In this video we explore the hot-button topic of pi digit music and its various musical and mathematical issues. Then, I present some crazy pi music based on infinite sequences!
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Just wanted to add: I don't think I did a good enough job in the video conveying that I think it's fine for people to take inspiration wherever they like from music, and that even random inspiration can lead to good musical results. (There's a long tradition of aleatoric music, and I use random numbers all the time in my music!) The point here is more that pi digit music is really just an exercise in shaping randomness, and we shouldn't pretend that it's not. There are interesting mathematical and scientific patterns to make music out of where the pattern itself has a quality and structure that can animate the music, and this isn't one of them. But I think that any inspiration someone wants to use for music is fine, and if the music is good, that's great!
Great video and I agree, playing the base 10 digits of pi is basically just an exercise in harmonization technique - which is a fun challenge but not some spiritual revelation. When I was younger, I wrote a short song that took the numbers of the Fibonacci sequence modulo 13 and mapped those to a chromatic octave (C to C), which produces a repeating 28 note sequence that happens to sound melodically decent due to repeated tones and some half-step motions that suggest a tonal center. Still not a revelation - I made arbitrary decisions along the way - but unlike pi, I can still easily hum this finite melody by memory decades later, and it's the melody rather than the harmony I added that is musically interesting.
I agree that it can be fun to make music from interesting mathematical paterns, or seamingly random data. but it does make it a little bit less 'artsy', just like AI music or pictures, because there wasn't really an artistic idea. not that there's anything wrong with doing it though. Anyways, great video! you brought up some interesting points.
I'm so glad someone else has been bothered by this. The magic of Pi is (among other things) the ratio it describes between a diameter and a circumference. 3.14... etc. is just how that maps to a base 10 irrational number. You don't even get to hear ALL of pi unless you play for eternity. Your method is certainly more mathematically interesting. But I get the feeling its just one of many ways pi could be used more thoughtfully when generating music. I wonder if there's a way it could be used with an actual circle, like the circle of fifths (although you might need microtones) 🤔
Absolutely agree! That's partly why I posed the question at the end. I feel like the circle-ness of if must be something that can lead to interesting music. The trick is that music needs to have that balance of predictability and unpredictability, and that's what I felt I found in the series at the end. The digits are too random, and the Leibniz series is too predictable, to be interesting musically.
no, you're just latching onto belief and are just incredibly stupid, and should stop trying to use your brain and maybe give up on life or something.
pi is stupid anyway, tau is cool
My comment might be 2 months late, but I agree, maybe get a 12base pi and play it inside an octave
Also, needs more Euler's number (e) music.
My main problem is that they were taking base-10 and mapping onto a 7-note scale, so some notes get repeated, removing octave flexibility
oh hey P82 guy
kzhead.info/sun/d6-RZdF7fIx8dZs/bejne.htmlsi=CFJRaMicCYIul8nX
Fix: write it in base-7
Or pick 10 notes from the chromatic scale, and use those
@@DrGreen2015 or write in 10 tone equal temperament
Since I’m lazy, I just play 22:7, which is a lovely flat 13th… if it’s good enough for Archimedes…
Pythagoras with his anvils would also approve this approach..
I've never seen the PI sonfication stuff as anything other than composers enjoying a fun constraint to their compositions. Maybe some people are treating it as giving some deeper understanding, but I haven't encountered it.
It's around, that and the fibonacci sequence. If music needs it use it like debussy, u know?
@@nomad_0036 Phi is genuinely my least favourite number. No other number has that level of overblown mysticism attached to it, and no other number gets invoked at random times to explain something that it doesn't really apply to. At least pi comes up a lot in mathematics - phi is useful at times, but largely irrelevant (although I'm sure a pure mathematician could tell me lots of mathematical applications for it, somehow I doubt they come up to the almost ubiquitousness of pi). Debussy is analysable with the golden ratio, and that's probably the biggest argument for its inherent aesthetic superiority in music. Music written specifically with the ratio in mind obviously doesn't count (because imposing it doesn't suggest anything inherent), and millions of other pieces just... don't have the golden ratio. I wrote a piece myself where the climax was more like four fifths through the music and it worked fine (imo at least - and it was apparently convincing enough to land me a masters lol). Anyway, sorry to rant about this. It's probably the least important topic that'll set me off lol
@@klop4228 In terms of math, phi is cool in a few ways. It's the unique real number such that 1/x = x-1. It's also often considered "the most irrational number" in that the ways to approximate it approach the true value at the slowest rate possible. There's a lot of geometric stuff, basically any time you're working with regular pentagons there's some golden ratio stuff going on. But in comparison to things like pi and e, or even the square root of two, it really isn't around much.
