Storing the last changed date for every single person on earth (even though not every person is an OpenAI customer) is something you could easily do on a laptop. It would be a rounding error for OpenAI.
I don't know what format they use for storage, but Iceberg would be a reasonable choice. A date in iceberg format is 4 bytes[1]. I checked postgres as well as a reference point. It also uses 4 bytes for a date, so whatever they use it's going to be about that.
Current world population is just shy of 8.3 Billion people [2].
4 bytes times 8.3 billion people gives 30.92 GiB. [3] OpenAI's training data will be in the petabyte range at least.
What you’re talking about is his proof of (a specialised version) of the Taniyama-Shimura-Weil conjecture[1] which had been proven to imply Fermat’s Last Theorem. The technique he used to prove this was adopted by his students to prove the conjecture in full generality so it now known as the modularity theorem. Given its importance to the Langlands programme it may be that when history looks back on this it will consider this a more important contribution than the fact that it proved FLT even though that is obviously the thing that grabs the headlines, but there’s nothing at all wrong with proving something that implies your goal rather than proving the goal directly. There’s a reason the words “it suffices to show” often turn up in proofs.
Also his physics explanation is not the best, and you can see if you just ask the next “why” question.
He talks about the harmonic series giving the basic ratios of the Pythagorean scale but why is that the case? When you solve the equations of motion of any sort of harmonic oscillator (including crucially, strings, vibrating columns of air from a wind instrument etc) you see that you can solve them using a Fourier series, so if you solve this in trigonometric form you get
a_1 * cos blah_1 + 1/2 * (a_2) * cos blah_2 + 1/3 * (a_3) * cos blah_3 + … + 1/n * (a_n) * cos blah_n [1]
…so those fractions end up being the partials of the harmonic series (a_n/n) where a_n is the n_th coefficient, which you find using an integral. Now if you have a normal western musical instrument, the higher overtones (later terms of the Fourier series) are not prominent so those coefficients are small. So the terms that matter have ratios a_1, a_2/2, a_3/3, a_4/4, a_5/5 corresponding to the primary intervals that he’s talking about.
In cultures (eg Balinese and Javanese music from Indonesia) where they use a different number of tones and different scale, it’s no coincidence that they play a lot of gongs and bells, which have much more prominent higher overtones, so a different set of Fourier coefficients so different ratios are going to be “congruent”/melodious-sounding.
[1] the “blah” terms are a function of pi and the length and stiffness of the string etc. Not really relevant here.
For metallophones used in Gamelan music, I don't think the key difference is emphasis on higher vs. lower overtones. Rather, their overtones don't follow the harmonic series but are still well-defined. Their tuning goes along with that, and it works given that particular non-harmonic timbre, but wouldn't work with western classical instruments, which tend to approximate the harmonic series in their overtones. In all cases the lower overtones remain the most audible and the most important ones for tuning and finding consonance.
This is (mostly) not music theory and what is music theory is mostly wrong or incomplete to the point of being wildly misleading. Source: have degree and postgrad in music, was a professional musician until RSI put paid to that career, wife is a professional musician and teaches to postgrad level at 2 conservertoires, most of our friends are professional musicians, have a house full of scores and music books.
If you actually want to learn music theory for the purposes of playing I strongly recommend you just follow whatever tutorials for your instrument and style and if you get to the point where feel you want to learn more and take it seriously in and of itself, buy “The Jazz Theory Book” by Mark Levine[1]. In spite of what it says, there really isn’t any such thing as Jazz theory - it’s just music theory, and this book is a great presentation with lots of good examples. If you like jazz (or the western popular music tradition including rock, pop, funk, etc) you’ll come out understanding how that music works better than most people. If you’re doing a music degree, there will be books recommended by your music programme, but honestly, Levine will cover most of what you need if you’re not doing a straight classical course in which case you’ll want to augment with a more conventional source so you understand the “rules” they want you to follow when writing pastiche counterpoint etc.
If you want to get big into composition and/or want to understand late romantic and 20th century music, get Harmonielehre and “Structural Functions of Harmony” by Schoenberg. Together they are by far the best harmony books I have ever seen and go super-deep into why the western classical tradition works the way it does. If you compose there’s a decent chance they will change your life forever as his approach is to not take anything for granted but exhibit everything with examples from masterworks of the western tradition. Amazing books both of them. Harmony is not a spectator sport though - to get full benefit you have to get the books and work through stuff on the piano. It will reward you immensely.
If you want something else that will blow your mind, read “The technique of my musical language” by Messiaen. If you read Levine first this will have the additional benefit of showing you where the “diminished” and “augmented” scales and the whole “harmonic major” thing come from.
Props for mentioning “The Jazz Theory Book”! It's an excellent book.
The only thing I'd add to your recommendations is: Listen! When you hear a song, some melody, a rhythm, listen carefully, try to deconstruct the components, how they interplay, and try to figure out what is it that you like. Was it a feature of the harmony? The melody? Pacing? Whatever it is, keep listening. Theory is just a way to try to explain what we hear and why we might like it. The more you listen, the more you have that you can base the theory on.
I'm sort of the opposite - when I can name something, then play it, then I can hear it. E.g., going from minor third to major third to root. I can't "unhear" that in blues-based music now. But before it had a "name" it was just an interesting sounding "thing" that didn't pop out to me in any specific way.
I originally read your comment as quite gatekeep-y and elitist. The article explained some of the "theory" behind certain things around music in a way that made sense to me, yet here was a professional telling me it was bad because it was bad.
However I've realised that "Music Theory" is a strictly defined term. If someone made an article called "Intro to Algebraic Geometry", and it was actually about geometric algebra, it'd be really annoying, even if to a uninformed person the meaning behind those terms would seem interchangeable.
