#Karplus-Strong algorithm

[synths-and-sensibility]

There's something vaguely disconcerting about the knowledge that one can stick a bunch of numbers into a circular buffer, do a little bit of feedback with averaging and it will come out sounding like a plucked string

Is this cosmic horror?

[sleep-token-confessions]

I suddenly realized that instrumentally Sugar and Caramel has similar intros that sound like it was made with a Karplus-Strong algorithm based synthesizer (the synth that makes sounds that sound plucked) or something.

I don't know what I'm saying where are the smarter people please help me make sense of this please please thank you

worship

.

[anphivenas]

and it was about Karplus-Strong algorithms LETS GO !!!!!!!!!

using ^_^ in an email to a professor Im unstoppable

[coconut2877-blog]

9/18/19 standing ground

This week I focus on the historical context of physical modeling. 

What has been done? 

What are the similarities and differences among the three commonly used approaches? 

To what extent are people modeling shapes and materials?

How are people simulating resonating bodies?

Am I sure about my own PDE (partial differential equations) formulations?

How to do sanity checks for the sounds I fabricated ?

My reference would be “Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method” by Lutz Trautman and Rudolf Rabenstein, and Dr. Julius O Smith’s online book “Physical Audio Signal Processing”. The former outlines theoretical proofs and applications of FTM, and the latter focuses on another method developed in CCRMA called DWG (Digital WaveGuide Networks).

How they used to do it

Classically physical modeling is done in roughly 4 ways - FDM (Finite difference method), DWG (Digital waveguide method), MS (model synthesis), and the relatively newer method FTM (functional transformation method), aka my approach(although not exactly as I discovered and would explain later). FDM and DWG are time-based synthesis while MS and FTM are frequency-based approaches. Both FDM and FTM relies on formal physical formulation, while MS and DWG start from analyzing existing recorded sounds. I will briefly describe all the approaches and then point out their limitations and possible combinations.

FDM

FDM starts from solving one or a set of partial differential equations with initial-boundary conditions that describe the given structure’s vibrational mechanism. Then it discretizes any existing temporal and spatial derivatives by Taylor expansion. This approach is straightforward, general, and works with most complex shapes, however tends to neglect higher-order terms. It is possible to improve its accuracy by using smaller discretization, although at the same time it would introduce heavy computations. It is often an offline method, not suitable to be implemented in real-time synthesis. The solution contains time-evolution of all the points on the object in question.

FTM 

FTM shares the same formulation as FDM but solves the equations differently. It eliminates the temporal and spatial derivatives by carrying out two transformations consecutively - Laplace transformation and SLT (Sturm-Liouville transformation). Both transformations turn the entire equation to be expressed in terms of another domain parallel to time-space, from (t,x) to (s,mu). In the alternate domain, derivatives on t and x are transformed to simple-to-solve algebraic equations in terms of s and mu. Afterwards, the solution maybe written in the form of a transfer function multiplying the activation function (derived from whatever force is exerted on the object). This transfer function may be inverted back to time-space domain and a solution would be obtained. The transfer function has its poles and zeros, from which we derive analytical solutions for each frequency partials and their decay rates. This approach is frequency-based in that the final solution is a summation of sinusoidal waves of different modes, with their own decay exponential terms. It accurately simulates the partials resulting from the sounding object however reaches its limitation when it comes to larger modes. It is more computational-friendly than FDM, however limits itself into simpler geometries - most of the time rectangular and circular shapes.

DWG

DWG analyzes a recorded sound and simulate the exact sound with bidirectional delay lines(for simulating traveling waves in both directions), digital filters, and some nonlinear elements. The method is based on Karplus-Strong algorithm and the filter coefficients+impedence of traveling waves are interpolated from the sound. This method is the most efficient but cannot describe a parametrized model. All changes in physical parameters need to be recorded again and be re-interpolated.

MS

MS considers objects as coupled systems of substructures and characterizes each substructure with their own mode/damping coefficient data. It then synthesizes sounds by summing all weighted modes. The modal data is usually obtained by measurements of the object itself rather than deriving from an analytical solution like FTM, and thus MS cannot react to parameter change in the physical model. Furthermore since no analytical solution is derived, MS requires measurements on discretized spatial points and the accuracy here is compromised.

