Source: https://docs.jmrp.io/phonometry/reference/glossary/ # Glossary The guides each open with the standard they implement, so a quantity is always defined where it is used. This page is the other direction: you have a symbol, from a report, a specification or a colleague's email, and you want to know what it is, what it is measured in, which document defines it and where in this documentation it is computed. A quantity that is not here is still defined where it is computed: every guide states its quantities before its code. Two conventions govern the line that says where a quantity is defined, and both matter more than they seem to. Where a clause, formula or table number appears, it is the one the implementation cites, taken from the standard the guide implements. Where only a designation appears, the standard is established but the defining clause is not stated anywhere in this documentation, and inventing a plausible one would be worse than leaving it out. A handful of quantities have no governing standard at all; their source is the paper or book the model comes from, named as such. A third convention governs the unit, and it is the one most often lost between a measurement and a report. A decibel is always a ratio, so an entry whose unit reads *re* something (dB re 20 µPa in air, dB re 1 µPa in water, dB re 1 pW for power, dB re 1 pW/m² for intensity, dB re 50 nm/s for a velocity level) is an **absolute level**, and the reference quantity is part of the unit. An entry whose unit is a bare dB is a **level difference or a rating**: $D$, $R$, $R_\mathrm{w}$, $C$, $C_\mathrm{tr}$, $\Delta L_\mathrm{w}$, $K_{ij}$, where the reference cancels and no reference applies. Two numbers can only be added or subtracted when they are of the same kind, and the commonest error in a report is subtracting two levels referred to different quantities, or adding a rating to a level. ## Symbols that collide Symbols collide across domains, and the glossary does not pretend otherwise. Some collisions are harmless because the two quantities never meet in one calculation; others change a number by tens of decibels, or by a whole rating step, and those are the ones below. Where two entries share a symbol, the qualifier in brackets after the notation says which one you are reading, and on the site a symbol index above the cards lists every meaning of a letter side by side: the answer for a reader who has the symbol and not the domain, which is the one case the grouping by domain cannot serve. | Symbol | Meanings that are not the same quantity | | :--- | :--- | | $C$ | The **decay curvature** $100\,(T_{30}/T_{20} - 1)$ in per cent, and the ISO 717-1 **spectrum adaptation term** in decibels. Both are defined on one page, [Rooms and buildings](https://docs.jmrp.io/phonometry/reference/theory/rooms-buildings/), a couple of sections apart. | | TL | A partition's **transmission loss** and a duct element's **transmission loss**: a different measurement, with an anechoic termination in the definition. The underwater quantity the sonar equation carries is not one of them, and is written PL: ISO 18405:2017 deprecates the two names as synonyms (3.4.1.3 Note 6, 3.4.1.4 Note 7). | | NR | The **noise rating** curve family of a room criterion, and the **noise reduction** $L_{p1} - L_{p2}$ between two rooms in noise control. | | $\alpha$ | The **absorption coefficient** of a surface, the **atmospheric attenuation coefficient** per unit length (dB/m here, dB/km in ISO 9613-2), the **volume absorption coefficient** of sea water (dB/km), and the **tortuosity** $\alpha_\infty$ of a porous model, which is not an absorption at all. | | $A$ | An **equivalent absorption area** in m², an **accelerance** in 1/kg, and the **total attenuation** of ISO 9613-2 in dB. | | $D$ | A **level difference**, the definition $D_{50}$, the withdrawn **D-weighting**, the directivity correction $D_\mathrm{c}$ and barrier screening $D_z$ of ISO 9613-2, the **acceleration dose** $D_\mathrm{z}$ of ISO 2631-5 (the same two letters, whose subscript is a path-length difference in one and a direction in the other, which is why one is italic and the other upright), the spatial decay rate $D_{2,\mathrm{S}}$ of an open-plan office, and a microphone's **directivity index** $D = 20\log_{10}(M_0/M_\mathrm{diff})$. | | $H$ | The **receptance** of ISO 7626-1, the **frequency response estimators** $H_1$ and $H_2$, and the **harmonic transfer functions** $H_n$ of a swept-sine measurement (where $H_2$ is the second harmonic, not the noise-on-input estimator). | | $\eta$ | The **loss factor** of a resilient element, the **coupling loss factor** $\eta_{ij}$ of a junction, and the **internal** and **total** loss factors of a building element. | | $\tau$ | The **transmission factor** of a partition, the **time constant** of a detector, the **lag** of a correlation, and the **air temperature** in CNOSSOS-EU. | | $T_\mathrm{s}$ | The **structural reverberation time** of a plate, which is seconds, and the number of **months per year that studded tyres are fitted** in CNOSSOS-EU. The ISO 3382-1 **centre time** of a room impulse response, tens of milliseconds, is $T_\mathrm{S}$, with the capital S its standard prints. | | $R$ | The **sound reduction index** in building acoustics, the **airflow resistance** in materials, the **roughness** in psychoacoustics, and the **cumulative stress variable** of ISO 2631-5. | | $\sigma$ | The **airflow resistivity** of a porous material, the **radiation efficiency** of a plate, and the **standard deviation** $\sigma_\mathrm{R}$ of a building-acoustics measurement situation. | | $L_N$, $L_\mathrm{N}$, $L_\mathrm{n}$ | $L_N$, with a sloped N, is a **percentile level** in environmental noise, where the N is the percentage. $L_\mathrm{N}$, with an upright one, is a **loudness level** in phon, which is how ISO 226:2023 prints it, and the level equivalent to a microphone's **inherent noise**. $L_\mathrm{n}$, with a lower-case subscript, is the **normalized impact sound pressure level** of ISO 10140-3. In building acoustics the case of the subscript is the whole difference; here so is its slope. | | $v_0$ | A **reference velocity** of 1 nm/s in EN 15657 and EN 12354-5, and of 50 nm/s in ISO/TS 7849 and ISO 9611 (34 dB apart, in one section of one area). | | $F_0$ | A **reference force** of 1 N in ISO 16283-2, and of 1 µN in EN 15657 (120 dB apart). | | $K_1$ | The ISO 3744 **background noise correction** in dB, and a CNOSSOS-EU **temperature coefficient** in dB/°C. | | $F$ | **Fluctuation strength** in vacil, the **Fast** time weighting, and the **modulation frequency** in $m(F)$ (all three on this page). | | $L_\mathrm{U}$ | The **magnitude of the linear transfer function** of ISO 226, normalized to zero at 1 kHz, and the level of the **upper contiguous critical band** of the prominence ratio (both on [Perception](https://docs.jmrp.io/phonometry/reference/theory/perception/), one section apart). | | $L_s$ | The **arithmetic mean of the two adjacent bands** a candidate tone is compared against in the Spanish tonal test, the **start level** an impulsive onset rises from, the **spherical spreading** term of the rotorcraft propagation chain, and the ISO 17208-2 **equivalent monopole source level** of a ship. The sonar equation's own source level is $L_\mathrm{S}$, with a capital. | | $C_\mathrm{P}$ | The **specific heat capacity at constant pressure** of the air in a porous absorber's thermal length (ISO 9053-2 Annex A), and the CNOSSOS-EU **propulsion coefficient** of a road junction (Table F-3), which sits beside $C_\mathrm{R}$ for rolling. | | $f_\mathrm{m}$ | The exact **midband frequency** of a fractional-octave band, and the **modulation frequency** of an amplitude-modulated tone or of a modulation transfer function. | Where two meanings meet inside one navigation section, the guide says so at first use; this table is the site-wide list. For the source of each definition rather than the definition itself, the [bibliography](https://docs.jmrp.io/phonometry/reference/bibliography/) lists every cited work with a DOI or publisher link, and the [conformance report](https://docs.jmrp.io/phonometry/reference/conformance/) shows the numerical check that pins each quantity to its standard's own expected value. ## Sound pressure, power and intensity levels | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $L_p$ | Sound pressure level: twenty times the base-10 logarithm of the r.m.s. sound pressure over the reference pressure. | dB re 20 µPa | IEC 61672-1:2013 | [Calibration and dBFS](https://docs.jmrp.io/phonometry/signals/metrology/calibration/) | | $L_\mathrm{eq}$ | Equivalent continuous sound pressure level: the level of the steady sound carrying the same mean-square pressure over the interval. | dB re 20 µPa | IEC 61672-1:2013 | [Integrated and Statistical Levels](https://docs.jmrp.io/phonometry/signals/levels/levels/) | | $L_\mathrm{Aeq}$ | The same integral applied to the A-weighted signal, the default descriptor of environmental and occupational noise. | dB re 20 µPa | IEC 61672-1:2013 | [Integrated and Statistical Levels](https://docs.jmrp.io/phonometry/signals/levels/levels/) | | $L_{\mathrm{A}E}$, SEL | Sound exposure level: the whole A-weighted energy of a single event normalised to one second. | dB re (20 µPa)²·s | IEC 61672-1:2013, Equation 8 (Table 4) | [Integrated and Statistical Levels](https://docs.jmrp.io/phonometry/signals/levels/levels/) | | $L_\mathrm{Cpeak}$ | C-weighted peak sound level: the absolute maximum of the C-weighted pressure, not a time-weighted maximum. | dB re 20 µPa | IEC 61672-1:2013, subclause 5.13 | [Integrated and Statistical Levels](https://docs.jmrp.io/phonometry/signals/levels/levels/) | | $L_N$ ($L_{10}$, $L_{50}$, $L_{90}$) | Percentile level: the level exceeded $N$ % of the measurement time, read off the time-weighted level distribution. | dB re 20 µPa | ISO 1996-2:2017 (Annex I uses $L_{90}$ as the residual level) | [Integrated and Statistical Levels](https://docs.jmrp.io/phonometry/signals/levels/levels/) | | $L_W$, SWL | Sound power level: the power a source radiates, referred to 1 pW. | dB re 1 pW | ISO 3745:2012, Clause 8 | [Sound Power](https://docs.jmrp.io/phonometry/devices/emission/sound-power/) | | $L_I$ | Sound intensity level: the magnitude of the intensity vector referred to 1 pW/m², with the flow direction reported separately as a sign. | dB re 1 pW/m² | IEC 61043:1993 | [Sound Intensity (p-p)](https://docs.jmrp.io/phonometry/devices/emission/intensity/) | | $L_p - L_I$ | Pressure-intensity index: the difference between the pressure and intensity levels at a position, the field indicator that qualifies an intensity measurement. | dB | ISO 9614-1:1993, Equation (A.3) | [Sound Intensity (p-p)](https://docs.jmrp.io/phonometry/devices/emission/intensity/) | | $K_1$ | Background