I've never met a jazz pianist that for example will work under the assumption that a 2-5-1 sounds sad-transition-happy, it sounds like a 2-5-1 because the pianist has a sophisticated enough musical understanding to have a concept on their brain that is a 2-5-1 and has a specific sound that is associated to it. It's the whole deal with ear training intervals, scales and chords. The whole major happy minor sad thing is like a pedagogy trick to get people started into getting those kind of sounds into their language. Same thing with intervals, a minor third is maybe sad but then a whole or a half step on the major scale are what? super sad? they sound like a train wreck harmonically but happy when you play them all together on the scale? What's happening is that people just associate musical phrases, sounds, harmony, to stuff and that's kinda outside of musical theoretic research and more like getting into the fields of cognitive science or psychology.

Have you actually asked any music theorist about this? I would be surprised if you hadn't gotten this kind of answer because in my experience talking to working theorists over lunch or on social events they usually agree on this.

I tend to think of things in consonance vs dissonance, and different colors for chord qualities and voicings. Where the goal is managing contrast/tension and release.

I am no expert in music theory but I've been playing for most of my life and write music for fun. I know that A4 is 440 and that's about it. I don't know how knowing any other frequency, or even that one for that matter, would ever be helpful in me reading a chord sheet and walking a bass line to it nor would it be very helpful in me writing a melody or chord progression for a song I might be working on.

As far as I know, the happy/sadness qualities of chords isn't a universal thing. It's likely not a question for music theory to explain.

I read through the article a bit and I think it's fine but the way most people learn music theory is by first learning an instrument and learning the relevant ideas associated with it and if still interested will likely move onto more advanced concepts. It's like any other field really it all sort of builds on each other. Some of it has to be rigorous I think. If you can't read music it's probably not going to be very useful to know G->B is a major 3rd. The author says they want to write music which you don't really need to know music theory to do but you need to learn to walk before you run and it's not clear to me whether the author even knows how to play an instrument.

This learning style is not universal and, in my view, why this article is specifically titled "Music theory for nerds". Programmers especially can make highly complex music without ever learning a classic instrument. Algoraves, chiptune, generative music, DAWs, real-time music programming environments etc. are all a thing and participants often don't need any concept of a "real" instrument to create quality music therein.

I think you're right about the happy/sad being a cultural quality but there might be portions of it that might be explained by other means. Here's my attempt, which is almost surely at least partly wrong: "Major" chords have more constructively interfering waves than do "Minor" chords, especially in the lower frequencies, where more of the power lays.

I would say this more as programming and math centered folks prefer subjects that are amenable to first principle analysis, which is what drew them to math and programming in the first place. And folks with that mental inclination will tend to use those tools to bear on all problems and subjects. When all you have is a hammer, etc.

But it's important to remember that not every subject is built from first principles. Not everything in the world is reducible to a simple system with emergent properties. There is no Grand Unified Theory of history, no five axioms of mammalian biology. And, while I like the mother sauces, there is no culinary theory that can logically prove which recipes will taste good.

We saw attempt to formalize in the 50s and 60s around spoken language. Chomsky and other linguists hoped to fully systematize spoken languages and analyze them according to formal grammars. Computer scientistics hoped to figure out all the rules of human languages so precisely that computers could parse them with perfect accuracy. The efforts failed. It turns out that while there are certainly patterns and grammars to how humans speak, the rules are fuzzy, ever-changing and deliberately broken.

Music theory is also particularly tempting for people who like thinking mathematically, because it does have some numbers and stuff around frequency, intervals, etc. But music is about 10% systematic and 90% arbitrary cultural history. One can certainly focus on the subset that fits in that 10% and have an enjoyable experience making music while doing so. But a whole lot of music won't "make sense" in any real way if you discount "because people did it that way and others got used to hearing it" as a valid justification for some musical practice.

There is no mathematically sound reason why we prefer the sound of a stretched out metal spring rattling against a taut piece of plastic on the second and fourth beat of every measure. Any explanation for why thousands of songs do that today has to involve discussions of goat skin, the Atlantic slave trade, the American fad for Hawaiian music in the 1930s, etc.