It's a fun webpage about a programmer dipping their toes in the very most basic elements of music and documenting some of their current understanding.Imagine I wrote an article called "Programming for musicians" that was mostly about how to turn your computer on and install homebrew[1] and finished by showing you step by step how to cut and paste "hello world" in javascript from stack overflow. You might rightly say that while "programming-adjacent" the article didn't really address programming.
Here[2] Is the syllabus for ABRSM Grades 1-5 music theory. So this is super-basic music theory of the level that you couldn't really expect to pass high school music without knowing. I've picked associated board because this is the most generic music theory syllabus possible, and grade 5 is very basic. If you were actually studying music you'd go way way beyond this.
To a first approximation none of this is in the article. It also doesn't have any more advanced topics (functional harmony, orchestration, voice leading, transposition, key/scale relationships, advanced rhythmic concepts etc). That's why I say the article isn't really music theory.
And then for completeness, when I say that what is music theory is wildly misleading I'm talking about things like "chords are notes stacked in thirds". There's so much wrong about about this it's hard to even start, but for starters it's an if and only if when it really shouldn't be. Notes stacked in thirds are chords, but there are a whole heck of a lot of chords that aren't stacked in thirds. It's like if I said "even numbers are 4 and 6". It's like sure, but there's more to it than that.
[1] without mentioning that this was only needed if you were using a mac
The author admits that this article applies to only a specific flavor of music theory, and says that it only covers a small part of it. The article even mentions at the end it does not cover some of the topics you think are missing.
The article is not a comprehensive syllabus of all elementary music theory, and it does not claim to be. I believe you are being too harsh, as this approach to understanding music feels much more intuitive to some (like the author, and myself), compared to traditional music education.
I would not call it harsh. The author don't even bother to assemble sentences themselves. And a title "Music Theory for Programmers" imply it is comprehensive even at an elementary scale.
The title does not imply it's comprehensive. If anything, a title like that suggests that it's only scratching the surface. If I read an article like "Haskell for C# Developers" I would not expect to be an expert in Haskell at the end. I would expect to have enough intuition to begin actually learning the language properly
PhD Candidate in music and computer science and gigging jazz musicain here. It is not too harsh. Articles like this confuse people who interested in learning a topic more than they help.
Yet another case of programmers thinking "I'm a programmer so I should blog about this thing I barely know anything about as if I'm an expert, what could possibly be the downside?"
There is "western music theory" ala Schenker, voice leading, serialism etc (to mention a couple of names that some people might have heard of) but that describes things to do once you've got a scale and chord system.
This is "12T music theory", describing how you might get to a scale and chord system.
I don't see how it is confusing. You can spend a lot of time doing "western music theory" without ever understanding most of what is in this article, that is certainly true. But the fact this this outlines a bunch of stuff that undergirds what a composing (or improvising) musician might consider "music theory" doesn't invalidate it, or make it confusing, IMO.
"Music theory" has a near universally accepted meaning. This article is not about that, it's about what we all call in music academia acoustics and digital synthesis (which of course I know you know as I know your work). The derivation of scales from acoustic principles is not in theory books; it's in acoustics books. I've taken numerous theory courses and also taken university acoustics courses and digital synthesis courses, so I can certainly comment on what was taught where! If people go here and think they are learning music theory and then want to go on, they will be frustrated by not finding what they want, they will have issues communicating with others in the field, and they will lose credibility by not knowing the standard nomenclature. That kind of redefinition of standard terms is not good pedagogy.
Look, it's like me writing an introduction to "colour theory" and then writing about something else that eventually leads to how we see colour.
I'm not debating that the article has useful content – it does – but it's title and framing is misleading, which is a disservice to the new student. I happen to personally believe everyone getting into music theory would be well served by knowing more acoustics and that this is useful material. But muddying the waters by using terms in weird ways is off.
And when you write about a field and use the wrong terms, you lose credibility. Sorry, I don't trust authors who can't be arsed to use the standard nomenclature for a topic, it really doesn't make them sound trustworthy.
Are Peano's axioms number theory? No one really uses them directly (other than induction) when working on practical number theory problems, but they are considered part of it.
Scales and chords build the fundamental basic blocks for Western music (I would introduce equal temperament third but that's only a matter of ordering). They are taken for granted in musical practice, I agree, but only because musical practice concerns itself about how/what to play and why. If somebody comes from the point of view that clefs and stems (which are undoubtedly musical tools) are gatekeeping and all you need is a piano roll, this article explains from first principles enough musical building blocks to tell them why they're wrong.
Sure, but none of that changes the fact that is someone reads that article and says "wow I like music theory!" and orders the best theory books or signs up for a course or lessons, they are going to be PISSED. They will get some books that don't cover what they think music theory is at all and that touch on basically nothing in this article.
On the other hand, if the author had said something like "Intro to the acoustics behind musical scales", then they might go on to order great books like Kyle Gann's or Gareth Loy's and be off to the races.
Redefining normal terms just makes people sound like they have no clue, and that is, 100%, a serious disservice to the reader/student.
Or maybe not... surely if you are shown figured bass you will be pissed, but on the other hand understanding triads and sevenths provides some intuition about inversions, voice leading, rootless voicings, upper structures, diatonic movement of voices. Certainly not enough to orchestrate a piece, but enough to listen to educational YouTube videos, follow lead sheets, think about what you're hearing.
Harmonics and temperament aren't really relevant to all this, though at some point you have to explain why certain intervals are naturally consonant but "boring", and others can be made to make sense but mostly within a more complex voicing (which reconnects to topics like inversions and voice leading).
(For disclosure I studied piano until ~20, both classical and jazz, and I would call my knowledge of jazz theory "decent" for someone with zero professional or academic experience. Obviously not comparable to yours and not even in English, so perhaps what I wrote above will sound really stupid).
> The derivation of scales from acoustic principles is not in theory books; it's in acoustics books.
And this is correct because ... ?
There are whole subsectors of "music theory" that cover precisely this sort of thing, even though they are fairly arcane. I'm thinking of things like pitch set theory.
