#harmonic series

[victusinveritas]

The top image is a graph of the first nine harmonics of a harmonic series. The bottom image is an x-ray of the inner structure of a conch shell.

[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.

[keepscrollinghun]

[ahorrorstorycircle]

The first episode of 'American Horror Story' aired 13 years ago.

[userfilmgifs]

THE QUEEN'S GAMBIT (2020)

[adeleine-everyday]

day 136

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

[diettcherryc0kee]

tomorrows outfit

˚　　　　✦　　　.　　. 　 ˚　.　　　　　 . ✦　　　 　˚　　　　 . ★⋆.

　　　.   　　˚　　 　　*　　 　　✦　　　.　　.　　　✦　˚ 　　　　 ˚　.˚　　　　✦　　　.　　. 　 ˚　.　　　　 　　 　　　　 　

[bullet-prooflove]

USS Allegiance Series Part One: Baby On Board - Harmon Rabb x Reader

Tagging: @kmc1989 @dizzybee03 @buckysteveloki-me @sca3a @burningpeachpuppy

Companion series to:

Flight Deck - It starts on the flight deck of the USS Allegiance.

Hourglass - You remember the moment you fell in love with Harm.

New Orleans (NSFW) - Harm wakes up the next morning to find you wearing his shirt.

The USS Allegiance is five hours away from port when Harm is notified about the newborn his Watch Commander finds in a rarely used storage hold. At first he thinks it’s a joke because to his knowledge he has no pregnant sailors upon his ship but it turns out to be the furthest thing from it.

“She’s in good health considering she’s a few weeks early.” He’s told by the ship’s doctor as he tickles the baby under the chin. “She needs airlifting to the nearest NICU, we’re not equipped to deal with her on board the carrier.”

“I’ll make the arrangements.” He promises as he looks down at the child.

A couple of hours old and all alone in the world…

It breaks his damn heart.

It’s only when he’s standing there, his fingertip clutched in the hand of the tiny newborn that the reality of the situation crashes down on him. They have possibly distraught mother AWOL on their ship. The urgency of the circumstances is compounded by the fact that they didn’t find the placenta with the newborn which means there’s a high chance of sepsis or haemorrhaging.  

It’s by a stroke of luck that you’re currently stationed nearby in Sydney, attached to Michelle Mackey’s team. His agent afloat is too green, he’s barely been with them a week and Harm can see his head practically spinning with the complexity of this problem. When Michelle sends you he’s relieved, not just because you have mental health training but because he knows the investigation is in safe hands.

He’s there to greet you when you step off the chopper and onto his flight deck. You have his duffle bag slung over your shoulder, the one with all his Aviation patches on. He’d given it to you when you’d made the transfer from LA.

“A little piece of me to keep with you.” He had whispered against your lips as he’d kissed you goodbye on the doorstep.

“Captain.” You greet as you pull off your helmet and his breath catches in his throat.

You’re just as beautiful as the day he deployed, a little more tanned, a little more freckled. Sydney seems agrees with you. The scent of the sea clings to your skin and he wonders if you’ve been surfing this morning. It’s something you’d taken up when you were residing back in Hawaii and it’s continued during your time in Australia. You and JD went out every couple of days, usually before work.

“I hear you had an unexpected visitor this morning.” You say interrupting his thoughts and he clears his throat, falling into step alongside of you.

“That would be correct.” He tells you heading towards the ship’s interior. “We’re keeping it quiet, we don’t want to spook the mom.”

He pulls open the door, gesturing for you to step inside. The back of your hand brushes against his and he captures your fingers, squeezing them for a second before releasing them.

“It really is good to see you.” He murmurs as you drift past him and you smile as you tilt your head towards him and say.

“I’m sure you’ll get to see a lot more of me after we get to the bottom of this.”

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[mediademon]

Anya Taylor Joy as Beth Harmon

[televsion]

Anya Taylor-Joy as Beth Harmon The Queen's Gambit (2020) Season 1

[rosebathe]

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

[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.

[haveyouseenthisseries-poll]