Chapter 10 Quiz: Electronic Sound & Synthesis
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Question 1 A sawtooth wave at 200 Hz is passed through a low-pass filter with cutoff at 600 Hz. Which harmonics of the sawtooth wave pass through the filter with minimal attenuation?
A) 1st harmonic only (200 Hz) B) 1st, 2nd, and 3rd harmonics (200, 400, 600 Hz) C) 1st through 5th harmonics D) All harmonics, but each reduced by the same amount
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**Correct Answer: B** The sawtooth wave contains harmonics at 200 Hz, 400 Hz, 600 Hz, 800 Hz, 1000 Hz, etc. A low-pass filter with cutoff at 600 Hz passes frequencies below 600 Hz with minimal attenuation and attenuates frequencies above 600 Hz progressively. The first three harmonics (200, 400, 600 Hz) fall at or below the cutoff and pass through. The 4th harmonic (800 Hz) and above are significantly attenuated. This is the fundamental operation of subtractive synthesis: sculpting the harmonic content of a rich source.Question 2 In FM synthesis, increasing the modulation index (I) primarily causes:
A) A higher pitch (higher carrier frequency) B) A richer, more complex harmonic spectrum with more sidebands C) A softer, quieter output D) A slower attack time
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**Correct Answer: B** The modulation index I controls the spectral complexity of FM synthesis. According to the mathematical description (amplitudes proportional to Bessel functions Jₙ(I)), as I increases, more Bessel function terms become significant — meaning more sidebands (fc ± n·fm) have non-negligible amplitude. At I = 0, you get a pure sine wave; at I = 5 or 6, you get dozens of significant sidebands with a dense, complex spectrum. I does not directly affect pitch (that is determined by fc), amplitude, or attack time.Question 3 The Karplus-Strong algorithm generates a convincing plucked-string sound by:
A) Summing dozens of sine waves at harmonic frequencies B) Applying FM modulation with a carrier:modulator ratio of 1:1 C) Initializing a delay line with noise and repeatedly applying a low-pass averaging filter with feedback D) Recording a real string and playing back the sample at variable speed
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**Correct Answer: C** The Karplus-Strong algorithm uses a delay line of length equal to one period of the target pitch, initialized with random noise (simulating a pluck). On each sample, the output is taken from the front of the delay line, and the new value fed back is the average of adjacent samples (a two-sample low-pass filter). This averaging attenuates high frequencies faster than low ones — exactly like a real string — causing the sound to "settle" from noise into a pitched, decaying tone. It is physical modeling synthesis at its most elegant: the physics of string wave propagation emerges from this simple recurrence.Question 4 Which oscillator waveform contains ONLY odd harmonics?
A) Sawtooth wave B) Sine wave C) Square wave D) Triangle wave
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**Correct Answer: C (and D)** Both the square wave and the triangle wave contain only odd harmonics (f₀, 3f₀, 5f₀, ...). The square wave has odd harmonics with amplitude 1/n; the triangle wave has odd harmonics with amplitude 1/n². The sawtooth contains all harmonics (both odd and even) with amplitude 1/n. This is why the square wave (like a clarinet) and sawtooth (like a violin/sawtooth) have different timbres despite both being "buzzy." For this question, the most commonly cited answer is C (square wave), as the triangle is not always presented as a primary example of "odd harmonics only."Question 5 The term "source-filter model" applies to which of the following pairs of synthesis components?
A) ADSR envelope and LFO B) VCO (oscillator) and VCF (filter) C) Digital delay line and reverb algorithm D) MIDI controller and audio interface
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**Correct Answer: B** The source-filter model describes a two-stage acoustic or electronic system in which a *source* generates raw, harmonically rich sound and a *filter* shapes its spectrum. In a synthesizer, the VCO (oscillator) generates the harmonic source (sawtooth, square, etc.) and the VCF (filter) shapes the spectrum by boosting or attenuating different frequency regions. This directly mirrors the voice's glottal source and vocal tract filter. The ADSR and LFO (A) are modulation tools; delay/reverb (C) adds spatial character; MIDI and audio interfaces (D) are signal routing infrastructure.Question 6 In John Chowning's FM synthesis, if the carrier frequency is 440 Hz and the modulator frequency is 440 Hz (C:M = 1:1), where do the sideband components appear in the spectrum?