My own take is that western musical pedagogy, at least historically, is one of the worst examples of pedagogy that exists, precisely because of what is taught, in what order, and why. It pretends (or used to) to have some sort of universality or inevitability, when even a scant familiarity with other musical cultures would make it clear that this is false. It is emphasizes a note-centric rather than interval-centric approach to melody (and chords) that ignores centuries of (folk) musical practice (most simply known as transposition, but the implications of it are staggering, and largely elided).
So, defending what that pedagogy calls "music theory" seems like weak sauce to me. Especially given, as many others have pointed out, western/european "music theory" is a codification of existing practice for the most, not a generative theory.
It seems you arguing how things should be, not what they are. I don't disagree that in music we have lots of inconsistent nomenclature that could have better names. But writing an intro to a topic and using non-standard nomenclature (without explaining that that's what you're doing) is still a source of confusion to learners.
Whether or not this info should be in acoustics books or theory books is not relevant to the new learner, that's where it is! I actually think a crash course in acoustics would be a good addition to a comprehensive theory book, but it doesn't change the fact that no theory course or book has this stuff (not even my pitch set texts!)
I teach music students regularly. I spend a lot of time explaining what something is called in various contexts. They need to know this to learn in a productive and not frustrating manner. They can then learn later why the terms are imperfect and used differently in different subcultures.
But no argument on that is going to convince me that it's good pedagogy to tell new readers that a post on acoustics and synthesis is on music theory. That's just counterproductive at best, or ignorant at worst.
What would you call the topic of "why are there 12 notes to the octave?" "why is the perfect fifth the most consonant chord?" "why do we use equal temperament?"
In the all the textbooks I have or have seen, those are called "acoustics" (and more specifically "tuning and temperament"). They are covered in the text book I had for acoustics, and not covered in any of the textbooks I used for theory (jazz or classical). For example, in Rossings "The Science of Sound", it's in a chapter called "Musical Scales and Temperament".
Look, I agree that they should be. I have literally had discussions with one of my PhD supervisors (who taught acoustics) about how much better some students would understand some of harmony if they started with some acoustics! But they aren't, so if one is going to redefine common uses of terms, at very least this should be explained in detail to the student prior to use.
My call on this stuff is always determined by "What will help my student learn most efficiently, without frustration or confusion". That article fails badly on that count.
While these are helpful topics to understand, they are not beginner topics. Not if you want to make music. They are fundamental questions in that they reside at the base of why things are the way they are, but they are not fundamental in the sense that you should teach them to a beginner who wants to make music.
The point is to make music. And the most practical way to do so is to teach instrument technique, intervals, scales, chords, and melody. Not low-level acoustic phenomena.
To make an (imperfect) programming analogy, you are proposing to teach low-level computation when most students would benefit from some Python, if/else statements, and functions. Not memory allocation and assembly. They're useful someday, but less useful when your first goal is to simply write a program.
Because music is pleasurable to play, to experience, and it's gratifying to be creative and to discover your creative potential.
If you have an alternative reason to learn music and to start learning through acoustic phenomena then let's hear it.
Most people don't get into molecular gastronomy if they don't intend to cook a meal. And I'm going to go out on a limb and say that 99% of aspiring cooks shouldn't learn cooking via that discipline without first starting with something more practical and immediate.
It’s also worth mentioning that these are very western ideas. Lots of other cultures derive alternative structures not based around 12 half steps to an octave and so on.
Oddly, or perhaps predictably, or both, most of them still converge on the same basic pitch classes.
The example I'm most familiar with is Carnatic and Hindustani music, where there are theoretically 22 tones per octave, and in fact the tones in most cases actually cover a range of frequencies rather than a single one. Nevertheless, the most common and most popular music from those traditions tends to only use about 7 tones per octave (equivalent to a western "scale"), and they still have a very central for tone ratios like 3/2.
That's sound design theory, not music theory. They're not the same thing.
Music theory is about chords, scales, rhythm, and - most importantly and elusively - how to fit them together to say something interesting.
Entry-level trad Western Theory gives you the concept of a basic grammar as a first introduction, but once you have that you can extend it fairly painlessly to jazz/funk/metal/pop/whatever.
Advanced classical grammar - baroque and modal counterpoint, extended harmony, and such - has some useful pointers for modern song-writing, but it's a specialised skill for experts. Movie and game score composers likely know it, but it's a degree-level skill.
Sound design theory is a subset of orchestration. The proof is that you can take most music and play it with simple sine wave bloops - no orchestration at all - and it remains completely recognisable.
Explaining equal temperament etc sounds clever and it's interesting if you like that kind of thing, but it's a distracting level of nerdery that doesn't help at all with basic song writing.
I agree. As a (hobbyist) musician and a (professional) programmer, I would not classify this web page as “music theory” given its widely accepted definition.
At UIUC, we had a class called Electronic Music Synthesis. It’s been over a decade since I took the class, but the first few lectures covered mostly everything in this web page. That content was never presented to us as “music theory”.
For people with the mind of a programmer, explaining the mathematical basis of equal temperament and then the major scale (the article doesn’t explain the major scale well, but simply says “it sounds better than a chromatic scale”) allows a programmer to understand not just the how but the why for the basics of western music.
For people that just want the how, one would start with “here is a pentatonic scale” followed by “here is a major chord”.
If we teach theory without first principles, all we have to do is say “C + E + G make up a major triad”; we may go as far as to explain that, in a major key, the I, IV, and V chords are major chords, the ii, iii, and vi chords are minor chords, and the vii chord is a very dissonant diminished chord.
However, first principles explain “why” a major chord sounds the way it does, and “why” a minor chord has more tension.
Let’s look at the five-limit just intervals: 2/1, 3/2, 4/3, 5/4, and 6/5. 2/1 is a perfect interval; two notes an octave apart sound nearly the same. 3/2 and 4/3 are also perfect intervals, but there’s a little more tension and beating than with 2/1. 5/4 has a little more tension than 4/3, and 6/5 has even more tension. I just explained, using first principles, the octave, perfect fifth, perfect fourth, major third, and minor third. That’s most of the scale right there.