noise correction: what is subtracted from the surface level to remove the background's own contribution, $-10\log_{10}(1 - 10^{-0,1\Delta L_p})$ from the source-on minus source-off margin. It is a cliff rather than a slope: above a 15 dB margin it is taken as zero, between 6 and 15 dB it is computed, and below 6 dB the standard caps it at 1,3 dB and warns that the result has lost accuracy. | dB | ISO 3744:2010, 3.16 and Equation (16) | [Sound Power by Pressure Methods](https://docs.jmrp.io/phonometry/devices/emission/sound-power-pressure/) | | $K_2$ | Environmental correction: what is subtracted to remove the energy the test room reflects back onto the measurement surface, $10\log_{10}(1 + 4S/A)$ from the surface area and the room's equivalent absorption area. Its ceiling is the grade of accuracy rather than a preference: an engineering-grade result is only valid where $K_{2\mathrm{A}} \le 4$ dB, the survey method allows 7 dB, and a qualified hemi-anechoic room gives zero. | dB | ISO 3744:2010, 3.17 and Formula (A.2) | [Sound Power by Pressure Methods](https://docs.jmrp.io/phonometry/devices/emission/sound-power-pressure/) | | $L_{WAd}$, $K_{WA}$ | The declared noise emission of a machine: either the dual-number form, the measured $L_{WA}$ and its uncertainty $K_{WA}$ stated separately, or the single-number form $L_{WAd} = L_{WA} + K_{WA}$, both rounded to the nearest whole decibel. The declared value is an upper limit a verification measurement is unlikely to exceed, not a best estimate, so it is never the number to feed into a propagation calculation. | dB re 1 pW | ISO 4871:1996, 3.15 and 3.16 | [Sound Power](https://docs.jmrp.io/phonometry/devices/emission/sound-power/) | | $L_{WA}$ (apparent, wind turbine) | Apparent sound power level of a wind turbine: the A-weighted level of a point source at the rotor centre that would radiate the same downwind emission as the machine measured. It is written like a sound power level but is not one in the usual sense: the ground-board measurement builds a downwind reflection into it, so feeding it to a propagation model that adds a ground effect counts that reflection twice. | dB re 1 pW | IEC 61400-11:2012+AMD1:2018, 3.1 and Formula (26) | [Wind-turbine noise: sound power and tonal audibility](https://docs.jmrp.io/phonometry/environment/sources/wind-turbine-noise/) | ## Environmental and occupational descriptors | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $L_\mathrm{den}$ | Day-evening-night level: the energy mean of the three periods with 5 dB added to the evening and 10 dB to the night. | dB re 20 µPa | ISO 1996-1:2016, 3.6.4 | [Environmental Levels (ISO 1996-1/-2)](https://docs.jmrp.io/phonometry/environment/assessment/environmental-levels/) | | $L_\mathrm{dn}$ | Day-night level: the same construction with the 10 dB night penalty only. | dB re 20 µPa | ISO 1996-1:2016, 3.6.5 | [Environmental Levels (ISO 1996-1/-2)](https://docs.jmrp.io/phonometry/environment/assessment/environmental-levels/) | | $L_\mathrm{r}$ | Rating level: the whole-day composite level after the source-character and time-of-day adjustments. | dB re 20 µPa | ISO 1996-1:2016, clause 6.5 (Formulae 5 and 6) | [Environmental Levels (ISO 1996-1/-2)](https://docs.jmrp.io/phonometry/environment/assessment/environmental-levels/) | | $L_{\mathrm{Ar},T}$ | Rating level of an impulsive source over a reference interval, $L_\mathrm{Aeq}$ plus the graduated impulse adjustment. | dB re 20 µPa | NT ACOU 112:2002, clause 8 | [Impulsive-sound prominence (NT ACOU 112)](https://docs.jmrp.io/phonometry/environment/assessment/impulsive-sound/) | | $K_\mathrm{I}$ | Impulse adjustment added to $L_\mathrm{Aeq}$, graduated by the predicted prominence of the impulses. | dB | NT ACOU 112:2002, clause 8 | [Impulsive-sound prominence (NT ACOU 112)](https://docs.jmrp.io/phonometry/environment/assessment/impulsive-sound/) | | $E$ | Sound exposure: the time integral of the squared A-weighted sound pressure over the exposure period. | Pa²h | IEC 61252:1993, 3.1 | [Integrated and Statistical Levels](https://docs.jmrp.io/phonometry/signals/levels/levels/) | | $L_\mathrm{EX,8h}$, $L_\mathrm{EP,d}$ | Daily noise exposure level: the steady level that, sustained over a nominal 8 h day, carries the same A-weighted sound exposure as the measured one. | dB re 20 µPa | IEC 61252:1993, 3.3 | [Occupational Noise Exposure (ISO 9612)](https://docs.jmrp.io/phonometry/perception/hearing/occupational-exposure/) | | $L_{p,\mathrm{A,eq}T}$ | A-weighted equivalent continuous level of a task, a job sample or a full day, the building block $L_\mathrm{EX,8h}$ is assembled from. | dB re 20 µPa | ISO 9612:2009, clauses 9 to 11 | [Occupational Noise Exposure (ISO 9612)](https://docs.jmrp.io/phonometry/perception/hearing/occupational-exposure/) | | NIPTS | Noise-induced permanent threshold shift: the median hearing loss attributable to a stated exposure level, duration and audiometric frequency. | dB | ISO 1999:2013 | [Noise-induced hearing loss (ISO 1999)](https://docs.jmrp.io/phonometry/perception/hearing/noise-induced-hearing-loss/) | | HTLAN | Hearing threshold level associated with age and noise: the NIPTS combined with the age component. | dB | ISO 1999:2013 | [Noise-induced hearing loss (ISO 1999)](https://docs.jmrp.io/phonometry/perception/hearing/noise-induced-hearing-loss/) | | $L_{\mathrm{Keq},T}$ | Corrected equivalent level: the A-weighted equivalent level of the interval plus the three penalties for tonal, low-frequency and impulsive character, $L_{\mathrm{Aeq},T} + K_\mathrm{t} + K_\mathrm{f} + K_\mathrm{i}$. It is the quantity the Spanish immission limits are written against, so an activity is judged on it and not on the bare $L_\mathrm{Aeq}$. | dB re 20 µPa | RD 1367/2007 (Spain), Annex I A.2 c | [Spanish Noise Regulation (RD 1367/2007)](https://docs.jmrp.io/phonometry/environment/assessment/spanish-noise-regulation/) | | $K_\mathrm{t}$, $K_\mathrm{f}$, $K_\mathrm{i}$ | The three character penalties added to $L_{\mathrm{Aeq},T}$: $K_\mathrm{t}$ for emergent tonal components, read from an unweighted one-third-octave spectrum against the arithmetic mean of the two adjacent bands; $K_\mathrm{f}$ for low-frequency content, from $L_\mathrm{Ceq} - L_\mathrm{Aeq}$; and $K_\mathrm{i}$ for impulsive content, from $L_\mathrm{AIeq} - L_\mathrm{Aeq}$. They are stepped, not continuous, so a spectrum just short of a threshold scores nothing. | dB | RD 1367/2007 (Spain), Annex IV A.3.3 | [Spanish Noise Regulation (RD 1367/2007)](https://docs.jmrp.io/phonometry/environment/assessment/spanish-noise-regulation/) | ## Outdoor propagation | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $A$ (octave-band attenuation) | Total octave-band attenuation between an outdoor point source and a downwind receiver: the sum $A_\mathrm{div} + A_\mathrm{atm} + A_\mathrm{gr} + A_\mathrm{bar} + A_\mathrm{misc}$ subtracted from the sound power level and the directivity correction. Everything the method knows about the path between source and receiver is in this one term. | dB | ISO 9613-2:1996, Equations (3) and (4) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $A_\mathrm{div}$ | Geometrical divergence: $20\log_{10}(d/d_0) + 11$ dB, the spreading of a point source radiating into free space with $d_0 = 1$ m. The 11 dB constant is what refers the level to a sound power level rather than to a level measured at one metre. | dB | ISO 9613-2:1996, Equation (7) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $A_\mathrm{atm}$ | Atmospheric absorption: the attenuation coefficient of the air times the path length. It is the term that removes the high bands over long distances, and it depends strongly on frequency, temperature and humidity (which is why a long-range prediction has to state the weather it assumed). | dB | ISO 9613-2:1996, Equation (8) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $\alpha$ (atmospheric) | Atmospheric attenuation coefficient: the excess loss per unit path length from classical absorption and the nitrogen and oxygen relaxation processes, a function of frequency, temperature, humidity and pressure. Watch the length unit: the library returns decibels per metre while ISO 9613-2 Table 2 tabulates decibels per kilometre, a factor of a thousand. | dB/m (ISO 9613-2 tabulates dB/km) | ISO 9613-1:1993, Equation (5) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $A_\mathrm{gr}$ | Ground effect: the interference between the direct path and the path reflected off the ground, split into a source region, a receiver region and the middle between them. Over hard ground it comes out negative (a net gain, not a loss), which is why it cannot be treated as an attenuation that is merely optional. | dB | ISO 9613-2:1996, Equation (9) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $A_\mathrm{bar}$ | Barrier attenuation: the screening $D_z$ of the diffracting edge minus the ground effect the barrier removes, floored at zero. The subtraction is the point: a barrier over soft ground buys much less than its raw screening, because the ground was already doing part of the work. | dB | ISO 9613-2:1996, Equation (12) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $C_\mathrm{met}$ | Meteorological correction: what is subtracted from the downwind level to obtain a long-term average over many wind directions, driven by the local factor $C_0$ and by the source and receiver heights against the distance. It is zero close to the source and grows only where the path is long compared with the heights. | dB | ISO 9613-2:1996, Equations (21) and (22) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $D_\mathrm{c}$ | Directivity correction: how far the level from the point source in the chosen direction departs from that of an omnidirectional source of the same sound power. It is the directivity index of the source plus an index for radiation into less than the full sphere, and it is 0 dB for an omnidirectional source in free space. | dB | ISO 9613-2:1996, Equation (3) | [Outdoor Sound Propagation](https://docs.jmrp.io/phonometry/environment/propagation/outdoor-propagation/) | | $N$ (Fresnel number) | Fresnel number of a screen: twice the extra path length the sound has to travel over the edge, divided by the wavelength. It is the single geometric parameter of the Kurze-Anderson insertion loss, which is why a barrier that works at 1 kHz can be worth almost nothing two octaves lower for the same geometry. | dimensionless | Bies, Hansen and Howard (2017), Equation 5.134; no governing standard | [Spherical ground effect and advanced barriers](https://docs.jmrp.io/phonometry/environment/propagation/ground-barriers/) | ## Frequency and time weighting | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | A, C, Z | The normative frequency weightings: the ear-response curves applied before integration, Z being