Also, I guess my comment does sort of imply that I meant a classical instrument but arguably some of the things you listed could also be described as instruments, in which case, my point still stands. If you want to learn western music theory with the intentions of writing music, which is what this article is describing more or less, you need to have a way to make western music, whether that be a cello, a tracker, or a gameboy it doesn't matter.

You're absolutely correct that we all learn differently but I would bet the people who learned and understood music theory well prior to learning and/or experimenting with some sort of sound generation first are in the minority. Most people will learn both at the same time. Playing music goes along way with reinforcing why things are done the way they are done and reading about the concepts after hearing them, playing them, experimenting with them goes a long way.

If you're getting a practical education in this stuff you learn bits of theory right at the point they make perfect sense and you "Grok" them quickly and internalize them without having to think of them as memorizable facts.

E.x. you are directly associating a particular part of the music theory with a direct link to muscle memory on your chosen instrument. It's burned into your muscle memory already and now you have just associated the theory with the practice. Every time you perform that technique or type of passage it just reinforces the theory.

Another example.. understanding the difference between a minor chord and major chord or 7th/diminished/augmented chord, or the difference in how two different intervals relate means a totally different thing to a person who has practiced those things till they can differentiate them by ear than a person who cannot differentiate them by ear.

Perhaps all this is a weakness in an age where a lot of people are making music on computers in ways that break this type of link.

It's all very analogous IMO to someone who has read a book about a sport but has never actually played the sport.

There IS a notation that they use among themselves about microtones above and below the standard pitch, and they have to agree what pitch, exactly, they're playing at any given note.

Furthermore, the pitch they would use depends on whether the musical line is going up or down; in other words, it could be different in different parts of the same piece.

There are a lot of things that serious musicians know well enough to explain, but almost no one ever asks them.

The reason they're the "same" is because of a limitation of musical instruments in their ability to play in multiple keys that led most Western instruments to be tuned in the 12-tone equal temperament system. If you select a different temperament, or use an instrument that can't be constrained by the 12-tone temperament, such as a computer, they can be different.

Some violin players will also tell you that they're not the same notes.

They're the same on an instrument that can only play a defined set of notes, e.g. a piano or fretted instrument. It has nothing to do with the piano being in equal temperament.

If a violinist is playing an F#, his finger isn't necessarily on the exact same spot as when he's playing a Gb. As he explained answering my question, it isn't even in the exact same spot for the same F# every time in the same piece. The string players have very slight variations that they can describe precisely to each other so they sound good together.

And yes, fretless instruments such as violins can be precise enough to differentiate between the two.

"nothing" other than the fact that there's only one black key which has to serve both purposes?

Or a guitar... I think multistring fretted instruments can't be in equal temperament.

First, no. I went hard into music in my early life, I both learned basic piano and intermediate saxophone, and I went through the full suite of band/orchestra/jazz/soloing, to the point where I was a fairly decent-ish musician. It's not until later that people get taught this stuff in my experience, I struggled with any practical connection to music theory probably until late middle-school.

But second, what you're describing is exactly why the article is useful; because the people who are trying to get into music haven't played an instrument for so long that they can improvise on it and start to put together intuitively that certain ratios or key signatures or whatever sound good.

What happens with people who are taught to play instruments is that they spend a lot of time honing those instincts by playing the instrument, but at the same time, what they're playing is constantly attached to this notation so that when they intuitively connect that minor/major/augmented chords sound good or bad in different situations, they simultaneously connect them to the notation as a way of expressing those concepts.

People who don't have formal instruction don't go through that process the same way. They might be composing music without ever thinking about the notation. And when they go to seek out instruction or learn more about techniques, they don't have a bridge to connect their intuitions about what does and doesn't sound good with the notation, everyone just expects them to find the notation intuitive.

I had a lot of formal instruction on playing jazz. A lot of it was about honing intuition, listening to jazz, replaying other famous improve tracks, improving over those tracks, memorizing licks. But that intuition and practical experience was also coupled with being able to break down and describe what those other musicians were doing. That required a shared notation that I could understand, it required being able to understand what an instructor meant when they talked about why certain riffs worked or common ways to resolve a run of notes if I got lost in the middle of an improv solo and didn't what to do next. But I could follow that instruction because I knew the notation and I had a connection between my practical experience of how music sounds and the formal notation about key signatures and chords and crud.