@@stevend285 it is an interesting number, I won't deny it, and I'll admit I have a little bias against it too lol. It's got some interesting things, and of course it comes up in pentagons (and it's always cool when you can find one number in seemigly unrelated places - like how pi comes out of both circles and triangles?), but it's not magic. Not even pi is given the same mysticism phi is. And the idea of the golden ratio being an "aesthetic ideal" is interesting, but not universal - the "silver ratio" was used in several Eastern countries iirc, and several works of art work almost ideally as they are, without conforming to either ratio.
@@klop4228 oh yeah, I really don't care much for it as some sort of mystical ideal ratio. Honestly, even with a degree in math, I had to think pretty hard to come up with anything that wasn't just "it's the positive solution to the quadratic x^2-x-1=0." But not every number can be pi or e, just showing up in everything.
I think you might be reading too much into those pi music things. Compositionally, it's a fun challenge to harmonize a random sequence of pitches in a way that sounds good, especially if you pick the pitches from a complicated scale. Years ago I tried to do it with the digits of tau (2pi) in base 19, tuned to 19-tone microtonal pitches. It doesn't really matter that it's pi, but it's more cute to make it pi than just a random sequence,
I'm on the hinge about it, because I see it as music inspired by pi but the videos always way somthing like "you are listening to pie". like no I'm not.
Do you have a link to that piece? sounds interesting!
I never finished it, but I could probably find it again
The first one I encountered, I just appreciated the smooth jazz. Also it works well as a memorization tool for music-savvy people, which is how I've been using it.
I'm a huge fan of procedural music and pi music could be great, but his complaints are valid. As a random number generator, it's not interesting on its own.
What’s also kind of ironic that the digits themselves we use for pi and any other mathematical constant are manufactured for the sake of having a way of communicating the approximation of the number. One might argue the significance of the digit sequence “141592653…” but those numbers could be any other sequence of numbers depending on which base you use, like binary or base 6. And all of a sudden your intervals and patterns are completely changed 🙃
I'm not sure you could get any sequence of numbers. You definitely can't, if you use an integer base.
I remember seeing someone make pi music (in the musical challenge sense) using base 12 (for the 12 notes in the octave). Interesting challenge but they unfortunately treat it like it's divine
Even the n-base system is human-bade. You can have fractional base, negative base, variable base. Introduce some weird rules like the the Roman numerals, or use the ancient Egyptian system of fractional numbers, you can use the English spelling of the numbers ("three point one four one five ...", or any other language) and map the letters to music notes. None of these sonofication methods are necessarily more natural than the other. Oh and also the frequencies of the musical notes are also just assigned by humans.
Yeah, we should use base-however many notes in the scale
@@nanamacapagal8342"Divine math" is so funny to me. It's just ancient Greek math half the time.
I think one pretty accurate way of using pi in music is to use it as what it is: a ratio. More specifically, we could use it as an interval ratio. Now, we don't have an interval that corresponds to pi in 12tet,but we have something that is about 99% close: the augmented 5th/minor 6th. Now, I don't know how you're going to make music out of a single interval, but at least you can hear what pi "sounds" like, I guess.
Use it as your equave?
