ADSR-based Polyphonic Synthesizer

This project is intended to be a polyphonic synthesizer for use in embedded microcontrollers. It features multi-voice synthesis for multiple channels.

The synthesis is inspired from the highly regarded MOS Technologies 6581 "SID" chip, which supported up to 3 voices each producing either a square wave, triangle wave or sawtooth wave output and hardware attack/decay/sustain/release envelope generation.

This tries to achieve the same thing in software.

Principle of operation

The library runs as a state machine. Synthesis is performed completely using only integer arithmetic operations: specifically addition, subtraction, left and right shifts, and occasional multiplication. This makes it suitable for smaller CPU cores such as Atmel's TinyAVR, ARM's Cortex M0+, lower-end TI MSP430, Microchip PIC12 and other minimalist CPU cores that lack hardware multipliers or floating-point hardware.

The data types and sizes are optimised for 8-bit microcontroller hardware.

The state is defined as an array of "voice" objects, all of the type struct voice_ch_t and a synthesizer state machine object of type struct poly_synth_t.

These voices combine an ADSR envelope generator and a waveform generator. A voice is configured by setting the waveform type and frequency in the waveform generator. This algorithmically provides a monophonic tone which is then amplitude-modulated using the ADSR envelope generator.

Under the control of the synthesizer state machine, the voices are selectively computed and summed to produce a final sample value for the output. The bit masks that enable and mute channels are defined by the uintptr_t data type, and so in most cases, 16 or 32 channels can be accommodated depending on the underlying microcontroller.

ADSR Envelope

ADSR stands for Attack-Decay-Sustain-Release, and forms a mechanism for modelling typical instrument sounds. The state machine for the ADSR waveform moves through the following states:

1. Delay phase: This is a programming convenience that allows for the state of multiple voices to be configured at some convenient point in the program in bulk whilst still providing flexibility on when a particular note is played. As there is no amplitude change, an "infinite" time delay may also be specified here, allowing a note to be configured then triggered "on cue".

2. Attack phase: The amplitude starts at 0, and using an approximated exponential function, rises rapidly up to the peak amplitude. The exponential function is approximated by left-shifting the peak amplitude value by varying amounts.

3. Decay phase: The amplitude drops from the peak, to the sustain amplitude. The decay is linear with time and is achieved by subtracting a fraction of the difference between peak and sustain amplitudes each cycle.

4. Sustain phase: The amplitude is held constant at the sustain amplitude. As there is no amplitude change, it is also possible to define this with an "infinite" duration, allowing the note to be released "on cue" (e.g. when the user releases a key).

5. Release phase: The amplitude dies off with a reverse-exponential function much like the attack phase. Again, it is approximated by left-shifting the sustain amplitude.

Typical usage

The typical usage scenario is to statically define an array of struct voice_ch_t objects and a struct poly_synth_t object. To set the sample rate, create a header file with the content:

#define SYNTH_FREQ		(16000)

… then in your project's Makefile or C-preprocessor settings, define SYNTH_CFG=\"synth-config.h\" to tell the library where to find its configuration.

The above example sets the sample rate to 16kHz… you can set any value here appropriate for your microcontroller.

The struct poly_synth_t is initialised by clearing the enable and mute members, and setting the voice member to the address of the array of struct voice_ch_t objects.

Having initialised the data structures, you can then start reading your musical score. To play a note, you select a voice channel, then:

• Call adsr_config with the arguments:
  • time_scale: number of samples per "time unit"
  • delay_time: number of time_scale units before the "attack" phase. If set to ADSR_INFINITE, the note is delayed until adsr_continue is called.
  • attack_time: number of time_scale units taken for the note to reach peak amplitude (peak_amp)
  • decay_time: number of time_scale units taken for the note to decay to the "sustain" amplitude (sustain_amp)
  • sustain_time: number of time_scale units taken for the note to hold the sustain_amp amplitude before the "release" phase.
  • release_time: number of time_scale units taken for the note to decay back to silence.
  • peak_amp: the peak amplitude of the note.
  • sustain_amp: the sustained amplitude of the note.
• Call one of the waveform generator set-up functions.
  • amplitude sets the base amplitude for the waveform generator.
  • freq sets the frequency for the waveform generator.
• Set the corresponding bits in struct poly_synth_t:
  • set the corresponding enable bit to compute the output of that synth voice channel
  • clear the corresponding mute bit for the output of that synth channel to be added to the resultant output.

