A slightly lower than x2 in frequency octave may sound horrible where as a slightly greater than x2 may sound brilliant

This psychoacoustic effect is even more prominent at double, triple octaves etc.


For example choosing a A3 note to be 220Hz, A5 at 880Hz will sound flat or a sick or an uninteresting multiple octave. A5 890Hz will be much better. It may depend on who is listening. It may even depend on which ear.


Experiments can be done with an online sinewave signal generator.


Acoustic intensity should be kept low as pitch depends on acoustic intensity too.


References:


Online tone generator
http://onlinetonegenerator.com


Engineering octave vs ear brain octave - euroelectron


Sound and Hearing - S. S. Stevens, Fred Warshofsky - Life Science Series


http://www.mmk.ei.tum.de/fileadmin/w00bqn/www/Personen/Terhardt/ter/top/octstretch.html