Tone Waveform and Monaural Beats

Since last Monday I’ve been enjoying watching the progress of my Picoscope 2203 USB oscilloscope/spectrum analyser/arbitrary waveform generator from (best price and shipping rates). UPS do a great job with their Quantum View tracking software – my little package has made its way from New York, to Kentucky, to Hawaii, to Australia, and to Auckland NZ before it disappeared into the NZ system and will hopefully emerge in Wellington on Monday.

In the meantime, I’ve been having a great time familiarising myself with the software. You can download the Picoscope Software free of charge and play with it in demo mode. This allows you to use two independently controllable tone generators to see what different frequencies and waveforms look like and how they interact. An especially powerful feature is the Maths Channel, which allows the two waveforms to be combined in all manner of ways. The software is a great toy all on its own, but, of course, the real fun starts when it’s used with the USB device that allows you to look at real-world signals, such as the output to headphones and glasses from mind machines and the likes of NP2/MWS.

To explore monaural beats (and, indirectly, binaurals), I set up one tone at 200Hz and the other at 210Hz – a 10Hz difference. I’ve set up a Maths Channel simply adding the two, as occurs in the formation of a monaural beat, to highlight the interaction in the display – it’s much harder to see with just the two source signals.

Here’s the output when both tones are sine waves…



What we see here is a very clear pair of peaks at 200Hz and 210Hz in the spectrum view (bottom) and a 10Hz pattern plainly evident through the higher tone frequencies in the oscilloscope view (top).

Note that the software is using 8-bit synthesis and measurement, so there is a certain amount of noise generated by the imperfect sine wave. The same effect will be found when examining the 8-bit or 16-bit output from mind machines or PC applications. Obviously 16-bit audio is going to be cleaner than 8-bit.

Replacing one of the sine waves with a square wave creates this…



The dominant peaks at 200Hz and 210Hz are still visible, but we also have harmonics at 10Hz spacing above and below the target. In the oscilloscope view it’s much harder to see the underlying 10Hz beat.

Changing both waveforms to square gives us this…



The spectrum is a complete dog’s breakfast of harmonics, with the 200Hz and 210Hz peaks barely holding their own. The oscilloscope view is massively different to the previous ones, with the 10Hz appearing more as pulse modulation than amplitude modulation.

I won’t bore you with samples using triangle waveforms – they are pretty much between sine and square, with more harmonics than sine, and less than square.

The upshot of all of this is that a monaural beat formed with anything other than sine waves will contain a lot of probably unintended frequencies. The sounds may be more interesting, but the targeting of effect will be lost. Any deviation from a pure sine wave will increase harmonics and reduce the definition of the beat. This is a matter of choice for monaurals, but is critical for binaurals – the likelihood of experiencing binaural perception diminishes rapidly as the waveforms depart from sine shape.

Keeping in mind that we are looking for evoked responses to the stimulus, it is clear that the less rubbish our brain has to pick through, the more likely it is to respond to our target frequency.

I’ll put together a similar examination of isochronic beat formation in a future post.


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