Then call poly_synth_next repeatedly to read off each sample. The samples are returned as signed 8-bit PCM. Each call will advance the state machines and so successive calls will return consecutive samples.

As each channel finishes, the corresponding bit in the enable member of struct poly_synth_t is cleared.

When all the machines have finished, the poly_synth_next function will return all zeros and the enable field of struct poly_synth_t will be zero.

Waveform generators

There are 5 waveform generator algorithms to choose from. The state machines have the following variables:

• sample: The latest waveform generator sample.
• amplitude: The peak waveform amplitude (from 0 axis, so half. peak-to-peak).
• period: The period of the internal state machine counter
• period_remain: The internal state machine counter itself. This gets set to a value then decremented until it reaches zero.
• step: The amplitude step size.

DC waveform generator (voice_wf_set_dc)

Configures the waveform generator to generate a "DC" waveform (constant amplitude). Not terribly useful at this time but may be handy if you wish to use the ADSR envelope generator only to modulate lights.

Square wave generator (voice_wf_set_square)

Configures the waveform generator to generate a square wave.

sample is initialised as +amplitude, and the half-period is computed as period=SYNTH_FREQ/(2*freq). period_remain is initialised to period.

Fixed-point 12.4 format (16 bit) is used to store the period counters, to allow tuned notes on low sampling rates too.

Each sample, period_remain is decremented. When period_remain reaches zero:

• sample is algebraically negated
• period_remain is reset back to period

Sawtooth wave generator (voice_wf_set_sawtooth)

Configures the waveform generator to produce a sawtooth wave.

sample is initialised as -amplitude, and the time period is computed as period=SYNTH_FREQ/freq. The step is computed as step=(2*amplitude)/T. period_remain is initialised at period.

Every sample, sample is incremented by step and period_remain decremented. When period_remain reaches zero:

• sample is reset to -amplitude
• period_remain reset to period

Triangle wave generator (voice_wf_set_triangle)

Configures the waveform generator to produce a triangle wave.

sample is initialised as -amplitude, and the time period is computed as period=SYNTH_FREQ/(2*freq). The step is computed as step=(2*amplitude)/T. period_remain is initialised at period.

Every sample, sample is incremented by step and period_remain decremented. When period_remain reaches zero:

• if step is negative, sample is reset to -amplitude, otherwise it is reset to +amplitude.
• step is algebraically negated.
• period_remain is reset to period

Pseudorandom noise generator (wf_voice_set_noise)

This generates random samples at a given amplitude. The randomness depends on the C library's random number generator (rand()), so it may help to periodically seed it, perhaps by taking the least-significant bits of ADC readings and feeding those into srand to give it some true randomness.

Sequencer

Since the synthesizer state machine is effective in defining when a "note" envelope is terminated, it is then possible to store all the subsequent "notes" in a stream of consecutive steps. Each step contains a pair of waveform settings and ADSR settings.

This allow polyphonic tunes to be "pre-compiled" and stored in small binary files, or microcontroller EEPROM, and to be accessed in serial fashion.

Each tune are stored in a way that each frame in the stream should feed the next available channel with the enable flag of the struct poly_synth_t structure reset.

In order to arrange the steps of all the channels in the correct sequence, a sequencer compiler has to be run on all the channel steps, and sort it correctly using an instance of the synth configured in the exact way of the target system (e.g. same sampling rate, same number of voices, etc...).

This compiler is not optimized to run on a microcontroller (it requires dynamic memory allocation), but to be run on a PC in order to obtain compact binary files to be played by the sequencer on the host MCU.

To save memory for the tiniest 8-bit microcontrollers, the sequencer stream header and the steps are defined in a compact 8-bit binary format:

// A frame
struct seq_frame_t {
    /*! Envelope definition */
    struct adsr_env_def_t adsr_def;
    /*! Waveform definition */
    struct voice_wf_def_t waveform_def;
};

where adsr_env_def_t is the argument for the adsr_config, and voice_wf_def_t is the minimum set of arguments to initialize a waveform.

In order to save computational-demanding 16-bit division operations on 8-bit targets, the waveform frequency in the definition is expressed as waveform period instead of frequency in Hz, to allow faster play at runtime.

This requires the sequencer compiler to known in advance the target sampling rate.

