I’d like to share a Csound user-defined opcode port of the “Virtual Analog Model of the Lockhart Wavefolder” by Fabián Esqueda, Henri Pöntynen, Julian D. Parker and Stefan Bilbao that was presented at SMC 2017. The paper reference is:
F. Esqueda, H. Pöntynen, J. D. Parker and S. Bilbao, “Virtual Analog Model of the Lockhart Wavefolder”, in Proceedings of the 14th International Sound and Music Computing Conference (SMC-17), Espoo, Finland, July 5-8, 2017, pp. 336—342.
The authors have placed a website with the original paper, errata, and a Max/MSP/gen~ implementation at:
The test instrument follows the recommendations of the paper to use a cascaded wavefolder structure with input gain and DC offset parameters. (See figure 9 in the paper.) The sampling rate is 88.2khz as mentioned in the paper to deal with anti-aliasing issues without having to use oversampling.
An example render of the test CSD file is below, modulating both the gain and DC offset parameters:
I’m very excited by all of the wonderful sonic possibilities! Bravo to the original authors for their work!
Practice session today using additive pitch hexbeat rhythms to generate melodic contours.
Each hexbeat() is generating sequences of 1’s and 0’s which are then multiplied to alternate between things like 7 and 0. So if I add one that alternates between 2 and 0, I get 9,7,2, and 0 as possibilities. Then with say 4 and 0, I get additional combinations. With the patterns of different lengths (I’ve been using mostly prime number lengths) it generates a nice long overall pitch pattern, which is then masked by the rhythmic hexplay() pattern. I then add a choose() to say “play 70% of the time” and I find all of that together is quick to write, generates good variety, but has an underlying structure that is stable. (It’s been on my mind how to mix randomness + stability in interesting ways and I’ve found these explorations have been leading to some interesting pattern generation.)
This desmos graph visualizes an example of a 3-part hex pitch rhythm added together:
(Click on the “Edit on Desmos” link in the graph to turn on/off visualization of the various individual hex pitch rhythms.)
Implementation of 1-dimensional (Elementary) Cellular Automata as a
stream using feedback and circular buffer delay line. Stream
generates 1 (Live) and 0 (Dead) values, according to initial state
Initial state may be any length array. Different array lengths
affects the rate of mutation, comparable to classical cellular
automata implementations that use a fixed array as value between CA
Rule numbers are implemented using Wolfram-style encoding where
number is interpreted as bits. This allows user to use Wolfram rule
numbers. For example, Rule 30 gives bit value of 00011110.
For this project, the CA stream values are used to turn and off a
held note of a specific frequency and amplitude. Actions occur only
when the stream values has transitioned from 0 to 1 or vice versa. The project runs indefinitely but was capped off at ten minutes here.
Using a feedback+delay-based approach could be interesting to allow for user input. The ca_stream user-defined opcode here could be modified to take in input and use bitwise-or with a generated value before writing it back into the stream. This could allow users to “play” the stream, and could make the Class 1 rules that evolve to 0’s be interesting for generating a limited amount of output in time to the user input. (I am curious to know if this could be useful, and will plan to investigate shortly by implementing an interactive web application.)
Live code session using csound-live-code and https://live.csound.com.
Initial code happens for about 2m40s, then sound begins.
For those interested in the code, the session uses:
1. start UDO for working with the different always-on instruments
2. vco2 square wave for enveloping (has a nicer quality to it than
using lfo with type 3, IMO)
3. portk for frequency glide
4. chnset for immediate setting of a channel value as part of performance
5. chnset within an always-on instrument (“Mod”) together with k-rate
randh to show how to approach using continuous values with channels
I have long avoided FM (Frequency Modulation) synthesis in my own musical practice as I never felt connected with the results I was able to get myself. However, I recently had the great pleasure to attend a talk about the 50th anniversary of FM synthesis, given by its creator, John Chowning, and I was very inspired to explore FM once again. In so doing, I came across the Yamaha reface DX synthesizer and became fascinated with reproducing its feedback system to morph an operator’s output from a Sine to either Saw or Square waveform.
Now, I do not own a reface DX, so most of my research into it was through looking at manuals and watching video demonstrations on YouTube to try to get an idea of how it might be done. I knew from going through literature on FM and PM (Phase Modulation) that using PM with feedback could get an operator’s signal to move from a Sine to Sawtooth wave, depending upon the amount of feedback. I was quickly able to setup a PM instrument in Csound and test this out and it sounded much like what I had heard for the reface DX.
In the code above, one can see that the acar output from tablei is also used as input into the opcode. The code above runs in a single-sample context (in Csound parlance, with ksmps=1).
