Tuesday, February 12, 2013

Arduino Notes, Frequencies and Scales plus a Bonus Filter.

A quick post with a file I use a lot to experiment with Audio projects.

The file contains the frequencies used to generate the midi notes 0 to 127 in your Arduino projects. The file doesn't quite provide the frequency, instead it provides the phase increment required to generate the frequency. If you are familiar with Direct Digital Synthesis you will know that this is what we use in our Auduino projects to generate sine and other interesting waveforms at a given frequency.

The Illutron B Uses Direct Digital Synthesis, there is an introduction to the technique here -
http://rcarduino.blogspot.com/2012/08/the-must-build-arduino-project-illutron.html

Saving Memory
The note tables file uses PROGMEM to efficiently store the frequency table out of the way in program memory -

http://arduino.cc/en/Reference/PROGMEM

In addition to the 128 midi notes, two scales are provided, the pentatonic blues scale that will be familiar to anyone who has built and Auduino and the equally widely used C Minor blues scale. To preserve memory, these scales are also stored in progmem. You can add your own scales by following the same pattern.

Accessing The Notes

To access a note you can use -

uint16_t unPhaseIncrement = getMidiNotePhaseIncrement(sNote);

where sNote is between 0 and 127

To access a note from one of the scales based on an analogInput you can use -

uint16_t unPhaseIncrement = getCMBluesPhaseIncrement(map(aInput,0,1024,0,CMBLUES_NOTES));

In the sample code above, we are using the map function to map an analog input value held in aInput the range of notes available in the C Minor Blues scale.

A Simple Test Synthesiser
At the end of this post is a very simple synth which uses the note tables and is based on the popular Auduino with one bonus feature. I have included the low pass filter from the Mozzi Arduino audio libraries. The Mozzi filter is better than the simple hardware filters I have tried and is very easy to add to a project.

In the test sketch the filter can be driven in two ways based on the position of an analog input. At the bottom end of the input range, the filter is controlled directly by the input, at the top end of the range, the filter is controlled by an oscillator, the frequency of the oscillator is  adjustable within this range.

To keep things simple, the test sketch uses the same hardware as an Auduino so if you want to have a play around with the mozzi filter or creating your own scales - load up and play away.

Mozzi

The Mozzi filter can be downloaded from http://sensorium.github.com/Mozzi/

The Mozzi sound samples are very good quality, the project implements a range of synthesizer building blocks and is something to take a closer look at.

Arduino Note Tables -

// Arduino Note Tables rcarduino.blogspot.com

#ifndef _NOTETABLES_
#define _NOTETABLES_

#include "avr/pgmspace.h"

