The Rhythm of The Primes  

you didnt make an inverted harmonic series, you made the normal harmonic series with a scalar lol

Awesome video! Can you help with a similar music project? Planets like Saturn have rings of asteroids. They remind me of a vinyl record or CD. If we had a high-res image of Saturn, could it set to music?

For those of you!

Quite a few years ago I made an array of primes and then using bitwise math triggered midi notes in the same key as bits 3 through 12 or so turned on in the integers as the array was cycled through, the bits acting like the pegs in a music box. It played an interesting song. I also painted a picture with the bits of primes in a strip. Low bits at the top. If the bit were on I drew a small line on the screen down to about 24 bits or so. The ribbon of primes was ghastly looking, bizarre, never repeating. With the same algorithm if you painted all integers the strip looks like a pristine orderly mountain range, but the prime version was ugly looking. I looked to see if I still had a copy of it, but no, I'd have to do it over again.

@@joe_z Cool so say we do that.

See also: en.wikipedia.org/wiki/Euclidean_rhythm

the Schillinger system is worth a look … his theory of rhythm is quite relevant here …

if you think about it a bed is the same as a bathtub only without a bed and with a bathtub and in the bathroom

@@ccshumshum8104 It's literally a waterbed.

Impossible

Das true Mon because I'm a drummer and I run out sometimes...so frustrating!🫤🪘

Sounds like something Douglas Adams might've written had he been a music critic.

You do only have 19.980 possible distinct usable sounds (although anything above 19.000Hz is nigh unhearable), that's if you're not counting cent differences which are hard to spot without a good ear.

You are only counting frequency (and just the fundamental). You can make a note, for example 440hz, with so many different timbre, adding more tan 19.980 possible sounds.

yeah, that would be great, just like the sorting algorithm sound videos made by someone else

Same

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-EsO9COuLPIE.html

Every time the commentery asked "can you hear..." about some aspect of the sound I was thinking "no, because I've only had a couple of seconds and you keep talikg over it". Unlike the video editor we've not heard the isolated sound pre-edit to be able to be reminded of the sound of each variant from a clip of a couple of seconds... It's worth the editor bearing in mind that viewers will be hearing these interesting sounds for the first time. Hopefully some more extended clips in the "making of..." video mentioned in the description.

if anyone's still looking for a no-commentary video of this, it's here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-M48319x1Kg4.html

There’s a lot of interesting musical references in Black and White. N’s full name is Natural Harmonia Gropius, and his father is Ghetsis Harmonia Gropius, pronounced as “G-cis” in the original Japanese translation. N represents a natural chord, while his father represents the chord of G and C#, which is the tritone, and “the devil in music”.

Thanks so much! Yeah... I have a similar reaction to those, since statistically the digits of pi aren't too different from a random number generator.

The only good one I've seen was one where the tempo is π/4.

The primes are inherently more interesting. Pi is just a bog standard irrational number, there's nothing special about it and the only reason it gets the recognition it does is because people with no understanding of math think its irrationality, which it shares with almost all other numbers, is some unique and magical property.

@@Oneiroclast I do agree with you, but pi is still important nonetheless, it's just that a lot of people think it's important for the wrong reasons.

@@Oneiroclast If you were as good at math as you’re implying then you would know that Pi is indeed a special number…

seconded, this is so nice to listen to. i'm not sure if i like a scale or the (inverted) harmonic series better but i want MORE

Count me in.

Im gonna try to make it, wish me luck

Try some G. F. Haas or Xenakis' Rebonds

@@phoenizboiisawesome Any luck?

