clavichord fretting

My clavichord project stalled when I realised it was just not going to work the way I’d done it.

This is partly because I’d naively gone for the full un-fretted design in the beginning, then later realised this would put too much pressure on the cheap bodywork and cause it to implode.

Changing the design afterwards to a fretted design wasn’t going to work either, because of how the keys were laid out.

So, the new plan is to rebuild the keyboard on the current clavichord, and hopefully get the thing finished as a triple-fretted, single-strung design.

Now, to explain…

If you have one string per note, this is called “unfretted”. In this design, every string is only ever hit by only one key.

The usual way to design a clavichord is “double-strung”, this means that every note actually has two strings for it. This makes double-strung clavichords louder than single-strung clavichords, because the combination of the two strings’ waves tends to alternately strengthen and dampen what’s happening at the soundboard.

Back to fretting – consider a guitar. Despite only having six strings, a guitar can play many more than only six notes. This is accomplished by “fretting” the strings. When you play a “G” on an “E” string, what happens is that you are shortening the wavelength of the overall string (with the fret and your finger), causing it to play a different note (G) than it would play if it was unfretted (E).

With a clavichord, the very act of striking the string with the key (or “tangent”, as the striking edge is called) causes fretting. The strings are damped at the ends with cloth or felt so when the key is not touching the string, the string doesn’t vibrate.

When you design your keyboard to multi-fret the strings, you need to do some calculation – let’s say you have a note, C, which is struck on the strings 100cm (let’s say) from the bridge. If your fretting involves the C# hitting the same string, then that key’s tangent must hit the string at about 94.4cm.

This is quite a small distance between the two tangents (5.6 mm), meaning that if you decide to triple-fret all your notes, then the keys for the high notes will be very close together, and the lower notes will be further apart (lower notes have larger wavelengths, so the distance between semi-tone frets increases as well as you get lower).

That explains the following image (a double-strung, triple-fretted clavichord – click for a larger image):

Note that the keys are all squashed together on the right side where the high notes are, and the spaces gradually increase as you move further left.

Notice as well that at the extreme left, the increase in spacing stops and all the keys are together again.

The reason for this is that when the notes get too low, there’s simply no more room for multi-fretting, so instead, the lower notes are all one per string.

There’s one more point to make about the keys.

Let’s say you create a key, which has its tangent 25cm from the fulcrum (a clavichord key is a lever). When the key is pressed, the tangent arcs up and strikes the string. It is still 25cm from the fulcrum in a 3D sense, but when measuring x/y from a top-down view of the clavichord, if the string is 4cm above the tangent (with key at rest), then the tangent strikes the string about 22.5cm from the fulcrum.

This must be taken into account when you design where the strings will contact the bridge and the hitchpins, as getting this wrong will cause the tangents to miss. Yes, you could just place the tangents after doing the strings, but my goal here is to be as perfect as possible. (there’s also the added problem that the tangent’s top is a certain height (3cm, say) above the level of the fulcrum, but you get the picture)

I’ve explained some of the problems to do with designing a fretted keyboard and string layout. Now, I’m off to write a program to design one automatically!

jQuery k3dCarousel plugin

I needed a “3D” carousel to rotate images. The currently available jQuery plugins for this purpose were either too large, too restricted (showing only 4 at a time is not good enough), or too old (not working in jQuery 1.4+).

So I wrote my own.


demo

In our CMS, WebME, this is available in the Image-Transition plugin. (If you’re interested in using WebME, you can either download it through SVN, or talk to us about our reseller deals.)

How the thing works, is that you add a list of images to an element like this:

[html]
<div id="k3dCarousel">
<img src="images/concrawood.jpg" />
<img src="images/fernheasty.jpg" />
<img src="images/mcnallys.jpg" />
<img src="images/northernstandard.jpg" />
<img src="images/soccertours.jpg" />
<img src="images/soundinsulation.jpg" />
<img src="images/textaroom.jpg" />
<img src="images/windhoist.jpg" />
</div>
[/html]

Then link to the jQuery library and the jquery.k3dCarousel plugin:

[html]
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
<script src="jquery.k3dCarousel.min.js"></script>
[/html]

And then tell jQuery to run the plugin after all the images have loaded:

[html]
<script>
$(window).load(function(){
$(‘#k3dCarousel’).k3dCarousel();
});
</script>
[/html]

If you want, you can vary the speed of the cycle by changing the sT (spin-time) variable, or the wT (wait time), which govern how long it takes for the images to move from point to point, and how long they pause once reaching there:

[html]
<script>
$(window).load(function(){
$(‘#k3dCarousel’).k3dCarousel({
wT: 500,
sT: 100
});
});
</script>
[/html]

Interested yet? Download it (tar.bz2, zip)