#define MIDI_NOTES 128
// used to convert midi note numbers into the increments required to generate the note in the ISR
PROGMEM unsigned int midiNoteToWavePhaseIncrement[MIDI_NOTES] =
{
 66 // 0,8.18,66.98,66                C
,70 // 1,8.66,70.96,70
,75 // 2,9.18,75.18,75
,79 // 3,9.72,79.65,79
,84 // 4,10.30,84.38,84
,89 // 5,10.91,89.40,89
,94 // 6,11.56,94.72,94
,100 // 7,12.25,100.35,100
,106 // 8,12.98,106.32,106
,112 // 9,13.75,112.64,112
,119 // 10,14.57,119.34,119
,126 // 11,15.43,126.43,126
,133 // 12,16.35,133.95,133            C
,141 // 13,17.32,141.92,141
,150 // 14,18.35,150.35,150
,159 // 15,19.45,159.29,159
,168 // 16,20.60,168.77,168
,178 // 17,21.83,178.80,178
,189 // 18,23.12,189.43,189
,200 // 19,24.50,200.70,200
,212 // 20,25.96,212.63,212
,225 // 21,27.50,225.28,225
,238 // 22,29.14,238.67,238
,252 // 23,30.87,252.86,252
,267 // 24,32.70,267.90,267           C - lowest note used on rcarduino ribbon synth
,283 // 25,34.65,283.83,283
,300 // 26,36.71,300.71,300
,318 // 27,38.89,318.59,318
,337 // 28,41.20,337.53,337
,357 // 29,43.65,357.60,357
,378 // 30,46.25,378.87,378
,401 // 31,49.00,401.40,401
,425 // 32,51.91,425.27,425
,450 // 33,55.00,450.55,450
,477 // 34,58.27,477.34,477
,505 // 35,61.74,505.73,505
,535 // 36,65.41,535.80,535           C
,567 // 37,69.30,567.66,567
,601 // 38,73.42,601.42,601
,637 // 39,77.78,637.18,637
,675 // 40,82.41,675.07,675
,715 // 41,87.31,715.21,715
,757 // 42,92.50,757.74,757
,802 // 43,98.00,802.79,802
,850 // 44,103.83,850.53,850
,901 // 45,110.00,901.11,901
,954 // 46,116.54,954.69,954
,1011 // 47,123.47,1011.46,1011       C
,1071 // 48,130.81,1071.60,1071
,1135 // 49,138.59,1135.32,1135
,1202 // 50,146.83,1202.83,1202
,1274 // 51,155.56,1274.36,1274
,1350 // 52,164.81,1350.13,1350
,1430 // 53,174.61,1430.42,1430
,1515 // 54,185.00,1515.47,1515
,1605 // 55,196.00,1605.59,1605
,1701 // 56,207.65,1701.06,1701
,1802 // 57,220.00,1802.21,1802
,1909 // 58,233.08,1909.38,1909
,2022 // 59,246.94,2022.92,2022
,2143 // 60,261.63,2143.20,2143       C
,2270 // 61,277.18,2270.64,2270
,2405 // 62,293.66,2405.66,2405
,2548 // 63,311.13,2548.71,2548
,2700 // 64,329.63,2700.27,2700
,2860 // 65,349.23,2860.83,2860
,3030 // 66,369.99,3030.95,3030
,3211 // 67,392.00,3211.18,3211
,3402 // 68,415.30,3402.12,3402
,3604 // 69,440.00,3604.42,3604
,3818 // 70,466.16,3818.75,3818
,4045 // 71,493.88,4045.83,4045
,4286 // 72,523.25,4286.41,4286      C
,4541 // 73,554.37,4541.29,4541
,4811 // 74,587.33,4811.33,4811
,5097 // 75,622.25,5097.42,5097
,5400 // 76,659.26,5400.53,5400
,5721 // 77,698.46,5721.67,5721
,6061 // 78,739.99,6061.89,6061
,6422 // 79,783.99,6422.36,6422
,6804 // 80,830.61,6804.25,6804
,7208 // 81,880.00,7208.85,7208
,7637 // 82,932.33,7637.51,7637
,8091 // 83,987.77,8091.66,8091
,8572 // 84,1046.50,8572.82,8572     C
,9082 // 85,1108.73,9082.58,9082
,9622 // 86,1174.66,9622.66,9622
,10194 // 87,1244.51,10194.85,10194
,10801 // 88,1318.51,10801.07,10801
,11443 // 89,1396.91,11443.33,11443
,12123 // 90,1479.98,12123.79,12123
,12844 // 91,1567.98,12844.71,12844
,13608 // 92,1661.22,13608.50,13608
,14417 // 93,1760.00,14417.70,14417
,15275 // 94,1864.65,15275.02,15275
,16183 // 95,1975.53,16183.31,16183
,17145 // 96,2093.00,17145.63,17145     C
,18165 // 97,2217.46,18165.16,18165
,19245 // 98,2349.32,19245.31,19245
,20389 // 99,2489.01,20389.70,20389
,21602 // 100,2637.02,21602.14,21602
,22886 // 101,2793.83,22886.67,22886
,24247 // 102,2959.95,24247.58,24247
,25689 // 103,3135.96,25689.42,25689
,27216 // 104,3322.44,27216.99,27216
,28835 // 105,3520.00,28835.39,28835
,30550 // 106,3729.31,30550.04,30550
,32366 // 107,3951.06,32366.63,32366
,34291 // 108,4186.01,34291.26,34291    C
,36330 // 109,4434.92,36330.32,36330
,38490 // 110,4698.64,38490.65,38490
,40779 // 111,4978.03,40779.41,40779
,43204 // 112,5274.04,43204.25,43204
,45773 // 113,5587.65,45773.32,45773
,48495 // 114,5919.91,48495.14,48495
,51378 // 115,6271.92,51378.79,51378
,54433 // 116,6644.87,54433.96,54433
,57670 // 117,7040.00,57670.76,57670
,61100 // 118,7458.62,61100.07,61100
,64733 // 119,7902.13,64733.26,64733
,3046 // 120,8372.02,68582.53,3046      C
,7124 // 121,8869.84,72660.64,7124
,11445 // 122,9397.27,76981.30,11445
,16022 // 123,9956.06,81558.77,16022
,20872 // 124,10548.07,86408.50,20872
,26010 // 125,11175.30,91546.65,26010
,31454 // 126,11839.81,96990.28,31454
,31454 // 127,11839.81,96990.28,31454 // this is wrong, need to calculate correct value, even though at 8Khz its wrapping around on every tick
};