It’s more a #12/b13 than a #5/b6
If you take a factor of 2 out of π its close to 1.57 which is within an octave now and corresponds closest to 8 semitones ie an aug5th so I concur. By the way a dim5th or tritone is 6 semitones which in 12 note ET is of course √2. Its also the harmonic mean of a third and a fifth: √((4/3)(3/2))=√2. The most geometrical aspect to music I think is how a 345 right triangle can represent major and minor triads with side lengths representing number of semitones since the difference between and minor is how they're stacked corresponding to traversing the same triangle in opposite directions. This fact is employed in tonnetz representations of music harmony on a 24 triangle grid and this is layed on the surface of a torus (seven colour map theorem has some relevance here I seem to recall, on a plane a max of 4 colours will suffice).
You could take Pi in base 12, so you can map the notes on the chromatic scale. Or in base 88, so you can map it on a piano. Then, coming up with harmonization would be wayyyy harder. But ultimately, I think that using math in music can be a tool to give you a starting point, but not an absolute rule to follow. Taking the first 20 notes of Pi in base 12 and then expanding the melody as you see fit is more interesting imo. On the last album I wrote, I used a lot of math : 142857, Conway's Game of Life, arithmetic progressions... but then I don't stop here ; it just gives me the basis, either a set of chords or a melody. Music is, and should always be, mostly a production of the brain. I use math only to find chords or melodies I wouldn't have thought about
Must say love the last interpretation, how to evolves from total chaos to sweet harmony.
Thank you! One of the things I like about it is that, since it's quantized to a major scale, you feel the tension of approaching the tonic as the values approach pi. :-)
Obviously the real masterpiece is to be found in Tau as a base 88. :) Hmm, wondering about the distribution of other bases I just came across the wonderful term “absolutely normal”.
@@RoverT65536 Care to post or link?
definitely cool to learn about all these little quirks in music and mathematics! though i will say even i made pi music as a teen, not because it felt like there was some mystical special music hidden in the number but just cause it was a good memorization tool (and i wanted to impress people with how much pi i could remember), and there is just something fun about coming up with ways of making a random sequence of notes sound good (and pi is pretty recognizable) so I'm not sure how many of the people who make pi music are trying to imply something about how it's an extra special number or anything, i feel like in a lot of cases it's really not that deep
this is definitely one of those things where people who aren't really keyed into math act like it's mystical and mysterious, instead of just... a set of (admittedly elegant) rules and logical deductions which lead to complex and often beautiful results. i hate the mysticism that surrounds math, it makes it feel unapproachable and as though it's passed down by god, instead of just... a process for solving problems, and at times those results converge in cool ways. so in that way, i definitely agree with the premise of this video. that being said-- i can appreciate typical 'pi music' for what it is-- an exercise in shaping something random to create art. when i was younger, i remember learning about a technique where an artist would draw scribbles, and then try and form those scribbles into a coherent shape. it's the same thing-- it shouldn't be some deep statement on 'the underlying structure of our universe'-- it's just a cool way to see how a creative human mind can make something unique. using pi specifically is also cool, because it is so common-- it means you get to see how different people shape the same underlying 'random' noise. either way, nice video!
I'd like to see Pi( and even Phi) used as musical ratios. They, being ratios, would be more meaningful expressed like this. It could be pitch ,rhythm...time signatures?
You might be interested in Conlon Nancarrow's Study No. 40a for player piano, which consists of the same melody, but played simultaneously in two different tempos with a ratio of e/π.
Listen to Paul David’s song called A Song from Pi. It uses Pi/4 as time signature. He also made a song with the golden ratio if you want to listen to that too.
@@xdtricknifer2752 Thanks
@@kazsolan thanks
Phi is sometimes used as a pitch. Websearch "Sevish golden ratio music interval"; they wrote an article about it.
I did a harmonization of tau in base 12 mapping to the chromatic scale a loooooong time ago. Partially because I felt like the chromatic scale was a less biased mapping of the notes, and partly just because I wanted to try to harmonize an essentially random chromatic melody. It was fun.
THANK YOU! Those videos bother me too. My only complaint about this is that each step was mapped to a pitch in our arbitrary 12-TET system; the most accurate way to represent the pitches is by not rounding them at all. Although the result might not sound very musical, maybe it just means that pi isn't SUPPOSED to be musical. Also, there are many different ways to formulate pi, and I think the best way to represent pi is by using the "most natural" formula for pi, whatever that might mean. Great video!