So what do we wanna use

Based on the summary from Trautmann and Rabenstein’s book I extracted:

“

frequency-based method are generally better than time-based methods due to the frequency-based mechanisms in the human auditory system

for more complicated systems simulations of spatial parameter variations is much easier in the FDM than FTM since eigenvalues can only be calculated numerically in FTM.

FDM is the most general and the most complex synthesizing method. It can handle arbitrary shapes.

FTM is limited to simple spatial shapes like rectangular or circular membranes

DWG is even more limited than FTM or MS. It can only simulate systems accurately having low dispersion due to the use of low-order dispersions.

human ear seems to be more sensitive to the number of simulated partials than to inaccuracies in the partial frequencies and decay times

“

How my approach is slightly different from FTM

My approach is technically a FTM approach however with slight modifications. FTM first formulates the physical model, perform Laplace and SLT transform, get transfer function, and then derive the impulse response by inverting the transfer function back to time-space domain. My approach follows the same formulation, however only perform the Laplace transform. At this point I would assume the solution to be of sinusoidal form and calculate explicitly what the spatial derivatives are. Due to properties of sinusoidal form, even high order derivatives wouldn’t escape their original forms. After that, I derive the transfer function and would only perform inverse-laplace transform to obtain the impulse response, instead of performing inverse-laplace transform and inverse-SLT transform.

Whether this approach yields utterly different results, why would people go through the trouble of performing SLT spatial transformation, and whether it’s safe to assume the solution be of sinusoidal form is still under investigation. 

What can be done 

FTM+DWG

From FTM we can derive accurate modes and their decay rate coefficients, however it costs computational power to synthesize the actual sound (summation of multitudes of mode, calculation of exponentials, sine operations etc) 

On the other hand from DWG we design filters based on pre-recorded sounds (not flexible to morph between different physical parameters), however very computationally-efficient to synthesize the sounds. 

The book mentions a promising solution of combining the two methods - use accurate modes/decay rate information obtained from FTM to design filters and leave the sound synthesis business to DWG. Next week I will explore further on the combination of these two approaches.

[stoersender]

Electronic Music and Sound Design

Electronic Music and Sound Design - Theory and Practice with Max8 Vol.2 is available. Digital Audio and Sampled Sounds: decimation, blocks technique, slicing, scrubbing, timing, polyphony and multichannel- Delay Lindes: echoes, looping, flanger, chorus, comb and allpass filters, phaser, pitch shifting, reverse, variable delay, Karplus-Strong algorithm - Creative Uses of Dynamixs Processors: envelope followers, compressors, limiters, live normalizers, expanders, gates, side chains, ducking - The Art of Organizing Sound: simple, complex and compound motion processes, motion within timbre, algorithmic control of motion, motion sequences - MIDI and Handling MIDI Messages in Max - Max for Live: audio effects, virtual instruments, MIDI effects, Live API and Live Object Model. 

“With their Electronic Music and Sound Design: Theory and Practice with Max/MSP (…) Alessandro Cipiriani and Maurizio Giri have produced a series of “interactive and enhanced books” that presents the student of computer music with the finest and most comprehensive electroacoustic curriculum in the world. By “illustrating” the text with a wealth of figures and clearly explained equations, they take the reader “under the hood” and reveal the algorithms that make our computing machines “sing”. By using David Zicarelli’s incredible powerful and intuitiv media-toolkit – Max/MSP to create hundreds of synthesis, signal processing , algorithmic composition, interactive performance, and audio analysis software examples, Cipiriani and Giri have provided the means for students to learn by hearing, by touching, by modifying, by designing, by creating, and by composing. (…) set the stage for the next generation of innovators. (…) In Electronic Music and Sound Design, Cipriani and Giri feed the hands, they feed the ears, and they feed the minds of the students in ways and to a degree that no computer music textbook has ever done.” From the Foreword by Richard Boulanger. Available at https://books.apple.com/it/book/electronic-music-and-sound-design/id1509968774?l=en  