A) At 220, 440, 880, 1320 Hz (subharmonics and harmonics) B) At 440 Hz only (FM with equal frequencies produces no sidebands) C) At 0, 440, 880, 1320, 1760 Hz (symmetric sidebands at n × 440 Hz) D) At random frequencies determined by the modulation index
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**Correct Answer: C** FM sidebands appear at fc ± n·fm for n = 0, 1, 2, 3, .... With fc = fm = 440 Hz, the sidebands are at 440 ± 0 (440), 440 ± 440 (0 and 880), 440 ± 880 (−440 and 1320), 440 ± 1320 (−880 and 1760), etc. Negative frequencies "fold" to positive frequencies (with a phase flip), so the components appear at 0, 440, 880, 1320, 1760 Hz — a harmonic series with the fundamental at 440 Hz. This is why C:M = 1:1 FM produces a harmonically complete spectrum.Question 7 What is aliasing in digital audio synthesis?
A) A copyright violation when sampling another artist's recording B) High-frequency harmonic content that folds back into the audio range because it exceeds the Nyquist frequency C) The tendency of digital filters to sound "cold" compared to analog filters D) An artifact of additive synthesis when too many harmonics are summed
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**Correct Answer: B** Aliasing occurs when a digital signal contains frequencies above the Nyquist frequency (sample rate / 2). Because the digital system cannot represent these frequencies accurately, they "fold back" (alias) into the audio range at incorrect frequencies, producing inharmonic noise. In synthesis, a naively implemented sawtooth wave contains theoretically infinite harmonics; those above the Nyquist frequency alias back into the audio band, creating harsh, buzzy distortion artifacts. Band-limited oscillator algorithms (such as the BLIT — band-limited impulse train) prevent aliasing by removing harmonics above the Nyquist frequency before they are generated.Question 8 The "ADSR" envelope in synthesis stands for:
A) Amplitude, Duration, Sustain, Resonance B) Attack, Decay, Sustain, Release C) Attenuation, Dynamics, Spectral content, Rhythm D) Analog, Digital, Synthesis, Recording
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**Correct Answer: B** ADSR stands for Attack (time to rise from silence to peak amplitude), Decay (time to fall from peak to sustain level), Sustain (amplitude maintained while key is held), and Release (time to fall from sustain to silence when key is released). This four-parameter model approximates the time-varying amplitude behavior of virtually any acoustic instrument. A piano, for example, has a very fast attack (~5 ms), a long exponential decay, no sustain (the amplitude falls continuously), and a short release when the key is released.Question 9 Which synthesis technique is described as "the direct implementation of Fourier's theorem in sound production"?
A) Subtractive synthesis B) FM synthesis C) Additive synthesis D) Physical modeling
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**Correct Answer: C** Additive synthesis directly implements the Fourier theorem: any periodic sound can be expressed as a sum of sine waves at harmonic frequencies. In additive synthesis, individual sine wave oscillators are combined at specified frequencies, amplitudes, and phases to build up the target timbre. This is Fourier reconstruction made audible. The pipe organ is the oldest additive synthesizer — it literally adds sine-wave-like tones from individual pipes. By contrast, subtractive synthesis (A) starts rich and removes; FM synthesis (B) uses frequency modulation to create complex spectra; physical modeling (D) simulates the differential equations of acoustic systems.Question 10 What mathematical functions describe the amplitudes of the sideband components in FM synthesis?
A) Sine and cosine functions B) Bessel functions of the first kind C) Exponential decay functions D) Gaussian probability distributions
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**Correct Answer: B** The amplitude of the nth sideband in FM synthesis is proportional to |Jn(I)|, where Jn is the nth-order Bessel function of the first kind evaluated at the modulation index I. Bessel functions are solutions to Bessel's differential equation, which appears in cylindrical wave propagation, vibrating circular membranes, and electromagnetic waveguide theory. The fact that FM synthesis generates Bessel-function amplitudes is not an engineering coincidence — it reflects the deep mathematical connection between frequency modulation and cylindrical wave physics.Question 11 In Section 10.8, Aiko Tanaka discovers that her resonant filter is governed by the same differential equation as the quantum harmonic oscillator. The fundamental equation is:
A) A first-order equation describing exponential decay B) A second-order linear differential equation with a restoring force proportional to displacement C) A wave equation describing transverse vibration of a string D) A Schrödinger equation in complex form
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**Correct Answer: B** The universal oscillator equation — the equation that governs the resonant filter, the quantum harmonic oscillator, a mass on a spring, an RLC circuit, and a vocal tract formant — is a second-order linear differential equation of the form: m·ẍ + b·ẋ + k·x = F(t). The restoring force (−k·x) is proportional to displacement (Hooke's Law in mechanics; Coulomb restoring force in the quantum well; the inductor-capacitor restoring voltage in the RLC circuit). This universality means that every physical system with a restoring force proportional to displacement oscillates in the same mathematical way.Question 12 The Hammond organ is best described as what type of synthesizer?
