Given a length of exactly 3 minutes, how many different songs

A lot

>>7705383
Depends on bitdepth and sample rate.

If you're talking about a more "analog" delivery / medium, not even modern physics knows the answer to that. Though you could, and likely would, take average data about human perception and human ear function, and derive an answer based on that.

It would only be an approximation.

Aleph 3

the powerset of the powerset of countable infinity

>>7705383

What does that even mean? 3 minutes of stored songs on a medium? Played? What about if you just increase the BPM to 200000? Do you want to factor that, too? Are they the same song? Different songs? I mean, that along would account for endless variations. Do you define songs by only their notes? Perhaps different instruments mean different songs?

Jesus fucking Christ, OP, define your parameters.

>>7705391
Except that's wrong, if you don't assume the generalised continuum hypothesis.

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>>7705391
Infinity is moronic. ie, I don't like it and demand that you don't either.

>>7705397
>not assuming things that are obviously true

shut up, nerd.

>>7705393
does he need ot spell it out for you?

A song is sound over time, and so a waveform, so there are at least as many songs as there are continuous functions over an interval

>>7705393
Well a song is just a bunch of frequencies, so

How many unique arrangements / patterns of frequencies can be created given a set time of 180 seconds

192kbit/s in a good mp3
180 secs are 3 minutes
Now calculate the possibilities, think its 180!*192

>>7705401
http://www.livescience.com/1212-sound-pulses-exceed-speed-light.html

I mean, technically.

>>7705419
Faggot smd. Music exists in the real world too faggot.

>>7705410
Like, literally infinitely many. The best you could do is up to Planck length, but that's not necessarily the smallest length.

>>7705524
This.

>>7705419
I think it's (2^192k)^180

>>7705524
But pop music provides heuristic evidence that only about four different songs exist, anon.

>>7705419
>192kbit/s in a good mp3
Maybe if you are fucking deaf.

>>7705386
>>7705391
>>7705448

check out Lambdoma and be amazed

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>>7705728
That is correct (unlike >>7705419 ,where did you even get the factorial from?)
2^(192000*3*60) evaluates to aboout 10^(10^7)
Anyone know how to put that in knuth's up arrow notation?

>>7705391
where are you getting countable infinity from?

i'm kinda going off of >>7705410 here to make my point but wouldn't there be an uncountably infinite amount of possible frequencies (like 2306.40395049... Hz or whatever) or am i missing something

>>7705524
Not infinite if you restrict the frequencies used in each song to the limits of human hearing, or the number of possible combinations of bits in a digitally-sampled audio file.

>>7705989
there are infinitely many frequencies within the range of human hearing

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>>7705999
no

>>7705999
yes, but you can most people cant tell the difference between 440.0Hz and 440.1Hz

bout tree fiddy

>>7705383

Sampling at 44KHz @ 8bits => 2^63360000

>>7705384

/thread

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kool

>>7705448
biject all real world sound to their electronic representation

The autism in this thread is through the fucking roof. Altering a frequency 1 billionth of a Hz does not make it a fucking different song. Seriously, you guys are pathetic to argue this shit.

>>7706548
it is if you're a math major
now go back to engineering

>>7706548
>Seriously, you guys are pathetic to argue this shit.
So at what point does the average human brain perceive something as truly unique? Not as a subset or derivative of some core original?

Not so easy now, is it, fucker. I've tried to write heuristics to do this. Psychoacoustic models are not easy, and they're inherently unsatisfying unless they're near perfect. Crude approximations simply will not do.

>>7705732
kek

>>7706548
It makes for a big number though. I bet you don't even wanna know how hot the sun is.

3^3=3 QED 3. 3 songs

How many audio-less videos of exactly 30 minutes length at a resolution of 1280 x 960 and a frame rate of 30 frames per second could possibly be made?

>>7709199
(1280 x 960 x ~65 000 000)! x 30 x 30 x 60

At least I think so.