Now, the part I could not find anywhere in literature or discussion online was how to use operator feedback to morph from Sine to Square. (This is done by using 0 to -127 range for feedback on the reface DX.) After a couple days of research and exploration, I stumbled upon a calculation that sounded to my ears very much like what I had heard on the reface DX videos.
This instrument is virtually the same as the first instrument with the exception of one additional calculation: the multiplication of the acar feedback by itself. (This is seen in the acar*acar calculation.) Adding this one additional multiplication made the signal move from Sine to Square.
I posted this to the Csound User list and Iain McCurdy gave great feedback that the waveform could be morphed between Saw and Square by interpolating between acar and 1. This made a lot of sense as when one of the acar‘s becomes 1, it reduces back down to the normal feedback addition to produce a Saw sound. After some further emails, I did some experiments to use a cosine-based mapping for the interpolation that resulted in a nice transition.
;; feedback PM - feedback moves from square to saw
;; Based on Iain McCurdy's comments on Csound User List
ifreq = p4
iamp = p5
kfb = 0.25
;;kfb = linseg(0, p3 * .5, 0.5, p3 * .5, 0)
kwaveshape = linseg(0, p3 * .5, 1, p3 * .5, 0) ;; range 0-1 for saw->square
kwaveshape *= kwaveshape ;; adjust curve
kwaveshape = $M_PI * (kwaveshape + 1) ;; adjust from PI->2PI
kwaveshape = (cos(kwaveshape) * 0.5) + 0.5 ;; adjust to 0-1
aphs = phasor(ifreq)
; init for feedback
acar init 0
acar = tablei(aphs+(ntrpol(acar, a(1), kwaveshape)*acar*kfb), 1, 1, 0, 1)
acar *= linen:a(1, 0.1, p3, 0.1) * iamp
I do not know if these calculations are what are used in the reface DX, but regardless, the sine->square sounded good to my ear and I felt it was usable for the kind of sound work I was interested in doing. For now, I have posted the Csound CSD project file here. The audio example at the top of this post is an MP3 version of the output rendered from this project.
Hexadecimal (base 16) has been used in various forms of computer music for a very long time, generally as a condensed way to notate values within a power-of-two range. For example, rather than write out “15” as a decimal value (base 10), one can use “F”, and rather than write out “255”, one can use “FF”. The notation of hexadecimal numbers, in general, take up less horizontal space on the screen than its base 10 counterpart.
The differences in screen real estate is even more pronounced when comparing the binary value (base 2) to the decimal and hex values. Let’s compare some values here:
A chart showing the binary, decimal, and hex values for number 0-255 are available here.
Now, one of the interesting challenges in live coding pattern-oriented music for me has been trying to have a very condensed notation for expressing beats (onsets). One way I’ve seen used is to notate values in a binary form within a string, such as “1000100010101000” which would mean “play notes where there are 1’s, but don’t play notes where there are 0’s”. In this case, on beat 1, 5, 9, 11, and 13.
Binary values in a string, on the one hand, quite clearly notates when an instrument should play. On the other hand, I’ve found it visually takes up quite some space and can be a bit slow to parse mentally.
One thing I’ve found rather useful is to notate onset patterns using hexadecimal strings. I first explored this in my Clojure systems Pink and Score, but recently translated the function I was using to Csound code. The Csound code turned out to be quite simple:
opcode hexbeat, i, Si
Spat, ibeat xin
;; 4 bits/beats per hex value
ipatlen = strlen(Spat) * 4
;; get beat within pattern length
ibeat = ibeat % ipatlen
;; figure which hex value to use from string
ipatidx = int(ibeat / 4)
;; figure out which bit from hex to use
ibitidx = ibeat % 4
;; convert individual hex from string to decimal/binary
ibeatPat = strtol(strcat("0x", strsub(Spat, ipatidx, ipatidx + 1)))
;; bit shift/mask to check onset from hex's bits
xout (ibeatPat >> (3 - ibitidx)) & 1
The above is saying: “within the hexadecimal beat string of f0d0d0f0, and given the current beat value between 0 and 32, check if the onset is a 1 and, if so, perform Synth 1”.
The code above may be a little tricky to grok at first glance. I’ve started a Github repository for this code and made an online web app for live coding with Csound and this library. The live web site is available at:
In working with the hex beat patterns, I found it took a little practice but the meaning of various hex values started to become intuitive over time. Hexadecimal works really well, in my opinion, for notating pattern onsets as each hex value maps to 4 bits, which works perfectly for 4 16th-notes. With this, 4 hex values can be used to notate a single measure of 16 16th-notes, 8 hex for 2 measures, and so on.