Added another great example of PWM pitch shifting (also volume/amplitude)
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Nick Westgate
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Probably the ultimate evolution of Apple II 1-bit audio are projects written using Michael Mahon's DAC522, including RT.SYNTH and Digital Music Synthesizer & Drummer:

DAC522 is a software digital-to-analog converter for the Apple II that plays a stream of 11.025kHz sound samples through the 1-bit Apple speaker port using a pulse-width modulated (PWM) stream at a pulse rate of 22.05kHz, or two pulses per sample. The 22kHz pulse rate renders the pulses themselves virtually inaudible to human ears, but the average output, changed by varying the pulse width in proportion to sample values, reproduces the sampled sound to a precision of 5 bits.

Regarding PWM and pitch, although RT.SYNTH is single voice, its instruments are resampled dynamically to any frequency and shaped with an envelope. Here's an overview:

The fundamental problem a music synthesizer must address is the production of notes of many frequencies and arbitrary durations having specified waveshapes (voices). Storing all the needed combinations in limited memory is not practical.

A workable solution is to store each waveshape needed as a single-frequency sample, then resample this waveshape on the fly to create any desired frequency.

Most instrument sounds change as a note sounds. For example, many sounds have an "attack" that sounds different from the rest of the note. And many instrument sounds change in amplitude as a note is held, usually decaying in amplitude or changing in "timbre" or spectral composition. Synthesis of notes with changes appropriate to particular instruments, therefore, requires that the synthesized waveform change as a function of the length of time the note is played.

RT.SYNTH performs all the calculations required to carry out these tasks while it is generating the pulses corresponding to the previously calculated sample.

Probably the ultimate evolution of Apple II 1-bit audio are projects written using Michael Mahon's DAC522, including RT.SYNTH and Digital Music Synthesizer & Drummer:

DAC522 is a software digital-to-analog converter for the Apple II that plays a stream of 11.025kHz sound samples through the 1-bit Apple speaker port using a pulse-width modulated (PWM) stream at a pulse rate of 22.05kHz, or two pulses per sample. The 22kHz pulse rate renders the pulses themselves virtually inaudible to human ears, but the average output, changed by varying the pulse width in proportion to sample values, reproduces the sampled sound to a precision of 5 bits.

Regarding PWM and pitch, although RT.SYNTH is single voice, its instruments are resampled dynamically to any frequency and shaped with an envelope. Here's an overview:

The fundamental problem a music synthesizer must address is the production of notes of many frequencies and arbitrary durations having specified waveshapes (voices). Storing all the needed combinations in limited memory is not practical.

A workable solution is to store each waveshape needed as a single-frequency sample, then resample this waveshape on the fly to create any desired frequency.

Most instrument sounds change as a note sounds. For example, many sounds have an "attack" that sounds different from the rest of the note. And many instrument sounds change in amplitude as a note is held, usually decaying in amplitude or changing in "timbre" or spectral composition. Synthesis of notes with changes appropriate to particular instruments, therefore, requires that the synthesized waveform change as a function of the length of time the note is played.

RT.SYNTH performs all the calculations required to carry out these tasks while it is generating the pulses corresponding to the previously calculated sample.

Added example routine.
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Nick Westgate
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Yes, it's possible to effectively change the volume if you're using Pulse Width Modulation (PWM), although the timbre of the note is also affected depending on playback hardware and psycho-acoustics. Dr. Blake Troise, who makes chiptunes under the moniker Protodome, describes how in a recent paper:

The 1-Bit Instrument: The Fundamentals of 1-Bit Synthesis, Their Implementational Implications, and Instrumental Possibilities

Even though the amplitude is a constant 1-bit waveform, the narrower pulses provide a way of varying volume. These narrower pulses have incrementally less power overall to the listener; as the duty cycle approaches 0% (or, by inversion, 100%) the perceptual volume decreases with it, even though the amplitude remains the same. This effect is not a consequence of the reduction of the pulsing signal's actual, electronic, or kinetic power. Instead, the reduction in volume is a product of bandlimiting—the effect whereby frequencies beyond a particular value are not heard. [...] Thinner pulses are constructed from more powerful high-frequency harmonics than lower ones. Accordingly, as the pulses get thinner, with extremely small or extremely large duty cycles, these higher frequencies increasingly fall outside the limits of what can be replicated by the speaker. Since these elements are not present, the result is a reduction of the waveform's overall power.

Some of the earlier uses of PWM on the platforms you mention were programs from around 1980 by Paul Lutus including Electric Duet. He states:

Decreasing the duty cycle of the generating waveform increases the amplitude of high-frequency components while reducing the overall volume.

