Pitches and Prime Numbers?

These days, the greatest problem in math is primes. If we only understood a pattern in primes, we could do so much more with math than we are already doing.

Anyways, primes are pretty interesting. There are some things we know, such as X^2 + 41X + 1 always generates a prime. But that doesn't account for all the other ones!

I wanted to plug prime numbers in as wavelengths into some sort of generator and work with the pitches they correspond to. I imagine that plugging primes in as wavelengths would generate mostly a series of randomly ascending pitches (which, because primes are generally close together would just get smaller going up until the differences in pitch were inaudible.) However, I only have Finale and see no obvious way to get it to play back a pitch per wavelength. Does anyone have a program / internet app that I could use / they could use to generate 100 or so pitches with prime wavelengths?

Who knows, maybe there is some inherent connection between primes and the series of harmonics, or has some inherent connection with some other aspect of music. It's doubtful, but it's worth a try!

(I doubt it actually is related to harmonics, since harmonics are all based on divisions of values, which is the antithesis of prime numbers!)

You could calculate the pitch yourself - I think, as the frequency determines the pitch, and frequency varies inversely to wavelength (f = V/λ, with V being the speed of sound perhaps?). Once you have your pitches I'm not sure how you would go about manipulating them - maybe try looking for some sort of computer program that would play back any frequency, then sample them and make a synth or something...

I have no idea if any of the above can be done, or even makes sense.



Good luck.

I hope you don't see the speed of light

f = (345m/s)/wavelength. (345 m/s is used here because we are talking about sound.) So you want to use numbers such as 2 3 5 7 9 etc to find a certain Hz? Hm so your first Hz would be around 172.5.

Then you want to play them? You'll have very small window to work with. Good luck though, you might have to program some of the stuff yourself. I just fail to see why you want to do this.

Side note, I hope you have fun calculating how these things occur outside a vacuum, but meh who am I to talk.

Side note number 2: I resent the notion that prime number is the greatest problem in mathematics. Correction: It's the greatest problem for number theorist. Last time I checked, that's a rather small group of mathematicians. For most of us, it's a neat thing, but not really oh so important.

Mark: I could calculate the pitch myself, but I need something to generate the actual pitches so I can hear them and manipulate them. The won't line up nicely with scale-tones, I don't think.

What I mean by going from wavelength to pitch is like, if A above middle C is 440. And the A above that is 880. That's wavelength, isn't it?

DOFTS: You're kind of mean. And the reason I want to do it is to see if any pattern emerges. It's like trying to see if Dark Side of the Moon lines up in a significant way with The Wizard of Oz.

I'm so sorry you resent me saying that primes are the biggest problem. If primes are not, what is the biggest problem for mathematicians?

I agree with DOFTS about the prime thing though - there are far more exciting things going on in maths than prime numbers

Originally Posted by Dan Gilbert

Mark: I could calculate the pitch myself, but I need something to generate the actual pitches so I can hear them and manipulate them. The won't line up nicely with scale-tones, I don't think.

What I mean by going from wavelength to pitch is like, if A above middle C is 440. And the A above that is 880. That's wavelength, isn't it?

DOFTS: You're kind of mean. And the reason I want to do it is to see if any pattern emerges. It's like trying to see if Dark Side of the Moon lines up in a significant way with The Wizard of Oz.

I'm so sorry you resent me saying that primes are the biggest problem. If primes are not, what is the biggest problem for mathematicians?

I'm kind of mean? I wished you luck, do you want me to program something for you? Not going to happen. Your best chance for doing this is to program something that can do this or find a program that simply produces pitches a modify it to suit your needs. (Since you only want to see a pattern, you can do this purely mentally. I've figured out the HZ for the first 1,000 primes without pen and paper, I'm sure you could do likewise and notice the same thing I have. And in cause you are wonder the Hz for 1,000 would be .0435666...)

I'm not sure what pattern you expect to find. Merely doing some pure theoretical work on this problem, it's fairly easily seen that the Hz you will find will be of the order of wave/prime which will produce a somewhat-prime pattern. It wouldn't take a genius. In a more particle sense, it won't produce that (unless is monocrhomatic) because the wavelength will have to change dramatically for the theoretical Hz to happen, but that cannot occur since you placed the limit on the wavelength.

As for prime numbers, I do not resent you, I resent the notion. Prime numbers is not the greatest problem presented in mathematics. There exist no such problem. It probably is the most important within number theory, but I fail to see how it matters to geometry, algebra, analysis, etc.

If you want my opinion, P VS NP is pretty damn important. More useful in the real world, and applies to everything from computer science, logic, graph theory, analysis, number theory, and many more.

I'm pretty sure you can input pure sine waves into Audacity at any frequency you wish... try that, I suppose. (Maybe Reaper does it too, I'm too lazy to check right now.)

Thanks Enigmus!

And DOFTS, prime numbers apply to all of those fields you mentioned.

Originally Posted by Dan Gilbert

Thanks Enigmus!

And DOFTS, prime numbers apply to all of those fields you mentioned.

Same with P vs NP. That isn't the point though. Prime numbers generate the greatest interest from number theorist. I fail to see how you can say it is the greatest problem in mathematics. Distribution of prime may be important, it may be interesting, and it may be hard, but I do not think it is the greatest. I also think it's absurd to say anything problem is the greatest.

Just like physics has pop-science, we have pop-math, and sadly, prime numbers have fallen into that realm.

Originally Posted by Dan Gilbert

These days, the greatest problem in math is primes. If we only understood a pattern in primes, we could do so much more with math than we are already doing.

Anyways, primes are pretty interesting. There are some things we know, such as X^2 + 41X + 1 always generates a prime. But that doesn't account for all the other ones!

Dan

Sorry

That is not always true. There is no algorithm that can generate a prime number with 100% probablity. There is always a doubt.

You can purchase prime numbers for codes and such that are over 200 digits long, but they can still not be positive that the number is prime. To prove that it is, it would take all of the computers in the world working for the lifetime of the universe and they would still need more time checking out a large number.

But if you could find an algorithm that was capable, using todays computers, to show whether or not if a large number (200 plus digits) was prime, you would become a millionaire overnight. But then a lot of people would want you dead as well.

Although no one has proven it yet, it is generally accepted in the math community that such an algorithm does not exist.

Most people still use Eratosthenes sieve to figure out if a number is prime or not and that is over 2000 years old.

I would say that one of the big tasks in Math today is not to find an algorithm to find prime numbers, but to prove that one does not exist.

Most of the guys here don't really know what Math is all about. They have probably never heard of Gauss or Euler or for that matter, Eratosthenes.

The upper levels of Math (especially number theory) are just a type of mental masturbation that mathematicians love to do.

BTW Guess what my major is?

Ron