// Pentatonic scale
// C D E G A C
// to map to midi note

#define PENTATONIC_NOTES 54

// provides an index of pentatonic notes in the midi note table

PROGMEM unsigned char sPentatonicNotes[PENTATONIC_NOTES] =
{
  0,   2,  4,  7,  9,
  12, 14, 16, 19, 21,
  24, 26, 28, 31, 33,
  36, 38, 40, 43, 45,
  48, 50, 52, 55, 57,
  60, 62, 64, 67, 69,
  72, 74, 76, 79, 81,
  84, 86, 88, 91, 93,
  96, 98,100,103,105,
 108,110,112,115,117,
 120,122,124,127
};

// C Minor Blues scale
// C D# F F# G A# C
// to map to midi note

#define CMBLUES_NOTES 65

// provides an index of pentatonic notes in the midi note table

PROGMEM unsigned char sCMBluesNotes[CMBLUES_NOTES] =
{
  0,   3,  5,  6,  7, 10,  // 6
  12, 15, 17, 18, 19, 22,  // 12
  24, 27, 29, 30, 31, 34,  // 18
  36, 39, 41, 42, 43, 46,  // 24
  48, 51, 53, 54, 55, 58,  // 30
  60, 63, 65, 66, 67, 70,  // 36  
  72, 75, 77, 78, 79, 82,  // 42
  84, 87, 89, 90, 91, 94,  // 48
  96, 99,101,102,103,106,  // 54
 108,111,113,114,115,118,  // 60
 120,123,125,126,127       // 65
};


unsigned int getMidiNotePhaseIncrement(unsigned char sNote)
{
 if(sNote >= MIDI_NOTES)
 {
   sNote = (MIDI_NOTES - 1);
 }

 return pgm_read_word(midiNoteToWavePhaseIncrement + (sNote));
}
unsigned int getPentatonicPhaseIncrement(unsigned char sPentatonicNote)
{
 if(sPentatonicNote >= PENTATONIC_NOTES)
  sPentatonicNote = (PENTATONIC_NOTES - 1);

 uint8_t sMidiIndex = pgm_read_byte(sPentatonicNotes + sPentatonicNote);

 return pgm_read_word(midiNoteToWavePhaseIncrement + sMidiIndex);
}

unsigned int getCMBluesPhaseIncrement(unsigned char sCMBluesNote)
{
 if(sCMBluesNote >= CMBLUES_NOTES)
  sCMBluesNote = (CMBLUES_NOTES - 1);
 
 uint8_t sMidiIndex = pgm_read_byte(sCMBluesNotes + sCMBluesNote);
 return pgm_read_word(midiNoteToWavePhaseIncrement + sMidiIndex);
}

#endif

The very simple, very lo-fi synth

// Very Lo Fi synth with Mozzi filter rcarduino.blogspot.com

#include "NoteTables.h"
#include "lowpass.h"