"can you hear the cycles of the larger primes come into focus now?" *sounds of a drum set crashing down the stairs*

​@@faland0069 😂

@@boncoderz1430 I started studying for a Bachelor in software engineering this year. Music and maths are just hobbies of mine. I play piano, transcribe and produce music in my freetime and studied 2 semesters of pure maths but I quit the latter.

hell ya

Someone made that under a different comment, but ill post the link here as well m.ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-sdhpyBGP1xI.html

That would be extremely hard to run for longer than a minute probably

Yes i would mike to hear that, we could state it as "the notes that makes one [row] when the row [x] times lower (in the graph) makes some constant rythm" the "x" have to be bog enough so that when larges tempo are heard as such, the row x time uphead is heard as a tone

This idea is ass. I'm screenshotting it, and I'll be back once I've done what you said

That's absolutely true --- probably should have mentioned it! Of course, if the idea is more of an infinite sieve, rather than one that stops at a certain point, then that's a different story, and that's kind of what I was ultimately going for

Cool

Yes but it’s still way too much…

@@pauselab5569 @pause lab yes, but not as much. Imaging having to seive a million times, when you could also do it for 1,000 only. That is litteraly over-powered.

Believe it or not but this optimization barely matters. To understand this, think about sieving the multiples of 2. You need to cross off half the numbers in your list. Now think about sieving the multiples of 101. This only takes 1/50th the work. This is where the real power lies in the sieve of eratosthenes. We find that sieving all multiples of the numbers 2,3,…,k in the numbers up to N takes (1/2+1/3+…+1/k)N=Nlogk time. All your optimization does is use k=N^1/2 rather than k=N. That only yields an optimization of 1/2. But it gets even better. We only sieve multiples of primes. This yields Nloglogk time instead. So as k gets larger, the optimization factor tends to 1 and becomes unnoticeable, let alone significant. There are even optimizations to the sieve of eratosthenes to achieve linear running time btw.

True! Thanks for labeling it in case anyone was wondering

@@marcevanstein I love that you used that prelude! It’s a little less known, but it’s one of my favorites

I figured it was Chopin! Just couldn't figure out what piece. Thanks!

takes hat off to sir

Thanks you!!!!

Yeah, that's an interesting point. Often in just intonation we talk about tunings having different prime limits (e.g. 5-limit, 7-limit), meaning we only allow frequency ratios that break down into prime factors below that limit. I guess in this video, I was more focused on the rhythmic aspect than the tuning, and by going with the nth prime I avoided getting too low to fast. I like your idea about times tables and ear training!

@@marcevanstein What about varying the tempo between each prime to make all of the primes sound equidistant

@@Anonymous-df8it wow, that would get incredibly high tempo, incredibly quickly. It would be a fun experiment! Considering the distance between primes grows logarithmically it would accelerate almost exponentially to make that distance perceived as linear. Now I'm curious how long you could play it before you exceed your bitrate!

@@lexinwonderland5741 Well, the more frequent polyrhythms (2,3,5 etc.) will eventually exceed the barrier of rhythm to pitch (20 Hz), so you could replace those with a sine wave. Similarly, when they become inaudible (20 kHz), you can stop playing them.

@@Anonymous-df8it I like how you think, friend. I made a version up to the 15th prime with overtones (4 octaves) and now you've got me wanting to play around even more haha. The bitrate question is still there with the increasing speed, but regardless this sounds like a fun weekend project!

Can you explain further?

@@droughdough Polymeter: Tracks that play in different meters, de-synchronizing themselves from each other (e.g a 5/4 time and a 4/4 time playing together) Polyrhythm: Subdivisions that fit within the same bar and whose accents always start on the downbeat of a bar (e.g triplets playing against eighth notes both in 4/4 time)

@@harry_dum7721 to be fair, there's a very natural correspondence which is to take the least common denominator, call that one bar, and only play beat 1 of each part. That then gives a polyrhythm corresponding to the meter. For example 2+3+5 corresponds to 6:10:15. In general the product of the polyrhythm and the meter giving it is that denominator.

This is exactly the type of comment I'd expect on a video like this.