A lot of people don't have that because they haven't spent X years learning to read sheet music. Articles like this are helpful for them.

It just doesn't work like that. Music could have gone in various directions, and Western music happened to pick the various directions it developed in, more or less arbitrarily.

They happen to emphasise a combination of parallel blocks and horizontal lines, and various quite complex kinds of motivic and structural elaboration and development.

Post-classical music - especially electronica - is much more focused on rhythm and timbre. It has more complex sounds and sound combinations and less complex structures.

There isn't much in the way of rhythm-and-timbre theory yet, but it's on its way and will be a thing within a few decades.

All of it is a mess because music has always been about styles, experiments, and conventions, and those have changed over time.

And it's also written from the musician's POV. Not a mathematician's POV. Or a dabbler's POV. Or a nerdy POV.

For example - sooner or later people get to transposing instruments and the obvious question is "Why would anyone sane do that?" And the answer is because it's convenient for the players.

That's it. That's the rationale. For all of it.

So while it's awkward and not very elegant, it has a kind of consistency that's somewhat useful across multiple styles.

It's impossibly hard to invent a system that is so much better for this that it's worth throwing the old system away. People keep trying and failing, because you can't just rationalise part of it, you have to improve all of it. And it's such a huge thing that's not a practical project.

So it persists - partly as a relic, partly as a developing system.

Electronica might be rhythm and timbre based but even looking at rhythm you can start to ask some basic questions (what note length frequency is more pleasing? Why? What frequency of two underlying beats sounds good? Why?).

Sometimes theory can be nothing more than a collection of discovered tricks. Sometimes it can be something more fundamental. To waive your hands and say that all of it is arbitrary is doing a disservice to anyone trying to learn and understand.

There are no fundamental rules to grammar, but we still teach writers what a simile is. Even in spelling, English has no consistency about a lot of this stuff. Are spelling rules useful though for non-native learners? Heck yes. Do we still have grammar books? Yes. It turns out that learning the exceptions is sometimes faster than memorizing everything. Music is a communicative medium based in large part around social norms of what combinations of sounds tend to feel good to people who grew up in a specific environment, and music theory is an attempt to break apart that social consensus into basic rules that can be imitated and built up into more complicated genres.

The rules are somewhat arbitrary and made up, but that doesn't mean they're not real, and that doesn't mean you can't sort-of derive some of them from more basic rules or from basic principles.

Music could have gone in multiple directions, but for whatever reason Western music went in the direction it did, and many people who are trying to learn music aren't trying to learn the full spectrum of every direction music could have gone. They're trying to learn how to imitate Western sounds, and for that purpose specifically music has rules -- many of them derivable from other rules, flexible and breakable as they may occasionally be.

Music theory is a language used to be able to have conversations about harmonic and melodic aspects of a piece of music. Rythmic aspects are less well supported (that's putting it mildly) by western musical theory, but the same is true there for whatever formalism or terminology/nomenclature you might pick: it's not a set of rules, it's a language to facilitate non-musical discusison.

For example, the vast majority of people who have taken Music Theory 101 have completed coursework that is the equivalent of "Hello, World!". That is barely scratching the surface and certainly give the aspiring programmer the skills necessary to create something non-trivial. The same is true of music theory. You don't instill in someone the musical understanding of Brahms with one music theory class.

I think that there are rules, but they're less about a teacher being an asshole. Musical styles evolve over time. We wouldn't have classical without baroque, and we wouldn't have romantic without classical. The style itself imposes a "rule" that is really a best practice. How do we in technology treat best practices? Well, they're basically rules that we shouldn't violate without careful thought. The same is true of music. People who study basic music theory learn about the cadences used most commonly in church music ... V-I ... IV-I ... and the deceptive I-IV-V-vi cadence! You feel where music is going because you've learned the rules by listening to other music and embedding yourself within its best practices. V-vi is deceptive because it violates a best practice, but used effectively, it works.