#define PWM_OUT_REG OCR2B

#define KEY_COUNT 20
#define KEY_WIDTH (1024/KEY_COUNT)

class CAudio
{
  public:
   CAudio(){}
   static void begin(uint8_t bStopTimer0Interrupts)
   {
     // Setup timer 1
     TCCR1A=0x0;          // set the timer prescaler to 8 = 16/8 = 2MHz
     TCCR1B=0x02;          // set the timer prescaler to 8 = 16/8 = 2MHz
     TIMSK1 |= (1<<OCIE1A);   // Enable output compare match interrupt on OCR1A
 
     TCCR2A=0B10110011;                                    //-8 bit audio PWM
     //TCCR0A=0x83;          // Set timer waveform generation mode to FAST PWM, clear OC0A On match, set at bottom - OC0A = digital pin 6.
     TCCR2B=0x01;          // Set to clock frequency, no prescaler

     pinMode(3,OUTPUT);
    
     if(bStopTimer0Interrupts)
     {
      // stops timer0 which triggers interrupts for the millis and micros functions
      // if we stop the timer, we get better audio, but loose millis and micros.
      TIMSK0 &= (~((1 << OCIE0A)| (1 << OCIE0B)));
     }
   }
};


#define SAW 0
#define SQUARE 1
#define RAMP 2


class COscilator
{
public:
  void setWaveform(uint8_t sWaveform)
  {
    m_sWaveform = sWaveform;
  }
  void setPhaseIncrement(uint16_t unPhaseIncrement)
  {
    m_unPhaseIncrement = unPhaseIncrement;
  }
  uint8_t hasTriggered()
  {
    return m_unPhaseAccumulator < m_unPhaseIncrement;
  }
  void trigger()
  {
    m_unPhaseAccumulator = 0;
  }
  void updatePhase()
  {
    m_unPhaseAccumulator += m_unPhaseIncrement;
  }
  uint8_t getSample()
  {
    uint8_t sSample = m_unPhaseAccumulator>>8;
    switch(m_sWaveform)
    {
      case SQUARE:
       (sSample >= 127) ? sSample = 255 : sSample = 0;
      break;
      case RAMP:
       sSample = ~sSample;
      break;
    }
    return sSample;
  }
protected:
  uint16_t m_unPhaseIncrement;
  uint16_t m_unPhaseAccumulator;
  uint8_t m_sWaveform;
};

COscilator Osc1,Osc2,LFO,LFOFilter;

uint16_t getPhaseIncrement(uint16_t aInput,uint8_t sOffset)
{
  uint8_t sKey = aInput/KEY_WIDTH;

  // find where on the ribbon the key starts 
  uint16_t unKeyStart = sKey * KEY_WIDTH;
 
  // find where on the ribbon the key ends
  uint16_t unKeyEnd = (sKey+1) * KEY_WIDTH;
 
  // map where the current input sits between the key start and key end to a frequency that sits at the same point between
  // the frequency of the key and the frequency of the next key
 
  return map(aInput,unKeyStart,unKeyEnd,getMidiNotePhaseIncrement(sKey+sOffset),getMidiNotePhaseIncrement(sKey+1+sOffset));
}

LowPassFilter lpFilter;
uint16_t gFilter;

void setup()
{
  Serial.begin(9600);
  CAudio::begin(true); 

  Osc1.setWaveform(RAMP);
  Osc2.setWaveform(RAMP);
  LFO.setWaveform(SAW);
  LFOFilter.setWaveform(RAMP);
}

void loop()
{
  uint16_t aInput = analogRead(1);
  if(aInput >= 1021)
  {
    Osc1.setPhaseIncrement(0);
    Osc2.setPhaseIncrement(0);
    LFO.setPhaseIncrement(0);
    LFOFilter.trigger();
  }
  else
  {
    uint8_t sOffset = 20;//((analogRead(1) >> 3)/12)*12;
    uint16_t unPhaseIncrement = getCMBluesPhaseIncrement(map(aInput,0,1024,0,CMBLUES_NOTES));
    Osc1.setPhaseIncrement(analogRead(2)<<2);
    Osc2.setPhaseIncrement(analogRead(3)<<5);