Oh my god I love your channel. Also that series at the end, it’s so peculiar, it’s unlike the vast majority of converging series. Crazy
Quality content! P.S. About the connection between pi and music, you can make a video about radians seen as beats (such as 2pi, which is an entire beat). It can be applied to time signatures with complex numbers, too. Andy Chamberlain talked about it in his video called "Imaginary Time Signatures".
One of the results of this is that I've never heard any pi music that is compelling or actually makes me feel anything. And while I respect the challenge of harmonizing arbitrary notes, that's essentially all it is when dealing with irrational numbers.
harmonizing arbitrary notes is fun though!
3:06 I love how you say "Mystical connection" and the same time it sounds Scriabin's Mystic Chord
Yay! Someone noticed!
A thing ViHart once had on her website was a music composition where the binary digits of pi were used as note/rest to set the rhythm of the melody and not the pitch. Of course, the point there isn't that pi is somehow special, it's a challenge in how to make a random and nonrepeating rhythm sound interesting and exciting.
There's a lot of ways we can make music that is directly related to pi, because pi is, in its outset, a ratio. There are a lot of things in music we describe as ratios, the first thing that comes to mind are intervals in pitch and polyrhythms in tempo. These aren't exactly unexplored, and it won't get you a very complex piece of music on their own, but if you want something that really gets to heart of what pi is, that does it.
Really good video, thanks for your work !!
we once made a song with a series of changing time signatures that followed the first few digits of pi (3/4, 1/4, 4/4, etc). nothing else about it was directly related, but it made an interesting and strange rhythm!
Something quite useful is the use of primes. Prime intervals would be each a unique interval generated over the product, starting from the more consonant end and increasing inharmonicity. It’s almost perfect that it’s constructed by product, as multiplying interval ratios is equivalent to addition in tonal space. Instead of mapping pitches, I’m curious of what each interval generated by prime ratios in the context of Euler’s product.
I really like that last series! There's something very soothing about it, but also slightly unsettling lol.
Excellent video! Summarized the majority of the first thoughts that came to mind when I saw those mathematical constant inspired piano music pieces. I personally didn't like how often people would just skip over a couple notes because there are 12 notes in an octave and only 10 digits to be represented in pi, so I would argue that creating a chromatic scale piece from pi in base 12 would be more "appropriate" or "true" when creating music from pi. Or maybe I'm just a dozenal freak.
You can always go full Pythagorean and convert digits to intervals. Like each interval is the next digit divided by its previous digit.
hehe, PIthagorian
I feel like there could be some nice pi connections connecting circles/periods with melodies. Or sound waves whose nodes/peaks/throughs are pi-away etc
i think it would be cool to do a sort of "macrotones" pi music piece, where the octave was divided into 10TET instead of western 12TET, therefore actually being able to play the base 10 digits
Marc, you quite well articulated my concern with the usual so-called "pi music". Good job. Any thoughts on a genuine and not overly-reductive approach to composing with Feigenbaum constants or Fibbonaci or Lucas numbers? (The usual Golden Mean stuff for determining the moment of climax is pretty reductive, in my opinion.) On a related note: In my own compositions, I want the music to not simply sound good and be true to a mathematical idea, but also to transparently convey the mathematical idea. That can be a challenge.
I appreciate that this video highlights that any musicality arises from specific aesthetic descizions which are independent of any universal structure hidden in mathematical forms. However every inspiration for any musical result is legitimate, being an emotion, feeling, philosophical, musical and conceptual idea, or a mathematical formula. In that regard, I would encourage experimentation with representing pi with different numerical bases (e.g. base 2, 5, 7, 12, 100) and mapping other musical parameters to numerical sequences (e.g. duration, dynamics, instrumental colors, articulation, specreal features etc.). Perhaps you can make a sonification that does a multi-dimentional mapping on all those musical parameters?