Now, let’s make a chord. Experience has shown that three notes is more interesting to the human ear than just two notes. That in mind, we want three distinct notes where the intervals between notes have a minimum of tension. Take the root, take 5/4 of that, then take 3/2 of the root. That’s a major chord. The reason we use 5/4 instead of 4/3 is because the interval between 5/4 and 3/2 is 6/5; the interval between 4/3 and 3/2 is 9/8. Since 9/8 has more tension than 6/5, that gives us a suspended chord, and it’s better to use a major chord with less tension to make a simple chord progression.
Now that we have our first chord, we can hear that having a 1-chord song becomes repetitive very quickly to the human ear. We can make the song more dynamic and interesting by giving it three chords: I, IV, and V. Take that chord: 1, 5/4, and 3/2 (a major chord). Move all three notes up 4/3, because 4/3 is a perfect interval with a minimum of tension. That’s our IV chord (F chord in the key of C major) Next, from the root position, instead of moving up the chord 4/3, we instead move it up 3/2. That’s a V (or dominant) chord—a G chord when played in the key of C major.
Now, from first principles, namely that the intervals 3/2, 4/3, and 5/4 sound pleasant to the human ear, that 6/5 has more tension, and 9/8 has even more tension (so we avoid suspended chords for now), we have a I IV V chord progression, which is the basis for countless rock and popular songs.
If we take all of the individual notes from the I IV V chord progression, that gives us the seven notes of the major scale, after explaining that, once we cross the octave threshold, we can transpose an octave down without affecting the musicality of the notes. We might even explain chord inversions here.
So instead of just parroting “I IV V makes a nice simple chord progression”, we now know the underlying physics which make I IV V sound so nice to the human ear, and how to get the major scale from those chords. I prefer understanding both the why and the how.
(I would have used two slightly detuned sawtooth waves instead of a sine wave for most of the examples if I were to write an article like the one this discussion links to, explaining this has a more pleasant, piano or violin like sound to it. Maybe even a low pass filter to tame the harmonics. Another option is to run a single sawtooth wave through a Solina style chorus, but explaining two detuned sawtooth waves is easier than trying to explain the Solina chorus effect)
Does music come from first principles, or is it a cultural product that's a result of a feedback loop between a listener/practitioner and an ambient culture and technological landscape? Parrotting is exactly how we learn music- we hear, and we reproduce what we hear. What you call "deriving music from first principles", I call, "post-facto justification for arbitrary aesthetic tendencies".
Whether the human ear naturally prefers 5/4 (5-limit) over 81/64 (Pythagorean) for the major third, and 6/5 over 32/27 for the minor third, is still something I don’t have solid research on.
As it turns out, the modern western scale is more closely aligned with Pythagorean tuning than with five-limit tuning. In particular, the Pythagorean thirds are closer to modern 12-tone equal tempered thirds than they are to five limit thirds.
>>>Around 1300, the English theorist Walter Odington proposes that major and minor thirds (81:64, 32:27) have ratios close to 5:4 and 6:5 respectively, and that singers lean toward these simpler ratios. His observation may reflect the style of much English polyphony of the period, where thirds often have a pervasive role in the texture and may even serve as closing sonorities.<<<
>>>Beginning with Ramos de Pareja in 1482,Fn11 the simple ratios of Just intonation began to be cited by theorists and used in their divisions of the monochord. [...] an octave is 2:1, a fifth is 3:2, a fourth is 4:3, a pure major third is 5:4, a pure minor third is 6:5. These “six-limit” ratios—the senarius, or senario, as Zarlino calls them—are the basic harmonic intervals. Zarlino attributed almost mystical significance to the senario<<<
This article is paywalled, but to summarize, it makes the case that the 5:4 and 6:5 ratios are ratios musicians naturally drift towards in polyphonic contexts.
Just wanted to say, thank you for the detailed response, I suppose my comment looks a bit glib in comparison. I appreciate this perspective- I knew about some basic elements of tuning and acoustics, but it's fascinating that there's this much structure that you can study in it, I understand the interest.
It reminds me a bit of regular polygons or simple geometry like circles- and it makes sense the Greeks would be interested in both- things that are pleasant and can combine and tile well because of their symmetric and regular properties.
I think my "pushback" was more just at the phrasing of "why" something sounds "good"- I do think when we listen to music, we bring our past and our culture into it, and whether a chord sounds "sad" or "happy" depends on a lot more than just the harmonic structure- I wonder about this concept of "tension" you bring up, I can't tell if you mean something emotional or more mechanical. Is that like something you understand just by crunching the numbers on the ratios?
I am missing the part where TFA said that the goal was to help with "basic song writing".
And what is "distracting level of nerdery" to someone can be the key that helps unlock a deeper level of understanding to someone else. I thought we understood neurodivergence a little better these days.
The western theory stuff you describe has almost no relevance at all when considered non-western musical cultures. The contents of TFA, while not strictly comprehensive when considering other musical cultures, is still pretty on point. Even though Carnatic and Hindustani music theoretically uses 22 tones per octave, the most common ones are still drawn from the same set of 12 used in western music, and the most common scales are remarkably similar.
> The western theory stuff you describe has almost no relevance at all when considered non-western musical cultures.
Say it louder for those at the back. People keep forgetting that western theory was unable to explain why the blues (the American music form by excellence) worked at all. And arguably, a lot of the western music theory is more akin to a codification of existing musical practices in the western world rather than some scientific model. But a lot of music theory fans seem to dogmatically treat it as THE science of ALL music.
> That's part of it, but you can make music with none of it.
Does anybody, though? Would anybody listen to it? Every culture on Earth has music. All of them use chords, scales, and rhythm, in various ways. Definitely not all of them use the Western diatonic system, but that's beside the point.
