretty much in the same way I would select a cymbal.
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