As music evolved, and as the world became smaller in terms of ease of travel and exposure to other cultures' music, we started to see new influences. Debussy and others were influenced by indonesian gamelan music. Without that influence, we might not have the jazz that we have today. Why? The impressionist style that Debussy practiced created floating pillars of sound, chromaticism, etc. that became important elements of early Jazz.

It's all connected and has evolved over time, just like technology. Personally, I do think they are rules, but like most rules, they're meant to be broken.

As another example, I've spent a ton of time learning game design rules, and all of them are optional, but they're still useful. "Rules" in this context means, yes, communicative terminology, but communicative terminology about particularly effective ways to build commonly understood musical motifs/phrases that affect Western listeners in somewhat predictable ways.

Music theory is a language for talking about a language, music itself. It is partially social convention that leads us to have a 12 tone scale, and it is definitely social convention that leads us to call that a "scale". However, the average Western listener will respond to the notes of that scale in predictable ways, and there are "rules" that you can learn that will allow you to more easily and predictably manipulate that listener's emotions and communicate broader ideas through your music -- many of those underlying rules about tuning, ratios between notes, and so on are derivable from mathematical principles or at least describable in mathematical terms, even if ultimately the reason why listeners respond to some of those ratios is social and arbitrary.

Of course, the rules are not concrete or immutable, they can be broken and often are. But the majority of rules we learn in most subjects are not concrete.

Similarly, there are no concrete rules in writing, and the terminology we use to describe story structure is arbitrary and made up. However, learning the "rules" of writing will make you a better writer for typical audiences that live near you, and those rules are expressed through common set of terms and concepts that many professional/hobby writers have decided to use -- many of which can be partially derived or explained by talking about psychology or history or whatever.

Sure, these are not immutable, scientific principles baked into the heart of the universe, but:

A) the author goes out of her way to say that she isn't claiming that, and

B) breaking down rules and building them back up from different starting points or looking at them mathematically is still a reasonable thing to do with rules that have a social origin, and

C) even though a lot of why certain chords sound good is baked into culture rather than biology, it's also a kind of strong claim to say that all of it is purely social. But I don't think it would matter much even if it was purely social, people who do music theory for a living still talk about math sometimes.

"Western musical theory" is full of ideas about harmony (OMFG, so many rules), often with non-musical semantics overlaid on top of the actual musical elements. These are the "rules" that you get play with as a musician, and the very best of them do in fact break them frequently (but expertly). Why do so many people remember "Take 5" ... because it's in 5 not 4! Why do people consider Coltrane to be a genius ... because of the games he played with harmonic relationships mostly connected to the circle of fifths but deeply subverted. Why do some of us still celebrate the "genius" of Schoenberg, Stravinsky or Bartok ... they upended traditional rules about harmonic resolution, even the very notion of tonal harmony in some cases. Even within this thread, we see people noting a striking detail of a recent Adele song that consists of (almost certainly deliberately) singing somewhat off-key to strong effect.

There is a huge amount of recorded music that plays entirely by "the rules" (the ones that go way beyond TFA), but a lot of what people think of as musical genius is precisely the stuff that flouts the rules (with enough knowledge of the rules to make this work).

I've commented to the same effect elsewhere, but people really underestimate how much the "barely anything" notation concepts are a real barrier to people who are unfamiliar with the domain. https://xkcd.com/2501/ comes to mind here; TFA is 5000 words and ends with multiple links to further tutorials and reading. That's a completely fine place to start. If you want to learn the rules of western music theory and get into the meat of what you're talking about, it is going to be a lot more work if you don't know what a scale or a chord is, and I don't see anything wrong with teaching those basic concepts from a mathematical perspective.

----

> with enough knowledge of the rules to make this work

That's the part that the author's target demographic wants. They want to be able to either:

A) imitate the rules well enough to write something passable (say for game soundtracks), but aren't looking to innovate, or to

B) learn the rules well enough to innovate.

In both of those cases, even the most basic notation concepts like "what scales and chords are" is a serious barrier to entry for many people.