Most music cultures work well without once thinking about frequency. The closest you get might be pitch. Starting from frequency is a very physics-oriented approach and will give you a hard time understanding why your favorite piece of music is so good.
I think what he means as music theory is the next step after what this (blatantly AI-written, but passable) article talks about. This is the part that you take for granted, but it certainly is music theory in the same way that Peano's axioms are number theory even though you don't use them explicitly.
The AI style gets boring very quickly, but I liked the explanation of what Western music notation is optimized for. For more information on this, there's a great and long video at https://youtu.be/Eq3bUFgEcb4.
(Edit: I wrote this around the same time as the reply, which more or less confirmed my hunch)
Music theory was originally a tool for music critics in the 19th century to talk about conservatory music of the time.
There's nothing rigorous, systematic or scientific in it; it's mostly a historical cultural artifact more than anything else.
For example, music "theory" is completely helpless when describing an EDM track or how to compose one. EDM is one of the most primitive music styles ever (barely even qualifies as music in my opinion) and yet music "theory" is worthless in this case.
Spoken like someone with absolutely zero grasp of music theory or modern electronic music. I almost want to congratulate you for the worst-informed comment I’ve read today.
Is music "theory" actually a theory? Can it be used to predict or construct something? Even just a two-note steady-pulse acid bass beat. I'm not asking for much.
It's not a scientific theory, but musical theory concepts are certainly used by players when playing. Would you rather it be called music ontology or something like that?
Music theory is absolutely an indispensable tool for musicians and composers. You can play music without it, but that’s just putting an unnecessary upper bound on what you can achieve.
More than anything, it’s a vocabulary to talk about the thing you’re doing with others.
Music's theory is something you really need to understand at an unconscious level. All the study of how the notes relate and frequencies, that's very interesting and it may help you understand things better, but the real question is not, can you do all the math to figure out why this note and that note work together, it's can you hear it with your ears and play the correct harmony note for whatever purpose the music leads.
I doubt there is any composer that actually is relying on music theory for their compositions. They may occasionally have something finished, but 'it doesn't sound right'. Then go back to music theory and say, oh, this chord is wrong. I can fix that chord because I know music theory and come up with something that works. But they're not doing that at first. They're composing from their unconscious mind.
> I doubt there is any composer that actually is relying on music theory for their compositions.
Would you expect an author to disregard all of the conventions we've discovered and codified through specified language because it's just "more natural" if they let it flow out of them? No, I don't think you would. You'd find it difficult to read and interact with, both as a reader and a fellow writer. Music is the same.
Music theory is just the natural language definitions of the sounds we hear. A composer is absolutely thinking in those terms and using them to construct the piece they hear in their head. It gives you a way to communicate, with words, the sounds you are hearing in your own head. It does not constrain music in any way.
You have it backward. The conventions were discovered first, music theory came after composers did things. Music's theory describes what we already know works, not how to make things work.
No composer I know thinks in the terms of music theory. They often use a chord progression that music theory describes why it works, but they're not thinking of it in terms of music theory. They're thinking in terms of chord progression, just like the composers of thousands years ago were thinking of their chord progressions the exact style changes and so a thousand years ago they went to thought in terms of modern chord progressions but they were still thinking in similar terms.
> The conventions were discovered first, music theory came after composers did things.
Broadly completely untrue.
If you're trying to say that humans were making music before we had a theory for it - absolutely. But every advanced musical tradition on the planet (including Western, but also Indian, Chinese, etc.) has developed alongside a system of analyzing that music, and for very good reason: It's a lot easier to teach music when you can actually talk about it.
I promise you, every single competent composer and musician on the planet - from every culture - has a fairly firm grasp on music theory, in whatever flavor is relevant to the form of music they practice. Every Indian musician who plays classical Indian music knows their ragas. Every Western musician can navigate the diatonic scale.
That’s like saying no programmer relies on computer science.
Sure, at some level of expertise you’re not sitting there saying “oh, I should name variables sensibly and encapsulate functionality because computer science says to”; they are doing those things because with training and experience that becomes innate and accessible in flow state.
But the fact that theory can become ingrained does not mean one isn’t using theory.
It's way more than that. They are just more fluent at creating things like melodies and harmonies that "work" without essentially starting from scratch on every composition.
I know music notation and can write things down, but I'm not a good composer. I'm at the mercy of others to write new material if that's what I'm interested in playing.
And writing it down in a way that other musicians can understand is of nontrivial value if you want people to play your stuff.
Definitely gatekeeping. I'm no wiz by any means, but I've done (and still do) a fair amount of paid work (gigs, studio recordings, teaching, etc.) and I would not describe Grade 5 ABRSM as "very basic"
I think there's still a pedagogical niche for what the article is doing. For someone coming from programming, "here's why these conventions aren't completely arbitrary" can be the thing that gets them interested enough to later learn harmony properly
Many subject matters are initially so confusing and inaccessible that I have often wished for an audio-visual video lecture series in the following format:
Part 1: Music theory explained in just 5 minutes
Part 2: Music theory explained in just 20 minutes
Part 3: Music theory explained in 80 minutes
Etc. Starting with an extremely simplified overview and then making the overviews progressively more detailed.
Many people instead try to give simple explanations without making them short. But no confused beginner wants to be overwhelmed by a huge wall of text, let alone by a long theoretical book.
Unfortunately most people who have become knowledgeable about some subject matter then quickly and thoroughly forget how confusing, overwhelming or intimidating it was before.
I started learning guitar last July, and I wanted to learn music theory (and standard notation) from day 1.
I am following Absolutely Understand Guitar[1] as my music theory lessons (and Hal Leonard method for notation) along side my regular tutorials. So far I am very impressed. Quite beginner friendly, and learning music theory while starting out with the instrument has not been difficult for me at least.
