Source: https://docs.jmrp.io/phonometry/signals/metrology/ # Calibration and uncertainty A level printed by software is not yet a measurement. Three things separate the one from the other: knowing that the record deserves to be **averaged at all**, knowing what the digital samples mean **physically**, and knowing how much the result could reasonably be **wrong**. This section covers all three, and they apply transversally to every other page of the documentation. A fourth page maps the evidence that backs the numbers: what a performance **class** asserts, the verifiers that grade a chain, and the published conformance report. [Calibration and dBFS](https://docs.jmrp.io/phonometry/signals/calibration/) handles the physical meaning. phonometry works in two reference frames: physical **dB SPL**, established from a recorded calibrator tone (the IEC 60942 field ritual), and digital **dBFS**, levels relative to full scale, appropriate when no physical reference exists or when characterising the digital chain itself. The page explains how each mode is set up and, just as important, which quantities are meaningful in which frame, and it grades the calibrator itself against IEC 60942:2017 from what a laboratory measured on it. [Measurement uncertainty (GUM and Monte Carlo)](https://docs.jmrp.io/phonometry/signals/gum-uncertainty/) handles the second, implementing the *Guide to the Expression of Uncertainty in Measurement* (**ISO/IEC Guide 98-3:2008**) and its Monte Carlo **Supplement 1**. The GUM route propagates standard uncertainties analytically through sensitivity coefficients into a combined and expanded uncertainty, with Welch-Satterthwaite effective degrees of freedom; the Monte Carlo route propagates whole probability distributions numerically and yields coverage intervals that stay honest when the model is non-linear or the inputs are far from Gaussian. The page shows both on the same models, including where they diverge and why. [Compliance and verification](https://docs.jmrp.io/phonometry/signals/compliance-verification/) carries the evidence story: what a performance class actually claims in IEC 61672-1 and IEC 61260-1 (same design goals, different acceptance limits), which public verifier grades each stage of a measurement chain against its tolerance tables, the conformance rule of IEC TC 29 that grades a measured instrument, how to read and cite the numerical conformance report the site publishes, and the honest boundary against the pattern-evaluation and periodic tests of IEC 61672-2/-3 and IEC 61260-2/-3: the measurements need an instrument in a laboratory rather than a library, and what the library does with them is grade the results (`metrology.verify_sound_level_meter_periodic` for the periodic tests of a sound level meter, `filters.verify_filter_periodic` for those of a band filter) and compute on a design the tests that need no specimen. [Data qualification](https://docs.jmrp.io/phonometry/signals/data-qualification/) guards the gate in front of both: every average - a Leq, a Welch PSD, every averaged input to an uncertainty budget - assumes the record is stationary, and the Bendat & Piersol reverse arrangement and runs tests decide that objectively from segment mean squares, with the book's own acceptance regions. The same page carries the Rice statistics of level crossings and peaks - apparent frequency, peak rates, the irregularity factor - that characterise a qualified Gaussian record and screen for one that is not. [Random-incidence and diffuse-field response](https://docs.jmrp.io/phonometry/signals/random-incidence/) takes the calibration of the meter itself beyond its reference direction: the IEC 61183 directivity factor from readings in an anechoic room, the random-incidence sensitivity level that follows from it, and the diffuse-field level by comparison with a reference meter in a reverberation room. [Free-field corrections](https://docs.jmrp.io/phonometry/signals/free-field-corrections/) bring a meter tested on a sound calibrator, a comparison coupler or an electrostatic actuator back to the free field it is specified for: the IEC 62585 adjustment value at the calibration check frequency, the correction at each frequency, the uncertainty budget that goes with it, and the maximum each clause permits. [Periodic tests of a sound level meter](https://docs.jmrp.io/phonometry/signals/sound-level-meter-periodic-tests/) grade what a laboratory measured on a working meter by IEC 61672-3: every clause from the frequency weightings to the high-level stability against the acceptance limits of IEC 61672-1 and the maxima of its Table B.1, what a complete test holds, and the statement Clause 22 prescribes for the outcome. [Calibration by comparison](https://docs.jmrp.io/phonometry/signals/comparison-calibration/) goes one step up the chain, to the microphone itself: a working standard microphone takes the sensitivity of a reference through the ratio of their output voltages, in a coupler by IEC 61094-5 or in a free field by IEC 61094-8, with the environmental, jig and free-field corrections each part asks for and the uncertainty budget of Table D.1 or Table 2. [Calibration by