the flat reference. | dB | IEC 61672-1:2013, Annex E (acceptance limits in Table 3) | [Frequency Weighting (A, C, Z)](https://docs.jmrp.io/phonometry/signals/levels/weighting/) | | G | Infrasound weighting, defined by its poles and zeros for the 0.25 Hz to 315 Hz range. | dB | ISO 7196:1995, Table 1 (nominal responses in Table 2) | [Special Weightings (G, B, D, AU)](https://docs.jmrp.io/phonometry/signals/levels/special-weightings/) | | B | Historical mid-level weighting, withdrawn from the current meter standard. | dB | ANSI S1.4-1983, Appendix C (Formula C2) | [Special Weightings (G, B, D, AU)](https://docs.jmrp.io/phonometry/signals/levels/special-weightings/) | | D | Historical aircraft-noise weighting, derived from the 40-noy perceived-noisiness contour. | dB | IEC 537:1976 (withdrawn) | [Special Weightings (G, B, D, AU)](https://docs.jmrp.io/phonometry/signals/levels/special-weightings/) | | AU | Weighting for audible sound measured in the presence of ultrasound. | dB | IEC 61012:1990, subclause 2.2 (Tables 1 and 2) | [Special Weightings (G, B, D, AU)](https://docs.jmrp.io/phonometry/signals/levels/special-weightings/) | | F, S, I | Fast, Slow and Impulse exponential time weightings: the detector ballistics that produce a displayed level. | s (time constant) | IEC 61672-1:2013 | [Time Weighting](https://docs.jmrp.io/phonometry/signals/levels/time-weighting/) | | Performance class (0, 1, 2) | Performance class of a filter or an instrument: the width of the tolerance corridor its response has to stay inside, band by band. Class 1 and class 2 share the same design goals and differ in the acceptance limits and in the operating temperature range, class 2 being the looser; class 0, the laboratory reference grade, comes from the withdrawn IEC 61260:1995 and ANSI S1.11-2004 and the current edition no longer defines it. A class is a property of the response, not of the result: a class 2 bank does not make a measurement wrong, it makes its band levels less certain. | dB (tolerance) | IEC 61260-1:2014, 1.2 and Table 1 | [Filter Class Verification (IEC 61260-1)](https://docs.jmrp.io/phonometry/signals/filters/filter-compliance/) | | K | K-weighting: the programme-loudness curve, a two-stage pre-filter that models the high-frequency boost a spherical head gives and then applies the revised low-frequency B-curve high-pass. It is applied per channel before the channel mean squares are summed and gated, and the LKFS designation records it. | dB | ITU-R BS.1770-5, Annex 1 | [Programme loudness and true peak (BS.1770 / EBU R 128)](https://docs.jmrp.io/phonometry/devices/broadcast/program-loudness/) | | ITU-R BS.468-4 weighting | The broadcast noise weighting: zero at 1 kHz, peaking at $+12{,}2$ dB at 6,3 kHz and falling to $-29{,}9$ dB at 31,5 Hz, shaped to how audible a noise is rather than how loud a tone is. The Recommendation pairs it with a quasi-peak detector and quotes results as dB(468); AES17 reuses the same curve with an r.m.s. detector, which is a different number from the same filter. | dB | Recommendation ITU-R BS.468-4, Table 1 | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | $W_\mathrm{b}$, $W_\mathrm{c}$, $W_\mathrm{d}$, $W_\mathrm{e}$, $W_\mathrm{f}$, $W_\mathrm{j}$, $W_\mathrm{k}$, $W_\mathrm{m}$ (whole-body) | The whole-body frequency weightings, one parameter row each of the same four-stage filter: $W_\mathrm{k}$ for the vertical axis and $W_\mathrm{d}$ for the two horizontal ones in health and comfort, with $W_\mathrm{b}$, $W_\mathrm{c}$, $W_\mathrm{e}$, $W_\mathrm{f}$, $W_\mathrm{j}$ and $W_\mathrm{m}$ for ride comfort, the seat back, rotational axes, motion sickness and the head. The weighted acceleration $a_\mathrm{w}$ is what comes out of them; the standard that names the curve is not the one that says where to apply it. | dimensionless | ISO 8041-1:2017, 5.6.1, Formulae (1) to (5) and Table 3 | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | | $W_\mathrm{h}$ (hand-arm) | The hand-arm frequency weighting: one curve, band-limited from 8 Hz to 1 kHz, applied to each of the three axes before they are combined into the vibration total value. Unlike the whole-body case there is no axis multiplier, so the three weighted values enter the total on equal terms. | dimensionless | ISO 8041-1:2017, 5.6.1, Formulae (1) to (5) and Table 3 | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | ## Spectral and system analysis | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $G_{xx}$, $G_{xy}$ | One-sided auto- and cross-spectral density: mean-square content per hertz, so the power in a band is the integral over it and not the height of a line. Everything else in this group is a ratio of these: the coherences, the two frequency-response estimators and the coherent output spectrum. | (unit of $x$)²/Hz | Bendat and Piersol (2010), Sections 5.2 and 9.1; no governing standard | [Calibrated spectral analysis](https://docs.jmrp.io/phonometry/signals/spectra/spectral-analysis/) | | $\gamma^2_{iy}$ (ordinary coherence) | Ordinary coherence: the fraction of the output autospectrum, at each frequency, that a linear time-invariant path from one input accounts for, $\|G_{xy}\|^2/(G_{xx}G_{yy})$. It is one where the pair is noiselessly linearly related, and with additive output noise it settles at $\mathrm{SNR}/(1+\mathrm{SNR})$ (so it reads as a quality figure, not as a cause). | dimensionless | Bendat and Piersol (2010), Equation (7.109); no governing standard | [Multiple and partial coherence](https://docs.jmrp.io/phonometry/signals/spectra/miso-coherence/) | | $\gamma^2_{y:x}$ (multiple coherence) | Multiple coherence: the fraction of the output that all the measured inputs together account for, one minus the residual spectrum over the total. It is the ceiling the partial coherences are apportioned under, and what is left of it is the part of the output no measured input explains. | dimensionless | Bendat and Piersol (2010), Equation (7.35); no governing standard | [Multiple and partial coherence](https://docs.jmrp.io/phonometry/signals/spectra/miso-coherence/) | | $\gamma^2_{iy\cdot(i-1)!}$ (partial coherence) | Partial coherence: the coherence of one input with the output after the inputs ranked before it have been conditioned out. It is what separates a genuine source from one that merely correlates with a genuine source, and it depends on the conditioning order, so the order has to be reported with the number. | dimensionless | Bendat and Piersol (2010), Equation (7.87); no governing standard | [Multiple and partial coherence](https://docs.jmrp.io/phonometry/signals/spectra/miso-coherence/) | | $H_1$, $H_2$ (FRF estimators) | The two averaged estimates of a frequency response function: $H_1 = G_{xy}/G_{xx}$, unbiased when the noise is on the output, and $H_2 = G_{yy}/G_{yx}$, unbiased when it is on the input. Their ratio is exactly the ordinary coherence, so they agree only where the measurement is clean, and the gap between them is a measure of how far it is not. | output per input | Bendat and Piersol (2010), Section 6.1; no governing standard | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | ENBW | Equivalent noise bandwidth of an analysis window: the width of the ideal rectangular filter that would pass the same broadband noise power. It is exactly 1 bin for a rectangular window and 1,5 for a Hann, and it is the factor that turns a windowed line spectrum into a density (a broadband level read off the lines sits $10\log_{10}(\mathrm{ENBW})$ dB high without it). | bins (or Hz) | Harris (1978), Table 1; no governing standard | [Calibrated spectral analysis](https://docs.jmrp.io/phonometry/signals/spectra/spectral-analysis/) | | Cepstrum and quefrency | Cepstrum: the inverse transform of the logarithmic spectrum, in which the periodic ripple an echo or a harmonic family leaves across the spectrum collapses onto a single peak. Quefrency is its independent variable, a time in seconds, at which that peak stands at the echo's own delay (which is why a bearing report quotes a quefrency and not a frequency). | quefrency in s | Havelock, Kuwano and Vorländer (2008), Chapter 27; no governing standard | [Cepstrum, echoes and the envelope spectrum](https://docs.jmrp.io/phonometry/signals/spectra/cepstrum-echoes/) | | Crest factor | Crest factor: the modulus of the ratio of the peak to the r.m.s. value over the measurement period. It decides whether an r.m.s. description is honest (above 9 the standard says the basic evaluation method is not sufficient and dose measures have to be reported beside it), and for a test signal it decides whether a device clips before the signal has delivered its energy. | dimensionless | ISO 2631-1:1997, 6.2.1 | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | ## Room acoustics | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $T_{20}$ | Reverberation time extrapolated to a 60 dB decay from a least-squares fit over −5 dB to −25 dB of the Schroeder curve. | s | ISO 3382-2:2008, Clause 6 and Annex C | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $T_{30}$ | The same extrapolation from a fit over −5 dB to −35 dB, the usual choice when the decay range allows it. | s | ISO 3382-2:2008, Clause 6 and Annex C | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $T_{60}$, RT | Reverberation time as such: the time for the sound energy to fall by 60 dB. Measured in practice as $T_{20}$ or $T_{30}$. | s | ISO 3382-1:2009 | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | EDT | Early decay time: the same slope taken over the first 10 dB of decay, which tracks perceived reverberance rather than the tail. | s | ISO 3382-1:2009 (just-noticeable difference in Table A.1) | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $C_{50}$ | Clarity for speech: the energy ratio between the first 50 ms of the impulse response and everything after it. | dB | ISO 3382-1:2009 | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $C_{80}$ | Clarity for music: the same ratio with the boundary at 80 ms. | dB | ISO 3382-1:2009 (just-noticeable difference in Table A.1) | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $D_{50}$ | Definition, or Deutlichkeit: the fraction of the total energy arriving in the first 50 ms. | dimensionless | ISO 3382-1:2009 (just-noticeable difference in Table A.1) | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $T_\mathrm{S}$ (centre time) | Centre time: the centre of gravity of the squared impulse response in time, a boundary-free alternative to the clarity indices. It runs to tens of milliseconds in a room; the building-prediction guides write $T_\mathrm{s}$, with a lowercase s, for something else entirely, the structural reverberation time of a plate, which is seconds. | s | ISO 3382-1:2009, Equation (A.13) | [Room acoustic parameters (ISO 3382-1/2)](https://docs.jmrp.io/phonometry/buildings/rooms/room-acoustics/) | | $A$ | Equivalent sound absorption area of a room: the area of a perfectly absorbing surface that would give the same reverberation time. | m² | ISO 354:2003, Equations (5) and (7) | [Sound Absorption Measurement and Rating](https://docs.jmrp.io/phonometry/materials/absorbers/absorption-measurement/) | | NC | Noise criteria rating of a background spectrum: the speech interference level selects the curve, and the tangency method rates the spectrum when a band exceeds it. | dB (index) | ANSI/ASA S12.2-2019, 5.2.2 and 5.2.3 (curves in Table 1) | [Room-noise criteria (NC / RC Mark II)](https://docs.jmrp.io/phonometry/buildings/rooms/room-noise/) | | SIL | Speech interference level: the average of the 500, 1000, 2000 and 4000 Hz octave-band levels. | dB | ANSI/ASA S12.2-2019, clause 3.2 | [Room-noise criteria (NC / RC Mark II)](https://docs.jmrp.io/phonometry/buildings/rooms/room-noise/) | | RC | Room criteria Mark II rating: the average of the 500, 1000 and 2000 Hz levels, with a rumble, hiss or neutral spectral tag. | dB (index) | ANSI/ASA S12.2-2019, Annex D (clauses D.3 and D.4) | [Room-noise criteria (NC / RC Mark II)](https://docs.jmrp.io/phonometry/buildings/rooms/room-noise/) | | NR (curve family) | Noise rating, the European counterpart curve family of NC. Discussed for comparison and deliberately not implemented. Not the NR of the noise-control guides, which is a level drop. | dB (index) | Kosten and van Os (1962); no governing standard | [Room-noise criteria (NC / RC Mark II)](https://docs.jmrp.io/phonometry/buildings/rooms/room-noise/) | | $D_{2,\mathrm{S}}$ | Spatial decay rate of speech: the drop in A-weighted speech level per doubling of distance along a line of workstations, taken from the regression of level against the logarithm of distance over positions between 2 m and 16 m. It is a slope only (it says how fast speech dies away, not how loud it starts). | dB | ISO 3382-3:2012, 3.2 | [Open-Plan Office Acoustics (ISO 3382-3)](https://docs.jmrp.io/phonometry/buildings/rooms/open-plan-acoustics/) | | $L_{p,\mathrm{A,S},4\,\mathrm{m}}$ | A-weighted speech level at 4 m: the nominal level of normal speech four metres from the talker, read off the same regression line rather than measured at that distance. It fixes the absolute height of the decay curve that $D_{2,\mathrm{S}}$ only gives the slope of, which is why the two are always reported together. | dB | ISO 3382-3:2012, 3.3 | [Open-Plan Office Acoustics (ISO 3382-3)](https://docs.jmrp.io/phonometry/buildings/rooms/open-plan-acoustics/) | | $r_\mathrm{D}$ | Distraction distance: the distance from the talker at which the speech transmission index falls below 0,50, beyond which concentration and privacy start to improve rapidly. It is the single number an open-plan office is usually specified on, and the only rating in the corpus that is a distance rather than a level. | m | ISO 3382-3:2012, 3.6 | [Open-Plan Office Acoustics (ISO 3382-3)](https://docs.jmrp.io/phonometry/buildings/rooms/open-plan-acoustics/) | | $r_\mathrm{P}$ | Privacy distance: the distance at which the speech transmission index falls below 0,20, beyond which speech is as private as it would be between separate rooms. In offices with small volume or poor privacy it can be out of reach entirely. | m | ISO 3382-3:2012, 3.7 | [Open-Plan Office Acoustics (ISO 3382-3)](https://docs.jmrp.io/phonometry/buildings/rooms/open-plan-acoustics/) | ## Speech and intelligibility | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $m(F)$ | Modulation transfer function: the fraction of the speech envelope modulation depth at modulation frequency $F$ that survives the transmission path. | dimensionless | IEC 60268-16:2020 | [Speech Transmission Index (STI)](https://docs.jmrp.io/phonometry/perception/speech/speech-transmission/) | | STI | Speech transmission index: the modulation transfer matrix converted to effective signal-to-noise ratios and weighted into a single value on 0 to 1. | dimensionless | IEC 60268-16:2020, A.5.2 to A.5.6 | [Speech Transmission Index (STI)](https://docs.jmrp.io/phonometry/perception/speech/speech-transmission/) | | STIPA | The direct STI measurement, made by playing a standardised two-modulation-per-band test signal through the real chain. | dimensionless | IEC 60268-16:2020, clause 6.3 and Table 3 (direct method, Annex B) | [Speech Transmission Index (STI)](https://docs.jmrp.io/phonometry/perception/speech/speech-transmission/) | | SII | Speech intelligibility index: the band-importance-weighted audibility of the speech spectrum against noise and the listener's threshold. | dimensionless | ANSI S3.5-1997, clause 6 (procedure in clause 5, importance function in Table 3) | [Speech Intelligibility Index](https://docs.jmrp.io/phonometry/perception/speech/speech-intelligibility/) | | STOI | Short-time objective intelligibility: the clipped per-band envelope correlation between clean and degraded speech. | dimensionless | Taal et al. (2011), Equations 5 and 6; no governing standard | [Objective Intelligibility (STOI & ESTOI)](https://docs.jmrp.io/phonometry/perception/speech/objective-intelligibility/) | | ESTOI | The extended measure, row- and column-normalised so that it tracks modulated maskers. | dimensionless | Jensen and Taal (2016), Equation 8; no governing standard | [Objective Intelligibility (STOI & ESTOI)](https://docs.jmrp.io/phonometry/perception/speech/objective-intelligibility/) | ## Sound insulation | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | NR (level drop) | Noise reduction: the sound pressure level in the source room minus the level in the receiving room, $L_{p1} - L_{p2}$. It is not the transmission loss of the partition: the two differ by a term set by the partition area against the receiving room's absorption, so a small partition into a well-absorbing room delivers more noise reduction than its transmission loss, and a large one into a hard room delivers less. | dB | Norton and Karczub (2003), Equation (4.101) | [Room to Room: Partition, Receiving Room, Criterion](https://docs.jmrp.io/phonometry/devices/noise-control/room-to-room/) | | $D$ | Level difference: the energy-averaged source-room level minus the receiving-room level, with no normalisation. | dB | ISO 16283-1:2014, 3.12 to 3.15 | [Field Insulation Measurement (ISO 16283)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-field/) | | $D_{\mathrm{n}T}$ | Standardized level difference: the level difference referred to a reference reverberation time, 0.5 s for dwellings. | dB | ISO 16283-1:2014, 3.12 to 3.15 | [Field Insulation Measurement (ISO 16283)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-field/) | | $D_\mathrm{n}$ | Normalized level difference: the level difference referred to a reference absorption area of 10 m². | dB | ISO 10052:2021 | [Sound Insulation Survey Method (ISO 10052)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-survey/) | | $D_\mathrm{n,e}$ | Element-normalized level difference of a small element or air path, referred to a reference area of 10 m². | dB | EN 12354-3:2000 | [Predicting Sound Insulation (EN 12354)](https://docs.jmrp.io/phonometry/buildings/design/insulation-prediction/) | | $R$ | Sound reduction index: the level difference corrected by the partition area over the receiving-room absorption area, measured in the laboratory with flanking suppressed. | dB | ISO 10140-2:2010 | [Laboratory Insulation Measurement](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-lab/) | | $R'$ | Apparent sound reduction index: the same construction measured in the building, so it includes every flanking path. The prime is the lab-versus-field marker. | dB | ISO 16283-1:2014, 3.12 to 3.15 | [Field Insulation Measurement (ISO 16283)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-field/) | | TL (panel) | Transmission loss: the airborne insulation of a partition predicted from its physical properties, ten times the base-10 logarithm of the reciprocal transmission factor, the same quantity as $R$ in a prediction context. | dB | Bies, Hansen and Howard (2017), Section 7.2; no governing standard | [Predicting Panel Sound Insulation](https://docs.jmrp.io/phonometry/buildings/design/panel-sound-insulation/) | | TL (duct element) | Transmission loss of a duct element: ten times the base-10 logarithm of the incident plane-wave power over the power transmitted into an anechoic termination, computed from the four-pole transfer matrix and the two port impedances. The anechoic termination is part of the definition, which is why this transmission loss describes the element alone and is not the noise reduction the same silencer delivers once it is installed between a real source and a real outlet. | dB | Bies, Hansen and Howard (2017), Sections 8.8-8.9; no governing standard | [Silencers](https://docs.jmrp.io/phonometry/devices/noise-control/silencers/) | | IL | Insertion loss: the level at a receiver before an element is inserted minus the level after, for a silencer the drop in radiated sound power level when a length of duct is replaced by it. Unlike a transmission loss it depends on the source and the termination as well as on the element, which is what makes it the number a client can hear and the transmission loss the number a catalogue can print. | dB | Bies, Hansen and Howard (2017), Section 8.2, Equation (8.1); no governing standard | [Silencers](https://docs.jmrp.io/phonometry/devices/noise-control/silencers/) | | $\tau$ | Transmission factor, or transmission coefficient: the fraction of the incident sound power a partition passes on. It is the quantity the whole group is a logarithm of, since $R = -10\log_{10}\tau$ and the transmission loss is the same logarithm; a $\tau$ of $10^{-5}$ is a 50 dB partition. Transmission factors of parallel paths add, which is why a prediction sums the direct, flanking and indirect airborne factors and only then takes the logarithm. | dimensionless | ISO 12354-1:2017, Formula (1) | [Detailed Per-Band Prediction (ISO 12354)](https://docs.jmrp.io/phonometry/buildings/design/detailed-prediction/) | | $R_\mathrm{w}$, $R'_\mathrm{w}$, $D_{\mathrm{n}T,\mathrm{w}}$ | The weighted single-number ratings: a fixed reference curve is shifted toward the measured spectrum until the unfavourable deviations reach their allowed sum, and the shifted curve is read at 500 Hz. | dB | ISO 717-1:2020 | [Insulation Ratings (ISO 717)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-ratings/) | | $D_\mathrm{n,e,w}$ | The same reference-curve rating applied to the element-normalized level difference. | dB | ISO 717-1:2020 | [Predicting Sound Insulation (EN 12354)](https://docs.jmrp.io/phonometry/buildings/design/insulation-prediction/) | | $C$, $C_\mathrm{tr}$ | Spectrum adaptation terms: the corrections that re-rate the measured curve against A-weighted pink noise ($C$) and against