Following my ongoing work on a theory of rhythms and a corresponding physical instrument using lasers, here is a version of the same idea implemented into an Arduino: a generative sequencer. The idea is to generate rhythms, and perhaps melodies, from one rhythm seed, then use mutated copies of it to create something more interesting, all this in realtime using knobs and buttons.

This is not ‘yet another step sequencer’, but really a generative music device, that builds a real time MIDI loop based on an underlying theory described in a previous post.

This is work in progress, and is shown ‘as is’ for the sake of getting feedback.

Approach

The approach is to generate a « seed » of rhythm that is then copied a few times into « instances », each instance being distorted in its own way. The controls for the human player (or programmer) are therefore all about adjusting the deformations (transforms actually) to apply to each instance, and of course defining the seed.

Eventually each instance is wired to a MIDI note, channel etc. to remote control a synthesizer or a drum machine or any MIDI setup, to generate actual sounds.

Principle: one seed, many transformed instances

Principle: one seed, many transformed instances

The maths

Given a seed of rhythm of lengh length composed of pulses, each of duration m, then:

for each instance k of the seed, each pulse i,
pulse(k, i) happen at time t = phase(k)  + i . m . stretch(k), t < length
where phase(k) and stretch(k) are the phase and stretch settings for the instance k.

Realtime control of the sequencer is therefore all about setting the phase and stretch values for each instance, once the pulse number and the pulse duration of the seed have been globally set.

Inversely, for a given instance k, at time t, we have a pulse if:

there exists an i, such as t = phase(k) + i * m * stretch(k)
i.e. i = (t - phase(k))/(m * stretch(k))

In other words, if

(t - phase(k))/(m * stretch(k)) is integer
(i.e. numerator % denominator == 0)

Thinking in MIDI ticks (24 per quarters), in 4/4, for 1 bar, length = 4 * 24, phase is in [-24 .. 24] and stretch is in [4:1 .. 1:4] and m in [12 .. 48] by steps of 12 ticks.

The implementation is the very simple: for each instance of the seed, and given its phase and stretch settings, whenever the modulo condition above is true, then we emit its MIDI note, with the set velocity on the set MIDI channel.

As usual, the pace of the loop is primarily based on the value from the Tempo potentiometer.

Overview of the circuit

Overview of the circuit, with the switches and the knobs

Adding some swing

8th note swing

8th note swing

The EMU SP-1200, early Linn machines, Roland 909, Akai MPC and many other machines are famous for their swing quantize, a feature that delays every other note by a certain amount in order to create a groovy feeling (see Swung Note).

Different machines express the swing factor in different ways, we will stick to the MPC format, expressed in percent from 50% (no swing, play straight) to 75% (hard shuffle).

For a swing for 8th notes, this swing factor represents the ratio of the period of the first 8th note over the period of the second 8th note, in percent.

In the Arduino code of our generative sequencer, we chose to do a fixed swing for 8th notes only.

A big constraint is that we are limited to a resolution of 24 ticks per quarter note, which is not a lot! By contrast, MPC have a 96 ppq resolution. Because a hard swing of 70% translates into hardly 2 MIDI ticks at 24 ppq, doing the swing on top of the ticks will not be accurate at all!

The only solution is to vary the internal tempo before and after each 8th note. The drawback (or advantage) is that the MIDI clock being sent will also move, reflecting the same swing. Since the Swing knob value is actually between 0 and 25 (to be read from50% to 75%), the tempo before (t-) and the tempo after (t+), are given by:

t+/- = (50 +/- swing) * t / 50
where t is the base loop period without swing

Video Demo

Here is a video demo. There are only 3 instances, selected by the switches 1, 2 and 3; the first switch selects the GLOBAL settings: step duration (quarter, 8th etc.), swing factor, tempo. Each instance can be set its Phase, Stretch, MIDI note, velocity and MIDI channel. Here I have preset the MIDI channels, instance 1 on channel 1 (the microKorg) and instances 2 and 3 on channel 2 (the MPC with a drum kit).

