posted 08 March 2003 20:42            

struckbars.kym

The two sounds simulate what happens when

(1) a bar is clamped at one end, and
(2) a bar is clamped at both ends.

Each sound uses up to 10 partials to synthesize the sound (more than enough!), in the correct proportions according to the modes excited by striking where you do. The sounds are pitched so you can play them across the keyboard. And some amount of amplitude normalization was applied to keep the output approximately the same loudness regardless of where the striking position is.

[But note... striking right at and very close to the clamps produces very little sound... and what is produced consists mainly of the highest modes, so you won't hear them unless you play in the first register of the keyboard down around C0!]

[Since some of the partials are as much as 300 times the fundamental frequency (for the bar clamped at one end), aliasing can become a big problem. Anti-aliasing was attempted with a hack; ensuring the frequencies of the oscillators are never allowed to go above Nyquist frequency, and assuming the amplitudes are almost always small. I certainly can't hear anything pinned at the Nyquist frequency...]

These Sounds implement the solutions of a 4th order differential equation for a uniform bar in the two clamping arrangements. This is something that Tassman cannot do live... while the magic of Smalltalk in Kyma allows us to continuously vary the strike point while we are playing. Very nice feature for Kyma to boast!

There is one other situation -- a bar without any clamps -- that I want to attempt, and while the solution is relatively simple in theoretical terms, it is much more difficult to express it in Smalltalk. It will be exactly the same Sound as the double-clamped bar, but the sound will be different with respect to striking position. The solution in this case is merely the 2nd derivative with position of the double clamped position.

Striking at various points along the bars excites resonant modes in the bar to varying degrees. For example, the double clamped sound approximates a Xylophone, and when you strike in exactly the middle of each bar (!CC01 = 0) you select out to play only the fundamental and odd partials -- the even partials cannot be excited by striking at that position. For other positions you can excite the higher partials in preference to the fundamental. Really neat!

The single-clamped case sounds more like doorbells and orchestral chimes, but an orchestral chime (I thought) was just a bunch of tubes suspended by a string -- so it ought to be the unclamped case??

Again, a completely unclamped bar sounds exactly the same as a bar clamped at both ends -- in terms of the overtones generated. The vibrational modes look entirely different. But there ought to be a place on each where you can strike and get identical sound from them.

Enjoy!

posted 09 March 2003 02:13            

struckbars.kym

1. Clamped at one end and struck anywhere along its length controlled by the mod wheel. Mod wheel 0 -> free end of bar, 1 -> clamped end of bar.

2. Clamped at both ends and struck anywhere along the length from the middle of the bar to one end, as mod wheel moves from 0 to 1.

3. Unclamped bar, mod wheel 0 -> end of bar, 1 -> middle of bar. A little Mathematica showed the simple way to this second order derivative.

4. Plucked bar clamped at one end. Almost the same as the struck bar with a strike at the very end, but not quite. No mod-wheel control on this one. Use for kalimba.

Amplitudes have been reworked to represent what would be heard in a mic at "infinite" distance from the bar -- the the sound emanating from every portion of the bar is collected by the mic. The only thing that changes the sound is where you strike the bar, and hence, what modes you excite.

Interestingly, while not a harmonic sequence, all of the partials add in 1/F proportion, where F is the frequency of the partial. In other words we have a 1/F line spectrum. I think that is interesting, don't you?

The only other thing that can control how much of a partial gets added in is where you strike the bar. Some fraction of all the modes gets excited, but never more than 1/F of any of them.

Hitting the free and doubly clamped bars in the middle brings out the fundamental and odd partials only. Even partials cannot be excited at this position.

Other positions along the bars will preferentially excite higher partials over the fundamental.

[loudness scaling compensation as a function of strike position has been removed... Do you want it back?]

- DM

posted 09 March 2003 03:05            

struckbars.kym

I took the free bar and added separate AD envelopes (attack-decay) to each partial. There is an overall !Decay parameter that controls the duration of the decay on the fundamental. A !Slope parameter controls the other partials in relation to this duration.

When the !Slope is negative the higher partials decay more rapidly than the lower partials, simulating wood and plastic.

When the !Slope is zero, we are back to our bars with equal decay times on all of the partials.

When the slope is positive (be careful not to make this too large!) the lower partials decay more rapidly than the higher partials, simulating metal and glass. In order to get everything to reasonable decay times you may need to drop the !Decay when making the !Slope positive. Remember we have 10 partials.

The scaling goes exponentially with respect to partial number. Hence

decay[n] = decay[1]*Exp[(n-1)*slope].

partial number n runs from 1 to 10, decay[1] is the !Decay parameter, and slope is the !Slope parameter.

I just pulled this scaling law out of a hat. I have no apriori physical reason for doing things this particular way, but it seems reasonable...