Loudness Analysis

Loudness quantifies the perceived intensity of a sound as experienced by a human listener. Unlike sound pressure level, loudness accounts for the frequency-dependent sensitivity of the auditory system, spectral masking, and temporal integration. V-Listen supports three internationally recognized calculation standards.

Supported Standards

Standard	Method	Scope
ISO 532-1 (2017)	Zwicker method	Stationary and time-varying signals
ISO 532-3 (2023)	Moore-Glasberg method	Stationary and time-varying signals
DIN 45631/A1 (2010)	Zwicker method with Amendment 1	Time-varying extension per Fastl

ISO 532-1 (Zwicker) is the most widely adopted method in automotive and consumer-product industries. ISO 532-3 (Moore-Glasberg) offers improved accuracy for sounds with strong tonal components. DIN 45631/A1 extends the original Zwicker model with a validated temporal integration scheme for non-stationary signals.

Theory

Critical-Band Rate Scale (Bark)

The auditory system divides the frequency range into approximately 24 critical bands. Each band spans one Bark on the critical-band rate scale. The transformation from frequency to Bark is defined as:

z = 13 · arctan(0.76 f / 1000) + 3.5 · arctan((f / 7500)²) [Bark]

Specific Loudness

Specific loudness N' describes the loudness contribution per critical band. It is derived from the excitation level within each band after applying the outer- and middle-ear transfer functions and accounting for spectral masking. Total loudness is obtained by integration:

N = ∫₀^{24 Bark} N'(z) dz [sone]

Temporal Integration

For time-varying signals, the instantaneous specific loudness is filtered through an attack/release model that simulates the temporal response of the auditory system. Attack time constants are shorter (~5 ms) than release time constants (~50 ms), matching human perception of sudden onsets and gradual decays.

Parameters

Parameter	Options	Description
Standard	ISO 532-1 / ISO 532-3 / DIN 45631/A1	Calculation method to apply
Signal Type	Stationary / Time-varying	Selects block-wise or running analysis
Field Type	Free field / Diffuse field	Outer-ear transfer function to use
Binaural Mode	Off / On	When on, left and right channels are processed independently and combined using a binaural summation model
Time Weighting	Block size in ms	Temporal resolution for time-varying analysis (default 2 ms)

Output Quantities

Quantity	Unit	Description
N	sone	Total loudness (time-averaged for stationary, instantaneous for time-varying)
N5	sone	5th percentile loudness, exceeded 5% of the analysis duration; commonly used as a single-value descriptor for time-varying signals
N'(z)	sone/Bark	Specific loudness spectrum over critical-band rate
N(t)	sone	Loudness vs Time (time-varying mode only)

Analysis Variants

Loudness vs Time

Computes instantaneous total loudness at each time step. The result is a time series of N(t) values with configurable temporal resolution. Use this variant to identify transient events such as door slams, relay clicks, or impulsive noise in pass-by tests.

Loudness vs RPM

When a tachometer channel is available, loudness can be plotted against rotational speed. This is essential for engine run-up/coast-down evaluations in NVH applications where loudness growth rate correlates with perceived powertrain refinement.

Interpretation Guidelines

Reference value: 1 sone corresponds to the loudness of a 1 kHz pure tone at 40 dB SPL in a free field (frontal incidence). A doubling of the sone value corresponds approximately to a doubling of perceived loudness.

< 5 sone — Very quiet; typical background noise in a recording studio.
5 – 20 sone — Moderate; passenger car interior at constant cruise speed.
20 – 50 sone — Loud; power tools, vacuum cleaners.
> 50 sone — Very loud; industrial machinery without enclosure.

Practical Application Notes

Always verify that the correct field type is selected. Using free-field correction on a diffuse-field recording (or vice versa) shifts the result by several sone.
For binaural recordings, enable binaural mode to obtain a single overall loudness that accounts for spatial summation.
N5 is the preferred single-value metric in most automotive specifications (e.g., OEM target catalogues). Report N5 rather than the arithmetic mean of N(t).
When comparing results across software platforms, ensure that the same standard, field type, and temporal resolution are used.

Standard References

ISO 532-1:2017 — Acoustics — Methods for calculating loudness — Part 1: Zwicker method
ISO 532-3:2023 — Acoustics — Methods for calculating loudness — Part 3: Moore-Glasberg method
DIN 45631/A1:2010 — Calculation of loudness level and loudness from the sound spectrum — Zwicker method — Amendment 1: Calculation of the loudness of time-variant sound
E. Zwicker & H. Fastl, Psychoacoustics: Facts and Models, 3rd ed., Springer, 2007