Physical Models

[JovianPyx]

Is anyone other than me doing physical model experiments?

Since I have a successful physical model synth (Karplus-Strong one dimensional string) working, I want to create more models for different sounds.

My own goal is not necessarily to make an exact model of a piano or any other existing natural instrument, rather, I would like to use principles of physical modelling and create new instruments with natural characteristics.

My current interest is a modification of my string model. Currently, it exists only as a C program that generates raw data which is then converted to .WAV using the "sox" program.

The model uses two delay lines, one is long, the other is short. The first's (the long one) output is coupled to the second's input, both delay line outputs are weighted and summed, IIR filtered and sent to the input of the first delay line. The idea was to create a digital waveguide with a "soft" reflection point. Ultimately, I would like to have multiple reflections by using many short delay lines after the long one, but for now its only two.

Anyone else done something like this?

[frijitz]

[mandrigora]

If want something sans DIY, see the Technics WSA-1, it is a modelling synth that does pretty much exactly what you describe.

[JovianPyx]

[frijitz]

[blue hell]

Maybe try to contact Chet Singer he is really into physical modeling (on the NM and IIRC reaktor). I'm sure he'll have some links for you.

[blue hell]

Also see: http://electro-music.com/pm_tutorial/

[blue hell]

And : http://www.cs.princeton.edu/~prc/AKPetersBook.htm

[williamsharkey]

Think of different arrangements for strings. For example, how would you model three strings connect to each other at the center, to form a Y.


Also think about introducing objects near the string. For example, how would you model placing a human finger near a string, to damp it?


Or how might you model a string, that part of lying on a table top. Like this

[JovianPyx]

[williamsharkey]

>Yes, I understand this much, I read somewhere that one should "think physical" or "think physics" when designing these models. Would that I could go back 35 years in time and re-educate myself in physics and a bit more math.

I agree with the idea of thinking physical.

>Ian and Blue Hell posted some good links, I may need to buy a book. For now, I've found information on models other than what was my initial interest when I started this thread (drums). It helps me to have the model well described, especially with block diagrams as clues. Articles on many models I've found have too little detail. However, recently I found a description for a "slide flute" model (Perry Cook) with almost enough information to try to implement a design. Once I do this, I can play with the model to change it (or learn by breaking it).

I do not use equations or models for strings or drum membranes. Because, to me that takes the physical, fun part out of it. I don't have an intuitive understanding of the equations.

I don't know if this is the way you're supposed to "do it", but I will explain my method:

What I do is create points.

Points are the building block of my models.

I understand points. They only have a few qualities: Mass, Position, and Velocity.

I know the equations for points. It kinetics that I learned in high school. F=MA , things like that.

Then, I think of a thing I want to model. Like a string.

So I simplify it. What is the minimum number of things/relationships that I need to model a string? Here's how I might answer it:

I need 2 dimensions.

I need about 20 points connected to each other.

I need to Fix the position of the start and end point.

I need to give each point two neighbors: Left and right.

I need to decide how the neighbors affect point. For me, I guessed neighboring particles were attached like bowling balls with springs between them.

Okay, so I put all this information into Matlab, or whatever language/system you use.

Then I "pluck" one of the points away from the rest, and run the string program. It starts to vibrate. I watch the graph.

Sometimes I store the position of a point versus time, and export this as a wave. Guess what, it sounds like a string! =)

The cool thing about this model, it that I can add more strings to it, or place objects (like a "finger") in proximity of it. Its really easy to do.

Now, my challenge to people who use a K-S model of a string, how would *you* place an object near the string? I just insert some points. But, i guess that for you, you must rework the entire model/equations. It is not easy to modify. (I think, I know very little in this area.)


I'm not sure if what I do is actually Physical modeling. It might be better described as physical simulation...

[JovianPyx]

Again, please pardon my ignorance...

I see what you're doing, you're thinking in an almost quantum manner it seems, predigitalizing things by resolving them to quantum points? That would fit the Karplus-Strong string model I implemented where the delay line that represents the string is actually 2048 points (the delay line) with the endpoints fixed. If I smack one of the points (the simplest way to energize the system), the string vibrates.

However, a string vibrating in one dimension with infinitely rigid endpoints seems easy to envision this way.

How would you, using "the points method" go about designing what Mr. Cook describes as a slide flute - with the ability to make "overblown" frequency changes?

From the Cook paper, it seems he started with a Karplus-Strong model and modified it with the embouchure delay line and nonlinearity and the coupling of the two systems.

[williamsharkey]

[JovianPyx]

[frijitz]

[frijitz]

[JovianPyx]

[doctorvague]

If you have access to Reaktor, there is a wonderful PM ensemble called Steampipe that is bundled with Reaktor. It sounds excellent and does some very cool overblown effects on the flutes. Perhaps you could look under the hood and see how it was built?