I can't possibly agree loudly enough with this recommendation. I started with Hal Leonard method classical guitar books(1 & 2) and that was one thing...great books, but nothing compared to Absolutely Understand Guitar. That guy teaches and explains music theory in a way so effective it's not even comparable to other systems. Fantastic teacher, fantastic material, nothing but praise for Scotty West's music program.
When I see my friends who are into music play and talk about different instruments, it actually feels like magic to me. I tried to learn Violin some years ago but I could never understand why the note was correct. I do know that if I had learnt Keyboard instead, I would know where the correct notes are but I am still not able to recognize a sound and understand what note that is. Any pointer as to what I can do? Because I dont think learning music theory is going to be enough for me.
At many western music schools, if piano isn’t your first instrument, it is compulsory to study piano as a second instrument. The reason for this is that it really helps when understanding harmony. You also do ear training, which is meant to solve the problem I think you’re describing. I expect you would find ear training resources on youtube or something now but I did it the old-fashioned way where you start by listening when people play major / minor chords, all the intervals, learn to recognize inversions etc and then move on to doing transcriptions of music you like. I have box files full of transcriptions I did when learning. But Levine (for example) includes some ear training advice.
That second point is spot on. The one thing I remember vividly - and that still helps me most - from all those years of classical piano training is the ear training. I don't have perfect pitch, but I remember A440 vividly (thanks to my electronic metronome) and the training left me with a strong sense relative pitch that helps me figure out pretty much any melody and chord progression relatively quickly.
I really wish I had studied piano for that reason. I put many years into flute and almost went to conservatory for it, so I can play pretty much any melody by ear after hearing it, but I have zero ability to do the same for harmonies/chord progressions. I've tried to learn some piano (and like the parent said, was forced to as part of music curriculum at college) but it's incredibly difficult to learn a new instrument to a satisfying level as an adult.
Can't agree more with that last sentence. I picked up guitar around 16yo, bass a couple of years later, and shortly tried my hand at drums. I'm now more than twice the age and I am indeed deeply unsatisfied with my technical ability at either.
> I am still not able to recognize a sound and understand what note that is
That is called "perfect pitch" and it is not necessary to play music. It's very rare to have perfect pitch, and it seems to be innate, not something you learn.
Contextual note recognition (relative pitch) is what musicians normally use to jam. It comes with practice and contextual clues that you pick up over tens of years (including familiarity with your jammate's instrument, even if it's not the one you play; familiarity with multiple eras of music theory; pure practice), so this shouldn't be your #1 priority since it just comes along for free (or a bit of practice), as you learn. Music playing 101 is just... playing music in your instrument. You don't need to recognize notes until you want to jam, which comes years after you start playing an instrument.
Some people seem to just be physically unable to distinguish relative pitch though.
You might want to start here: https://www.musictheory.net/ (not affiliated, I just think it's a very good resource for Music Theory 101).
Isn't perfect pitch just when you can tell a note without having a reference tone?
Once you have a point of reference things just go up and down and from there it should be manageable to identify each note.
Also, not sure about the innate thing. Seems to me that it's just a neural pathway that can be created by playing or listening to a whole lot of music while being aware of which tone is which, for example by reading the score alongside.
Perfect pitch is quite debated. What we know is that: 1) Most people with perfect pitch have it mostly on their main instrument, and they translate the pitch in their inner ear if they hear a different instrument, and 2) Many with perfect pitch report that it gets less reliable with age.
There seems to be many different ways of having perfect pitch. For example, some singers may connect it more to the physical sensation of applying tension to their vocal cords (so they have to be singing the pitch or imagine singing it to be able to tell). For others it's purely auditive.
There's nothing magic in it. Any two pitches that have a rational number ratio with a small denominator sound "correct".
It's just a quirk of human physiology. The real creativeness and ingenuity comes from rhythm and the interplay of repetitive and surprising sounds. The pitches are not important.
Off topic, but given your credentials you might be a good person to ask. Any recommendations on how I should go about learning to play piano? I am just starting out. I have no music background except playing some basic self taught guitar in my teenage years. I can't read music fluently yet. I have access to a nice Yamaha with weighted keys.
The tried and true approach is to find a piano teacher in your area, schedule weekly appointments, set aside at least one hour of practice every day between lessons.
I am hoping you can get pretty far by self studying if your study material is made by experts and vetted by peers, and you are diligent in practicing an hour a day using a practice routine recommended by experts.
Personally I am aiming towards becoming a low-intermediate guitar player over the course of a full year by self studying. My biggest fear is that I develop bad habits, but I am hopeful that the bad habits can be trained out of me with a lot of effort during the intermediate phase.
Doesn't look like really a "v2" to me, rather v1 a bit re-arranged. A true "theory" able to explain present music (or even Jazz from the seventies) and also support its creation is still widely lacking, or just a naive variation of what was used for classical music. Tymoczko & co go a bit in a more general/useful direction where the theory eventually can also be used to define algorithms which can "compose" credible contemporary music, but still a long way to go. The latter is like the "litmus test" from my humble point of view whether a theory is indeed useful.
Thank you for sharing this (and your other reactions downthread) with such depth and care.
Setting your off-the-cuff comment alongside TFA’s Claudish muddle reminds me—as if I needed reminding—about the hazardous parts of self-education, particularly when that education is, as it seems maybe to have been in the author’s case, led by LLM…
I appreciate a programmer hacking on sound and music—that’s awesome, and I’m really grateful the author did so and shared his experience. The trouble comes from the unearned air of authority.
When I worry about the broader question of subtle truths getting lost in the slop cycle, it feels reassuring when authentic expertise like yours still stands out clearly. I’ll take what optimism I can find!
As a non-musician non-Western programmer, the only music book that is making sense to me (still reading) is Robert Snyder's Music and Memory[1]. It's the first book that doesn't trick me by trying to pass cultural artefacts (notes, scales, raga, etc.) as some universal truth, or douse me in medieval pseudo-science (Pythagorean small ratios, etc.)
