Hi db, I don't think high-ordered odd harmonics do add to our lives. The current state of high-end audio suggests that they don't. Their rarity in nature might mean that less brain power is required to detect the change in volume, but what is important is not the 'why?' but the fact of 'what is'.
That we react this way is easy to demonstrate BTW. If you have access to test equipment, set up a sine wave and run it through an amplifier at 0VU and listen to the result. Now run down the volume, switch to square wave, and turn it up until you get the same perceived volume level. Now look at the meter- you will be about 20-24db down compared to the original sine wave. That's 1/100th the level or so depending on your perception. If you add a filter to filter out the lower orders, you will find there is almost no change in perception.
That we react this way is easy to demonstrate BTW. If you have access to test equipment, set up a sine wave and run it through an amplifier at 0VU and listen to the result. Now run down the volume, switch to square wave, and turn it up until you get the same perceived volume level. Now look at the meter- you will be about 20-24db down compared to the original sine wave. That's 1/100th the level or so depending on your perception. If you add a filter to filter out the lower orders, you will find there is almost no change in perception.