Cheers
Phil

[JovianPyx]

[JovianPyx]

I now have a working fixed point model using integer arithmetic in C that I've translated from the first cut code which used double precision floating point arithmetic. It works down to 18 bit signed fixed point which means it's ready for the FPGA. Most of the structure for the FPGA is in place and I will be ready to test it perhaps today. The state machine uses 1 clock for init and 11 clocks for each pass. I will use decimation of a 2 MHz sample rate (running the state machine twice for each DAC enable) to down convert it to 1 MHz. It's fast enough that I could do 4 to 1 (picollo?).

It was indeed a challenge (as usual) to move from double float to fixed point arithmetic using integers, but at least I've proved the concept for the target environment.

As for the DCkiller, it is just a specially designed simple digital high pass IIR type filter. I found the filter specifics on Stanford's Julius O. Smith website where it is called a "DC Blocker". Here.

A funny thing happened to me - I had set the bore length to an arbitrary value and then when I got it working, I noticed that it took a rather long time to come up to full amplitude when resonation began. Then I realized that I had a very l-o-n-g bore... Shortening it fixed the slow amplitude climb.

What surprised me was how little energy is required to sustain resonant behavior once it starts. Due to this fact, a very clear tone is possible even though the system is energized by wideband noise.

[bugfight]

this is very interesting, scott
looking forward to hearing it.
"soon" i will actually set up my fargin 3e...
so many projects, etc etc

[JovianPyx]

Some success today, the FPGA version of the phLUTe appears to be working. It looks like I need to implement a fractional delay filter in the design. The system works at relatively short waveguide lengths. Getting it to hit the fundamental for the waveguide length requires lower jet energy as the waveguide length is increased. Too much, and it overblows and locks onto a harmonic, usually an octave or a fifth. The more the overblow, the higher the harmonic. Using 18 bit arithmetic, I'm having difficulty getting a bore with a length of 256 to oscillate at it's fundamental because it's overblown even with very low input. Shorter wavelengths lock to the fundamental more easily. I'm trying different things with the jet envelope and that's helping, but I doubt that I can get the length to over 10,000 as I had planned. Hopefully I can find enough information on fractional delays to implement that and then run it at a lower sample rate consistent with the shorter waveguide. If I can get all that working, I may be able to get 8 pipes polyphony.

[JovianPyx]

A couple of days worth of PDF collecting and reading resulted in a choice between the Thiran Allpass and the LaGrange Interpolator for providing fractional delays. The LaGrange Interpolator (an FIR type filter) of first order is a simple linear interpolator and as such is not computationally burdensome (the Farrow structure is 2 adds and one multiply). Articles regarding waveguide bore instruments having tone holes indicates that a first order filter should be adequate to model waveguides of nonintegral lengths. This type of filter is said to work best when the signal is well oversampled. If 400 delay units is considered to be the lowest note of the phLUTe, (approx 261 Hz), a sample rate of about 100KHz will be used which keeps the highest frequency (around 2400Hz) as 0.024 of the sample rate. Bass flute range, from 130Hz to 1200Hz could be realized using a sample rate of about 50 KHz at the same proportion of sample rate. If 50 KHz is used for both, the proportion is still only 0.048, more than sufficient for using this type of filter.

Regarding the FPGA design, I've been able to get reliable resonation of a waveguide 400 delay units long by careful adjustment of the design parameters, especially the reflection filter. Longer waveguides tend to lock to harmonics instead of the fundamental when the reflection filter bandwidth is too high. This design will require a table to drive the filter bandwidth parameter as well as waveguide length and LaGrange Interpolator parameter for each note of the scale. Also the bore feedback scale factor set to a nominal value of .55 causes the the amplitude of a new note at long waveguide lengths to build slowly. This can be corrected by increasing from 0.55 by an amount that depends upon the waveguide length. This will affect the character of the attack portion of the sound produced.

[JovianPyx]

The FPGA design has been modified to include 2 LaGrange Interpolators, one on the bore delay output and one on the jet delay output. The system is working, but needs some help because parameters that resonate well, producing a very near sine output at short wavelengths don't work with lower notes. Some notes don't appear to work at all - this could be some error in my tuning tables or it could be a problem with the LaGrange Interpolator(s). I may also discover a problem of inaccuracy with the interpolators, the bore must be exactly twice as long as the jet. I created the tuning tables with this in mind, but I believe that the interpolator is most accurate with values farther away from 0.5. It may require hand tuning each note, but that just requires a new tuning table.

This method (first order LaGrange Interpolator) was suggested in Perry Cook's web information so that's where I'm starting. It was certainly very easy to implement.

[blue hell]

It's good to see you have some progress.