# Homework Help: Asymmetric tuning fork, and fender rhodes

1. Jul 30, 2008

### zorgzorg2

Hi all,

First of all, thanks for the great forum !

Second, the question I am about to ask is not homework, but due to my poor level in physics, I thought this part of the forum would be the best.

I am a computer scientist, and I would like to make a physical model of the Fender Rhodes piano, the goal being to make a realtime implementation of the model and make something like a vst plugin. That's why I need some insight on how it physically works.

1. The problem statement, all variables and given/known data

Ok, here we go. A fender rhodes piano is an electric piano consisting of a hammer hitting a tuning fork.
The tuning fork is asymmetric (see http://www.fenderrhodes.org/rhodes/manual/ch1.html" [Broken])

I have been searching the equation for the movement of the end of the thin end of the fork (called the tine), but all I could find was the movement of the cantilever beam. I suppose that the case of the tuning fork is different, since there must be an interaction between the two beams.

2. Relevant equations

Thus I found this page http://em-ntserver.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm" [Broken] that gives equations, but as I said earlier, I am not a physicist, so I'm not sure how to get the equation of the vertical movement of the tine from there. Also, in my case, the beam is cylindrical, does it change something ?

And above all, am I on the right way ? or is the tuning fork movement totally different from the cantilever ?

Cheers,

Last edited by a moderator: May 3, 2017
2. Jan 20, 2010

### AcouSchtick

I am also in a similar position to you because I am writing a small music dissertation on the Fender Rhodes which includes a large section on the physics of the instrument and would like an equation for the vibration instead of just takings sonograms and comparing to other simlilar instruments. If i am able to develop an equation (some how) i will post it on here. I am at the University of the West of England on BSc Audio and Music Technology.

cheers :-)

Last edited: Jan 20, 2010
3. Jan 23, 2010

### zorgzorg2

Hi there,

In the long time that separate us from the first message of this thread, I did some research and did not find anything on asymmetric tuning forks unfortunately.

My assumption is now that the equation of motion is approximately similar to an excited cantilever beam, the excitement decaying in time.

Let me know if you have something !

Cheers,
Martin

4. Jan 25, 2010

### AcouSchtick

A funny thought...Never know Harold Rhodes could have got some of his theory from cantilever beams as he did major in Architecture ... but dropped out to look after his family and take over a piano school ;-)

cheers will let you know if i come up with anything

5. Feb 7, 2010

6. May 9, 2011

### EntRhodes

Is anyone still watching this topic? If so I have some information to contribute. I had it all typed up but there was a submission problem and I don't mind retyping everything so long as there's someone out there who cares. :)

Last edited by a moderator: May 5, 2017
7. May 10, 2011

### AcouSchtick

Go for it, should be interesting. :-)

I hate that when there's an issue with a forum page and you've just written everything, know the feeling "Grrr Arggh".

8. May 10, 2011

### EntRhodes

Full disclosure. I became fascinated with chromatic percussion a few years ago with a primary interest in building my own instruments. I have scoured the net for knowledge, wisdom, and guidance. I am an elec engineer with a lifelong love of music, but can't read a note of it.

Just picked up my 1st rhodes piano last week. I quickly put it down again as it is quite heavy (125 lbs, ha) but I have studied it quite a bit. I'm going to take a stab at this.

The Fender Rhodes piano uses tuning forks as tone generators. Tuning forks are extremely well balanced resonant systems and have excellent sustain, but have some drawbacks. The lightweight plastic/wood hammers used in the Rhodes cannot really impart much energy into the relatively thick arms of a tuning fork, and the forks would have to be quite long to present adequate motion to the electromagnetic pickups. The compromise was to use an asymmetrical fork - the hammers directly strike a thin short metal tine, and that tine is coupled to a larger tonebar. The tine and tonebar pair vibrate at the same frequency even though they are of different weight, length, and thickness. But at it's heart this is still a tuning fork.

The tine and tonebar can each be modeled as a beam that is free on one end and clamped at the other. Here are equations that are in play.

TINES: modeled as a cylindrical solid
frequency of fundamental = fn = (pi * v * K * m^2) / (8L^2)
n=1
where v = speed of sound in the material of tine
L = length of the tine
m = 1.194 when n = 1 (fundamental freequency)
K = (tine radius) / 2

TONEBARS:

Almost the same as for tines, but since they are rectangular in profile, they have a different value for K.
v = speed of sound in the material of tonebar
L = length of the tonebar
m = 1.194 when n = 1 (fundamental freequency)
K= (tonebar thickness) / 3.46

There is a resonance factor involved, some folks call it Q, that is not represented in this model. I am not sure if there is a way to mathematically predict the Q. I have dug up these links which may help. I give the google docs quick view links so please excuse the long links.

Q principles:

computerized experiments with a tuning fork:

Caveats: I believe rhodes pianos use swagged tines, which taper slightly along their length. And then, don't forget about the tuning spring. These factors produce different harmonics that are no doubt part of the gestalt that is the Rhodes piano sound. This means that a model of a cylindrical tine is a simple approximation.

Thats all I have for now :)

Last edited: May 10, 2011
9. Oct 14, 2011

### Tofustw

Cool thread, I'm really interested in this too!

EntRhrodes: where did you find those equations? Citation, please!

Thanks guys,
Greg

10. Jun 27, 2012

### EntRhodes

I lost track of this forum. Hope someone is still watching.

The following link is to a .pdf for a book called "The Physics of Musical Instruments"
Page 99 has the free end bar equations that I referenced above.