Hi Marc! About the last pi example, Maybe a new intersing approach is to view the time exponentially. I mean that the more you play the faster you plot the numbers. The question is then, will keep being explosive like the beginning? or will it want to be "kinda" linear like when it approached to the end in your example?
I really appreciate the aesthetic of finding music in math formulae. Xanakis did some cool things. Take a track like the one above and think counterpoint.
This is such an intuitive argument to me: I use Eurorack synthesizers, and in that case it's common to pull in random voltages to represent pitch -- when you need that to be musical, there's a type of module called a quantizer whose entire purpose is constraining random voltages to a specific musical scale. It's possible - and common - to get pleasantly musical results from randomness, but the technique is always to apply constraints to it.
It's a fun constraint or prompt. I've seen a video on similar ideas to use math to generate story prompts. Wish I could remember what video it was, I think something Numberphile. But this video got me thinking about doing repeating fraction music, since those are regular periods, like n/7, where n-|-7. I suppose Pi Poetry would also receive a similar critique, since it'd be exchanging intervals or chord numbers for syllables or word length.
I think the best way to map pi into music is, at least in the case of traditional western scale the one we're most used to, is to convert pi into base 87 and assign each digit from 0 to 87 to the keys on a piano, arguably the most popular instrument in western music and the one with the widest frequency at least in terms of human/technical capabilites (im sure you can hit a C9 on a tuba if you try hard enough). Do that and then play the music and there you have pi music mapped to the western 12 TET scale. Im sure you canget different but fundamentally similar result by mapping pi to the number of notes a specific culture's scale have like the pelog or slendro in Javanese or the many different Ragas from Hinduism and the indian subcontinent
the pitch choices for the sound visualizations around the 6 minute mark might do really well with just intonation, starting with simple ratios from a fundamental, and converging on pi times that fundamental
As someone greatly intrigued by the music of Xenakis and the like, this is incredible work! Glad to see I'm not the only one annoyed by this
Have you tried taking the Leibniz series and assigning the terms to relative harmonic pitches in just intonation
strangely for some reason it reminds me of Andrew Norman's style :) Good job!
Reminds me of a video by tantacrul where he also criticises composers who unimaginatively map some numbers from some statistics to some notes to make the music seem meaningful.
This video is rad as usual, but the sound of your voice seems way better. Did you do some of that stuff we talked about?
I think you could express pi as a (neumatic) melody faithfully by converting it into base 12 and assigning each symbol in ascending order to an ascending chromatic scale. C could be 0, C# 1, D 2, etc. This would be consistent because the order the notes in western music go up would correspond to the order numbers go up. The note you assign 0 to is arbitrary, but you can just change that to be in whatever key or mode you want. However, I don't know what could be done with harmony and rhythm. Maybe it should just be a Gregorian chant?
i personally used Pi as a dictation of intervalls in my music. My aim was completely different though: it was not an accurate depiction of Pi in music, but more an exercise of counterpoint and experimentation of a given theme.
