Measures / dBA Introduction
[Part-III: Loudness. 2020/1/7]
[Part-II: SLMs & Resolutions. 2019/12/18]
[Part-I: dBA Introduction Graphs & Tables. 2019/12/13]
[References]
Part-III Loudness
Part III, II, I deal with how we perceive sound loudness at frequency, and how that generally correlates to sound pressure levels from just audible—the threshold of hearing—to everyday comfortably quite home and office-level sounds. The main takeaway is that our perception of loudness at low-levels are anything but flat or linear.
loudness is our perception of sound intensity—what we “know” post sensation and body/brain processing. And rather than hack away at this rather complex term, I’ll just quote the intro of the seminal paper:
Loudness is a psychological term used to describe the magnitude of an auditory sensation. Although we use the terms “very loud,” “loud,” “moderately loud,” “soft” and “very soft,” corresponding tot he musical notations ff, f, mp, p and pp, to define the magnitude, it is evident that these terms are not at all precise ad depend upon the experience, the auditory acuity, and the customs of the persons using them. If loudness depended only upon the intensity of the sound wave producing the loudness, then measurements of the physical intensity would definitely determine the loudness as sensed by a typical individual and therefore could be used as a precise means of defining it. However, no such simple relation exists. –Harvey Fletcher and W. A. Munson, Bell Telephone Laboratories. August 28, 1933
Referenced earlier were James Jean’s table on the threshold of hearing. I am still not able to find the reference work and its methodology, but the correlation between it and Fletcher-Munson are quite close, particularly within hard data bandwidth of Fletcher and Munson.
Fletcher-Munson v Jean—Threshold of Hearing
Y Axis = dB-SPL (Ref: O dB-SPL = 20µPa) / X Axis = Hz
F-M: Harvey Fletcher and W. A. Munson, Loudness, Its Definition, Measurement and Calculations. Bell Telephone Laboratories (Received August 28, 1933). JASA Volume V, 1933
Jeans, James, Sir. Science & Music. Cambridge University Press, 1937
Deviation between F-M and Jeans is within the test sample margin. Data below 62Hz is not shown as statistical extrapolation in the F-M curves has been removed, and testing and methods have not be confirmed for Jeans.
Part-II SLMs & Resolutions
The method of usage has at least as much effect on the outcome as the quality of instrument itself. –Acoustical Society of America
Before I get into how we relate to sound at various levels, frequencies and forms—on which the dBA hinges—we need to talk about measurement resolutions and how we might relate with and test against the numbers. At the very least we should recognize what it is we might not know about. My facial muscle coordination, but when data references hit my desk at a tenth of a dB resolution I get an automatistic eyebrow rise. Most of the sound level meters and systems out there comply to ANSI Type-2, and without further lab-level characterization, your SLM has an amplitude resolution of about 2 dB, or more precisely plus/minus 2.3 dB, and that’s only in the meaty-middle decade of the audible spectrum. Simple sound level systems including the app for your phone can be useful, but they are not really referenceable. Specifications for a sound level meter should be ANSI referenced [ANSI S1.4-1983 (R2006)/ANSI S1.4a-1985 (R2006)], and occasionally be recalibrated and certified. They also need to be handled with care, if the SLM, or mic is dropped or impacted recertification is advisable. The tolerance specifications (ANSI) when used in steady-state sinusoidal diffuse sound-field within the frequency range of 100 to 1250Hz:
Type-0 instrument (laboratory reference standard)
Type-1 instrument ± 1.5dB
Type-2 instrument ±2.3dB
Since the ANSI calibration standards of a microphone specify random-incidence response, calibration of angle of incidence should be know, which is the angle of incidence from axis of symmetry for plane waves in free space which provides a frequency response that most closely approximates random incidence. If unknown, measurements of directional sounds should be made at 70˚ angle of incidence which generally approximates random-incidence calibration.
For complex sounds with significant spectral content above 3kHz, such as music, with rapidly varying temporal characteristics, a Type-1 instrument will give improved measures.
The standard requires each type to have three frequency weightings, A, B, and C; and two exponential time-averaging characteristics, slow and fast. Impulse response may also be an option within temporal characterizations. I don’t have the reference handy but I believe fast is based on a 200ms window and slow is based on a 500 ms window. B-weighting is a comprise and is rarely referenced or used.