    //lpFilter.setCutoffFreq(analogRead(4)>>2);
    lpFilter.setResonance(analogRead(5)>>2);
   
    LFO.setPhaseIncrement(unPhaseIncrement);   
   
    uint16_t unFilter = analogRead(4);
    if(unFilter < 512)
    {
     LFOFilter.setPhaseIncrement(0);
     unFilter>>=1;
    
     uint8_t sreg = SREG;
     cli();
     gFilter = unFilter;
     SREG = sreg;
    }
    else
    {
     uint8_t sreg = SREG;
     cli();
     gFilter = unFilter;
     SREG = sreg;
    
     LFOFilter.setPhaseIncrement((gFilter-512));
    }
  }
}



#define DELAY_LENGTH 1024

// iterate the grains and LFO
SIGNAL (TIMER1_COMPA_vect)
{
  static uint8_t sDelayBuffer[DELAY_LENGTH];
  static uint16_t sDelayIndex;

  sDelayIndex++;
  if(sDelayIndex >= DELAY_LENGTH)
  {
    sDelayIndex = 0;
  }
 
  OCR1A += 125;

  Osc1.updatePhase();
  Osc2.updatePhase();
  LFO.updatePhase();
  LFOFilter.updatePhase();
 
  if(LFO.hasTriggered())
  {
    Osc1.trigger();
    Osc2.trigger();
  }
   
  if(gFilter < 512)
  {
    lpFilter.setCutoffFreq(gFilter>>1);
  }
  else
  {
   lpFilter.setCutoffFreq(LFOFilter.getSample());
  }
 
  uint16_t nOutput = lpFilter.next((Osc1.getSample()>>1)+(Osc2.getSample()>>1));
  if(nOutput > 255)
   nOutput = 255;
  PWM_OUT_REG = nOutput;

  // not being mixed in to output but easy to add, see rcarduino.blogspot.com
  sDelayBuffer[sDelayIndex] = PWM_OUT_REG;
}




And don't forget the Mozzi filter 'lowpass.h' from https://github.com/sensorium/Mozzi

Duane B

3 comments:

  1. Hi,

    this blog is truly an inspiration!

    Im wondering if its possible for the following code http://rcarduino.blogspot.co.uk/2012/01/how-to-read-rc-receiver-with.html to do a sanity check, ie only update nThrottleIn on 3 consecutive values that are identical or +-2% or something?

    My receiver spits out the odd glitch I think on channel 3 when I poke the throttle. I look at the serial output and amongst the good values, once or twice every three seconds a value that is really wrong is printed.

    Im using it to control a RC police car I built my kid. At this stage its a simple lights, siren deal...

    ReplyDelete
  2. Would be better if you asked this question following and RC Related post, but, here is a post that gives you a ready made solution - http://rcarduino.blogspot.ae/2012/03/reading-from-rc-reveiver-do-you-need.html

    Unless the car is behaving erratically I would not bother to address the occasional glitch as if you weren't measuring it with an Arduino you probably didn't notice it was there in the first place.

    If you using brushed motors, they can generate a lot of electical noise, people had been using these motors in RC Cars for 40 years without noticing the noise - its only when you plug and Arduino in and look at the numbers that you start to notice.

    Duane.

    ReplyDelete
  3. Thanks Duane for your response, I'm already using a 2.4G Futaba transmitter/receiver.
    Basically AUX channel was used to turn lights/siren on at either extreme, and off in the middle.
    I found that with them off, wiggling the steering and punching the throttle would glitch, and cause the siren and lights to come on for a millisecond maybe 3 times over 4 seconds...
    I managed to resolve the issue by using the RCArduinoFastLib instead of the initial code you had created.
    I was putting off trying that, I am by no means fully understanding much of this, but with your comments in the code and helpful nature I have a perfectly working toy for my son (and me)
    Thanks again, I've just compiled and tested it and it works a treat...

    ReplyDelete