user2178: I want to try to make my own musicbox. The picture below shows what I mean:

I was wondering how to determine the length of the metal tone generating plates (shown in dark grey). I assume it is a function of the length and thickness, I just don't know the exact relationship.
Could someone please provide me with a formula relating the plate dimensions with the frequency?

user35861: tI am building a music box comb ( and everything else ) to make a musicbox. I have found little answers out there but this is what I KNOW from trial and error. Get a cheap , used miter saw blade. and using an angle grinder cut a square or rectangle out of it , ensuring that it does not get hot. Have a spray bottle of water or bowl of water to cool it every few seconds Choose how many notes you will need and with a sharpie and ruler draw lines about 1/8th inch wide but allow for the width or cut of your blade ( 40, ks ) I have used my angle grinder for years and using the  cutoff blade  is second nature... but be careful,  Draw a line at about 60 degrees at an angle for your cut teeth ensuring each one is a bit longer by cutting to that line. Drill 3 holes near the top and bolt it down to a sound carrying box of any kind. You can buy a clip on guitar tuner for under $10 . with that clipped on near the comb pluck a tooth and see what notes you have. By cutting a bit deeper the note will become lower.   Get it close for now. After I have a clean , deburred comb I heat it nearly red hoe and then quickly drop it into water. This tempers the steel. Any blacksmith shop can explain annealing... if you dont know simply lay it in your oven at 499 for a few hours... that will make the steel harder , but not brittle.

user1890: The tuned teeth (or lamellae) of the steel comb is typically set to a chromatic scale. To change the tuning would require adding or subtracting material to an individual tooth with some trial and error and a good ear. Changing the length would cancel the action of the pins on the revolving cylinder so that is not a good idea.
If you think the scale you have meets your tuning definition then it would be far easier to make a new scroll to change to the melodic and harmonic content you desire. If you are starting from scratch and have the tools you should make a system to be able to change the scrolls so you have a diversity of songs.
Here is a reference to tuning the reeds on a harmonica since this is adding and subtracting material related:
http://www.angelfire.com/music/harmonica/mikesretuning.html
Information on how to tune lamellae as used in a Karimba:
http://www.nscottrobinson.com/mbiratunings.php
Here's a place where you can make your own music box tunes by using 
punchable paper strip musical movement:
http://www.deanorgans.co.uk/order_musicalmovements_mbm30hp.htm
Math part:
http://en.wikipedia.org/wiki/Tuning_fork#Calculation_of_frequency
UPDATE:
I am not entirely certain that using tuning fork math is the right place for a series of metal bars as found in a music box comb so I have done some more searches and found a reference that covers much more here:
http://windworld.com/features/tools-resources/exmis-free-bar-length-calculator/

2178: <p>I want to try to make my own musicbox. The picture below shows what I mean:
<img src="https://i.stack.imgur.com/UvfPs.jpg" alt="enter image description here"></p>

<p>I was wondering how to determine the length of the metal tone generating plates (shown in dark grey). I assume it is a function of the length and thickness, I just don't know the exact relationship.</p>

<p>Could someone please provide me with a formula relating the plate dimensions with the frequency?</p>
 35861: <p>tI am building a music box comb ( and everything else ) to make a musicbox. I have found little answers out there but this is what I KNOW from trial and error. Get a cheap , used miter saw blade. and using an angle grinder cut a square or rectangle out of it , ensuring that it does not get hot. Have a spray bottle of water or bowl of water to cool it every few seconds Choose how many notes you will need and with a sharpie and ruler draw lines about 1/8th inch wide but allow for the width or cut of your blade ( 40, ks ) I have used my angle grinder for years and using the  cutoff blade  is second nature... but be careful,  Draw a line at about 60 degrees at an angle for your cut teeth ensuring each one is a bit longer by cutting to that line. Drill 3 holes near the top and bolt it down to a sound carrying box of any kind. You can buy a clip on guitar tuner for under $10 . with that clipped on near the comb pluck a tooth and see what notes you have. By cutting a bit deeper the note will become lower.   Get it close for now. After I have a clean , deburred comb I heat it nearly red hoe and then quickly drop it into water. This tempers the steel. Any blacksmith shop can explain annealing... if you dont know simply lay it in your oven at 499 for a few hours... that will make the steel harder , but not brittle.</p>
 1890: <p>The tuned teeth (or lamellae) of the steel comb is typically set to a chromatic scale. To change the tuning would require adding or subtracting material to an individual tooth with some trial and error and a good ear. Changing the length would cancel the action of the pins on the revolving cylinder so that is not a good idea.</p>

<p>If you think the scale you have meets your tuning definition then it would be far easier to make a new scroll to change to the melodic and harmonic content you desire. If you are starting from scratch and have the tools you should make a system to be able to change the scrolls so you have a diversity of songs.</p>

<p>Here is a reference to tuning the reeds on a harmonica since this is adding and subtracting material related:</p>

<p><a href="http://www.angelfire.com/music/harmonica/mikesretuning.html" rel="nofollow">http://www.angelfire.com/music/harmonica/mikesretuning.html</a></p>

<p>Information on how to tune lamellae as used in a Karimba:</p>

<p><a href="http://www.nscottrobinson.com/mbiratunings.php" rel="nofollow">http://www.nscottrobinson.com/mbiratunings.php</a></p>

<p>Here's a place where you can make your own music box tunes by using 
punchable paper strip musical movement:</p>

<p><a href="http://www.deanorgans.co.uk/order_musicalmovements_mbm30hp.htm" rel="nofollow">http://www.deanorgans.co.uk/order_musicalmovements_mbm30hp.htm</a></p>

<p>Math part:</p>

<p><a href="http://en.wikipedia.org/wiki/Tuning_fork#Calculation_of_frequency" rel="nofollow">http://en.wikipedia.org/wiki/Tuning_fork#Calculation_of_frequency</a></p>

<p>UPDATE:</p>

<p>I am not entirely certain that using tuning fork math is the right place for a series of metal bars as found in a music box comb so I have done some more searches and found a reference that covers much more here:</p>

<p><a href="http://windworld.com/features/tools-resources/exmis-free-bar-length-calculator/" rel="nofollow">http://windworld.com/features/tools-resources/exmis-free-bar-length-calculator/</a></p>