One thing that often goes "wrong" with this is that the mathematics of frequency ratios is a huge barrier that's most often irrelevant to actual music making. If you literally know nothing about music, there's a good case for just letting the tuners deal with it for the time being, and starting from the old Do, Re, Mi etc. that teaches you both solfège (sight reading/aural skills) and the musical syntax of scale degrees. Then sing a whole lot of music in (movable do; fixed do is pointless except for specialists) solfège and try to make up simple embellishments and variations on what you sing. There's a "programmer's favorite" way of learning these too (these are called diminutions) based on the scale-degree leap that you're traversing, hypothetical elementary operations of musical syntax and whatnot; but good musical intuition will always be helpful. Guess what, now you're well on your way to improvising simple music at the keyboard, and later on you can even get started on learning counterpoint without being lost in all the details. Because, unlike actual college students who are forced to take a counterpoint class as part of studying bookish "music theory", you'll have the fundamentals down pat.

The problem with teaching them from the particular mathematical perspective taken in this work is that...it doesn't actually teach them, and it throws up it's hands and says I don't really know about fairly basic stuff. This isn't an alternate pedagogical route chosen by someone who has a different view of how to get people up to speed for the domain, it's a smattering of trivia that isn't directed at learning the rest because the author doesn't understand the basics, much less have a particular pedagogical approach to them.

I think that's a separate conversation from whether this article specifically should be the entire basis for someone learning how to compose music. I agree that I would not point someone at this article and say, "this will be enough to get you on the road to learning how to compose music", I would want something more involved by someone who has more experience.

But that's different from saying it's wrong for the author to talk about sound frequencies.

----

To your point in specific, I don't see where the author ever claims that this is an alternate pedagogical route to learning music, the author actively discourages people who already know music from reading the post. The post explains a few basic concepts like what a scale is -- and fairly accurately (or at least about as accurate as most of the other explanations that you'll find online). It openly works through the stuff that the author understands, and openly admits what the author doesn't understand, while sympathizing with the target reader that it's hard to pick up a new subject when it sounds like everyone else is speaking a different language from you.

So basically, it is every single technical blog post written on any subject by anyone who is openly learning about a thing online, and that is something that should be encouraged, not derided.

I also still kind of disagree with people who are saying that this is just trivia or too basic to even talk about, commenters are still underestimating how little normal people know about music.

If people come out of this article understanding stuff like:

- There are 12 "steps" in an octave

- An octave is doubling the frequency of a pitch

- Written down on a staff, we compress those 12 "steps" into roughly 7 spaces.

- A scale is 7 different notes.

- Because of weird ratio stuff and social consensus about which "steps" in an octave are most commonly used, some parts of the scale move 2 "steps" and some move 1

- Transposition exists as a concept, you can play the same song starting at different pitches

- Notes like B# and C can overlap, except some really professional players might treat them differently because it turns out the math we use for different pitches doesn't completely work out correctly in all scenarios.

That's all stuff that people who are unfamiliar with music don't know. Okay, the author doesn't really understand what's going on with minor keys, but this isn't a textbook, and there is value even in something as simple as "an octave is doubling the frequency of a pitch."

I'm weirded out by how upset HN is being about an amateur blog post with reasonably correct information by someone who is actively trying to teach themselves how to write music. This is exactly the content that we should want people to write about online, and it's written in exactly the style that we regularly encourage bloggers to write in when they're exploring new concepts/domains.

Starting off an explanation of music theory by talking about whole number frequency ratios is like starting off English class with a diagram of the glottis.

> Western music has twelve distinct pitches. This is somewhat arbitrary — twelve has a few nice mathematical properties, but it’s not absolutely necessary. You could create your own set of notes with eleven pitches, or seventeen, or a hundred, or five. There are forms of music elsewhere in the world that do just that.

[...]

> I get the feeling that treating the whole chord/key ecosystem as a set of rules is like studying Renaissance paintings and deciding that’s how art is. It’s not. Do what you want, if it sounds good. I’m gonna go try that. Consensus seems to be that the real heart of music is managing contrast — like every other form of art.

----

> Starting off an explanation of music theory by talking about whole number frequency ratios is like starting off English class with a diagram of the glottis.

I would say it's more like starting out an explanation of color theory by talking about wavelengths, even though you don't really need to know any of that to understand composition, and even though most of the rules of image composition are contextual to specific cultures and aren't hard requirements that artists have to obey.