A) Subtractive (starts with noise and filters it) B) FM synthesizer (uses frequency modulation) C) Additive synthesizer (uses drawbars to add sine-wave-like harmonics) D) Physical modeling synthesizer (simulates pipe organ acoustics)
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**Correct Answer: C** The Hammond organ uses tonewheel generators — spinning electromagnetic wheels that generate approximately sine-wave tones at specific harmonic frequencies. Drawbars select which harmonics (fundamental, 2nd, 3rd, 4th, 5th, 6th, 8th harmonics) are added to the output, and at what amplitude. This is textbook additive synthesis: building a complex timbre by summing sinusoidal components. The Hammond was not designed with Fourier theory in mind — it was an engineering solution to the problem of building an affordable substitute for a pipe organ — but it is nonetheless a direct implementation of additive synthesis principles.Question 13 Why does an FM synthesis patch with carrier:modulator ratio of 1:1.414 produce an inharmonic (bell-like) spectrum?
A) Because 1.414 ≈ √2, an irrational number, so the sidebands fc ± n·fm are not integer multiples of fc B) Because 1.414 Hz is in the ultrasonic range C) Because the modulation index must be exactly 1.414 to produce inharmonic spectra D) Because bell sounds always require a C:M ratio of exactly 1:1.414
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**Correct Answer: A** Sideband components in FM synthesis appear at fc ± n·fm. If fm = 1.414 × fc, then the sidebands are at fc ± n × 1.414 × fc = fc(1 ± 1.414n) for n = 0, 1, 2, .... Since 1.414 ≈ √2 is irrational, the multiples 1.414n are never exactly integers, meaning the sidebands are not at integer multiples of any common fundamental. The resulting spectrum is inharmonic — it does not correspond to any repeating waveform's harmonic series. Inharmonic spectra are characteristic of metallic percussion (bells, gongs, metal bars) rather than bowed strings or wind instruments.Question 14 The "proximity effect" in microphone technique refers to:
A) The tendency of microphones to distort at high volumes B) An increase in low-frequency output when a directional microphone is placed very close to a sound source C) The acoustic coupling between a singer's chest and a nearby microphone D) Aliasing that occurs when the microphone capsule vibrates in proximity to the speaker
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**Correct Answer: B** The proximity effect is a physical property of directional (cardioid and figure-8) microphones: when placed very close to a sound source, low frequencies are boosted relative to high frequencies due to the pressure gradient detection mechanism of the microphone at close distances. This gives the recorded voice a "warm," bass-heavy quality different from the live acoustic sound. Pop and rock vocalists singing into a close microphone typically rely on the proximity effect for a rich, intimate tone — a different acoustic reality from projecting to a concert hall.Question 15 "Voltage-controlled" synthesis (VCO, VCF, VCA) means that:
A) The synthesizer must be plugged into a wall socket to operate B) Pitch, filter cutoff, and amplitude can all be controlled by voltage signals, allowing any module to control any parameter C) The synthesizer uses vacuum tubes (which require high voltage) for its characteristic sound D) The sound is converted from voltage to audio only at the final output stage
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**Correct Answer: B** The "voltage-controlled" architecture means that parameter control (pitch, filter frequency, amplitude) is done by applying control voltage (CV) signals. Because all parameters are voltage-controlled, any voltage-producing module can control any parameter: an LFO can modulate pitch (vibrato), filter (tremolo), or amplitude; an envelope generator can control pitch sweeps, filter sweeps, or amplitude; a sequencer can control all of these in rhythmic patterns. This universal voltage = control paradigm is what makes modular synthesis — and the creative routing of signals — possible.Question 16 How does a resonant filter (high Q setting) differ from a non-resonant filter (Q = 0.707, Butterworth response)?