For this reason, a stream header contains the information to avoid issues during reproduction:

struct seq_stream_header_t {
    /*! Sampling frequency required for correct timing */
    uint16_t synth_frequency;
    /*! Size of a single frame in bytes */
    uint8_t frame_size;
    /*! Number of voices */
    uint8_t voices;
    /*! Total frame count */
    uint16_t frames;
    /*! Follow frames data, as stream of seq_frame_t */
};

The frame_size field is useful when the code in the target microcontroller is compiled with different setting (e.g. different time scale, or different set of features that requires less data, like no Attack/Decay, etc...).

Typical usage

The sequencer can be fed via a callback, in order to support serial read for example from serial EEPROM or streams.

/*! Requires a new frame. The handler must return 1 if a new frame was acquired, or zero if EOF */
void seq_set_stream_require_handler(uint8_t (*handler)(struct seq_frame_t* frame));

/*! 
 * Plays a stream sequence of frames, in the order requested by the synth.
 * The frames must then be sorted in the same fetch order and not in channel order.
 */
int seq_play_stream(const struct seq_stream_header_t* stream_header, uint8_t voice_count, struct poly_synth_t* synth);

/*! Use it when `seq_play_stream` is in use, one call per sample */
void seq_feed_synth(struct poly_synth_t* synth);

MML compiler

A very common language to define tunes in a quasi-human-readable fashion is the Music Macro Language (MML).

The project contains an implementation of a MML parser that creates a sequencer stream. In that way, it is possible to 'compile' tunes into binary streams, embed it in the microcontroller and play it from the sequencer stream with the least as computational power as possible.

The MML dialect implemented supports multi-voice: each voice can be specified on a different line, prefixed with the voice number (from A to Z).

command	meaning
cdefgab	The letters a to g correspond to the musical pitches and cause the corresponding note to be played. Sharp notes are produced by appending a + or #, and flat notes by appending a -. The length of a note can be specified by appending a number representing its length (see l command). One or more dots . can be added to increase the length of 3/2.
p or r	A pause or rest. Like the notes, it is possible to specify the length appending a number and/or dots.
n<n>	Plays a note code, between 0 and 84. 0 is the C at octave 0, 33 is A at octave 2 (440Hz), etc...
o<n>	Specify the octave the instrument will play in (from 0 to 6). The default octave is 2 (corresponding to the fourth-octave in scientific pitch).
<, >	Used to step up or down one octave.
l<n>	Specify the default length used by notes or rests which do not explicitly define one. 4 means 1/4, 16 means 1/16 etc... One or more dots . can be added to increase the length of 3/2.
v<n>	Sets the volume of the instruments. It will set the current waveform amplitude (127 being the maximum modulation).
t<n>	Sets the tempo in beats per minute.
mn, ml, ms	Sets the articulation for the current instrument. Stands for music normal (note plays for 7/8 of the length), music legato (note plays full length) and music staccato (note plays 3/4 of length). This is implemented using the decay of ADSR modulation.
ws, ww, wt (*)	Sets the square waveform, sawtooth waveform or triangle waveform for the current instrument.
|	The pipe character, used in music sheet notation to help aligning different channel, is ignored.
#, ;	Characters to denote comment lines: it will skip the rest of the line.
A-Z (*)	Sets the active voice for the current MML line. Multiple characters can be specified: in that case all the selected voices will receive the MML commands until the end of the line.

(*) custom MML dialect.

The MML compiler is not optimized to run on a microcontroller (it requires dynamic memory allocation), but to be run on a PC in order to obtain the data to create a binary stream for the sequencer. The typical usage is a compiler for PC.

Typical usage

The MML file should be loaded entirely in memory to be compiled.

// Set the error handler in order to show errors and line/col counts
mml_set_error_handler(stderr_err_handler);
struct seq_frame_map_t map;
// Parse the MML file and produce sequencer frames as stream.
if (mml_compile(mml_content, &map)) {
    // Error
}
// Compile the channel data map in a stream
struct seq_frame_t* frame_stream;
int frame_count;
int voice_count;
seq_compile(&map, &frame_stream, &frame_count, &voice_count);

// Save the frame stream...

// Free memory
mml_free(map);
seq_free(frame_stream);

Ports

The code is written with portability in mind. While it has only ever been compiled on GNU/Linux platforms, it has successfully worked on AVR and Linux/x86-64. The code should compile and work for other processor architectures too.

To build a port, run:

$ make PORT=port_name

ATTiny85 port (attiny85)

The ATTiny85 port was the first microcontroller port of this synthesizer library. The demonstration port tries to operate as a stand-alone synthesizer. The PWM output is emitted out of PB4 and PB3 is used as an ADC input.

