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Equal Loudness Curves for Music Program

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I am curious how the determine the 3 gain (and output power) curves. I understand that there are several formulas for this, but the audiogram only measures your hearing threshold. Even if 2 persons have the same audiogram, their hearing may differ above the hearing threshold. Are such differences ignored? Is the same formula used for differing audiograms?

The reason I ask is that the Equal Loudness Curves (ELC) are based on a formula. One input to this formula is the hearing threshold of a person with ”normal” hearing. The output is 10 power curves that are separated by the same amount at the frequency 1000 Hz. So I was wondering what happens if I put in my audiogram in this formula instead of the ”normal”. I decided to implement the formula in Mathematica and found that It distorted the ELCs significantly at lower powers, but not so much at higher powers.Then I sampled the formula to get the 50, 65 and 80 db curves and plugged them into the output power curves (not the gain curves) of the Music program in SmartFit just to see what happened. I tried it on my classical guitar. To my surprise it sounded very natural. Has anyone tried this?

No,I never tried this. For the piano I always went with decreasing the G50 curve by 6-10dB, to allow for the larger crest factor in music than in speech. Following with setting the G65 and G80 curves at a compression ration of 1.4. (Literature states 1.3, but that is still too loud for me and results in headaches.)

This works for me and results in a piano that has no distorted or painful notes.

Could you elaborate on the mathematics and the formula’s used? I am always willing to experiment.

It’s always nice to get a more natural sound. However, our hearing losses are significantly different. I have a cookie bite , resulting in a dreary and plain piano at the 3 middle octaves. Yours is a downsloper, removing most high frequencies. Restoring those fully wouldn’t have to give you a natural sound, if your natural got used to less high frequencies in the years your hearing was losing its high notes. So the question to me isn’t whether it’s more natural. It’s more whether it is another viable approach to programming aids for the piano.

Ok, i will try to elaborate.

The Equal Loudness curves (ELC) are based on the ISO 226:2023 standard. If you Google ISO 226 pdf you will find links to that document. The mathematical formula is in equation (1). It is based on the arrays in Table 1. One of the arrays is the “normat” threshold Tf. The formula gives the ELCs the figure in Annex A. I implemented formula (1) as an interpolating function in Mathematica, which lets you sample the curves at any frequency. Note that the curves are equally spaced at 1 kHz, but not at other freaquencies.

So what I did was to replace the array Tf with my (mirrored in the frequency axis) To do this I converted the audiogram into another interpolating function (also in Mathematica) that I resampled at the same frequencies as Tf. The result was curves with a higher threshold than the original curves, especially in the high frequency range (due to my specific hearing loss). This led to a compression of the curves there.

The next step was to use the modified formula to pick out 50, 65 and 80 (at 1 kHz) curves. These 3 curves were then sampled at the 10 frequencies used by Smart Fit. The gave suggested output power values that I tried to put into Smart Fit. It was not possible to do this exactly (due to the fitting formula of Smart Fit not being exactly the same as my modified formula), so I settled on getting it close to the suggested values. To my suprise my guitar sounded much better than with the default music program.

Maybe one reason that this worked suprisingly well for me is that a classical guitar has a limited frequency range as well as a limited dynamical rannge compared to, for example, a piano.

I hope my experiment is easier to understand now.

One variation could be to replace Tf not by the audiogram but by, for example, 1/3 of the audiogram. This semms to be used in other methods.

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