I am not an expert, so maybe this book has its own shortcomings which I am being blind to. But this is the first book on music I have been able to read this far without having to fight the urge to fling it against a wall.
I don’t think it’s unreasonable to say 2/1, 3/2, 4/3, 5/4, and 6/5 are intervals which sound pleasant to the human ear. [1]
Once that is established, as per the linked article, 12-tone equal temperament makes a lot of sense (but isn’t universal, obviously) because it’s resulting tuning gives us a really close 3/2 and 4/3, and having a simple 12-tone scale reasonably in tune everyone can agree on makes sense.
We can then explain that 5/4 and 6/5 are a bit off in 12-tone, but are “good enough” that we tolerate them being slightly out of tune when using equal temperament. Once we accept that 12-tone has imperfect thirds, we can then look at the I IV V chord progression (I IV V comes from 3/2, 5/4, and 4/3 sounding pleasant to the human ear), and explain why that chord progression is so common in western popular music.
These aren’t universal truths—12-tone equal temperament is a compromise, but, as per the linked article, a reasonable one. Just intonation is, of course, another possible compromise.
[1] 2/1: Octave; 3/2: Perfect fifth; 4/3: Perfect fourth; 5/4: Major third; 6/5: Minor third
And in many cases we don't need to tolerate this because most instruments barring guitar and piano allow musicians to tune chords to just temperament, and players will do this automatically and completely subconsciously.
I’m convinced that “Safe and Sound” by Capital Cities became a major hit because it uses an actual trumpet for the lead, causing the perfect intervals to be exact instead of the every so slightly off intervals 12-tone equal temperament has.
The linked article makes the case for equal temperament by showing that 12 just fifths played in sequence is flat compared to seven octaves.
I'm not saying a real, recorded trumpet doesn't make an appreciable sonic difference, but if it were a sampled trumpet "Safe and Sound" would most likely still be a hit.
Attributing it's hit status to the perfect intervals is ignoring all of the other choices (and supporting infrastructure) that go into making a hit. It's like saying that the Dodge Charger was a successful car because the windshield wipers are of a certain make.
“"Safe and Sound's" trumpet line is partly responsible for the popularity Capital Cities is currently enjoying”
>>>The trumpet line in ‘Safe and Sound’, for example, didn’t appear in the production until nine versions into the song. The final version, on a whim, we decided to try using a trumpet, a live trumpet, to play that line and it stuck. We ended up actually using the trumpet a lot throughout the album after we included it in ‘Safe and Sound’.
"It was trial and error, right? We felt like that line was an epic line and we thought about different instruments that sounded epic, and the trumpet is obviously one of them,<<<
The thing about trumpets is this: Their fifth is a little “sharp” because it’s a perfect just intonated fifth (i.e. a perfect 3/2 ratio).
West Asian maqam has 24 notes, Indian classical has 22 notes, Indonesian gamelan has 5 or 7 notes. What would be the ratios that sound pleasurable now?
What is or isn't pleasurable is a matter of cultural training, and treating them as absolute facts is what I found frustrating in the books that I was complaining about.
Indeed. Bobby McFerrin has a demonstration where, regardless of culture, the pentatonic scale is universal. For the record, a just major pentatonic scale is the notes with the intervals (from the root note) 1, 9/8, 5/4, 3/2, and 5/3.
If you like that book, you might also enjoy David Huron's books on voice leading and anticipation. I have not read the book you referenced, but from the description it seems like a similar approach.
It is presented with a tone of "music theory, the way a musician could never understand it, because they do not know what a sin wave is" which makes it so infuriating.
It’s really good at explaining the octave, the fifth, it shows the mathematical basis for why just intonation has “wolf notes”, and why we use 12-tone equal temperament.
Once it hits the 12-tone scale, and explains why we generally avoid the tritone, it doesn’t explain very well why we generally use diatonic instead of chromatic scales (well, OK, great music can use chromatic scales, but there’s a reason “Entrance of the Gladiators” sounds like a clown show).
I would had, after explaining how 12-tone gives us an almost perfect fifth and fourth, explained that a major third is 5/4, and a minor third is 6/5, and that the thirds are noticeably but tolerably out of tune in 12-tone equal temperament.
Once we have the fifth and the major third, we then explain the major chord (Base note, 3/2, and roughly 5/4). Next, we explain the perfect fourth. From there, we can show the I IV V chord progression. And once we have I IV V we can then demonstrate the major scale. (The linked article shows us a major scale but doesn’t explain why the major scale is tone-tone-semitone-tone-tone-tone-semitone—it’s that way because if we take all of the notes that exist in a I IV V chord progression, we get the seven notes of a major scale)
After I IV V, I would then look at a basic 4/4 rhythm, quarter notes, eight notes, the kick drum, the snare drum, and the closed hi hat.
I IV V, the major scale, and a simple 4/4 rhythm is enough music theory to write a good number of rock and pop songs.
I IV V and the major scale is roughly equivalent to understanding variables and variable assignment. Adding the structure of a 4/4 rhythm, with kick, snare, and high hat is equivalent to if-then-else and while.
From there, if I were to continue, I would next explain the minor third (6/5) and minor scale, the pentatonic scales (minor pentatonic gives us a large number of rock guitar solos), and probably show the I V vi IV chord progression.
Obviously, this is very basic, but things like ABRSM Grade 5 are the music equivalent of Forth-like and Lisp-like languages: They can be useful, but just as the majority of programs aren’t written in Forth or a Lisp dialect, the majority of music doesn’t use, say, an irregular time signature.
A counter argument to the typical "piss on TFA" HN top voted comment: (musician of many decades) the post IS music theory of the kind it purports to be, it's not misleading in the least, at worst it's incomplete (but never claimed to be complete) and simplified.
It's just not conventional music theory (which is just a set of rules thrown at you). But the whole point that the parent missed, is that it is told in a way to arrive to music theory from first principles as understood by computer programmers and math nerds.
