Scott wrote:I don't know how people subjectively determine twice as loud...
1) it's scientifically known as the "G factor". G as in "guitar".
"Your guitar is twice as loud as my keyboard" is an objective assesment
"No, my guitar is just as loud as the drums, which are twice as loud as the bass" is on the contrary an arbitrary and ridiculous pretense.
2) on a more jocular tone: "feeling loudness" means "perceiving air pressure on the ear".
This is why it becomes painful above a certain, albeit approximate, treshold.
Low frequencies apply the same pressure as high frequencies, but being the pressure equal, they give less information (you have lesse repetition of the waveform "sampling" by the brain).
This is why you think you "ear" high frequencies "louder" than low frequencies.
You hear them BETTER, not louder.
eg. you ear a violin waveform 2000/4000 times a second, while in the same second you hear a bass 100/400 times. So, the pressure on the hear is the same, but the violin makes itself more easily recognized, then more easily "heard".
The point where they break your tympanus is the same though. And it depends on PRESSURE (at least until you go to frequencies so high that physical resonance damages the ear's tissues).
The point where you DECIDE you want it to stop because you're afraid it will damage you, comes on the violin first, because you perceive better that the sound is getting louder. The danger doesn't change , the alert is more audible. The bullet is the same, but the higher frequency is a "traceable".
This is why a bass can shatter a guitar ampli, and the contary is less easy.
ABOVE a certain frequency this changes. Too long a discussion to post here.
Pardon the funny offtopic.
But from the above one should recognize why ANALOG acoustic content, not midi scale, is paramount to loudness.