The goal is to build a simple beat by only adjusting the parameters.


(Arduino) Interactice Generative Sequencer from cyrille martraire on Vimeo.

The code

You can download the Arduino project here: generativesequencer1; below is the same source code for convenience. The code includes the knob pagination described in a previous post.

Please note that some parts of the code are not used any more, such as the big constant arrays, and some comments are not up to date (e-g no prime number anymore).

All analog inputs are wired to simple knobs. Digital inputs 8, 9, 10 , 11 are the four buttons used to switch pages. Digital output 12 is the activity LED (showing when the knob is active within the knob pagination). MIDI out is on the Tx pin.

/*
 * Generative rhythm sequencer, more details at: http://cyrille.martraire.com
 *
 * Knob mapping according to a grid 2^n . prime^m, against the MIDI 24 ticks/quarter.
 *
 * Knob pagination to multiplex the knobs several times with LED to show activity.
 *
 * Memory-less event handling thanks to maths relationships.
 *
 * MIDI note on output on every 16 channel and MIDI clock according to tempo.
 *
 *
 * Creative Commons License Cyrille Martraire cyrille.martraire.com
 */
// DEBUG
int debug = false;
//---------- USER INPUT AND PAGINATION -----------
#define PAGE_NB 4
#define KNOB_NB 6
#define FIRST_PAGE_BUTTON 8
#define PROTECTED -1
#define ACTIVE 1
#define SYNC_LED 12
// the permanent storage of every value for every page, used by the actual music code
int pageValues[PAGE_NB][KNOB_NB];
// last read knob values
int knobsValues[KNOB_NB];
// knobs state (protected, enable...)
int knobsStates[KNOB_NB];
// current (temp) value just read
int value = 0;
// the current page id of values being edited
int currentPage = 0;
// signals the page change
boolean pageChange = false;
//temp variable to detect when the knob's value matches the stored value
boolean inSync = false;
// ---------- KNOBS CALIBRATION AND MAPPING ---------
// rhythmic scale, to select globally
int scale2[] =  {1, 2, 3, 6, 6, 12, 12, 24, 24, 48, 48, 96, 192, 384, 768};
int scale3[] =  {1, 2, 3, 6, 9, 12, 18, 24, 36, 48, 72, 96, 144, 384, 768};
int scale5[] =  {1, 2, 3, 6, 12, 15, 24, 24, 30, 48, 60, 96, 120, 384, 768};
int scale7[] =  {1, 2, 3, 6, 12, 21, 24, 24, 42, 48, 84, 96, 168, 384, 768};
int scale9[] =  {1, 2, 3, 6, 12, 12, 24, 24, 27, 48, 54, 96, 108, 384, 768};
int scale11[] = {1, 2, 3, 6, 12, 12, 24, 24, 33, 48, 66, 96, 132, 384, 768};
//int scale13[] = {1, 2, 3, 6, 12, 24, 12, 24, 39, 48, 78, 96, 156, 384, 768};
int maxValue = 890;
int scaleLen = 15;
int *scale = scale3;
int step = 60;
int center = 30;
int coeff = 10;
//---------- GENERATIVE MUSIC CODE ---------
unsigned int cursor = 0;
int bars = 1;
int length = bars * 4 * 24;
// INPUTS
int PHASE = 0;
int STRETCH = 1;
//int DIRECTION = 2;
int NOTE = 2;
int DURATION = 3;
int VELOCITY = 4;
int CHANNEL = 5;
// GLOBAL KNOBS (seed and global settings)
int seedDuration = 24;
int seedTimes = 8;
int instanceNb = 4;
int swing = 0;//0..25% (on top of 50%)
//
int loopPeriod = 125/6;//120BPM
int actualPeriod = loopPeriod;
//instance i
int phase = 0;
int stretch = 1;
int note = 48;
int duration = 24;
int velocity = 100;
int channel = 1;
void setup(){
  if(debug){
   Serial.begin(19200); //debug
  } else {
    Serial.begin(31250);
  }

  pinMode(13, OUTPUT);

  setupKnobMapping();

  setupPagination();
}
void setupKnobMapping(){
  step = maxValue / scaleLen;
  if (step * scaleLen < maxValue) {
     step++;
  }
  center = step / 2; // for phase only
  coeff = step / 8; // +/-3 ticks, for phase only
}

void loop () {
    midiClock();

