Back in my phreaking days, I was grounded so often that out of sheer boredom I learned to whistle DTMF tones. I could dial a number simply by whistling it.
You're thinking in the frequency ___domain, which is natural. Try to think, instead, of what a dual-sideband suppressed-carrier signal looks like in the time ___domain. It looks for all the world like a single frequency with rapid variations in amplitude (which can be accomplished by bubbling the air through a carefully-controlled reservoir of saliva). If you can mimic the time-___domain signal, you can mimic the frequency-___domain signal, since they're just two ways of looking at the same thing.
I tried to find a friend to train with me so we could do DTMF, or rather CCITT #5.
I could whistle the 2400hz and 2600hz reasonably well (not at the same time) which allowed me to hang up on international calls if I wanted to.
Oh, I was also pretty adept at war-dialing manually in the dark. Dialing numbers in sequence, but then switched the light on and wrote down the details if I found a modem or a controllable voice mail or pbx system.
I don't know about whistling, but tone mis-detections were fairly common in the early days with some folks' voices, and they still arise in a few of the systems.
We tried to reduce this mis-detection within the hardware and software of a voice response system back in the early 1990s. This commonly involved intentionally requiring longer tone input detection before the tone action was triggered, but it was left programmable for the end-users.
I know someone that still triggering a tone detection in a conferencing system within the last few years; she'd end up muting herself in the call, which lead to appreciable frustration.
If you look at the standard 3x4 phone number grid, each row or column had a specific frequency assigned to it. A single button would play both the row and column tones simultaneously.
edit: I just remembered, it's actually 4x4. There is a fourth column labelled ABCD. Forget what it's used for. I was mostly a theoretical phreak :)
The 6 extra keys (*, #, A, B, C, and D) where meant to be used for remote control of devices attached to the telephone network. They were heavily used for test equipment. Another use was in the old Army AUTOVON system where the letters were mapped to call precedence levels.
You can't generate DTMF tones with throat singing. I do some throat singing, and a better name for it is overtone singing. You're not producing two different fundamental tones as DTMF would require, you're producing one fundamental tone and then emphasizing and suppressing various harmonics (overtones).