[programmingsolver]

Project 2 Guitar Solution

Overview

In this project, you will write a program to simulate plucking a guitar string using the Karplus-Strong algorithm. This algorithm played a seminal role in the emergence of physically modeled sound synthesis (where a physical description of a musical instrument is used to synthesize sound electronically). The Karplus-Strong models the vibration of a guitar string with a remarkably…

[myprogrammingsolver]

Project 2 Guitar Solution

Overview

In this project, you will write a program to simulate plucking a guitar string using the Karplus-Strong algorithm. This algorithm played a seminal role in the emergence of physically modeled sound synthesis (where a physical description of a musical instrument is used to synthesize sound electronically). The Karplus-Strong models the vibration of a guitar string with a remarkably…

[blickensynths]

Available now! The 2hp Pluck⠀ ⠀ The Pluck is a physical modelling synth voice. It uses the Karplus-Strong algorithm to create plucked string sounds. The dampening control sets the size of the string and allows for dramatic timbral shifts.⠀ ⠀ The decay control changes note length from percussive transients to infinite harp sounds. In addition, four voice polyphony provides complex layered tones; all from a single sound source.⠀ ⠀ Strum a new chord with Pluck.

[thetapelessworld]

Softube Releases EDEN WT-800 BASS AMP plugin , and MUTABLE INSTRUMENTS BRAIDS and DOEPFER A-188-1 BBD for Softube Modular Plugin

Softube Releases EDEN WT-800 BASS AMP plugin , and MUTABLE INSTRUMENTS BRAIDS and DOEPFER A-188-1 BBD for Softube Modular Plugin

EDEN WT-800 BASS AMP We’re introducing the Eden WT-800 bass amp on our native platform. An absolutely top-of-the-line tool for modern bassists due to its versatility in finding tones for big, hi-fi styles like hip hop, soul, metal, and R&B. Two phenomenal cab models, four high-end classic microphones, easy bi-amping, powerful built-in eq and compressor, and a special ‘enhance’ knob all help to make Eden a must-have for the modern music-maker

Innumerable pro players, including Mike Rutherford of Genesis and Mike Gordon of Phish, have come to treat this amp as essential. It’s great for the grungey dirty vintage sounds, of course, but for the heft and clarity required by modern hip-hop, R&B, pop, metal, and jazz, there aren’t many that can compete.

Our plug-in is fully endorsed and authenticated by Eden, and features physical modelling of two of their best-loved cabinets, a 1x15 and a 4x10, each miked with four different high-end classic microphones, selected and positioned by Troy Antunes, producer and bassist famous for his work with Pharrell Williams and Justin Timberlake.

And with a three-channel mixer section, you can blend the two cabs with the direct signal to find just about anything you could ever want to hear.

With a far more sophisticated EQ than many competitors, a built-in compressor, and a specially designed and optimised ‘enhance’ knob, which boosts the high and low frequencies while cutting the mids for that ultra-modern ‘scooped’ smiley-face sound, the WT800 represents the best-of-the-best, in sound quality and versatility alike.

In short

Fully-featured bass amp simulation to cover every need, vintage and modern

Faithful modelling of class-leading, top-quality equipment

Five-band EQ

Make-sound-better ‘enhance’ knob

In-built compressor

Not one but two cabinet models

Easy bi-amping; select your cutoff frequency and send your low and high frequencies to different cabinets

Choice of four classic microphones per cabinet, expertly selected and placed

Great for rough stuff, but amazing for hyper-rich hi-fi modern tones

https://www.softube.com/index.php?id=eden_wt800

https://www.softube.com/index.php?id=eden_wt800

MUTABLE INSTRUMENTS BRAIDS Modular, our software Eurorack synth, has a new macro-oscillator – Braids, by Mutable Instruments – which emulates dozens of classic synthesis techniques with ‘under-the-hood’ digital algorithms, allowing the user to quickly flip through an encyclopedia of synth, touring the sweet spots with a simple two-knob control set-up.