A) A resonant filter has a steeper roll-off slope; a Butterworth filter has a gentler slope B) A resonant filter has a pronounced amplitude peak near the cutoff frequency; a Butterworth filter is maximally flat (no peak) C) A resonant filter works only in the digital domain; a Butterworth filter only works in analog D) A resonant filter passes high frequencies; a Butterworth filter passes low frequencies
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**Correct Answer: B** A Butterworth (Q = 0.707, or "critically damped") filter is designed to have the flattest possible passband response with no amplitude peak at the cutoff — it is "maximally flat." A resonant (high Q) filter has an amplitude peak near the cutoff frequency — the filter actively boosts signals at that frequency before attenuating them. In synthesis, this resonant peak is what creates the "synthesizer filter sweep" sound — as the cutoff frequency is swept, the resonance peak moves through the spectrum, emphasizing different harmonics dramatically. In acoustic analogy, the resonance peak corresponds to a vocal tract formant.Question 17 Physical modeling synthesis is considered the most "physically principled" synthesis method because:
A) It always produces the most realistic-sounding output B) It implements the actual differential equations (wave equations, resonance equations) that govern acoustic instruments C) It requires the most computing power D) It was invented by physicists rather than musicians or engineers
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**Correct Answer: B** Physical modeling synthesis is "physically principled" because it implements the actual differential equations that govern the physics of acoustic instruments — wave propagation equations for strings and bores, vibrating membrane equations for drums, modal synthesis equations for plates and bars. By solving or approximating these equations, the synthesizer produces sound that responds to parameter changes in physically correct ways (e.g., a longer "string" plays at a lower pitch; a softer "blow" into a "reed" produces a softer, breathier tone). This physical grounding means the model responds correctly to playng gestures that acoustic instruments respond to — something neither FM nor subtractive synthesis can do as naturally.Question 18 In Aiko's experiment (Section 10.8), her resonant low-pass filter operating on a sawtooth wave to approximate a bowed string corresponds to which two components of the source-filter model of the voice?
A) The vibrato (source) and the pitch (filter) B) The glottal pulse source and the vocal tract resonance filter C) The subglottal air pressure and the mucosal wave D) The fundamental frequency and the harmonic roll-off
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**Correct Answer: B** Aiko's sawtooth oscillator corresponds to the glottal pulse source in the voice: both are periodic, harmonically rich signals generated by a vibrating element (bow-string friction for the sawtooth model, vibrating vocal folds for the voice). Aiko's resonant low-pass filter corresponds to the vocal tract resonance filter: both are frequency-selective systems that boost certain frequency regions (formants / resonances) and attenuate others. The key difference is that the vocal tract has multiple formants while Aiko's simple filter has one resonance peak, but the structural parallel is exact: source × filter = output timbre.Question 19 The Nyquist-Shannon theorem guarantees that digital audio at 44,100 Hz sample rate can accurately represent:
A) All sounds from 0 Hz to 44,100 Hz B) All sounds from 0 Hz to 22,050 Hz (half the sample rate) C) Sounds above 20,000 Hz for high-resolution listening D) Only sounds that are multiples of the sample rate frequency
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**Correct Answer: B** The Nyquist-Shannon sampling theorem states that to accurately represent a signal with maximum frequency content fmax, you must sample at a rate of at least 2·fmax. Equivalently, given a sample rate fs, you can accurately represent signals up to fs/2 — the Nyquist frequency. At fs = 44,100 Hz, the Nyquist frequency is 22,050 Hz. All frequencies from 0 Hz to 22,050 Hz are accurately represented in the digital signal; frequencies above 22,050 Hz are either filtered out before recording (anti-aliasing filter) or will alias into the audio band as artifacts.Question 20 The thought experiment "If a synthesizer perfectly simulated a Stradivarius, would it BE a Stradivarius?" is primarily a question about:
A) The technical feasibility of physical modeling synthesis B) Whether acoustic quality fully determines instrument identity, or whether identity also depends on history, materiality, and cultural meaning C) Patent law and the ownership of acoustic instrument designs D) Whether digital synthesis is superior to analog synthesis