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.

:D

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 :P

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.

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.

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

I kind of wish this thread was locked. I don't want to be criticized any more for saying that primes are the biggest problem. Nevermind, OK? And yes, there is doubt that that equation I gave always generates a prime, because you can't really inductively prove things with primes. I sorely apologize for my ignorance having to do with math, and I hope that I'm not banned from the forum.

I kind of wish this thread was locked. I don't want to be criticized any more for saying that primes are the biggest problem. Nevermind, OK? And yes, there is doubt that that equation I gave always generates a prime, because you can't really inductively prove things with primes. I sorely apologize for my ignorance having to do with math, and I hope that I'm not banned from the forum.

Dan

Please do not worry about this. I was not criticizing you either. You obviously know some math, and most work in math today revolves around prime numbers. That is in algebra, geometry (which few work in today) and analysis. Prime numbers are a focal point in all aspects of math. Making codes and more importantly, breaking codes, is the largest realm of Math today and that is all prime numbers and abstract algebra.

All interesting stuff.

Ron

Dan

Please do not worry about this. I was not criticizing you either. You obviously know some math, and most work in math today revolves around prime numbers. That is in algebra, geometry (which few work in today) and analysis. Prime numbers are a focal point in all aspects of math. Making codes and more importantly, breaking codes, is the largest realm of Math today and that is all prime numbers and abstract algebra.

All interesting stuff.

Ron

Really? I never knew prime numbers came into play in my research of non-linear PDE and Chaos Dynamics. Please don't make absurd statements.

P versus NP

The Hodge Conjecture

The Poincar

That list with major maths problems is a complete ripoff off wikipedia :(

You could just take a prime number and add "Hz" next to it and make it into a frequency. And for frequencies below/above the audible range, you could just multiply it by two (i.e. raise it by an octave) until it's inside the range.

Although I'd find such a procedure a bit meaningless - primes are interesting but using primes just for the sake of using primes can be a bit silly. I used irrational numbers to derive the pitches (their decimal points, actually), and I used prime numbers to shape the form of the piece. The reason I used these two numbers is because a) the string instruments can produce a seemingly infinite stream of sound, so the infinity of irrational numbers fits their nature, and prime numbers are the opposite of irrational numbers in a way: primes are numbers which can't be represented as the multiple of two integer numbers (other than themselves and 1) whereas irrational numbers are numbers which can't be represented as the quotient of two integer numbers.

But that's a bit more specialised and thought for than just using primes with pitches.

But then again, you can do whatever you want, no one's restricting you. However, if you want to use primes in your music, then make sure that you know everything you need to know in order to use primes in your music (and if you don't know, then go find out just like other people have in the past) instead of asking other people about it, otherwise it will make you look like a fool, just like DOFTS showed :)

That list with major maths problems is a complete ripoff off wikipedia :(

Actually it's a rip off of the millennium problems. I'm not sure why these problem sure are millennium problems. I guess Hilbert's speech was quite moving (oddly enough no one went to hear him). Oh well!

and I hope that I'm not banned from the forum.

Wha...?

...

Where do you come from (forum or real life) where they 'ban' you for "ignorance"...?

WTF?

So you want to use numbers such as 2 3 5 7 9 etc to find a certain Hz?

Tsk, tsk. A mathematican speaking of 9 as a prime number? :P

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?

If somebody already said it, I missed it: No, that's not wavelength, but frequency, i.e. the number of times the wave "passes your ear" per second. Wavelength would be the length of the wave in metres.

But here's the first 100 prime numbers (up to 541 Hz) as frequencies in a row: Click here to watch Prime-numbers-as-Frequencies I stopped at 100 because typing numbers is boring, but I don't think it would sound significantly different with higher numbers. And of course you won't hear anything the first few seconds as those prime numbers are in sub-audio range.

Thanks so much gardener! I really appreciate it.

And I was being sarcastic about being thrown off the forum for my sheer ignorance.

Oh thank christ for that.

Yawn

I don't see the appeal of mixing and matching natural numbers (discrete) and sound frequencies (continuum). The mystique of primes would be lost because of arbitrary (though conventional) frequency units (i.e. Hz depends on the definition of second, nm depends on definition of meter).

Tsk, tsk. A mathematican speaking of 9 as a prime number? :P

Figured something was funny about that. Oh well!

I don't see the appeal of mixing and matching natural numbers (discrete) and sound frequencies (continuum). The mystique of primes would be lost because of arbitrary (though conventional) frequency units (i.e. Hz depends on the definition of second, nm depends on definition of meter).

The arbitrariness of what 1 Hz is doesn't really matter though, since the proportions between the primes still stay the same. If, say, Hertz was defined as oscillation per 2 seconds, the resulting tone row would be just an octave lower, but the intervals would stay the same.

I don't find prime numbers as frequencies very interesting musically per se but they do have musical uses: Sometimes you need to use numbers that have no common denominator in computer music, for which prime numbers are of course an excellent source.

My only thought is that as primes occur at a somewhat close-to-predictable pattern (near a logarithmic function i cant remember right now, when plotted as a graph) the music would sound too predictable. I think using functions without a "fractal" component most of them creates boring stuff. Not being an expert the idea in the original post is worth at try.

Check some sites on fractal music if you find computer (or algorithmic) generated music as a topic interesting. I did want to write such a program once, but my knowledge is not really updated recently ;)

True, they are slightly predictable. (not completely, other wise there would be function to out put only/all prime numbers)

if you want a more interesting graph, (might produce more interesting music), graph the rate of change of the prime numbers. looks kindof sinusoidal (if i spelt that right). this reminds me more of sound than just straight prime numbers.