#log-a-rhythms

[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.

[pownicmania5000]

GO MY WHITE TUTORIAL CHILDREN

NEXT YEAR IS OUR TIME

[junior-spaceclaw]

for a while until one rewatch of npmd where i was actually looking at the subtitles during the line - i had always thought until that point the line during 'literal monster' went 'he's the whore in every rumour' not 'horror' and i did not question it at all i mean considering the other lines like 'the hottest girl yeah he knocked her' and 'you have a girl he'll seduce her' i just completely went 'yeah ok he's a whore that makes sense'

[sleeping-realist-waking-dreamer]

please let frye struggle to dance again

please let her try and struggle to do all the things she wants to do and itches to do but is physically unable to

please let her realise that being healthy isn't just going to fix her knee and shes going to keep pushing herself but its only going to make things worse and she just has to accept herself for who she is now and her capabilities now.

even if she dances again it wont be the same and it can never be the same because of her knee. she has to rest so much more despite how she wishes to just be able to move and dance.

ALSO LET MECHANIC SHIVER AND BIG MAN BE HER THERAPIST

otherwise ill have to be a fanfic writer is all 🤧

[ettawritesnstudies]

maybe its not strictly legal to renew your childhood library card using your parents' home address but it makes me happy that I still have the barcode digits memorized

[rotglass]

Beat Saber // Wet Dream - Wet Leg

getting back into more of a VR routine, which means im cycling back into beat saber yet again :3 love this song

i'm very much out of practice from how i used to be, but getting back to that level is part of the fun !

def need to adjust camera settings for recording beat saber, but thats always a long process ahah

[salty-an-disco]

brain huuuurrrrrts

but I managed to start writing a thing

[heatwa-ves]

guys I miss her

[nomiyakazehaya]

the way i just randomly want to see dragon mama!megatron with her little sparklings (hatchlings?)… 🥺😭

[brbuttons]

Do expect, as we use Tumblr more, to see the odd system ramble and roam. The call of the static, embracing the void, a flow of thought that calls like home.

The true unmasked. But only for some of us.

We are fine. Maybe. Perhaps.

But I am happy. Maybe. Perhaps.

What is happy?

[rubyrhythmposts-archive]

i just logged in wtf is going on

[pepimeinrad]

list of TV shows I watched in 2023: (bold: shows that had new episodes out this year, brackets: I only watched the new eps, not the whole show again)

Murder Rooms The Night Manager Why didn't they ask Evans? Cambridge Spies Star Trek TNG Star Trek Picard Tage, die es nicht gab Star Trek Prodigy Succession (Ted Lasso) Kohlrabenschwarz Arcane Good Omens Heartstopper (Only Murders in The Building) (Star Trek Lower Decks) Sex Education Our Flag Means Death BBC Ghosts (Doctor Who) BBC Rev. TV shows I (re)watched a substantial part of (with some system behind it): Wizards of Waverly Place Star Trek DS9 Boston Legal Star Trek Voyager The Thick Of It

[caramelmochacrow]

BANDORI PLEASE SPARE ME AND MY LOW STORAGE PHONE!!!!!!!

[shoutlikethewolf]

I am physically unable to stop replaying dd’s new song

[sisyphusshrugged]

so i think smoking does actually help me fall asleep, but makes it harder to wake up. gotta keep tinkering with all this until i can get my rhythm working how i want.

[aogmgoose]

Week 11 (Lecture Reflection) – Rhythm Games

For many years, rhythm games have been an afterthought for me, but they've experienced a resurgence in recent years, driven by the popularity of Clone Hero and OSU – some of these games even have their own esports scenes. These rhythm games are inherently arcade and tactile (despite being played in the household). For clone heroes, the tactile functions and feedback are delivered through a guitar arcade controller. As for OSU, many players swapped out their mice and mousepads, opting instead to use graphic design drawing tablets to better track movements. This became so popular that tablet manufacturers like Wacom actually embraced (and promoted) their tablets for OSU.

References -

(Carpenter 2019) - "Gamers with godlike reflexes are racing to break world records in this rhythm game." PC Gamer, 2019. Accessed 23/05/2025. https://www.pcgamer.com/two-teens-are-on-a-crazy-world-record-race-in-extremely-challenging-rhythm-game-osu/.

(Clone Hero 2023) - "CH esports: CSC:CS3 and Birdman Drum Tournament." [Website]. Accessed 23/05/2025. https://clonehero.net/2023/01/07/csccs3-birdman.html.

(KoiFishu 2021) - "RANKING EVERY OSU! TABLET." YouTube, 13/03/2021. https://www.youtube.com/watch?v=mUaZxp4Uj6Q.

(Wacom 2024) - "Wacom pen tablets – preferred by osu! players worldwide." Accessed 23/05/2025. https://estore.wacom.com/en-us/osu