as you said any way to convert a digit to a sound is some sort of mapping, which rather is the key point than the digit itself i believe a more natural way to produce pi-music could be the following. and i still believe this is a mapping and it has some parameters, which might completely change the music, but i think it is still better (one shouldnt say "better"... different) you utilize a converging series and map each step to a specific pitch on a continuous spectrum e.g. the "exact" value of pi equals some chosen frequence f_pi let us say pi_n is the nth element of the leibniz series. i.e. pi_n = 4 * sum(from: k = 0, to: n, of: [...]) f_n is the corresponding frequency, which is being played for some amount of time then you could have two algorithms: (1) Difference f_n = f_pi + k * (pi_n - pi) (2) Ratio f_n = f_pi * k * pi_n / pi for both there is some parameter k in (1) it is quite necessary to scale the difference, because otherwise (depending on f_pi) it wouldn't be very audible in (2) it is not as necessary, because frequency is exponential and therefore difference in pitch becomes ratio in frequency I think this continuous range of pitches is much more realistic, because the set of real numbers is continuous however (without having tried it), i believe it will sound quite.... "special"
I love this! I've also viewed with skepticism the attempts to musically realize such "magical/transcendental" numbers. As a composer I've tried this myself, but not with π. My dealing of frustration with π is so-called "Pi-Day" March 14, significant because it is also Einstein's birthday (though what did ha have to do with π? It bothered me that it just assigned the 3 to March out of the arbitrarily-divided into 12 months, and then the first two decimals as the day. What?? What if the year was divided into 10 months (as it once was) or 14? What if the first digit in π was 0, or the first two decimals were .76? My solution was to ask what the significance of π was, and could that be expressed as a day of the year? Well, it is a ratio of the circumference of a circle to its diameter. Hmm, a year happens to be a (nearly) circular orbit of a planet (earth) that has an average distance to its sun (radius). So if you take the average diameter of our orbit and inscribe that distance into our orbit, starting midnight at January 1, where does that take us? I've done the math, but I forget the actual answer, but it is somewhere in April. No matter how often I mentioned this my Pi Day never caught on. People were more attached to or convinced by the superficial connection of the raw numbers arbitrarily superimposed onto the calendar. Yay! (In addition I also once took issue with the so-called infinite series of digits in π. My problem was, assuming this number had some bearing on reality, it occurred to me that it must be able to describe the ratio of the LARGEST circle and diameter we can imagine: the known universe. Also another lost calculation, I figured even with that vast size of 17 billion light years (is that right) with the smallest measurement of the Planck length, π's decimal accuracy goes FAR beyond what is required. I think something like only 62 decimals were required, or at least less than 200. What else would those smaller digits ever actually describe other than hypothetical circles INFINITELY LARGER than the universe?) In my music I was more enamored with the Golden Mean/Ratio and Fibonacci series, although I wasn't quite sure how to do this so I experimented with various methods involving pitch, rhythm and even form. My last attempt used alternate tuning systems to better approximate the numbers. Other than that I've experimented with 12-tone music, confronting the charge that "you can't hear the row" - which isn't the point of it - by vowing only to ever use ONE row. It would be like there only being one song in each key or mode. Would they sound as familiar to us? Why then use a different row for every piece. I also experimented with using the row in different ways, but that is another story.
Great sonifications!
What about additionally considering some pi related number or formula determine the duration of notes to allow for more than a uniform fluctuation of frequency alone? Also perhaps something more to determine accompanying chords?
Maybe you should map pi to overtones. So you take a root frequency like 440Hz. You multiply it by 3, the first digit, which is 1320 Hz. This is a note between the octave 880Hz and 1760Hz. So you could half it once to bring it back between 440Hz and 880Hz. But that step is only really important when the multiplication gives a frequency higher than audible. Then you take that frequency and multiply it by 1. And the result of that x4, x1, x5, etc. Or just make a pi sound. Start with 3Hz, add 3 x1 Hz, add 3x4 Hz (12) add 12x1Hz, add 12x5Hz, add 60 x 9 Hz, add 540 x 2 Hz, 1080 x 6 etc.
My trust has been broken too many times in this video, I shall never believe another mathe-/musician (great video, loved it)
I mean, one of the biggest problems I find with mapping pi to music is a matter of numerical base: music could be thought of as in base 8 (if you are limiting yourself to a single scale), base 12 if you are using the chromatic scale. neither of these are base 10, which is the form we are used to looking at pi in. as a result, ANY attempt to map the digits to music, even without adding harmony of any sort, will be editorialized by what note you map each digit to. given that the way a piano is tuned uses increments of 1/12, what if you were to map the digits to the notes you would get by replacing the 1/12 in the piano tuning formula with 1/10?
You can also use chain ratios representation, though you need to remap numbers with care, as they are not digits but natural numbers
6:40 Starting here, it just sounded like Vihart- all the way to 7:25 (the increasing softness in your voice at the end, especially!) What if you used e or phi?
I also think another problem with this digit way of doing thing is in the grand scale of things, number 10 is quite random as a base to be assumed to give pi its meaning out of a sudden.