    //TODO partition inputs reading every other cycle if required by CPU load
    poolInputWithPagination();

    poolGlobalSettings();

    // parameters for each instance (pages 1 to 3)
    for(int index = 1; index < instanceNb; index++){
        processSeeInstance(pageValues[index]);
    }

    cursor++;
    cursor = cursor % length;
    delay(actualPeriod);
}
void poolGlobalSettings(){
    // global parameters
    seedDuration = mapC(pageValues[0][0], maxValue, 1, 4) * 12;
    seedTimes = mapC(pageValues[0][1], maxValue, 1, 16);
    instanceNb = 4;//mapC(pageValues[0][2], maxValue, 1, PAGE_NB);
    // = mapC(pageValues[0][3], maxValue, 1, PAGE_NB);
    swing = mapC(pageValues[0][4], maxValue, 0, 25);
    loopPeriod = mapC(pageValues[0][5], maxValue, 63, 2);// 12.5 ms - 62.5
    if (cursor % 24 <= 12){
      actualPeriod = (50 + swing) * loopPeriod / 50;
    } else {
      actualPeriod = (50 - swing) * loopPeriod / 50;
    }
    //TODO prime number selection and scale switch
}
// custom map function, with min value always 0, and out max cannot be exceeded
long mapC(long x, long in_max, long out_min, long out_max)
{
  if (x > in_max) {
    return out_max;
  }
  return x * (out_max - out_min) / in_max + out_min;
}
void processSeeInstance(int * params){
  phase = mapC(params[PHASE], maxValue, 0, 24);
  stretch = mapC(params[STRETCH], maxValue, 0, 4);
  stretch = pow(2, stretch);// 4:1 to 1:4, in fourth
  note = mapC(params[NOTE], maxValue, 36, 48);
  //duration = mapC(params[DURATION], maxValue, 6, 96);
  velocity = mapC(params[VELOCITY], maxValue, 0, 127);
  channel = mapC(params[CHANNEL], maxValue, 0, 4);

  if(isPulse(phase, stretch)) {
     noteOn(channel, note, velocity);
  }
}
// for each instance, and for the given cursor, is there a pulse?
boolean isPulse(byte phase, byte stretch){
  int num = cursor - phase;
  int denum = seedDuration * stretch / 4;
  return num % denum == 0;
}
// Sends a MIDI tick (expected to be 24 ticks per quarter)
void midiClock(){
  Serial.print(0xF8, BYTE);
}
//  plays a MIDI note for one MIDI channel.  Does not check that
// channel is less than 15, or that data values are less than 127:
void noteOn(char channel, char noteNb, char velo) {
   midiOut(0x90 | channel, noteNb, velo);
}
//  plays a MIDI message Status, Data1, Data2, no check
void midiOut(char cmd, char data1, char data2) {
   Serial.print(cmd, BYTE);
   Serial.print(data1, BYTE);
   Serial.print(data2, BYTE);
}
//********************************************
void setupPagination(){
  pinMode(SYNC_LED, OUTPUT);
  for(int i=0; i < KNOB_NB; i++){
    knobsValues[i] = analogRead(i);
    knobsStates[i] = ACTIVE;
  }
}
// read knobs and digital switches and handle pagination
void poolInputWithPagination(){
  // read page selection buttons
  for(int i = FIRST_PAGE_BUTTON;i < FIRST_PAGE_BUTTON + PAGE_NB; i++){
     value = digitalRead(i);
     if(value == LOW){
         pageChange = true;
         currentPage = i - FIRST_PAGE_BUTTON;
     }
  }
  // if page has changed then protect knobs (unfrequent)
  if(pageChange){
    pageChange = false;
    digitalWrite(SYNC_LED, LOW);
    for(int i=0; i < KNOB_NB; i++){
      knobsStates[i] = PROTECTED;
    }
  }
  // read knobs values, show sync with the LED, enable knob when it matches the stored value
  for(int i = 0;i < KNOB_NB; i++){
     value = analogRead(i);
     inSync = abs(value - pageValues[currentPage][i]) < 20;