Operational techs should know and follow the instruction set out by the instrument manufacturer and also know ANSI S1.4-1983 (R2006)/ANSI S1.4a-1985 (R2006). Further how and why questions specific to SLM are very likely address in that document.
Ska—it’s what a thirteen year-old boy hears when he gets extra mozzarella sticks. —Harvey Day
Part-1: dBA
dBA is a precisely defined unit relating to sound. The dB on the other hand is a unit that without an additional symbol assigned only expresses logarithmic relationships or change in value without any specific respect to sound. There are many other defined sound units but dBA is ubiquitous, far and way the most used and most referenced.
Many sound levels/quality scales exist due to our need to communicate, the nonlinearity of our hearing and the quality of information being sent and received. The vast majority of information sonically conveyed is centered in the bandwidth and sound pressure levels of speech—dBA is designed around this premise [1].
About a year ago I wrote here in a blog post, “A-weighted sound level measure has solid relevance for speech and speech-level sounds including environmental acoustics at speech levels, the dBA unit has little relevance to music, film and the performing arts and is rarely used.” While that might be true in some situations it was defiantly written from an audio engineer’s frame of reference and made some rather large assumptions. So here we go with dBA - revisited.
dBA (deci-Bell, referenced to a lower limit, A-weighted) appears to be the oldest as well as the most widely used unit of sound measure. This “A” weighted function on frequency characteristics was engineered to mirror the phon equal loudness-level contours based on the 1933 Fletcher-Munson data[1]. As this dataset has proven to be useful and accurate, dBA units continue to be referenced in the design and usage of performing arts venues, recording studios and lecture halls throughout the world, as well by every municipality with written ordinances. Even many hard hitting international touring bands reference dBA within their contracts and riders.
So why then are there other units and scales for sound and how we perceive them? I think it comes down to three main reasons, and maybe fourth:
Our nonlinear sensitivity to pitch, timbre and amplitude.
Our extremely large scale sensitivity to sound pressures.
And most importantly our need to communicate with fidelity.
A subset of the above is also this, that specialized situations and conditions need increased rigor and refinement.
Understanding dBA will allow the user of any sound level metering device not only get reliable data but will also facilitate a much deeper appreciation of hearing and our use of sound. A great starting point is with the phon scale and the beginning days of psychoacoustics. We start there because that is roughly the beginning, and while many of us have an idea of the Fletcher-Munson curves[1] many more do not, let alone ever learning about the phon scale.
The above 16-bit, 44.1kHz set of curves and the impulse response are interesting as it shows that level of resolution, either in the wave or in the processing, effects the resulting measures.
The above table is found in Science & Music by Sir James Jeans[2]. I find it interesting as it reflects the musical interests of the subbass region. While the contour appears to be a conflation of other work or some lost work, Jeans does site it as the work of Fletcher and Munson. Jeans also references the work of Andrade and Parker (1937) and states that results between studies, as well as other works unnamed “are in very close agreement.” Many studies have followed and there have been discrepancies, especially at the extreme ends of the audible bandwidth, most likely due to the way the tests were performed; head-on vs side, plane wave vs amorphus, headphones vs loudspeakers. But within the speech and the power spectrum of the vast majority of music, Jean’s table is still relevant and quite close to current international standards.
REFERENCES
[1] Harvey Fletcher & W. A. Munson / Bell Telephone Labs. Loudness, Its Definition, Measurement and Calculation. Journal of Acoustic Society of America, 1933. [JASA. 5, 82 (2005); https://doi.org/10.1121/1.1915637]
[2] Jeans, James, Sir. Science & Music. Cambridge University Press, 1937
[] Kinsler, Frey, Coppens, Sanders. Fundamentals of Acoustics, 4th ed. Wiley
[] IS0-226:2003
[] ANSI S1.4-1983 (R2006)/ANSI S1.4a-1985 (R2006)
[] ANSI S1.4-1983 (Rev of S1.4-1974) ASA 47-1983
[] ITU: ITU-R BS.1770-4. Algorithms to Measure Audio Programme Loudness and True-peak Audio Level. 2015.
[] Charbonneau, Jeremy. Theses: Comparison of Loudness Calculations Procedure Results to Equal Loudness Contours. University of Windsor, 2010
[] Parmanen, Juhani. Some Reasons to Revise the ISO 226:2003: Acoustics—Normal Equal-Loudness-Level Contours. Open Journal of Acoustics, 2012, 2, 143-149