Technical Reference Dictionary
Plain-language explanations, mathematical formulas, and interactive tool cross-references for essential concepts in audio engineering, psychoacoustics, signal synthesis, and acoustic measurement.
A double-blind comparative listening test protocol where subjects are presented with known references A and B, and must identify whether unknown target X is identical to A or B. Used to establish statistical significance (p < 0.05) and eliminate expectation bias.
P(X \ge k) = \sum_{j=k}^{n} \binom{n}{j} (0.5)^nAn unwanted digital distortion artifact created when an analog frequency exceeds half the digital sampling rate (the Nyquist frequency). The exceeding frequency folds backward across the Nyquist limit as an inharmonic phantom tone.
f_{\text{alias}} = |f - N \cdot f_s|A standardized chart displaying an individual's hearing threshold sensitivity across discrete octave frequencies (typically 125 Hz to 8,000 Hz), measured in decibels relative to normal hearing thresholds.
An auditory illusion perceived in the superior olivary complex of the brainstem when two pure sine tones of slightly different frequencies are presented separately to each ear via isolated stereo headphones.
f_{\text{beat}} = |f_1 - f_2|The number of binary bits allocated per sample in digital pulse-code modulation (PCM). Bit depth dictates the theoretical dynamic range and signal-to-quantization-noise ratio (SQNR).
\text{SQNR} \approx (6.02 \times N + 1.76) \text{ dB}A stochastic acoustic signal characterized by a power spectral density that rolls off at -6 dB per octave (-20 dB per decade) with increasing frequency. Named after Brownian motion random walks.
\text{PSD}(f) \propto 1/f^2A family of traditional open tunings for the Brazilian 10-string viola caipira (most commonly Cebolão em Mi or Cebolão em Ré), sounding a resonant major chord across five paired courses with octave and unison stringing.
A logarithmic unit of measure for musical intervals, where one equal-tempered semitone equals 100 cents and an octave equals 1,200 cents. Used to quantify microtonal pitch deviation and intonation accuracy.
\Delta\text{cents} = 1200 \times \log_2\left(\frac{f}{f_0}\right)A grouping of two or more adjacent strings positioned close together on a stringed instrument, tuned in unison or octaves and struck simultaneously as a single musical voice (common on 12-string guitars, mandolins, and lutes).
The ratio of the peak amplitude of a waveform to its root-mean-square (RMS) effective level. A pure sine wave has a crest factor of 3.01 dB (1.414:1), while uncompressed orchestral recordings can exceed 18–20 dB.
C = 20 \log_{10} \left( \frac{V_{\text{peak}}}{V_{\text{RMS}}} \right)The frequency threshold where an audio filter network splits an input signal into separate bands for specialized transducers (e.g. routing sub-80 Hz to a subwoofer and above 80 Hz to satellite monitors).
Unwanted leakage of acoustic or electrical signal from one stereo channel into the adjacent channel, measured in negative decibels. High crosstalk narrows the perceived stereo soundstage width.
A logarithmic measurement unit for digital audio signals where 0 dBFS represents the maximum possible digital numerical value before hard clipping occurs. All levels below clipping are expressed as negative values.
\text{dBFS} = 20 \log_{10} \left( \frac{|x|}{x_{\text{max}}} \right)The intentional injection of randomized, un-correlated microscopic noise into digital audio prior to word-length reduction (e.g. 24-bit to 16-bit) to linearize quantization and completely eliminate harmonic distortion.
The decibel ratio between the maximum undistorted signal level an audio system can produce and its residual analog noise floor or digital quantization threshold.
A series of curves (Fletcher-Munson / ISO 226) plotting the sound pressure levels across the frequency spectrum required for human listeners to perceive equal subjective loudness.
The phenomenon wherein the frequency response of human hearing flattens as overall listening volume increases. At quiet volumes, human hearing is significantly less sensitive to low bass and high treble.
The lowest frequency in a periodic waveform that establishes its musical pitch. Integer multiples of the fundamental are known as harmonics or overtones.
The safety margin in decibels between nominal operating level and the point of clipping or non-linear saturation. In digital audio, 1 to 2 dB of headroom prevents inter-sample peak distortion during lossy encoding.
A traditional Japanese pentatonic tuning mode for the 13-string koto (and adapted to shamisen and guitar), built from intervals of 2, 1, 4, 1, and 4 semitones (e.g. D–E–F–A–B♭) that produce a contemplative, minor-modal character.
The standard root tuning for traditional Japanese three-string plucked lutes (shamisen and sanshin), consisting of an ascending perfect fourth followed by a perfect fifth (e.g. D3–G3–D4 or C3–F3–C4) relative to the singer’s pitch.
The microsecond time delay between when a sound wavefront strikes the nearer ear compared to the further ear. ITD is the primary psychoacoustic cue used by the brain to localize low-frequency sounds (< 1.5 kHz).
Non-linear distortion occurring when two or more distinct input frequencies interact within an amplifier or transducer, generating spurious sum and difference frequencies not present in the original signal.
f_{\text{IMD}} = |m \cdot f_1 \pm n \cdot f_2|Loudness Units relative to Full Scale (ITU-R BS.1770 / EBU R128). A standardized psychoacoustic measurement incorporating K-weighting frequency filters and gating to reflect human perception of integrated loudness.
Half of the digital sampling frequency ($f_s / 2$). According to the Nyquist-Shannon sampling theorem, an analog signal can be perfectly reconstructed without aliasing only if it contains no frequencies exceeding this boundary.
f_{\text{Nyquist}} = \frac{f_s}{2}The psychoacoustic illusion where identical, correlated mono audio signals played simultaneously from left and right stereo speakers are perceived as originating from a physical point centered directly between them.
A random acoustic signal with a power spectral density proportional to 1/f (-3 dB per octave). Because it delivers equal energy per musical octave, pink noise sounds subjectively flat to human hearing and is the universal reference for acoustic calibration.
\text{PSD}(f) \propto 1/fThe electrical wiring orientation (+ and -) of an audio circuit. Swapping speaker leads inverts electrical polarity by 180°, causing low-frequency cancellation and destroying stereo soundstage imaging.
The progressive, age-related sensorineural hearing loss occurring predominantly in the highest audible frequencies due to cumulative mechanical wear and metabolic attrition of outer hair cells in the basal cochlea.
A stringed instrument tuning where the open strings do not progress monotonically from low to high across the fingerboard, such as the high-G fourth string on standard ukuleles or the fifth drone string on banjos.
The standardized acoustic frequency assigned to middle A (A4), from which all other semitones across an instrument’s scale are mathematically derived. Standard concert pitch is defined as 440 Hz by ISO 16.
f = A_{\text{ref}} \times 2^{(m - 69)/12}Acoustic standing waves formed in an enclosed space when the distance between parallel walls, floor, and ceiling coincides with integer multiples of a sound wave's half-wavelength. Results in localized bass peaks and nulls.
f = \frac{c}{2} \sqrt{\left(\frac{p}{L}\right)^2 + \left(\frac{q}{W}\right)^2 + \left(\frac{r}{H}\right)^2}The percentage or decibel ratio between the combined root-mean-square amplitude of all generated harmonic distortion components and the amplitude of the fundamental input signal.
\text{THD} = \frac{\sqrt{\sum_{n=2}^{\infty} V_n^2}}{V_1} \times 100\%A stochastic signal containing equal acoustic energy per Hertz of bandwidth across all frequencies (flat power spectral density, 0 dB/octave). Sounds bright and hissing to human ears due to logarithmic octave summation.
\text{PSD}(f) = \text{constant}