     // enable knob when it matches the stored value
     if(inSync){
        knobsStates[i] = ACTIVE;
     }

     // if knob is moving, show if it's active or not
     if(abs(value - knobsValues[i]) > 5){
          // if knob is active, blink LED
          if(knobsStates[i] == ACTIVE){
            digitalWrite(SYNC_LED, HIGH);
          } else {
            digitalWrite(SYNC_LED, LOW);
          }
     }
     knobsValues[i] = value;

     // if enabled then miror the real time knob value
     if(knobsStates[i] == ACTIVE){
        pageValues[currentPage][i] = value;
     }
  }
}
void printAll(){
     Serial.println("");
     Serial.print("page ");
     Serial.print(currentPage);

     //Serial.println("");
     //printArray(knobsValues, 6);
     //Serial.println("");
     //printArray(knobsStates, 6);

     for(int i = 0; i < 4; i++){
       Serial.println("");
       printArray(pageValues[i], 6);
     }
}
void printArray(int *array, int len){
  for(int i = 0;i< len;i++){
       Serial.print(" ");
       Serial.print(array[i]);
  }
}

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2 Responses to “(Arduino) Interactive Generative Sequencer”

  1. on 01 mai 2009 at 4 h 45 minLaurence

    Great post!!
    Very interested in the hard swing example you’re covering in this article. I arrived here after google searching for hard shuffle midi clock. Basically I want to do the same thing, except I already have a step sequencer (mam sq-16) which has no swing, and I want to hard swing it.
    The trouble is, I’ve found that it has pretty rubbish timing as far as simultaneous notes go. It’s probably mostly the fault of MIDI, but I reckon some of it has to do with the cpu in the sq-16. I tested it on a tight system by the way (not quite an Atari ST, but I used an old mac beige g3 running oms and os 9, using an emagic unitor 8 over serial, not usb. Quite good timing).
    I want to ask you, how snappy do you find the arduino serial input/output? I’ve read a bit about trying to get it do act as a serial interrupt device, without much success. How do you find it when it is just used in a tight inner loop?
    I have an arduino I want to integrate into my setup for live sequencing with the sq-16 (can’t afford one of those fancy all-in-one machinedrums just yet) and I can’t decide whether to put it before or after the sq-16 in the chain — before would feed in hard shuffled clock (haven’t tried this yet, the sq-16 might not like it); after would accept midi notes and clock from the sq-16, requantize and hard-shuffle the lot (probably have to write some serious buffering code which may jitter the timing of the midi output from the arduino).
    Apologies for my long-winded and rather tangental post!

  2. on 01 mai 2009 at 12 h 06 mincyrille

    Hi Laurence,
    So far I have only used Arduino for MIDI output, and for that there is no need for interrupt and it works fine (I took care not to run extensive calculations in the loop to reduce jitter). However I did not test the jitter at all. What I read about interrupt etc. was especially critical for MIDI in, MIDI out is so much simpler.

    It is a pity I did not demonstrate that in the video, but along with the MIDI notes the code also sends MIDI clock correctly, i.e. at 24ppq. I have used that together with a microKorg sync’ed to external MIDI clock, and it works: the arpeggiator of the microKorg follows the tempo and the swing sent by the Arduino.

    I would then recommend to start with this simplest approach (have Arduino be just a master MIDI clock with built-in swing, driving every other MIDI device, including your step sequencer), and also because the other approach (MIDI in then requantize etc.) would require plenty of efforts, together with a high risk of disappointing results. The code for an Arduino master MIDI clock with shuffle would have definitly no jitter, being extremely simple (just remove everything in my code but the « send midi clock » part and you got it). Tell us a bit when you’ve done what you want, will be interesting for sure…