# How to keep the same power (sonority) between pure sines?

I have a list of sine waves in 1/3 Octave (63,80,100...1k,1.25k,etc) that I want to reproduce with the same power. Right now I just have a global gain that applies to all this freqs, but of course the high frequencies are louder that the lower ones.

I am not sure how to keep the same power between them, I suppose I can use the principle of the pink noise and convert the gain (normalized 0-1) to dB, lower 3dB per octave as I go up in the list and go gack to normalized. But I am not sure if this is the correct way to achieve what I need.

How can I Keep the same power/Sonority?

Edit: By equal power I mean they sound with "the same volume" to person listen to them.

For info, the user will be using mostly headphones. This is running on mobile phones.

• Please be clear: By the same power, do you mean electrical voltage/current at the amplifer input or the acoustic pressure wave power at the output of the loudspeaker, or the percepted power of the sensation in the human hearing system? Dec 26 '17 at 21:05
• You should consider that of two tones exactly equal in power, the one at the higher frequency (up to like 3 kHz?) will sound louder to the human ear. Look up "equal loudness contours" to see this concept visualized. Dec 27 '17 at 9:16
• @Fat32 I was not sure how to translate this, in spanish it is "Sonoridad". I used "power" just because it is what Wikipedia uses when explaining about the characteristics of the Pink Noise. I added an edit. It is about the percepted power. Dec 27 '17 at 12:15
• @goldrik I now the Fletcher Munson curves but I do not know how to apply it here because the work with SPL and I Do not have direct control with that. Dec 27 '17 at 12:15

## 1 Answer

From the comments on the question I gather that you want the individual sine waves to appear to be at the same volume. Unfortunately, there is no single EQ setting you could apply to achieve this. As for the reasons, let's look at the equal-loudness contours:

What these contours tell us is that for a specific level of phones there exists an EQ setting that would make your sine waves sound at equal loudness. Unfortunately, the human perception of loudness not only depends on frequency but also on SPL—what that means is that your EQ settings that you meticulously set up for a certain level of phones won't work any more if you change the overall gain of your playback system. To compensate for the SPL-dependency of the human hearing you would need an adaptive EQ that takes into consideration the SPL of the signal at 1000 Hz (or any other reference frequency) by measureing it with a sound level meter and setting the EQ parameters accordingly.

• I was looking in get just something like a gain "correction" for each freq. So when 1Khz has a gain of 0.4 then 250Hz will have a gain correction of -for example- 1.4 (so a total of 0.56 volume units). Those does not need to be really accurate just enough to not be annoying for the user to say "I can not hear 100 hz". Maybe will I try to measure it with an SPL meter just to get a reference. But I am not really sure how to measure earbuds... Dec 27 '17 at 15:27