#harmonic series

[greetings-inferiors]

It really fucks with me that the area under the curve y=x^-1 is undefined between [1,infinity].

Like look at the curve

The area gets smaller and smaller

But it still tends to infinity?

This is mostly a gripe with the harmonic series because what the actual fuck

You’re telling me that the harmonic series is equal to ln(n) with just some random constant added to it? What the fuck? When I found out that was such a cop out. Like c’mon really?

Euler’s constant is my least favourite constant solely because this offends me

[minotaurmerkaba]

[orchidsslideontongues]

[oneefin]

i usually find youtube comments sections pretty low-brain, but one of my favorite bits of cleverness i've ever seen came from a youtube comment under a math video of someone explaining how they did it using music theory. and this is right up my alley so i'm going to break it down.

the problem in the video was "approximate log_2(3) without a calculator", and they did it using purely mathematical methods and a tiny bit of memorization. but you can actually do this with a basic understanding of tuning theory:

basically, there's this thing in music called the harmonic series. its a sequence of notes starting from some root pitch and ascending in whole number multiples of that pitch. for example, if you start from C:

each note in this sequence has a frequency n times the frequency of C5. get it?

now, even though this would be the "perfect" way to tune things, we don't actually tune notes this way - because it doesn't work if you change your root note. instead, western music is tuned to what's called 12-tone equal temperment (12tet), in which the ratio between two adjacent notes is exactly the same:

the ratio x is picked such that an octave is still x2. so x turns out to be the 12th root of 2.

anyway, how does this help with the original problem? well, these concepts give us two ways to think about a similar musical interval. consider the difference between C and G:

in the harmonic series, this distance is a x3 multiplication. however, in 12tet, this is 19 steps, each multiplying by the 12th root of 2. written another way, that gives 19/12 = log_2(3).

19/12 is 1.58333..., while log_2(3) is about 1.585. that's accurate to two decimal places.

in fact, the approximation isn't just really close - it can be considered optimally good among other fractions of a similar length. that's because mathematicians have a way to derive best fractional approximations for any irrational number, and on that list for log_2(3), 19/12 is there:

that's a cool solution to an arbitrary math problem, but also it's quite cool from a music theory perspective! it gives a reason for why it's not only appropriate for the western scale to has 12 notes in it, but that it'd be surprising for it not to have 12 notes in it, given that 19/12 approximates the 3rd note in the harmonic series so well.

[kelemengabi]

golden ratio

[adeleine-everyday]

day 136

funky piano (based on that one 64 minigame concept art)

[mediademon]

Anya Taylor Joy as Beth Harmon

[best-character-named-x-poll]

have you done your daily click

[rosebathe]

The Queen's Gambit (2020) dir. Scott Frank

[haveyouseenthisseries-poll]

[bullet-prooflove]

Chevy Corvette: Harmon Rabb x Reader

Tagging: @keyweegirlie@dizzybee03@snowlover250@kenbechillin@too-strong-to-lose

You are the only woman that Harm has ever let drive his 1969 Cherry Red Corvette ‘Betty’. He’s away six months out of the year and you are the only person he trusts to give her a run around to keep the engine tipping over.

“Drive her to work a couple of days a week or take her out at the weekend.” He requests as he hands over the keys before his latest deployment.

“I’ll make sure to keep your darling happy.” You tease as you place the keys in the drawer by the front door. “Just make sure to keep this darling happy too.”

He smiles at you then with that wolfish grin of his before he takes you bed.

“How’s my baby doing?” He asks when he calls a month later from the USS Allegiance.

You’re standing outside in the sun back in Washington. You have his aviators perched on your head, pushing back your loose hair as you sit inside the Corvette in the parking lot at work.

“Do you mean me or the car?” You ask him and he can’t help but laugh.

“Why not both?” He responds as he adjusts the picture he has beside his bunk. It’s the one of you leaning against the Chevy in nothing but a denim shorts and a white vest top. It had been taken a couple of months ago when he’d told you about the deployment.

“Let me give you something to think about while you’re away.” You’d whispered in his ear, as your fingers curled in his hair. “Any fantasy, anything that’s going to keep you thinking of me when you’re away.”

“There is one thing…” He’d said.

He’s always had a thing for pretty girls and fast cars.  

You’d fulfilled that fantasy and then some. You’re the only woman he’s ever fucked in the Corvette. If that isn’t love, he doesn’t know what it is.

“Have you given any thought to the other thing we talked about?” He asks you as he sits down on the edge of his rig and runs his hand through his dark hair.

“I have.” You say quietly, looking at the antique engagement ring on your finger, the one Harm had left on your nightstand the morning before he left.

“Just think about it.” He’d whispered as he’d smoothed the hair away from your sleepy features. “There’s no pressure.”

“I’ve given it a lot of thought.” You tell him, your thumb chasing over the pretty silver band.  “And I think I’m ready to marry you Captain Rabb.”

Love Harm? Don’t miss any of his stories by joining the taglist here.

Like My Work? - Why Not Buy Me A Coffee

[giftedpoison]

It boggles my braincells sometimes thinking about how some people just weren't heavily influenced by their media as I was??? Like when i was kid i grew up reading Gallagher Girls and watching House of Anubis so duh I learned to pick locks, want to learn as many languages as possible, and martial arts. (And also is why I never see lying as a bad thing but a skill.) (Reading Alias and Red Blazer Girls was also a heavy contributor)

Or I started learning ASL because of a tv show I watched in middle school (switched at birth- unsurprising) but now I love the language because I love being able to communicate without talking (although that's more small words that i teach people the meaning so i don't have to use my voice) and learning about the Deaf community.

Or learning sleight of hand because of Kaz Brekker. Chess because of Beth Harmon (I'm determined I'd be pretty good at it if I could just figure out the middle game) Like pick a hobby i have and i'll tell you which fictional character gave it to me. (with the exception of reading, music, writing, researching, and art) These are all exceptionally useless capabilities (other than maybe language learning and lying and you can make an argument that martial arts is a lifetime fitness) and yet they mean a fuck ton to me.

[naota-gray]

The Queen's Gambit (2020)

[kelemengabi]

Flower of life pentagon octave

[mediademon]

The Queen's Gambit (2020)

Openings