But you don't really care for music, do you?
I actually like this. A tip, however: it's obvious you're talking about Smile, and the likelihood that you'll get raked over the coals for a Thing What Makes you Crazy is near to 100%. Also, what's so important about frequency σ that it's specifically what the Foundation is going to unspeakably great lengths to contain? You don't even mention what that frequency does. (Unless you're saying that cancelling out that one frequency undoes the entire effect, but then again, how did the Hebrews generate that sound in the first place?)
I would also change the time parameters; that's a little too arbitrary. Maybe the effects manifest after 3-4 seconds and drive you crazy at 30 seconds, something like that. Give it a little more leeway.
If you cancel any one of the frequencies, the five-tone chord can't be produced so you're safe. Since you have to generate the antiphase tone in order to cancel a given frequency, you'd hear the antiphase tone (think of how noise-cancelling headphones work) unless it and the frequency you're cancelling are already ultrasound. Frequency sigma is ultrasound so you can broadcast frequency zeta, really loudly all the time and all over the place, also in ultrasound without bothering people. (This also has the side benefit of producing the Taos Hum).
I'm aware that Thing What Makes You Crazy is a flaw, any alternate suggestions?
Since I'm assuming you don't want this to be a "brown note" you could leave it as ecstacy. It makes you orgasmicly happy - and leaves you there forever. Or is the resonant frequency of bone.
Drop the bit about outside of dog hearing. There's a lot of creatures out there with better hearing, and it's not very sciencey.
And drop off the tenth of a second part of the timings. Humans would react at different speeds but within a range ("Stage 1 lasts between 10 and 15 seconds, stage 2 between 5 and 40 seconds….")
Finally, what about the deaf?