There were routines published in a few Apple II magazines that made use of this volume technique. Here's one in Nibble magazine:

Software Volume Control Goetz, Philip November 1984

It's called VOLUMETONES.DEMO on disk NIB22B.dsk.

Yes, it's possible to effectively change the volume if you're using Pulse Width Modulation (PWM), although the timbre of the note is also affected depending on playback hardware and psycho-acoustics. Dr. Blake Troise, who makes chiptunes under the moniker Protodome, describes how in a recent paper:

The 1-Bit Instrument: The Fundamentals of 1-Bit Synthesis, Their Implementational Implications, and Instrumental Possibilities

Even though the amplitude is a constant 1-bit waveform, the narrower pulses provide a way of varying volume. These narrower pulses have incrementally less power overall to the listener; as the duty cycle approaches 0% (or, by inversion, 100%) the perceptual volume decreases with it, even though the amplitude remains the same. This effect is not a consequence of the reduction of the pulsing signal's actual, electronic, or kinetic power. Instead, the reduction in volume is a product of bandlimiting—the effect whereby frequencies beyond a particular value are not heard. [...] Thinner pulses are constructed from more powerful high-frequency harmonics than lower ones. Accordingly, as the pulses get thinner, with extremely small or extremely large duty cycles, these higher frequencies increasingly fall outside the limits of what can be replicated by the speaker. Since these elements are not present, the result is a reduction of the waveform's overall power.

Some of the earlier uses of PWM on the platforms you mention were programs from around 1980 by Paul Lutus including Electric Duet. He states:

Decreasing the duty cycle of the generating waveform increases the amplitude of high-frequency components while reducing the overall volume.

Yes, it's possible to effectively change the volume if you're using Pulse Width Modulation (PWM), although the timbre of the note is also affected depending on playback hardware and psycho-acoustics. Dr. Blake Troise, who makes chiptunes under the moniker Protodome, describes how in a recent paper:

The 1-Bit Instrument: The Fundamentals of 1-Bit Synthesis, Their Implementational Implications, and Instrumental Possibilities

Even though the amplitude is a constant 1-bit waveform, the narrower pulses provide a way of varying volume. These narrower pulses have incrementally less power overall to the listener; as the duty cycle approaches 0% (or, by inversion, 100%) the perceptual volume decreases with it, even though the amplitude remains the same. This effect is not a consequence of the reduction of the pulsing signal's actual, electronic, or kinetic power. Instead, the reduction in volume is a product of bandlimiting—the effect whereby frequencies beyond a particular value are not heard. [...] Thinner pulses are constructed from more powerful high-frequency harmonics than lower ones. Accordingly, as the pulses get thinner, with extremely small or extremely large duty cycles, these higher frequencies increasingly fall outside the limits of what can be replicated by the speaker. Since these elements are not present, the result is a reduction of the waveform's overall power.

Some of the earlier uses of PWM on the platforms you mention were programs from around 1980 by Paul Lutus including Electric Duet. He states:

Decreasing the duty cycle of the generating waveform increases the amplitude of high-frequency components while reducing the overall volume.

There were routines published in a few Apple II magazines that made use of this volume technique. Here's one in Nibble magazine:

Software Volume Control Goetz, Philip November 1984

It's called VOLUMETONES.DEMO on disk NIB22B.dsk.

Source Link
Nick Westgate
  • 6.4k
  • 1
  • 19
  • 53

Yes, it's possible to effectively change the volume if you're using Pulse Width Modulation (PWM), although the timbre of the note is also affected depending on playback hardware and psycho-acoustics. Dr. Blake Troise, who makes chiptunes under the moniker Protodome, describes how in a recent paper:

The 1-Bit Instrument: The Fundamentals of 1-Bit Synthesis, Their Implementational Implications, and Instrumental Possibilities

Even though the amplitude is a constant 1-bit waveform, the narrower pulses provide a way of varying volume. These narrower pulses have incrementally less power overall to the listener; as the duty cycle approaches 0% (or, by inversion, 100%) the perceptual volume decreases with it, even though the amplitude remains the same. This effect is not a consequence of the reduction of the pulsing signal's actual, electronic, or kinetic power. Instead, the reduction in volume is a product of bandlimiting—the effect whereby frequencies beyond a particular value are not heard. [...] Thinner pulses are constructed from more powerful high-frequency harmonics than lower ones. Accordingly, as the pulses get thinner, with extremely small or extremely large duty cycles, these higher frequencies increasingly fall outside the limits of what can be replicated by the speaker. Since these elements are not present, the result is a reduction of the waveform's overall power.

Some of the earlier uses of PWM on the platforms you mention were programs from around 1980 by Paul Lutus including Electric Duet. He states:

Decreasing the duty cycle of the generating waveform increases the amplitude of high-frequency components while reducing the overall volume.