Connected to PB3 is a voltage divider network, with the segments connected to Vcc via pushbuttons. When a button is pressed, it shorts a section of the resistor divider out, and a higher voltage is seen on the ADC input.

The voltage is translated to a button press and used to trigger one of the voices, each of which have been configured with a different note.

The code is a work-in-progress, with some notable bugginess with the ADC-based keyboard implementation.

The remaining pins are available for other uses such as I²C/SPI or for additional GPIOs.

ATTiny861 port (attiny861)

This code is forked from the ATTiny85 port when it was realised that the ATTiny85 with its 5 usable I/O pins would be incapable of driving lots of lights without a lot of I/O expansion hardware.

Here, four I/O pins on port B are allocated:

• PB3: PWM audio output
• PB4: audio enable pin
• PB5: PWM light output
• PB6: GPIO enable pin

The audio amplifier used in the prototype is the NJR NJM2113D, and features a "chip disable" pin that powers down the amplifier when pulled high. The audio enable signal drives a N-channel MOSFET (e.g. 2N7000) that pulls the pin low against a pull-up resistor to +12V.

A logic high on the audio enable signal turns on the amplifier.

All of the pins on port A (PA0 through to PA7) are used for interfacing to MOSFETs and pushbuttons by way of a multiplexing circuit driven by the GPIO enable pin. The multiplexing circuit consists of two 4066-style analogue switches (I am using Motorola MC14066Bs here because I have dozens of them with 8241 date codes) and a 74374 D-latch.

The GPIO enable line connects the clock input of the 74374 and the switch enable pins on all switches in both 4066s. The 4066 and 74374 inputs are paralleled.

When GPIO enable is driven low, this turns off the 4066s allowing us to assert signals for the 74374. On the rising edge of GPIO enable, the 74374 latches those signals and the 4066s re-connect port A to the outside world. By doing this, port A is able to be used both for control of digital outputs hanging off the 74374 and for analogue + digital I/O through the 4066s.

The light PWM signal on PB5 connects to the 74374's "output enable" line, and thus by using pull-down resistors on the outputs of the 74374, it can drive N-channel MOSFETs to control the brightness of 8 lights.

Individual control of lights can be achieved with ⅛ maximum duty cycle by choosing a single output then driving that line with the desired PWM amplitude.

PC port (pc)

This uses libao and a command line interface to simulate the output of the synthesizer and to output a .wav file. It was used to debug the synthesizer.

The synthesizer commands are given as command-line arguments:

• voice V selects a given voice channel
• mute M sets the synthesizer mute bit-mask
• en M sets the synthesizer enable bit-mask
• dc A sets the selected voice channel to produce a DC offset of amplitude A.
• noise A sets the selected voice channel to produce pseudorandom noise at amplitude A.
• square F A sets the selected voice channel to produce a square wave of frequency F Hz and amplitude A.
• sawtooth F A sets the selected voice channel to produce a sawtooth wave of frequency F Hz and amplitude A.
• triangle F A sets the selected voice channel to produce a triangle wave of frequency F Hz and amplitude A.
• scale N sets the ADSR time unit scale for the selected channel to N samples per "tick"
• delay N sets the ADSR delay period for the selected channel to N "ticks"
• attack N sets the ADSR attack period for the selected channel to N "ticks"
• decay N sets the ADSR decay period for the selected channel to N "ticks"
• sustain N sets the ADSR sustain period for the selected channel to N "ticks"
• release N sets the ADSR release period for the selected channel to N "ticks"
• peak A sets the peak ADSR amplitude for the selected channel to A
• samp A sets the sustained ADSR amplitude for the selected channel to A
• reset resets the ADSR state machine for the selected channel.

Or, alternatively, you can pass all the above commands stored in a text file:

• -- NAME loads and run the script, and skip all the remaining arguments.

Once the enable bit-mask is set, the program loops, playing sound via libao and writing the samples to out.wav for later analysis until all bits in the enable bit-mask are cleared by the ADSR state machines.

When the program runs out of command line arguments, or the script ends, it exits.

In addition, the PC port can be used to compile MML tunes to the sequencer binary format:

• compile-mml FILE.mml compiles the .mml file and produces a sequencer.bin output

and to play sequencer files as well:

• sequencer FILE.bin loads and plays the sequencer binary file passed as input.