I was asking for a mathematical proof of how a 900hz tone and a 350hz tone resolve to a beating at 550hz?

Do you understand that what you just explained applies to any combination of two tones?

The implication of that being that you may find that many of the pleasing combinations have already been identified.

I'm curious to learn how 900hz and 350hz resolve to 550hz.


I have a friend who was selected 3 Tibetan singing bowls out of a collection of hundreds that he was able to choose from. He knows that the ones he selected are particularly ancient and imbued with spiritual magic.

He places the bowls on and around people in near proximity and sets up beating waves that he feels offer a sort of acoustic therapy.

I have analyzed his three special bowls on a spectrum analyzer... what I found is that he has discovered the G C F triad.

They do sound very nice together.

He can not even begin to fathom what the spectrum analyzer and I am trying to explain to him about the science behind his instinctive choice. It's magic.

Here is an example of his work... this done with another set of bowls:

http://www.harmoniccycle....nastary%20approach.mp3

Leaving artistic questions aside (How can anyone judge something that hasn't been created yet and they've never heard?), I'd say you just need a synth/sampler that produces very pure sine waves and, very importantly, allows for alternative tunings. I'd probably look at an FM synth, as sine waves are their stock and trade, and I'd expect them to be fairly "pure" sine waves.

You then need to adjust the tuning of each key to the exact mathematical frequency you're looking for. Some synths don't allow you to tune each key but have a number of preset tunings. But you may find that a preset tuning, like "just tuning" is exactly what you're looking for:
http://en.wikipedia.org/wiki/Just_intonation

I'm curious to learn how 900hz and 350hz resolve to 550hz.

Intermodulation. 900-350=550.
Actually, both the sum and the difference components are created (900+350=1250). So if two signals of 900 and 350 hz are added, two new beating frequency components appear at 550 and 1250 Hz.
 

But don't the two frequencies have to be close in frequency in order for a "beat" frequency to be heard? I'd suspect that 900 and 350Hz are way too far apart for this effect. But I'd love to know otherwise.

Thanks Jose.

I see the article mentions a 10hz shift as sweet combo of paired tones.

It makes me think of BB King and his trilling hand.

If you use a MIDI synth that responds to microtuning you might be set on what you want to do.

The MIDI standard does have messages to control micro-tuning capable synths.

It can be hardware of software synth, but it has to have the micro-tuning capability.

if a 900 Hz sine wave is played into the right ear and a 350 Hz one into the left ear, the brain is entrained towards the beat frequency 550 Hz

Well, I wasn't going to ask but now you've got my curiosity sparked.

To answer Mike's question, 550 is simply the difference between 350 and 900. There will also be a sum frequency generated at 1250Hz. Of course, if the two tones are anything other than sine waves, there will also be many other frequencies generated representing the sums and differences of all the harmonics plus the resulting sum and difference frequencies of the other synthesized sums and differences. Mixing just two tones can result in a surprisingly large number of of beat frequencies - most of which are inharmonic and most of which are unpleasant!

Google the name Diana Deutsch if you want to hear some mind-blowing audio phenomena. She is an expert in psychoacoustics at the University of California San Diego. Here's an interesting list of some of the better-known audio illusions, including some of Deutsch's discoveries. Trippy stuff.

I'd be curious to know if there is any magic frequency or combination of frequencies or critical bands that can trigger instant nirvana in anyone who hears them. I suspect there is not. Our perception of sound is as uniquely individual as all of our other senses.

It would really suck if we found out that the frequency that lowers blood pressure is 18KHz, when I can only hear 16.

Hey Bit that ascending chord (Shepard's paradox) illusion really is weird.... I cant stop playing it and trying to figure out how that goes !

I'd be curious to know if there is any magic frequency or combination of frequencies or critical bands that can trigger instant nirvana in anyone who hears them. I suspect there is not. Our perception of sound is as uniquely individual as all of our other senses.

that would be the "lost chord"  - it exists, you just can't find it...






I'd better put a smiley in just so everyone knows I'm joking...

Hey Bitflipper - freaky stuff cheers mate!
"...No brain no gain no rain dont wait wont work no wait go grain no way...."