According to Leo Beranek's book, Acoustics, eqn (9.33), the percent
2nd harmonic distortion for an infinite horn is given by
1.73(f/fc)*It^(.5)*10^(-2) where It is the power/square meter at the
throat. Thus, if a horn cut off is 200 Hz with an extreme slope crossover at that frequency, and we want the horn to
cover up to 3200 Hz for 4 octives, we have to consider how much distortion we would
accept. Assuming a 2" throat and a 1 watt acoustical 3200 Hz signal, that equates to It = 493 w/sq m so that the 2nd harmonic distortion would be about 6.1%. I recall that about 50% of music power is below 350 Hz and that the power drops off quickly above 1000 Hz. With "large" horn systems capable of handling over 100 watts (electrical), it would appear that distortion is a design factor.
Comparing a 2" diameter throat with a 1" diameter throat, we note (assuming both dimensions are exact) the smaller throat causes twice the distortion.
Thanks,
nat