This old video made a different and more interesting approach. Not trying to harmonize an infinite cuasi-random melody, but overlapping the first 32 digits of pi with different figures. kzhead.info/sun/qq9wpNVvg2KEa30/bejne.html
I dunno about the questions. I dug what you did.
i actually had this video idea about pi music since like last year lol. but i havent gotten around to making it and when i did want to make it, i got busy with exams. maybe for next year or for tau day ill make it? anyways. i had a few ideas for how to make pi into music. the first one is this. pi at the end of the day is just the ratio between the circles outer thing and the circles inner thing. so... theoretically you can make compose music that only uses notes that are a multiple of pi. like, you know how one octave is just multiplying by 2, what if instead you only multiply and divide by pi? what does pi as an interval sound like? is it good? but... i cant compose music so that brings me to the second idea. to highlight how hekin arbitrary pi music is, what if you use other scales with it? since usually its in decimal, why not use 10 equal divisions of an octave? or maybe the other way around? since the traditional piano has 12 notes, why not just use pi in base 12? okay yeah thats it basically lol this is a cool vid. that curve doesnt look like its converging to pi at all XD
Another thought occurred to me: what about using the continuous fraction version of pi? That would at least eliminate the arbitrariness of using base 10.
I've looked at sonifying pi, but not come up with anything that I liked. That last infinite product is interesting though. Maybe work with successive terms mapping onto notes and durations, rather than successive partial products?
Interesting idea!
Wonderful
If I were to attempt to explore any mathematical relationship I would see if there is a way to convert pi digits to base 12 for the 12 tone scale. That would be the truest representation of pi. Or alternatively use Tau in place of Pi. Which would be more 'mystical' as it represents a full circle. IF we're tying to be 'mystical', then we would need to look at and understand how ancient people mathematically defined shapes and their usage. In which case I would look at Ancient Babylonian metrology and their base 60 system that we use to this very day to tell time.
how about converting pi to base 12 and then mapping each digit to a note?
Pi and python, thats amazing.
Im not sure the weird prime series was possibly found not by dabbling into primes but rather experimental mathematics approach "what happens if". Plouffe is known for such attempts
most melodies range two octaves, so perhaps taking the base 23 expansion of pi and mapping it chromatically from C4 to C6.
Thanks for calling out the stupidity of Pi Music. I loved your version!
Where can I find the Python code so I can sonify other stuff myself?
Pi is a ratio. Musical intervals are also ratios. One interval can be used to define a scale by repeatedly multiplying by it and then reducing by octaves. Building a scale this way and then composing music that emphasized the pi/2 interval would be the most "real" way to musicalize pi.
To a close approximation, this is 23edo, which is notoriously awkward and dissonant. It approximates π well, as well as φ, but not 3, 5, 7 or even 11.
All I want is a true, avant-garde Iannis Xenakis style pi music. Is that so much to ask for?
All the examples given seemed to be using 12TET. Maybe you could try a different tuning system or the harmonic series?
I agree! I did try rounding to a harmonic series, but somehow I liked the major scale a little better in the end because of the leading tone that it kept approaching and leaving. But I wonder what kind of tuning system would be meaningful for pi. I mean there's the pi ratio, which is close to a minor 6th, but how do you weave that into a temperament, and would it be meaningful?
i agree. the internets err towards sensationalism inevitably leads to pareidolia.
I just learned a new word today 🙂
All that chaos at the beginning became a movie soundtrack
(Drummer here) What about looking at PI as a series of beats instead of pitches?
Bartok iria adorar isso
Surely there must exist more interesting ways to sonify pi. What about e.g. interpreting the digits as tonal functions and generating melody/harmony/voice leading based on those. It's still completely pi, but it's not a one-to-one mapping of digit to note (and most likely a bit more interesting to listen to).
Ok ok but why ain't anybody talkin about this, it freaking killed me 0:25
Nasty ringing noise sometimes on your vocals, should I wave my fist at KZhead's encoding? Fascinating video anyway, well done!
oh wonderful
Is it quite random that Western Music divided tones into 12 aka 12-TET? and why not any other numbers?