A-weighted urban road traffic ($C_\mathrm{tr}$). | dB | ISO 717-1:2020, Annex A | [Insulation Ratings (ISO 717)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-ratings/) | | $L_\mathrm{n}$ | Normalized impact sound pressure level: the receiving-room level under the standard tapping machine, referred to a 10 m² absorption area. | dB re 20 µPa | ISO 10140-3:2010 | [Laboratory Insulation Measurement](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-lab/) | | $L'_{\mathrm{n}T}$ | Standardized impact sound pressure level, referred to a reference reverberation time. Note the sign: more reverberation lowers it, the opposite of $D_{\mathrm{n}T}$. | dB re 20 µPa | ISO 16283-2:2015 | [Field Insulation Measurement (ISO 16283)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-field/) | | $L_\mathrm{n,w}$, $L'_{\mathrm{n}T,\mathrm{w}}$ | The weighted impact ratings. The reference curve is shifted the same way, but an unfavourable deviation is now one where the measurement exceeds the reference. | dB | ISO 717-2:2020 | [Insulation Ratings (ISO 717)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-ratings/) | | $C_\mathrm{I}$ | Impact spectrum adaptation term, from the energetic sum over 100 Hz to 2500 Hz. The enlarged-range $C_{\mathrm{I},50\text{–}2500}$ extends it down to 50 Hz. | dB | ISO 717-2:2020 (enlarged range in A.2.1 NOTE) | [Insulation Ratings (ISO 717)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-ratings/) | | $\Delta L_\mathrm{w}$ | Weighted reduction of impact sound pressure level given by a floor covering, measured as the improvement over the bare reference floor. | dB | ISO 717-2:2020 (measurement in ISO 16251-1:2014, Formulae (3) and (4)) | [Floor-Covering Impact Improvement (ISO 16251-1)](https://docs.jmrp.io/phonometry/buildings/design/impact-improvement/) | | $\Delta R_\mathrm{w}$ | Weighted improvement of airborne insulation contributed by a lining or additional layer, added to the element rating in the prediction. | dB | EN 12354-1:2000, Formulae 27 and 28a | [Predicting Sound Insulation (EN 12354)](https://docs.jmrp.io/phonometry/buildings/design/insulation-prediction/) | | $K_{ij}$ | Vibration reduction index of a junction: the direction-averaged velocity level difference corrected by the junction length and the equivalent absorption lengths. | dB | ISO 10848-1:2006, Formula (13) | [Laboratory Flanking Transmission (ISO 10848)](https://docs.jmrp.io/phonometry/buildings/insulation/flanking-lab/) | | $f_\mathrm{c}$ | Critical frequency: the frequency at which the bending wavelength of a panel equals the wavelength in air, where the coincidence dip appears. | Hz | Bies, Hansen and Howard (2017), Equation 7.3; no governing standard | [Predicting Panel Sound Insulation](https://docs.jmrp.io/phonometry/buildings/design/panel-sound-insulation/) | | $\sigma$ | Radiation efficiency of a plate: the airborne power radiated per unit mean-square surface velocity, normalised by the plane-wave value. | dimensionless | Hopkins (2007), Equations 2.227 to 2.230; no governing standard | [Predicting Panel Sound Insulation](https://docs.jmrp.io/phonometry/buildings/design/panel-sound-insulation/) | | $D_{2\mathrm{m,n}T}$ | Standardized facade level difference: the level 2 m in front of the facade minus the indoor level, standardized to a reference reverberation time of 0,5 s for dwellings. The 2 m position sits in the field the facade itself reflects, so it is not a free-field level, and the notation records the source ($D_{\mathrm{tr},2\mathrm{m,n}T}$ for road traffic, $D_{\mathrm{ls},2\mathrm{m,n}T}$ for a loudspeaker). | dB | ISO 16283-3:2016, 3.15 | [Façade Sound Insulation](https://docs.jmrp.io/phonometry/buildings/insulation/facade-insulation/) | | $D_{\mathrm{ls},2\mathrm{m,n}T,\mathrm{w}}$ | The weighted facade rating: $D_{2\mathrm{m,n}T}$ measured with a loudspeaker put through the ISO 717-1 reference-curve procedure. The `ls` subscript is not decoration (it records that the source was a loudspeaker at 45 degrees rather than real road traffic), and a facade rated with one source is not interchangeable with the same facade rated with the other. | dB | ISO 717-1:2020 | [Façade Sound Insulation](https://docs.jmrp.io/phonometry/buildings/insulation/facade-insulation/) | | $R'_{45°}$ | Apparent sound reduction index of a facade element under loudspeaker sound at 45 degrees: the level difference corrected by the specimen area over the receiving-room absorption area, with a further $-1{,}5$ dB that carries the single-angle geometry. It is apparent, so flanking and any other component of the facade are inside the number. | dB | ISO 16283-3:2016, 3.12 | [Façade Sound Insulation](https://docs.jmrp.io/phonometry/buildings/insulation/facade-insulation/) | | $R_\mathrm{A}$, $R_\mathrm{A,tr}$ | Global airborne index: the A-weighted level a partition transmits when it is excited by a normalised spectrum (pink noise for $R_\mathrm{A}$, road traffic for $R_\mathrm{A,tr}$), summed energetically over eighteen one-third-octave bands from 100 Hz to 5 kHz. It is a close relative of $R_\mathrm{w} + C$ and $R_\mathrm{w} + C_\mathrm{tr}$ but is computed directly, not by shifting a reference curve, and it uses two bands the ISO 717-1 range does not. | dBA | CTE DB-HR, Annex A, Formulae (A.5) and (A.6) | [Spanish Building Code (CTE DB-HR)](https://docs.jmrp.io/phonometry/buildings/insulation/spanish-building-code/) | | $D_{\mathrm{n}T,\mathrm{A}}$, $D_{2\mathrm{m,n}T,\mathrm{Atr}}$ | The same global index applied to a standardized level difference: between two rooms ($D_{\mathrm{n}T,\mathrm{A}}$, pink noise) and between the outside and a protected room ($D_{2\mathrm{m,n}T,\mathrm{Atr}}$, road traffic or aircraft). These are the quantities the DB-HR requirement tables are written against, so a project is checked in them and not in the ISO 717-1 ratings. | dBA | CTE DB-HR, Annex A, Formulae (A.5) and (A.6); requirements in clause 2 | [Spanish Building Code (CTE DB-HR)](https://docs.jmrp.io/phonometry/buildings/insulation/spanish-building-code/) | | $R_I$ | Intensity sound reduction index: the source-room level minus the intensity level scanned over the radiating face, so the transmitted power is measured directly instead of inferred from the receiving room. It is the method of choice where flanking is strong; add the $K_c$ adaptation to get $R_{I,\mathrm{M}}$, the value the ISO 10140 pressure method would have produced. | dB | ISO 15186-1:2000, 3.8, Equation (7) | [Sound Insulation by Intensity (ISO 15186)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-intensity/) | | $D_{I,\mathrm{n,e}}$ | Intensity element-normalized level difference: the small-element counterpart of $D_\mathrm{n,e}$, measured by scanning the element and normalised to a reference absorption area of 10 m². It is rated through the same ISO 717-1 procedure, as $D_{I,\mathrm{n,e,w}}$, so a ventilator or a transit sealing system can be compared with a wall on one scale. | dB | ISO 15186-2:2003, Formula (12) | [Sound Insulation by Intensity (ISO 15186)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-intensity/) | ## Materials and surfaces | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $\alpha$ | Sound absorption coefficient at normal incidence: the fraction of incident energy not returned by the surface, obtained in the impedance tube from the reflection factor. | dimensionless | ISO 10534-2:1998, Equations (17) to (19) | [Impedance Tube](https://docs.jmrp.io/phonometry/materials/absorbers/impedance-tube/) | | $\alpha_\mathrm{s}$ | Random-incidence sound absorption coefficient measured in a reverberation room, from the change in equivalent absorption area with and without the specimen. | dimensionless | ISO 354:2003, Equations (8) and (9) | [Sound Absorption Measurement and Rating](https://docs.jmrp.io/phonometry/materials/absorbers/absorption-measurement/) | | $\alpha_\mathrm{p}$ | Practical sound absorption coefficient: the one-third-octave data grouped into octave bands and rounded to steps of 0.05. | dimensionless | ISO 11654:1997, Clause 4.1 | [Sound Absorption Measurement and Rating](https://docs.jmrp.io/phonometry/materials/absorbers/absorption-measurement/) | | $\alpha_\mathrm{w}$ | Weighted sound absorption coefficient: the fixed reference curve shifted toward the practical values and read at 500 Hz. | dimensionless | ISO 11654:1997, Clause 4.2 | [Sound Absorption Measurement and Rating](https://docs.jmrp.io/phonometry/materials/absorbers/absorption-measurement/) | | Absorption class | The A to E letter class the weighted coefficient maps to, or "not classified". | class letter | ISO 11654:1997, Table B.1 | [Sound Absorption Measurement and Rating](https://docs.jmrp.io/phonometry/materials/absorbers/absorption-measurement/) | | $R$ | Airflow resistance: the pressure difference across a specimen divided by the volumetric airflow rate through it. | Pa·s/m³ | ISO 9053-1:2018, Clause 3 | [Airflow Resistance](https://docs.jmrp.io/phonometry/materials/absorbers/airflow-resistance/) | | $R_\mathrm{s}$ | Specific airflow resistance: the airflow resistance referred to the specimen face area. | Pa·s/m | ISO 9053-1:2018, Clause 3 | [Airflow Resistance](https://docs.jmrp.io/phonometry/materials/absorbers/airflow-resistance/) | | $\sigma$ | Airflow resistivity: the specific airflow resistance per unit thickness, the primary input to every empirical porous model. | Pa·s/m² | ISO 9053-1:2018, Clause 3 | [Airflow Resistance](https://docs.jmrp.io/phonometry/materials/absorbers/airflow-resistance/) | | $Z$ | Surface impedance: the complex ratio of sound pressure to particle velocity at the face of the sample, usually reported normalised by the characteristic impedance of air. | Pa·s/m | ISO 10534-2:1998, Equations (17) to (19) | [Impedance Tube](https://docs.jmrp.io/phonometry/materials/absorbers/impedance-tube/) | | $s$ | Scattering coefficient: the fraction of reflected energy that is not returned specularly, measured at random incidence on a turntable in a reverberation room. | dimensionless | ISO 17497-1:2004+A1:2014, Formula (5) | [Diffusers and Their Coefficients](https://docs.jmrp.io/phonometry/materials/diffusers/diffusers/) | | $d$ | Diffusion coefficient: the uniformity of the polar response of a surface, from the autocorrelation of the free-field goniometer measurement. | dimensionless | ISO 17497-2:2012, Formula (5) (normalised form in Formula (7)) | [Diffusers and Their Coefficients](https://docs.jmrp.io/phonometry/materials/diffusers/diffusers/) | | $s'$ | Dynamic stiffness per unit area of a resilient layer: a dynamic force per unit area divided by the resulting change in thickness. | MN/m³ | EN 29052-1:1992 (ISO 9052-1:1989), Formula 1 | [Dynamic stiffness of resilient materials](https://docs.jmrp.io/phonometry/materials/resilient/dynamic-stiffness/) | | $\phi$ (porosity) | Open