Any statement made in TFA is true (at least to a basic level, and, for some of claims, when focusing on western music).
You'll learn nothing of the sort you learn in TFA by reading "The Jazz Theory book" suggested by the parent. The opening paragraphs of TFA explicitly address why that doesn't cut it:
"The problem was never the practice. It was that every explanation of music theory seemed to miss out the fundamental reasons for how and why things are the way they are. Here is a staff. Here are the notes on it. This is a major scale, memorise the pattern. Why those notes? Why that pattern? Because that is the convention. Which is a strange way to teach a system that essentially comes out of physics and arithmetic. There are twelve notes for a reason. The major scale has the shape it has for a reason. Chords that sound good sound good for a reason, and you can compute those reasons."
The parent comment is stuck on trying to sell the conventional music theory nomenclature and its extensions, which, despite the name "theory", is a descriptive set of norms and rules based on historical practices.
The author of the above comment's "postgrad in music" and experience in conservertoires make then unable to see the worth of TFA, because they're too invested in the conventional description and "how things are done".
If you want to understand music theory as a construction, not merely as "here's a set of arbitrary rules and other rules that build on them", ignore jazz/classical musicians and people with music degrees trying to sell you on what they've been taught, as it will be near useless. This requires a different type of mindset.
There are books on musicology that address the concerns of TFA in an official and deep way, but TFA is a good programming-nerd oriented introduction to the matter.
I'm a programmer with a degree in musicology as well.
This ain't it.
I'm reading your comment with a certain disdain for analysis and theory, which I get - a lot of people come out scarred from music theory training, and I'm sorry someone hurt you that way.
But music theory is fundamentally a way to talk about music. Nobody is trying to "sell" you anything, but it does become much easier to work together as musicians when we share a language we can use to talk about the music. "Take it from the candenza", "a bit more ritenuto", etc. is just more efficient and precise than "take it from the place where it goes dun-dun-dunnnn", or "go more slowly-like".
Seriously, you're doing yourself a huge favor as a musician and broadening your conceptual thinking about music by learning this stuff.
>I'm reading your comment with a certain disdain for analysis and theory, which I get - a lot of people come out scarred from music theory training, and I'm sorry someone hurt you that way.
I'm fine with contentional music theory training. Know my music theory, had official music training, been at it for some decades.
It's not the purpose of this. Traditional music theory training or a jazz theory book wont tell you about harmonics and timbre. It wont tell you how come we divided the octave like this, and things this tries to tackle.
It was written to serve a fundamentally different purpose. A purpose which apparently familiarity with regular music theory makes most blind to.
It's like someone wanting to learn about acoustics, and someone given them an earful about diatonic chords and how to read notation. It's simply not what they want to now about. Or it's like someone wants to know about the chemistry of cement or the physics behind structural engineering, and people try to tell him all about construction and construction terms. Not what he is interested in knowing, even if it's essential for building a house, just like music theory is essential (or at least useful) in playing and composing music.
>But music theory is fundamentally a way to talk about music. Nobody is trying to "sell" you anything, but it does become much easier to work together as musicians when we share a language we can use to talk about the music.
That's neither here nor there. The purpose of TFA is not for musicians to talk about music with one another, or to help someone analyze that this piece of music is in that key or uses that mode, and modulates there, or that "this chord here is used as a chromatic mediant", or borrowed chords, or counterpoint, and all that.
>"Take it from the candenza", "a bit more ritenuto", etc. is just more efficient and precise than "take it from the place where it goes dun-dun-dunnnn", or "go more slowly-like".
That's explicitly NOT what TFA wants to be useful for.
> if you get to the point where feel you want to learn more and take it seriously in and of itself, buy “The Jazz Theory Book” by Mark Levine[1]. In spite of what it says, there really isn’t any such thing as Jazz theory - it’s just music theory
Your recommendation seems to mostly apply to western music (I assume so since you only mentioned western music), no? Will Jazz Levine's book help with ragga or gamelan?
People in the cubing community often call all twisty puzzles "cubes".
In this parlance, the "pyraminx" (regular tetrahedron twisty puzzle) is a cube, the face-turning octohedron is a cube, and the "Megaminx" (dodecahedron) is a cube. I've even heard Rubik's Clock[1] called a cube.
He doesn’t say quadratic time, he says infinite time. He is talking about the probability of any given string arising from a random sequence of letters. As t goes to infinity that probability approaches 1.
The monkeys don’t understand hamlet. They just bash enough keys that it appears by chance (eventually). Hence “‘It was the best of times, it was the blurst of times…’ Stupid monkey. “
Here's something to ponder. Assuming the Riemann Hypothesis is true, would that monkey type out a proof of the RH before it got to Hamlet? I guess it depends on if the proof can be expressed in fewer words than the word count of Hamlet.
I love the fact he mentioned the Riemann rearrangement theorem [1] briefly in his examples about analysis. That is (in my opinion) one of the coolest and least intuitive consequences of infinities. Requires some intro to different types of convergence to fully appreciate. More about the theorem here if you’re interested. [2] Weird as it seems it’s definitely true and one of the things you would prove in a typical undergrad sequence on analysis.
[2] Formally, I think the normal way to state the theorem is if you have an infinite series of real numbers which is “conditionally convergent”[3], then the terms can be rearranged so that the sum converges to any arbitrary real number, or diverges https://en.wikipedia.org/wiki/Riemann_series_theorem
[3] Meaning it converges but does not converge absolutely. a_n = 1 - 1/2 + 1/3 - 1/4 + … is an example of such a series. It converges but if you take sum of the absolute values of each term you get the harmonic series which does not coverge.
You can also think of conditional convergence as convergence under the condition of a specific order. It then turns out that unconditional convergence (that is, convergence where it doesn't matter what order you choose) is equivalent to absolute convergence (that is, the sum over the absolute values converges).
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