@@droughdough If you were to write out this music, it would all be 8th notes, they are just at different pitches. With polyrhythms that's not the case, as each different instrument/voice would have to be written as a different tuplet (like a triplet, or quintuplet). Here's the easiest way I can put it: Polymeter means there are multiple meters (time signatures) happening simultaneously, but we keep the tempo and the note divisions constant. This means the different instruments do NOT start together at the beginning of each measure, and instead it might take a few bars for them to get back together. As an example, imagine a piano playing 3 8th note pattern played on top of a guitar playing a 4 8th note pattern. The patterns are different lengths but the same speed. Polyrhythm means it's all the same time signature, but the different instruments are playing different speeds (or tuplets). In other words, within the space of one measure, one instrument might play 4 notes while the other instrument plays 5 notes, but they always start at back together at the beginning of each measure. The patterns are all the same length but different speeds but the same length

Thanks so much! I just looked you up, and your channel is wonderful. (Watched your video on knots, which I've always been curious to know more about.) If you ever want to collaborate on a mathematical sonification of some sort, I'd definitely be interested!

This is a *very* interesting idea! Kind of like a Shepard tone, but for prime rhythms

Extra cursed shepherd tones

dude I'm absolutely stealing your idea it's amazing

@@bonbondojoe1522 Don't forget to share with us!

@@bonbondojoe1522 I request an update

the note frequencies vs primes rhythms are offset by one. so 31 -> 37 is actually 30 -> 36, which is 6->5 once you take out the common factors of 2 and 3, a minor third descent.

:-) Do you have any videos of yourself playing percussion?

Very poetic .

If you play this rhythm fast enough, it becomes a sound. An overtone series with just the primes resembles a lot a clarinet - except there is the 2nd partiaö, and the 1st missing (as well as all non-primes).

not necessarily the same thing because then you'd just get infinite per unit time because of so many primes?

and this video did not run until the heat death of the universe, so what?

@@burkhardstackelberg1203 I never would have guessed that would sound like a clarinet, but somehow it makes sense.

@@torydavis10 But you have to represent something infinitessimally close to the start while not having to run the video until the heat death of the universe self-corrects because the really big primes don't have to be represented before the heat death of the universe and would be represented at its own pace. While for this the really big primes would have to be represented incredibly quickly. With that said, it would be really interesting to try this with the first n primes (with n being a finite number)

You may enjoy reading Haskell school of music, if not already familiar

@@quinnherden Thanks for the tip! I'm aware of Haskell but have never used it. I've added the book to my shopping list :)

@@macronencer Sweet! Just subscribed~ I look forward to a potential update

Gee, sorry, I made the same joke two days later

8 months later and I thought I was a genius for coming up with this too. 😅

This is an *excellent* idea -- I love it! I think I'll probably try it

I was looking through the comments for someone else who thought of this. I want to hear this sequence represented as a tone. Play the "2" rhythm at some audible frequency (>20Hz). I presume the resulting sound would start as a recognizable pitch but dissolve into noise fairly quickly.

I remember seeing you somewhere

Ooh, sounds very cool. How do you control the wind chime rhythmically? Or is it in pitch?

@@marcevanstein I intend to control only the pitch. A vertical helical blade (probably) on top will capture the wind and spin a vertically stacked set of cams spaced according to the first handful (out of the presumed infinite number) of primes. The cams will then actuate hammers that strike tubular bells surrounding the structure.

It is microtonal! The inverted harmonic series is interesting though, because it still has a lot of pure intervals

Good idea --- I'll try to put one together! I was thinking of maybe also including a downloadable link to a midi file, in case people wanted to play with it

@@marcevanstein That sounds great, I won't miss that!

Fibonacci's tend to the golden ratio, which is the *most* irrational number there is (phi = 1 + 1/(1 + 1/(1 + 1/(1 +...... and that would be maximally dissonant.

@@DrDeuteron It depends on how its sound is represented, and the mapping algorithm. But I guess you're pretty much right

I need help writing out the Math patterns for the prime numbers. May i please have your assistance doing this?

@@christopherrice891 I might not understand your question, but I'm afraid I'm the wrong guy to ask. I only have a passing knowledge of number theory, no working knowledge.

He meant 4000Hz