Astonishingly Sophisticated Sound-Generation

Braids, by French Eurorack pioneers Mutable Instruments, is not an oscillator.

It sort of looks like one, with fine and coarse pitch/frequency controls, a v/oct input, and voltage-controllable tone/timbre controls.

It even sort of sounds like one, in as far as it outputs audio.

Mutable Instruments call it a macro oscillator, but even that is an understatement. It’s a hugely sophisticated digital synthesis engine, able to produce and manipulate complex sounds – classic waves from vintage synths, bells, resonant filters, plucked and bowed strings, vocals and vowel/formant sounds, wind instruments, percussion, noise, granular clouds and more – by means of 45 or so fully-realized algorithms, featuring multiple oscillators, wavetables, filters, VCAs, ring modulators, and so on under the hood.

Each mode is a different algorithm, and produces a different variety of sounds as you turn the two tone controls, Timbre and Colour. These controls are pre-programmed to do different things per algorithm, often adjusting multiple parameters in the set-up at once to tour the sweet spots. And of course they can be CV controlled.

Using the trigger input and built-in AD envelope, each algorithm can even become a self-contained synth voice. No other modules required. But bring other modules in and you can make pretty much any instrument you could imagine.

In a sense, Braids can be looked at as both an encyclopedia of classic synthesis techniques, and a tool to bring them into the present-day, with tremendous sound-quality and ease-of-use to match.

It is also shockingly, spectacularly rich, varied, and complicated, with each mode being an instrument unto itself.

n short

Macro oscillator featuring 40+ fully-realized digital synthesis algorithms

Produce millions of different sounds easily – classic waves and telecoms babble, bells and whistles, percussion and ambience

Just two controls morph through the sweet spots of each algorithm

Great for triggered percussion

Awesome for crazy complex waveform synthesis

Phenomenal for glitchy out-of-control modulated sounds

Incredibly deep, but easy to use

It’s like a library of the greatest synth sounds of all time

Requires Modular

https://www.softube.com/index.php?id=mi_braids

https://www.softube.com/index.php?id=mi_braids

DOEPFER A-188-1 BBD

Dopefer’s A-188-1 Bucket Brigade Device also comes to Modular, bringing gritty seventies solid-state delay-based effects into play. Build your own chorus, flanger, doubler, or ensemble, and CV control delay time for spacey pitch effects (including Karplus-Strong plucked-string synthesis).

It’s time to take control of time itself, with the Doepfer A-188-1 Bucket Brigade Device for Modular.

Produce and CV-control gritty, distorted delays, flanging effects, choruses and more with this unusual, proto-digital add-on module for Modular, our software Eurorack synth. A BBD uses a chain of capacitors to sample and delay your signal, with increasing loss of fidelity as the delay line gets longer. This can give rise to an enormous range of creative options, and add extra dimensions to any sound, from drums, guitars, and vocals to synth waves.

https://www.softube.com/index.php?id=doepfer_bbd

Before digital delays became the cheapest and most versatile option in the late 70s and early 80s, echo effects in recorded or live music were achieved by a variety of creative analog means. Short tape loops with adjustable playback heads, or variable speeds, were favoured for a while, despite the downside of needing to replace the tape now and again. Designs featuring magnetic drums or discs aimed to solve that issue, but never dominated the market.

Solid state designs enjoyed a brief but fruitful period of vogue in the mid-to-late seventies. These devices, featuring long chains of voltage sampling ‘buckets’ controlled and released in time by a high speed oscillator, lent their unique characteristics not only to electronic, techno, and emergent dance styles, but to guitar rigs the world over.

By passing the signal along a line of capacitors, the sound is delayed in time, but also degraded with high-frequency loss and additional noise (as well as noticeable sample-rate reduction and aliasing at high delay times). This creates a warm and dirty sound, much sought after at the time, and still loved as a creative effect despite the practical disadvantages a BBD unit has compared to more versatile, cleaner digital delays.

Not only can this kind of delay produce tight slapbacks, grungey echoes, and smokey ambience, but by exploiting high feedback and very short delay times Karplus-Strong style plucked string synthesis is also possible.