porosity: the fraction of the material's volume that is air connected to the outside, $\phi = V_\mathrm{a}/V_\mathrm{T}$. A closed bubble counts as frame, not as pore, because sound cannot enter it; for most fibrous materials and foams $\phi$ lies very close to one, which is why a one-parameter model that assumes so can still work. | dimensionless | Allard and Atalla (2009), Equation (2.25); no governing standard | [Porous and Multilayer Absorbers](https://docs.jmrp.io/phonometry/materials/absorbers/porous-absorbers/) | | $\alpha_\infty$ (tortuosity) | Tortuosity: how much longer the winding path through the pores is than the straight line, squared (exactly $1/\cos^2\varphi$ for pores inclined at an angle $\varphi$, and one for straight cylindrical pores). It sets the high-frequency limit of the effective density, and despite the $\alpha$ it is not an absorption coefficient of any kind. | dimensionless | Allard and Atalla (2009), Equation (4.143); no governing standard | [Porous and Multilayer Absorbers](https://docs.jmrp.io/phonometry/materials/absorbers/porous-absorbers/) | | $\Lambda$, $\Lambda'$ | The two pore sizes the Johnson-Champoux-Allard model needs: $\Lambda$ weights the pore surface by the squared flow velocity, so it is set by the narrow constrictions where the viscous losses happen, and $\Lambda'$ is the plain surface-to-volume length that governs the thermal exchange with the frame. $\Lambda'$ is normally the larger, and the two are equal only for identical straight cylindrical pores. | m | Allard and Atalla (2009), Equations (5.24) and (5.27); no governing standard | [Porous and Multilayer Absorbers](https://docs.jmrp.io/phonometry/materials/absorbers/porous-absorbers/) | | $Z_\mathrm{c}$, $k$ | Characteristic impedance and complex wavenumber: the pair that describes a porous medium as an equivalent fluid (the ratio of pressure to particle velocity in a travelling wave inside it, and the wavenumber whose imaginary part is the attenuation per metre). Every empirical or semi-phenomenological model produces this pair, and it is what the transfer-matrix method stacks layer by layer. | Pa·s/m and 1/m | Allard and Atalla (2009), Chapter 5; no governing standard | [Porous and Multilayer Absorbers](https://docs.jmrp.io/phonometry/materials/absorbers/porous-absorbers/) | ## Vibration and structure-borne sound | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $Y$ | Mobility: the complex ratio of a velocity response to the force that produces it. | m/(N·s) | ISO 7626-1:2011, 3.1.2 and Table 1 | [Mechanical mobility and the FRF family (ISO 7626-1)](https://docs.jmrp.io/phonometry/vibration/structural/mechanical-mobility/) | | $Z$ | Mechanical impedance: the reciprocal of mobility, force per unit velocity. | N·s/m | ISO 7626-1:2011, Table 1 | [Mechanical mobility and the FRF family (ISO 7626-1)](https://docs.jmrp.io/phonometry/vibration/structural/mechanical-mobility/) | | $H$ (receptance) | Receptance, or dynamic compliance: displacement response per unit force, the pivot the whole family converts through. | m/N | ISO 7626-1:2011, Table 1 | [Mechanical mobility and the FRF family (ISO 7626-1)](https://docs.jmrp.io/phonometry/vibration/structural/mechanical-mobility/) | | $A$ | Accelerance, or inertance: acceleration response per unit force. Its reciprocal is the apparent mass. | 1/kg | ISO 7626-1:2011, Table 1 | [Mechanical mobility and the FRF family (ISO 7626-1)](https://docs.jmrp.io/phonometry/vibration/structural/mechanical-mobility/) | | $k_{21}$ | Dynamic transfer stiffness of a resilient element: the blocking force on the output side divided by the displacement on the input side. | N/m | ISO 10846-1:2008, 3.7 | [Transfer stiffness of resilient elements (ISO 10846)](https://docs.jmrp.io/phonometry/vibration/structural/transfer-stiffness/) | | $L_k$ | Level of the dynamic transfer stiffness, referred to 1 N/m. | dB re 1 N/m | ISO 10846-2:2008 and ISO 10846-3:2002, 3.17 | [Transfer stiffness of resilient elements (ISO 10846)](https://docs.jmrp.io/phonometry/vibration/structural/transfer-stiffness/) | | $\eta$ (resilient element) | Loss factor of a resilient element: the tangent of the phase angle of its dynamic transfer stiffness. | dimensionless | ISO 10846-1:2008, 3.8 | [Transfer stiffness of resilient elements (ISO 10846)](https://docs.jmrp.io/phonometry/vibration/structural/transfer-stiffness/) | | $\eta_\mathrm{int}$ (internal) | Internal loss factor of a building element: the fraction of its vibrational energy dissipated per radian inside the material itself, before anything is radiated or leaves through the junctions. It is an input to the prediction, not a measured output: Table B.3 of the same standard gives 0,005 for concrete and about 0,01 for most masonry. | dimensionless | ISO 12354-1:2017, Annex C, Formula (C.1) | [Detailed Per-Band Prediction (ISO 12354)](https://docs.jmrp.io/phonometry/buildings/design/detailed-prediction/) | | $\eta_\mathrm{tot}$ (total, in situ) | Total loss factor of an element as built in: the internal loss factor plus the losses radiated into the air and absorbed at the perimeter junctions. It is what damps the resonant transmission above the critical frequency, and it fixes the structural reverberation time through $T_\mathrm{s} = 2{,}2/(f\,\eta_\mathrm{tot})$ (so a laboratory value measured in a heavy test frame does not transfer to the building unchanged). | dimensionless | ISO 12354-1:2017, Annex C, Formula (C.1) | [Detailed Per-Band Prediction (ISO 12354)](https://docs.jmrp.io/phonometry/buildings/design/detailed-prediction/) | | $a_\mathrm{w}$ | Frequency-weighted acceleration: the root sum of squares of the band accelerations after the human-response weightings. | m/s² | ISO 2631-1:1997, Equation (9) | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | | $A(8)$ | Daily vibration exposure: the exposure magnitude normalised to a reference 8 h day, combined over the operations of the day. | m/s² | ISO 5349-1:2001, Equations (2) and (3) | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | | VDV | Vibration dose value: the fourth-power time integral of the weighted acceleration, which weights shocks far more heavily than an r.m.s. does. | m/s^1.75 | ISO 2631-1:1997, Equation (5) | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | | MTVV | Maximum transient vibration value: the largest 1 s running r.m.s. of the weighted acceleration. | m/s² | ISO 2631-1:1997, Equation (4) | [Human Vibration](https://docs.jmrp.io/phonometry/vibration/human/human-vibration/) | | $R$ | Cumulative stress variable of the multiple-shock model: the daily compressive stresses accumulated over the years of exposure, which the lumbar injury probability is read from. | dimensionless | ISO 2631-5:2018, Annex C (Formulae C.1 and C.3 to C.5) | [Multiple-shock whole-body vibration (ISO 2631-5)](https://docs.jmrp.io/phonometry/vibration/human/multiple-shock-vibration/) | | $L_v$ | Velocity level: twenty times the base-10 logarithm of the surface velocity over the reference velocity. | dB re 50 nm/s | ISO/TS 7849-1:2009, Formula 3 | [Sound power from surface vibration (ISO/TS 7849)](https://docs.jmrp.io/phonometry/devices/emission/vibration-sound-power/) | | $\varepsilon$ | Radiation factor, or radiation efficiency, of a vibrating machine surface: the airborne power radiated per unit mean-square velocity and area. | dimensionless | ISO/TS 7849-1:2009 and ISO/TS 7849-2:2009 | [Sound power from surface vibration (ISO/TS 7849)](https://docs.jmrp.io/phonometry/devices/emission/vibration-sound-power/) | | $L_\mathrm{Ws}$ | Structure-borne sound power level injected by equipment into a reception plate. | dB re 1 pW | EN 15657:2018, Formula 14 | [Structure-borne sound power of equipment (EN 15657)](https://docs.jmrp.io/phonometry/buildings/design/structure-borne-power/) | | $\eta_{ij}$ | Coupling loss factor: the fraction of energy per radian that a statistical energy analysis subsystem loses into a neighbouring one across a junction. | dimensionless | Hopkins (2007), Equation 2.154; no governing standard | [Plate junctions: wave approach and experimental SEA](https://docs.jmrp.io/phonometry/vibration/structural/junction-transmission/) | | $\tau_{ij}$ (junction) | Junction transmission coefficient: the fraction of the bending-wave power arriving at a junction from plate $i$ that continues into plate $j$, angle by angle and then averaged over a diffuse field. Both the coupling loss factor $\eta_{ij}$ and the vibration reduction index $K_{ij}$ are derived from it, so it is the wave-approach quantity the junction family bottoms out in. | dimensionless | Hopkins (2007), Equations 5.12 and 5.13; no governing standard | [Plate junctions: wave approach and experimental SEA](https://docs.jmrp.io/phonometry/vibration/structural/junction-transmission/) | ## Psychoacoustics | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $N$ | Loudness: the perceived magnitude of a sound, anchored so that a 1 kHz tone at 40 dB SPL is exactly 1 sone. | sone | ISO 532-1:2017, clause 5 (stationary) and clause 6 (time-varying) | [Loudness](https://docs.jmrp.io/phonometry/perception/psychoacoustics/loudness/) | | $N'$ | Specific loudness: the loudness density along the critical-band scale, whose integral is $N$. | sone/Bark | ISO 532-1:2017 (sone/Cam form in ISO 532-2:2017, Formula 7) | [Loudness](https://docs.jmrp.io/phonometry/perception/psychoacoustics/loudness/) | | $L_\mathrm{N}$ | Loudness level: the level of the 1 kHz free-field tone judged equally loud as the sound. | phon | ISO 226:2023, Formula (2) (contours in Formula (1)) | [Loudness](https://docs.jmrp.io/phonometry/perception/psychoacoustics/loudness/) | | $S$ | Sharpness: the position of the centre of gravity of the specific loudness on the critical-band scale, normalised so that the reference narrow-band noise is exactly 1 acum. | acum | DIN 45692:2009-08, clause 6 | [Sound Quality Metrics](https://docs.jmrp.io/phonometry/perception/psychoacoustics/sound-quality/) | | $R$ | Roughness: the perceived harshness of fast amplitude modulation, around 70 Hz, normalised so that the reference modulated tone is 1 asper. | asper | ECMA-418-2:2025, clause 7 (Formula 104) | [Sound Quality Metrics](https://docs.jmrp.io/phonometry/perception/psychoacoustics/sound-quality/) | | $F$ | Fluctuation strength: the perceived slow amplitude modulation, around 4 Hz, normalised so that the reference modulated tone is 1 vacil. | vacil | ECMA-418-2:2025, clause 9 (Formula 163) | [Sound Quality Metrics](https://docs.jmrp.io/phonometry/perception/psychoacoustics/sound-quality/) | | $T$ | Tonality: the perceived tonal content of a sound, derived from the autocorrelation of the band envelopes. | tu | ECMA-418-2:2025, clause 6 | [Sound Quality Metrics](https://docs.jmrp.io/phonometry/perception/psychoacoustics/sound-quality/) | | TNR | Tone-to-noise