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Related: Why is the candela a base unit of the SI?

In the answers given in the previous question, the candela is included because lighting is important for humans. By the same argument, hearing is also important for humans, so there should also be an SI unit for subjective loudness of sound.

So why is none of the subjective loudness units, such as sone, phon, or some similar units, included in SI units?

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In addition to the greater variance of the human ear compared to the human eye, I think there is at least one other reason sones (or whatever) aren't SI units and it boils down to this: while all candles of the same color and brightness look the same, not all strings of the same pitch and loudness sound the same.

While loudness corresponds to brightness and pitch corresponds to color, sound has a third quality, let's call it "timbre", that doesn't really have an analogue in light. The closest, for our purposes, is color mixing but here the differences between optic perception and acoustic perception cause a serious divergence.

For optic perception, only three colors of light get their own receptor, and even these have some serious overlap (so much so that calling them "red", "green" and "blue" is more than a little disingenuous). As a result, color mixing is simply how most colors are perceived. For acoustic perception, every (or near enough) pitch of sound gets its own receptor, none of this "oh, look, the green and red cones were both set off, but there's more red than green, must be orange" nonsense. No; each pitch gets its own hair cell.

So what happens if more than one hair cell is set off by one note? This is (our definition of) timbre. The lowest-perceived or "fundamental" pitch is the nominal pitch, but the higher "harmonic" pitches tell you what kind of sound it is. This is what distinguishes pianos from harps, flutes from clarinets, plain vowels from nasal vowels from rhotic vowels, and content purrs from disgruntled growls.

Pitch and loudness interact analogously to the way color and brightness interact (the threshold of hearing, ie, the quietest sound a human can perceive, depends on pitch), but timbre also interacts with both. A sound that carries multiple distinct pitches will sound louder than a sound with only one pitch at the same amplitude; the "fuzzier" and "noisier" the note, the louder it sounds, up to a point, although "pure" tones can also be quite piercing. And of course "noisier" sounds can't really be said to even have a pitch.

This is where the difference between color-mixing and timbre really shines (pun very much intended). Because all colors except the reddest of reds and the bluest of blues are perceived as mixed colors, even if they were originally pure, color mixing can be smoothed away to give a fairly consistent luminosity function, even for white light, the "noisiest" of light. (Heck, the candela used to be defined by the brightness of a certain black body, which by definition emits light that is as mixed as possible.)

But pure tones are perceptually distinct from mixed sounds, and timbre is, if anything, more exaggerated than frequency-mixing. A proper "sonosity function" would have to take into account pitch, loudness and timbre and all the messiness that comes with it; the fact that "noises" don't actually have a pitch, that many pitches played at once tend to be louder than if each were played separately, that timbre can't really be properly ordered, even in the way color can in two or three (or more) dimensions.

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Ultimately, you'd have to ask the BIPM.

However, there's a strong case to be made that the average human eye's subjective response to illumination as a function of wavelength (the so-called luminosity function) is relatively uniform over the entire human population (if one ignores inconvenient facts like the existence of different kinds of colorblindness, in the several-percent level of prevalence), and that this remains relatively stable over any given individual's life.

By contrast, the human ear's spectral response shows appreciable evolution, and it shows a degradation over the high-frequency part of the spectrum starting as early as the twenties and thirties (hence e.g. "ultrasonic" ringtones, and other such ways to annoy an entire high-school classroom to the bafflement of the teacher, or their weaponized form). Producing a standardized equivalent of the luminosity function for subjective loudness is therefore much more difficult.

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  • $\begingroup$ There is "Equal-Loudness contour" which seems to be the equivalent of the luminosity function for sound. There is also ISO 226:2003 which defines an Equal-Loudness contour. I did not read the details, but that this ISO document exists suggests that a standardized loudness may be defined. $\endgroup$ – MaudPieTheRocktorate Dec 7 '17 at 13:27
  • $\begingroup$ @MaudPieTheRocktorate As I said already, you can "define" whatever equal-loudness contour you want, and enshrine it into however many official standards you care for, but none of that changes the fact that it will generally only apply to a fraction of the population, and the applicability of the curve to a given individual will change over time; both effects limit the usefulness of those curves. As to why those "standards" are recognized by ISO and not by the BIPM, as I said, you'd have to as the BIPM. $\endgroup$ – Emilio Pisanty Dec 7 '17 at 13:35
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Because the SI only takes in acount the most basic units. Sound is vibration of presure, and presure, whith the basic unit being the pascal, is https://en.wikipedia.org/wiki/Pascal_(unit) 1pascal=1kg⋅m−1⋅s−2, thus you can decompose it in kilos, meters and seconds, which are IU. The candela is by definition a unit so it can not be decomposed further. You must take in account that this is normally decided by the precision at which the definition of the unit can be measured in the calibration, so that the result is as precise as posible.

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  • $\begingroup$ What you said about sound can also be said about the Candela. You can express radiant intensity in W per sterradian and square meter just as you can with vibrations of air. However just as with expressing sound in pressure related units it does not tell you the human perception of brightness or sound because it depends on physiological sensitivity of humans. There must be another argument. $\endgroup$ – Jan Bos Sep 19 '16 at 1:03
  • $\begingroup$ The argument migth that be taking in account the actual methods to calibrate and measurement,the definition of Candela and the other IU gives rises to a set of references that can be use in order to calibrate the measurement devices with the highest precision posible. From that arises the IU system and measurements as sound could be very well calibrated using the definition of kilo, second, meter, and some physical property related to them and sound or pressure. However the best way to measure irradiance is...well, take the definition of Candela and compare your irrandiance with it. That's all $\endgroup$ – Victor Sep 19 '16 at 2:09
  • $\begingroup$ Huh? But irradiance is measured in the unit W/m^2 $\endgroup$ – MaudPieTheRocktorate Sep 19 '16 at 2:48
  • $\begingroup$ yeah, sorry, luminosity, not irradiance. Here you have more information about the topic: quora.com/… physics.stackexchange.com/questions/183210/… $\endgroup$ – Victor Sep 19 '16 at 2:55
  • $\begingroup$ @Victor Vibrations in air as a human perceives (i.e. sound) can be calibrated in a similar way to some reference as how a human perceives radiant intensity (i.e. luminous intensity). Or not? The question is why the Candela made it in the SI system and something similar for sound not. $\endgroup$ – Jan Bos Sep 19 '16 at 3:58

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