The length of the delay line – the number of buckets in the brigade – has a significant effect on the sound and capabilities of the effect. The hardware module is available in six versions, each featuring a different number of stages (128, 256, 512, 1024, 2048, and 4096). But our software version contains all six, and can switch between them with one click.

In a sense it’s six modules in one, four of which, due to component scarcity, are limited editions in hardware (all but the 1024 and 2048-stage versions).

Another change, as compared to the hardware, is the option to simply switch off the audible bleed from the high frequency clocking oscillator. What would have required careful filtering after the event is now a simple flip of a switch.

Use this module to design your own flanging, doubling, chorus, and depth effects by blending a modulated delay signal in parallel with the dry, unprocessed sound. Or take the wet output separately from the dry and work with them individually.

In Short

Ultra-precise model of rare and exciting style of analog delay effect.

Can be used within synth patches in Modular, or for processing external audio in Modular FX.

Six different models in one module.

Great for dirty delays, sharp slapbacks, whooshing swirly ambience, or utter craziness.

Build your own flanger/chorus for guitars, drums, or any other audio source.

Take advantage of the disadvantages of this special design – use the BBD as a bitcrusher or distortion unit.

Keep the original noise bleed, or simply switch it off.

Requires Modular

https://www.softube.com/index.php?id=doepfer_bbd

[kirch]

Patchení s Nikol - Karplus-Strong algorithm https://youtu.be/fZ1rviedGvc

[synths-and-sensibility]

(Python isn't my native language, so please pardon my code)

It's not a very usable version of the algorithm, but the goal tonight was to generate a sound, so mission accomplished!

[affinitydivine-blog]

Mini-Report #2 Physical Modeling

For his Mini-Report, Theodore presented on Physical Modeling.

Theo covered a lot of interesting concepts pertaining to the synthesis and modeling of sound and the algorithms used in the process. Physical Modeling is a method in which a sound wave is generated and modeled to simulate a musical instrument. One of the first methods of achieving that was the Karplus-Strong algorithm: A burst of white noise is sent to a delay line. Afterwards, the sound is simultaneously output and fed into delay line that is L samples long. Lastly, a low pass filter is applied to the signal, which is then simultaneously mixed back into the output and fed back into the delay line. The Yamaha VL1 modeling synthesizer (released in 1994) uses this method to emulate different instruments.

A more modern version of physical modeling is exemplified in Logic’s Sculpture.

Sculpture provides three unique options to shape a sound:

String: This section allows us to choose the material of the exciter, media loss or how much sound is lost from the environment and we can also modulate the tension of the string, thus changing its momentary detuning after its plucking.

Object: Here we can set up to three parameters that affect the string and consequently change its timbre.

Pickup: This section emulates the pickups of an electric guitar and allows us to choose where they are placed along the string. We can also change where the three objects from the previous section affect the string.  The rest of the sections work as expected and allow for a fine modeling of the newly generated sound.

Theo's presentation has definitely given the class a spark of inspiration and has certainly inspired me to look into physical modeling for my future projects. He finished his mini-report with the world’s first “singing computer”:  https://www.youtube.com/watch?v=XIrX8YpiJgA

[synths-and-sensibility]

Found another book at the library that broke out the KS algorithm pretty well

[synths-and-sensibility]

Help! Too many projects clamoring for my attention:

- DCO (in progress)

- VCA (prototyped, needs fine tuning)

- Envelope generator (not started)

- MIDI controller (built, needs coding)

- MIDI to gate/CV (not started)

- Karplus-Strong (algorithm needs refinement and expanding)

- Clock (need parts)

- Sequencer (need parts)

- Flanger/chorus (initial concept stage)

[synths-and-sensibility]

I've written like three different Karplus-Strong algorithms this week that produce identical rudimentary results... Girl! You've been fixating on digital filters all week! Don't you think it's time to implement the stupid filters in the feedback path instead of running in circles on the core functionality??

[synths-and-sensibility]

Oh, Extended Karplus-Strong Algorithm, we're really in it now...