The math behind color is definitely not a requirement that artists should be forced to learn, but some people find it helpful to know what mathematical formulas were used to create a given color wheel.

Do you play the piano? I think the piano is the best vehicle for grokking music—it allows for melody and harmony (and rhythm) all in one instrument, in sort of a visual way, that is hard to get in monophonic instruments, or even with guitar (for more complicated reasons). I think I developed my musical sense in two main ways: 1. listening to songs on records and on the radio, and figuring out how to replicate them at the piano, and 2. playing lots of music on the piano from sheet music, where I was constantly exposed to chord progressions and the like in other people's music; the "tropes" of Western classical and popular music, if you like. Neither of these are trivial, but both are within reach of most people, I think. I will posit that there are few shortcuts to musical mastery. Grokking music is definitely not like (as easy as) learning a new programming language.

6 years ago, I accidentally abandoned my preferences and disengaged disgust in an attempt to stop automatically judging. And then I returned to music for the first time in 18 years with the idea that there is no wrong note. Here are some of my observations:

- I wasn't deeply/actively/mindfully listening to music when I was younger. This was part of a cycle of an attention-degrading cycle where I'd hear music and then distract myself with judgements of it, emotions that followed the judgments, and judgments about those emotions.

- Songs that "feel sad" don't. How a person hears/attends to music, how their body has been conditioned to receive different notes/chords/progressions, the meaning given to the sounds/words, the judgments around those things, and how they learned to feel in response to those judgments is what's being described when someone says a song feels a certain way to them. It's not universal and those feelings can be disengaged.

- How I feel in response to music has gotten way deeper and more expansive as a result of releasing all those conditioned feelings. I did this, in part, by pressing a bunch of random keys down on an organ and sitting with the feelings that came up and let them pass. Part of the practice involves letting up on one key at a time and then pressing it again, back and forth, until I can distinguish the note in the cacophony and have reached a feeling of contentment with the sounds. Rinse and repeat for each note.

- Music theory is absolutely unnecessary and in many ways hinders the learning process. I play improvisationally and not necessarily to play a song I've heard. Doing this for a year led to the emergence of a skill where I can start picking out melodies I remember.

- Styles and genres are largely based around preferences. I have a friend whose connective tissue disease (Ehrler-Danlos Syndrome) keeps them from feeling music. As a result, they've developed a strong liking of noise music, which would likely feel very uncomfortable in the body to people whose bodies have been trained on more traditional forms of music.

- The discomfort with dissonance is largely a learned thing, due to cultures of being unwilling to sit with dissonance. It can be turned off.

- If what you're looking to do is make music people can easily like based on commonly cultivated body feels around different sounds and preferences, focus on rhythms that don't change much, avoiding dissonance by default, repetition and also on novelty.

- If you want to make music people can easily ENJOY, repetition, improvisation, and novelty are keys. If you don't know any music theory, novelty will be easy. If you can make some sounds and then vaguely make the same sounds again, repetition will come (this can take a bit of practice, especially if not very connected with the body). Improvisation is such a broad idea because there's improvising around a melody or theme, around rhythm, around volume, around whatever the inspiration is (whether it be sounds, rhythms, feels, words, stories, colors, whatever), and probably more. Allowing and accepting whatever happens is a key to improvisation.

- Music can be enjoyable, even with abrupt transitions from slow to fast, soft to loud, harmonious to dissonant, rhythmic to droning.

- If I want to play what's in my mind, I can sing it and play along with how I'm singing.

- "Wrong notes" played rhythmically can fit into anything.

- If there's no wrong sound, I can play any instrument.

- Everything is a drum.

- Everything is music. Including silence. They cannot compel the silence to cease. So you are music trying to music in some ways and making music without trying. Trying to do that in a way that gains approval or caters to preferences is one way to live. Experimenting in the ways I describe here is another.

I happened to go to an experimental concert just last week, involving organs (since you mentioned them). You might enjoy it. It's available for streaming here: https://roulette.org/event/cleek-schrey-and-weston-olencki-o...