reciprocity](https://docs.jmrp.io/phonometry/signals/reciprocity-calibration/) is the top of that chain: the reference itself, a laboratory standard microphone, calibrated with no other microphone to compare it with, from three pair measurements and the acoustic transfer impedance of a coupler by IEC 61094-2 or of a free field by IEC 61094-3. The same discipline extends into the frequency domain: the [Signals and spectra](https://docs.jmrp.io/phonometry/spectra/) pages apply the Bendat & Piersol error analysis to Welch spectral estimates, so every PSD carries its effective number of averages, its normalized random error and a chi-square confidence interval. The pages meet in practice: an uncertainty budget for an acoustic measurement almost always contains a calibration term, and several standards implemented elsewhere in the library (ISO 9612, ISO 12999-1) ship uncertainty budgets that are specialisations of the GUM machinery described here. ## Pages in this section - [Calibration and dBFS](https://docs.jmrp.io/phonometry/signals/calibration/): physical SPL calibration from a calibrator tone, the stability check it applies to that recording, the IEC 60942:2017 verdict on the calibrator itself, and the digital full-scale mode. - [Compliance and verification](https://docs.jmrp.io/phonometry/signals/compliance-verification/): what a performance class asserts, the verifiers that grade weightings, filter banks and intensity spectra against their tolerance tables, the conformance rule of IEC TC 29, the conformance report, and the scope of IEC 61672-2/-3 and IEC 61260-2/-3. - [Measurement uncertainty (GUM and Monte Carlo)](https://docs.jmrp.io/phonometry/signals/gum-uncertainty/): the law of propagation of uncertainty and the Monte Carlo method, expanded uncertainty and coverage intervals. - [Data qualification](https://docs.jmrp.io/phonometry/signals/data-qualification/): the reverse arrangement and runs stationarity tests on segment statistics, and the Rice level-crossing and peak statistics with the irregularity factor. - [Random-Incidence and Diffuse-Field Response (IEC 61183)](https://docs.jmrp.io/phonometry/signals/random-incidence/): the directivity factor of a sound level meter from readings in two planes, one plane or 38 equal-area elements, its random-incidence and diffuse-field sensitivity levels, and Table B.1 of the reference microphone. - [Free-Field Corrections of a Sound Level Meter (IEC 62585)](https://docs.jmrp.io/phonometry/signals/free-field-corrections/): the adjustment value, the corrections for a calibrator, a coupler and an actuator, the budget of Annex I and the verdict of clauses 9 to 14. - [Periodic Tests of a Sound Level Meter (IEC 61672-3)](https://docs.jmrp.io/phonometry/signals/sound-level-meter-periodic-tests/): the verdict on a laboratory's results, clause by clause, with Tables 4, 5 and B.1 of IEC 61672-1, and the statement of Clause 22. - [Microphone Calibration by Comparison (IEC 61094-5/-8)](https://docs.jmrp.io/phonometry/signals/comparison-calibration/): the simultaneous comparison with the interchange of Annex C, the sequential one against a monitor, in level and phase, the environmental, WS3 jig, different-diameter and acoustic impedance corrections with the air between two microphones, the validation of a jig or coupler, the budgets of Table D.1 and Table 2 with k = 2, and the time-selective processing of IEC 61094-8 Annex B. - [Microphone Calibration by Reciprocity (IEC 61094-2/-3)](https://docs.jmrp.io/phonometry/signals/reciprocity-calibration/): three microphones calibrated in pairs, the transfer impedance of a plane-wave or large-volume coupler with the heat conduction of Annex A and the capillary tubes of Annex B, the free field with the attenuation of Annex B and the acoustic centres, and the budgets of Table 1. ## What this section does not cover Nothing here measures an instrument or a calibrator. No IEC 60942 test is performed: `verify_sound_calibrator` grades the numbers a laboratory measured on a calibrator, and the static-pressure correction of an LS/M or 1/M pistonphone comes from its manual, so pass an already corrected `target_spl` when the manual asks for one; the IEC 61672-3 periodic tests are not run either, and `verify_sound_level_meter_periodic` grades the results a laboratory returns; [Compliance and verification](https://docs.jmrp.io/phonometry/signals/compliance-verification/) draws that boundary precisely, part by part. The dBFS half of the calibration page sits outside any standard and makes no physical claim: it is a reference frame, not a measurement. Data qualification implements the quantitative core of Bendat & Piersol's section 10.3 only: classifying a record's type, validating it against physical limits and editing out glitches remain manual steps, as the book describes them. And an uncertainty budget is a model of *your* measurement: the library propagates whatever you declare, and never invents the terms. Where a standard publishes its own budget the guides say so, as ISO 9612 does for [occupational exposure](https://docs.jmrp.io/phonometry/perception/hearing/occupational-exposure/) and ISO 12999-1 for [sound insulation](https://docs.jmrp.io/phonometry/buildings/insulation/).