ratio: the level of a discrete tone above the masking noise in the critical band around it. | dB | ECMA-418-1:2024, clause 11 (Formulae 9 to 11) | [Prominent Discrete Tones (ECMA-418-1)](https://docs.jmrp.io/phonometry/perception/psychoacoustics/tone-prominence/) | | PR | Prominence ratio: the level of the critical band containing the tone above the mean of the two adjacent bands. | dB | ECMA-418-1:2024, clause 12 (Formula 23) | [Prominent Discrete Tones (ECMA-418-1)](https://docs.jmrp.io/phonometry/perception/psychoacoustics/tone-prominence/) | | $\Delta L$ | Audibility of a tone in noise: the tone level minus the critical-band masking level minus the masking index. | dB | ISO/PAS 20065:2016, Formula 14 | [Objective audibility of tones in noise (ISO/PAS 20065)](https://docs.jmrp.io/phonometry/perception/psychoacoustics/tone-audibility/) | | PA | Psychoacoustic annoyance: the percentile loudness scaled by sharpness and by a fluctuation-plus-roughness term. | dimensionless | Fastl and Zwicker (2007), Equation 16.2; no governing standard | [Psychoacoustic annoyance and fluctuation strength](https://docs.jmrp.io/phonometry/perception/psychoacoustics/psychoacoustic-annoyance/) | | Critical band | Critical band: the frequency span within which the ear sums energy as one event, about 100 Hz wide below 500 Hz and roughly a fifth of the centre frequency above it. Masking, sharpness and the two tone-prominence ratios are all computed band by band on this scale, which is why none of them can be read off a fixed fractional-octave spectrum. | Hz | Fastl and Zwicker (2007), Sections 6.1 and 6.2; no governing standard | [Loudness](https://docs.jmrp.io/phonometry/perception/psychoacoustics/loudness/) | | $z$ (critical-band rate) | Critical-band rate: the auditory frequency scale on which one unit is one critical band, running 0 to 24 Bark over the audible range. Specific loudness is a density along it, which is why its unit is sone/Bark and why a loudness pattern is plotted against $z$ rather than against frequency. | Bark | Fastl and Zwicker (2007), Section 6.2, Table 6.1; no governing standard | [Loudness](https://docs.jmrp.io/phonometry/perception/psychoacoustics/loudness/) | | $ERB_N$ (Cam scale) | Equivalent rectangular bandwidth of the auditory filter, and the Cam scale built from it by counting one unit per $ERB_N$: about 132 Hz at 1 kHz, so the step from 934 Hz to 1066 Hz is one Cam. It is narrower than the Bark band at low frequencies, and it is the scale ISO 532-2 and ISO 532-3 compute specific loudness on, so a sone/Cam density is not numerically a sone/Bark one. | Hz (scale in Cam) | ISO 532-2:2017, 3.13 and 3.14 | [Advanced Loudness (ISO 532-2/-3, ECMA-418-2)](https://docs.jmrp.io/phonometry/perception/psychoacoustics/advanced-loudness/) | | $N_5$ | Percentile loudness: the loudness exceeded 5 % of the time, read off the time-varying loudness of the ISO 532-1 model. It is the stationary stand-in for a fluctuating sound that psychoacoustic annoyance is built on, and it is a loudness in sone, not a loudness level in phon. | sone | Fastl and Zwicker (2007), Equation 16.2; no governing standard | [Psychoacoustic annoyance and fluctuation strength](https://docs.jmrp.io/phonometry/perception/psychoacoustics/psychoacoustic-annoyance/) | | Short-term and long-term loudness | The two smoothed loudness time series of the Moore-Glasberg-Schlittenlacher model: short-term loudness is the loudness of a brief segment (a syllable, a single note, typically up to 500 ms), and long-term loudness that of a longer one, a whole sentence or musical phrase, typically up to 5 s. The loudness of a sound lasting two or three seconds is predicted by the maximum of the long-term series, not by its average. | sone | ISO 532-3:2023, 3.10 and 3.11 | [Advanced Loudness (ISO 532-2/-3, ECMA-418-2)](https://docs.jmrp.io/phonometry/perception/psychoacoustics/advanced-loudness/) | ## Electroacoustics and programme loudness | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | THD | Total harmonic distortion: the harmonic content of the output relative to the fundamental ($\mathrm{THD}_\mathrm{F}$) or to the total signal ($\mathrm{THD}_\mathrm{R}$). | % or dB | IEC 60268-3:2013, 14.12.2 to 14.12.11 (the R form in 14.12.3.2) | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | THD+N | Total harmonic distortion plus noise: everything left after notching out the fundamental, within the standard measurement bandwidth. | % or dB | AES17-2015, clause 6.3.1 (notch and bandwidth in 5.2.5 and 5.2.8) | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | SINAD | Signal to noise and distortion ratio, the reciprocal expression of THD+N. | dB | AES17-2015, clause 6.3.1 | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | IMD, $d_{m,n}$ (modulation) | Modulation intermodulation distortion: the sidebands a strong low-frequency tone produces around a weak high-frequency one. IEC 60268-3 defines several intermodulation families with different test signals, so a bare "IMD" has to say which one it is, and the single number an SMPTE-type analyzer prints combines the modulation sidebands in r.m.s. and is none of them. | % | IEC 60268-3:2013, 14.12.7 | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | $d_{d,n}$ (difference frequency) | Difference-frequency intermodulation distortion: the products two closely spaced high-frequency tones of equal amplitude create at their difference and its multiples, referred to the fundamentals. Its test signal and its products are both different from the modulation form, so the two numbers are not comparable. | % | IEC 60268-3:2013, 14.12.8 | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | TDFD | Total difference-frequency distortion: the second- and third-order difference products of the two-tone test combined into one figure and referred to the sum of the two fundamentals, the single number the difference-frequency family reports. | % | IEC 60268-3:2013, 14.12.10 | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | $H_n$ (harmonic order $n$) | Harmonic transfer function of order $n$: the impulse response that an exponential-sweep deconvolution places $L\ln n$ seconds *before* the linear one, so a single sweep separates the linear response and every harmonic order into its own window. The distortion of order $n$ at excitation frequency $f$ is then read as $\|H_n(nf)\|/\|H_1(f)\|$. | output per input | Farina (2000), no governing standard | [Swept-sine distortion and phase utilities](https://docs.jmrp.io/phonometry/devices/electroacoustics/swept-sine-distortion/) | | DIM | Dynamic intermodulation distortion, measured with a 15 kHz sine against a filtered 3.15 kHz square wave. | % | IEC 60268-3:2013, 14.12.9 | [Electroacoustics: distortion and frequency response](https://docs.jmrp.io/phonometry/devices/electroacoustics/electroacoustics/) | | $L_\mathrm{K}$, LUFS | Programme loudness: the channel-weighted sum of K-weighted mean-square powers, gated in 400 ms blocks. LUFS and LKFS name the same unit. | LUFS | ITU-R BS.1770-5, Formula 2 (gating in Formulae 3 to 7) | [Programme loudness and true peak (BS.1770 / EBU R 128)](https://docs.jmrp.io/phonometry/devices/broadcast/program-loudness/) | | LRA | Loudness range: the spread between the 10th and 95th percentiles of the gated short-term loudness distribution. | LU | EBU Tech 3342 | [Programme loudness and true peak (BS.1770 / EBU R 128)](https://docs.jmrp.io/phonometry/devices/broadcast/program-loudness/) | | dBTP | True peak level: the peak of the signal reconstructed by oversampling, which catches the inter-sample peaks a sample-domain maximum misses. | dBTP | ITU-R BS.1770-5, Annex 2 | [Programme loudness and true peak (BS.1770 / EBU R 128)](https://docs.jmrp.io/phonometry/devices/broadcast/program-loudness/) | ## Aircraft and airport noise | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | PNL | Perceived noise level: the 24 one-third-octave band levels converted to noisiness in noys and recombined. | PNdB | ICAO Annex 16, Vol. I, Appendix 2 (noisiness law in Table A2-3) | [Aircraft noise: Effective Perceived Noise Level](https://docs.jmrp.io/phonometry/aircraft/aircraft-noise/) | | PNLT | Tone-corrected perceived noise level: PNL plus the penalty for spectral irregularities such as fan and turbine tones. | PNdB | ICAO Annex 16, Vol. I, Appendix 2 | [Aircraft noise: Effective Perceived Noise Level](https://docs.jmrp.io/phonometry/aircraft/aircraft-noise/) | | EPNL | Effective perceived noise level: the maximum PNLT plus the duration correction over the 10 dB-down window, the noise-certification metric. | EPNdB | ICAO Annex 16, Vol. I, Appendix 2 | [Aircraft noise: Effective Perceived Noise Level](https://docs.jmrp.io/phonometry/aircraft/aircraft-noise/) | | PNLTM | Maximum tone-corrected perceived noise level: the largest PNLT of the half-second time history, after the bandsharing adjustment. It is the peak the certification metric is built on, since $\mathrm{EPNL} = \mathrm{PNLTM} + D$ and the 10 dB-down integration window is measured down from it. | PNdB | ICAO Annex 16, Vol. I, Appendix 2, 4.4 | [Aircraft noise: Effective Perceived Noise Level](https://docs.jmrp.io/phonometry/aircraft/aircraft-noise/) | | NPD | Noise-power-distance table: the event level of one aircraft ($L_\mathrm{Amax}$ or SEL) tabulated against distance for a handful of engine power settings, measured in steady flight along a notionally infinite straight path at a reference speed. A calculation interpolates it linearly in power and logarithmically in distance, then corrects that baseline segment by segment. | dB | ECAC Doc 29, 4th ed., Volume 2, section 4.2 | [Airport Noise (ECAC Doc 29)](https://docs.jmrp.io/phonometry/aircraft/airport-noise/) | | ANP database | Aircraft Noise and Performance database: the international collection of NPD tables, aircraft and engine performance coefficients and default departure and approach profiles, supplied mostly by the manufacturers, that an airport-noise calculation is normally run from. | | ECAC Doc 29, 4th ed., Volume 2, Appendix G | [The ANP fleet database](https://docs.jmrp.io/phonometry/aircraft/anp-fleet/) | | $d_p$ | Slant distance: the perpendicular distance from the receiver to the flight-path segment, which is the abscissa of every NPD table. It is not the distance along the ground and not the aircraft's altitude, and to the side of the track it is the minimum distance to the segment rather than to the whole path. | m | ECAC Doc 29, 4th ed., Volume 2, section 4.5.2 | [Airport Noise (ECAC Doc 29)](https://docs.jmrp.io/phonometry/aircraft/airport-noise/) | | $L_\mathrm{Amax}$ | Maximum A-weighted level of a single event: the largest instantaneous value $L_\mathrm{A}(t)$ reaches while the aircraft passes, the simpler of the two event metrics an NPD table carries. Doc 29 reads $L_\mathrm{A}$ on the Slow sound-level-meter scale, so the time weighting is part of the quantity; it is not the peak level, which has no time weighting at all. | dB re 20 µPa | ECAC Doc 29, 4th ed., Volume 2, section 4.1 | [Airport Noise (ECAC Doc 29)](https://docs.jmrp.io/phonometry/aircraft/airport-noise/) | ## Underwater acoustics | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $L_p$ (underwater) | Underwater sound pressure level, referred to 1 µPa rather than 20 µPa. An airborne level never converts to it by subtraction alone. | dB re 1 µPa | ISO 18405:2017 (mean-square level in ISO 18406:2017, Formula 7) | [Underwater acoustics: radiated noise and pile driving](https://docs.jmrp.io/phonometry/underwater/underwater-acoustics/) | | SEL (underwater) | Underwater sound exposure level, the time integral of squared pressure referred to 1 µPa²·s. | dB re 1 µPa²·s | ISO 18405:2017 | [Underwater acoustics: radiated noise and pile driving](https://docs.jmrp.io/phonometry/underwater/underwater-acoustics/) | | $L_\mathrm{RN}$ | Radiated noise level of a ship: the level of the product of the far-field r.m.s. pressure and the source distance. | dB re 1 µPa·m | ISO 17208-1:2016 | [Underwater acoustics: radiated noise and pile driving](https://docs.jmrp.io/phonometry/underwater/underwater-acoustics/) | | $L_\mathrm{s}$ | Equivalent monopole source level: the radiated noise level after the Lloyd's-mirror surface correction, so that one number describes the source itself. | dB re 1 µPa·m | ISO 17208-2:2019, Formula 3 | [Underwater acoustics: radiated noise and pile driving](https://docs.jmrp.io/phonometry/underwater/underwater-acoustics/) | | PL, $N_\mathrm{PL}$ (underwater) | Propagation loss, the quantity the sonar equation uses: the difference between the source level and the mean-square sound pressure level at the receiver, $N_\mathrm{PL}(x) = L_\mathrm{S} - L_p(x)$, in practice a geometrical spreading law plus the volume absorption $\alpha R$. Clause 3.4.1.3 keeps the name transmission loss for the reduction in level between two stated points, and both entries deprecate using one name as a synonym of the other, which is why so much of the literature calls this one a transmission loss. | dB | ISO 18405:2017, 3.4.1.4 | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | SL, $L_\mathrm{S}$ | Source level: the level of the source factor, equal to the level 1 m from a hypothetical point source radiating into an infinite lossless medium, so it is back-projected from a measurement made much further away and never measured at 1 m. The reference value carries a squared metre, which is why the widespread "dB re 1 µPa at 1 m" is the same number written loosely. | dB re 1 µPa²m² | ISO 18405:2017, 3.3.2.1 | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | NL, $L_\mathrm{N}$ | Sonar noise level: the background the signal has to be detected against, in the band of interest, from wind, thermal agitation, distant shipping and the platform's own self-noise. It has to be quoted over the same bandwidth as the source level, since an ambient spectrum level and a broadband level differ by $10\log_{10}B$. | dB re 1 µPa | ISO 18405:2017, 3.6.2.5 | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | DI (receiving array) | Directivity index of a receiving array: the array gain in the special case the sonar equation assumes, a plane-wave signal in isotropic background noise. It is the signal-to-noise ratio the beam buys over a single omnidirectional hydrophone, and it enters the equation as a credit against the noise level. | dB | ISO 18405:2017, 3.6.2.4 (Note 4) | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | DT | Detection threshold: ten times the base-10 logarithm of the signal-to-noise ratio at which a signal counts as just detectable, for a stated probability of detection (often 0,5) and probability of false alarm. It is where the processing gain and the operator's tolerance for false alarms enter the sonar equation. | dB | ISO 18405:2017, 3.6.2.1 | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | TS, $N_\mathrm{TS}$ | Target strength: the level of the target's differential scattering cross section, the free-field ratio of what it scatters back to what is incident on it. It is the one term that separates the active sonar equation from the passive one, and it depends on both the incidence and the scattering direction, so a backscattering value is the monostatic special case. | dB re 1 m²/sr | ISO 18405:2017, 3.6.2.8 | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | SE, $\Delta L_\mathrm{SE}$ | Signal excess: the amount by which the signal-to-noise ratio at the processor output exceeds the detection threshold. It is what the sonar equation returns; the target is detectable where it is positive, and the range at which it crosses zero is the detection range. | dB | ISO 18405:2017, 3.6.2.2 | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | FOM | Figure of merit: the propagation loss a passive system can afford before the signal excess reaches zero, that is, the loss at which SE = 0. It is read as the loss at which the probability of detection falls to 50 % only under the usual convention that the detection threshold is itself referred to that probability; SE = 0 fixes no probability on its own. Inverting any loss law at $PL = \mathrm{FOM}$ gives the detection range directly, which is why it is quoted instead of the whole curve. | dB (re 1 m² as a propagation factor) | Ainslie (2010), Equations (3.48) and (3.111); no governing standard | [Underwater sound propagation](https://docs.jmrp.io/phonometry/underwater/underwater-propagation/) | | $W(f)$ | Auditory weighting function: a generic band-pass filter shaped to one hearing group's susceptibility to noise-induced hearing loss, with its gain chosen so the flat central part sits at 0 dB. It is applied to the spectrum before an exposure is summed, so the same physical sound weighs differently for a porpoise and for a baleen whale. | dB | NMFS (2024) v3.0, Equation 1 (parameters in Table 5); no governing standard | [Marine-mammal noise exposure](https://docs.jmrp.io/phonometry/underwater/marine-mammal-exposure/) | | TTS onset | Onset of temporary threshold shift: the exposure at which a recoverable loss of hearing sensitivity begins, published per hearing group as a weighted sound exposure level and, for impulsive sound, together with an unweighted peak level. Both metrics have to be tested; whichever is reached first decides. | dB | NMFS (2024) v3.0, Table 8; no governing standard | [Marine-mammal noise exposure](https://docs.jmrp.io/phonometry/underwater/marine-mammal-exposure/) | | AUD INJ onset (PTS onset) | Onset of auditory injury, the 2024 guidance's name for what earlier versions called permanent threshold shift onset: the exposure above which the shift no longer recovers. For non-impulsive sound it is the TTS onset plus 20 dB for every group; for impulsive sound the guidance sets it 15 dB above in exposure and 6 dB above in peak level. | dB | NMFS (2024) v3.0, Table ES3; no governing standard | [Marine-mammal noise exposure](https://docs.jmrp.io/phonometry/underwater/marine-mammal-exposure/) | | $\mathrm{SEL}_\mathrm{cum}$ | Cumulative sound exposure level: the weighted sound exposure of every event of an activity (every strike of a piling campaign, say), summed over its whole duration. The onset criteria are written against this accumulated quantity, not against a single event, so halving the strike energy and doubling the strike count changes nothing. | dB re 1 µPa²·s | NMFS (2024) v3.0, Table ES3; no governing standard | [Marine-mammal noise exposure](https://docs.jmrp.io/phonometry/underwater/marine-mammal-exposure/) | ## Numerical simulation | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $C_N$ (the cfl argument) | Courant number: how far a wavefront travels in one time step, measured in grid cells, $c\,\Delta t\sqrt{1/\Delta x^2 + 1/\Delta y^2}$. An explicit scheme is stable only up to one and meaningless above it, so it is the number the time step is chosen from rather than the other way round; the library defaults to 0,6. | dimensionless | Attenborough and Van Renterghem (2021), Equations (4.13) and (4.14); no governing standard | [2D FDTD wave simulation](https://docs.jmrp.io/phonometry/simulation/fdtd-simulation/) | | Numerical dispersion | Numerical dispersion: the error the discrete scheme makes in the propagation speed, which grows with frequency and depends on the direction of travel (largest along a coordinate axis, and zero along the diagonal of square cells at a Courant number of one). It is why ten cells per shortest wavelength is the working rule, and why an FDTD arrival time drifts if the grid is too coarse. | % (speed error) | Attenborough and Van Renterghem (2021), Equation (4.15); no governing standard | [2D FDTD wave simulation](https://docs.jmrp.io/phonometry/simulation/fdtd-simulation/) | | PML (perfectly matched layer) | Perfectly matched layer: a boundary region whose absorption is graded so that, in principle, it reflects nothing at any angle or frequency, which is what lets a finite grid stand in for open space. What this library ships is the graded sponge layer, its simple precursor, so a grazing-incidence residue at the edge is expected rather than a bug. | | Attenborough and Van Renterghem (2021), Section 4.2.3; no governing standard | [2D FDTD wave simulation](https://docs.jmrp.io/phonometry/simulation/fdtd-simulation/) | ## Measurement uncertainty | Symbol | Definition | Unit | Defined in | Computed in | | :--- | :--- | :--- | :--- | :--- | | $u(y)$ | Combined standard uncertainty of a result, propagated from the standard uncertainties of its inputs by the law of propagation of uncertainty. | unit of the result | ISO/IEC Guide 98-3:2008 (JCGM 100:2008), clause 5 | [Measurement uncertainty (GUM and Monte Carlo)](https://docs.jmrp.io/phonometry/signals/metrology/gum-uncertainty/) | | $U$ | Expanded uncertainty: the combined standard uncertainty multiplied by a coverage factor, which defines a coverage interval. | unit of the result | ISO/IEC Guide 98-3:2008 (JCGM 100:2008), clause 6 and Annex G | [Measurement uncertainty (GUM and Monte Carlo)](https://docs.jmrp.io/phonometry/signals/metrology/gum-uncertainty/) | | $\sigma_\mathrm{R}$ | Reproducibility standard deviation of a sound-insulation quantity: the standard uncertainty ISO 12999-1 assigns to situation A, the widest of the three. The same clause assigns $\sigma_\mathrm{situ}$ to situation B and the repeatability $\sigma_\mathrm{r}$ to situation C (for $R'_\mathrm{w}$, 1,2 dB against 0,9 and 0,4), so the situation has to be stated with the number. | dB | ISO 12999-1:2020, Clause 5.2 (coverage factors in Table 8) | [Field Insulation Measurement (ISO 16283)](https://docs.jmrp.io/phonometry/buildings/insulation/insulation-field/) |