9:04 May the fourth be with you! 😂
More interesting and perhaps more meaningful would be to have π represented in base-12 numbers, then map its digits to the 12 pitches. My guess is that highly irrational numbers like π and ϕ would sound LESS musical, or at least less diatonic.
As an engineer I’d just play the third note and call it a day. Close enough = good enough.
I've long decided that when you represent pi in base 10 you can use a chromatic 10EDO.
I'm a music composer myself and I've always been one of those who wanted to make microtonal music in some systematic and predictable ways (oh yeah, I was never a big fan of consciously involving randomness in my music). So I have two suggestions for you. #1. Interestingly enough, in the history of microtonal music, there was the English clock maker John Harrison who had the idea which went something like: "If one octave were to represent one full circle, what about making a temperament where a major second would correspond to one radian exactly?" And that's what he did. So if I convert this to some familiar logarithmic units like cents, this means that the size of a major second is then equal to 1200 cents ÷ (2×π). So this offers a representation of π which is not contained in a specific sequence of pitches but in the specific size of the major third in that particular temperament (i.e. a major third is nothing other than two major seconds stacked on top of each other). In the 20th century, Charles Lucy decided to realize Harrison's temperament on todays instruments. More about that here: www.harmonics.com/lucy/tuning.html #2. John Wallis had this formula for π÷2 which went like: 2/1 × 2/3 × 4/3 × 4/5 × 6/5 × 6/7 × 8/7 × ... Now imagine that you would take a specific frequency, like 220 Hz meaning the pitch of A3, and you would then multiply this frequency by each of those factors while still keeping the initial frequency sounding together with each of the resulting frequencies. This way, one would first hear an octave (2/1), then a fourth (4/3), then a minor seventh (16/9), then actually a diminished fifth (64/45) and so on. The further you go in that sequence, the closer the interval gets to the target interval that sounds slightly larger than a perfect fifth.
I wish you had took longer (or any time at all) in showing how people do say that the "pi pieces" are a meaningful way of listening to pi itself, instead of just a compositional challenge based on an arbitrary interpretation of it.
It's not exactly an arbitrary mapping they are using, though. It's usually the pitches of a major scale, which western musicians already tend to map to specific numbers.
3:03 that first 9 is correct though
the fact that at the start he just wrote 3.14159 and then random digits
oh he mentioned that inthe video
I understand wanting to get in as much of the sequence as possible, but the tempo makes it hard to recognize any musical aspects of the result. Sure, you start to notice a pattern as it starts to get more regular, but it's the parts that vary more that tend to be considered more musically interesting.
Yeah, I wanted to show the long term convergence and I enjoyed it at the fast tempo, but you're right that at a slower tempo you would hear different things. And with this sequence in particular, there are interesting patterns to appreciate at the slower tempo.
There's that one video that uses pi as a time signature, which isn't really based on randomness.
What about the key signature pi/26
And what if we read pi in a duodecimal system and converted that to notes on the chromatic scale
i see music like this more like an interpretation of pi. I dont see it like theyre trying to show us some hidden harmony, but they are taking pi and using it as the foundation for music
Could you do a deep dive into dropping a steel pipe from a MathiMusical™️ perspective
Hey, love your video! I just did my own take on Pi sonification (kzhead.info/sun/Z5exgNNwooZ3oaM/bejne.html), that illustrates how the musical result is very much determined by the scale and rhythm you use for the mapping. I am still kind of wondering whether there might be some musically perceivable difference between random numbers and irrational numbers, or between 'less irrational' numbers like pi and tau on the one hand and 'more irrational numbers like root 2 and phi on the other hand. I guess that will be my subject for next year's pi day video :)
>I am still kind of wondering whether there might be some musically perceivable difference between random numbers and irrational numbers Pi is normal, so stastically there's not really a difference between pi's digits and a random sequence of integers. But pi's digits are fixed of course
Your pi music is a lot more interesting than the music originally referenced in the video.
It's so impressive that people are able to use essentially arbitrary numbers and create something as good as they do
Kinda how all music. Works
I honestly like that music at the end... though its impossible to play
This is interesting and all but where’s the first licc?
3:06 I love you