Here's the instructions for doing the nonjudgment practice that led to all these realizations. I highly recommend them. The effects are quite literally lifechanging, unlocking/unblocking joys I didn't even know were possible.

https://news.ycombinator.com/item?id=29764591

I've had to really staunchly stand up for myself and my music to other musicians and to my past notions of music, and have definitely gotten defensive around playing music like this.

No more. I'll just send people to this. And I'm definitely going to focus on playing more like this again.

Thanks again for bringing this into our lives! <3

I sometimes feel like one could take this sentence and substitute just about anything for "music."

"Science is what we understand well enough to explain to a computer. Art is everything else we do."

There is nothing wrong with trying to turn an art into a science. Music just has a bunch of implicit rules that people want to make explicit. Musicians find this frustrating because they aren't interested in understanding music this way. Both perspectives are fine.

And yet I get the feeling that if someone does investigates that (and adjacent topics) in depth with success there would be a bunch of interesting consequences to it.

Maybe, I have got no knowledge in the field - it just sound like something interesting, why the heck wouldn't we want to know it?

Thanks, I misunderstood you.

It's a craft, not a rigid system that you have to follow. What's called 'Rules' in music is more like patterns that have been found to sound good. For example, the famous 'Rule of the Octave' is a pattern based originally on playing thirds and sixths ("first inversion chords" if you want to phrase it that way) over a "walking" baseline. But the rule is far from fixed, and almost immediately the basic pattern using thirds and sixths was altered to use thirds and fifths ("root position chords") on the tonic and dominant degrees. Then the other chords were altered in turn, giving each bass scale degree a sonic identity of its own, with ascending and descending, major and minor varieties etc. Thus what literally started as a simple and basic rule has become incredibly complex. This just shows how a craft can evolve to become more interesting; rigid, foolproof rules cannot. And the "rule of the octave" is a tiny part of music as a whole (though it's pretty foundational, all things considered); but guess what, other "rules" work the exact same way!

'Music theory' is much more of a working practice musicians use to communicate with each other and document their work and discoveries. How programmers feel about their notation systems isn't something working musicians should be concerned with, I don't think.

There is no fundamental thing that makes some notes or combinations pleasing and others not. It is all culturally mediated. I know that possibly seems unlikely and uncomfortable, but nonetheless it is true. If you drill down far enough into music you find the harmonic ratios, and human culture. That's it, there is nothing else down there at the foundations.

IMO asking why a melody sounds pleasing would be like asking why a plot of the Mandelbrot set is interesting; math isn't going to be able to answer that.

I would be fine with a music theory that is a set of tools to deal with sounds, just as math is a set of tools to deal with numbers. Whether certain properties are desirable are up to the theorist.

Music theory can tell you why a specific combination of notes and a chord progression in a musical piece are pleasant to the ear, but does not guarantee that using similar combinations and progressions will result in pleasant sounds.

Part of the reason is subjectivity, in the sense of music is intended to be heard by subjects. And these subjects have their own experiences of music, which in turn conditions their expectations and their reactions to sounds. What sounds good is different from person to person, let alone from culture to culture. Coming from a classical background, when I heard jazz at a young age, I considered it chaotic and awful. Today, it's the most pleasant style of music for my ears. I've seen people who had never, ever heard opera music listen to an aria and laugh to tears because for them it was comically awful.

Another is reason, I think, is that music is embodied by who plays it. I can play Blackbird in the exact same way Paul McCartney does, but when I do it the best I can expect is people saying "that's nice!". When McCartney plays it, the entire stadium hold their breath and get chills, some are in tears. I don't see how that level of emotion can be explained in a scientific way.

GP didn't say there are no rules.

“The rules are culturally, and path, dependent and are not derived or derivable from a simple set of universal first principles” is very far from “there are no rules”.

It does mean that certain approaches to learning the rules that might fit well with people's abstract preferences for how they’d like to approach the field don't work well in practice, though.

What "there are no rules!" is kinda the excuse for music theorists to keep on working on a field that has had so far little applications on how music is created. Maybe yeah on how some people learn it, but that's it. It's basically them admitting that actually successful musicians usually work under a set of rules and techniques so simple from the theoretical standpoint that the whole field gets invalidated.

If anything, it's just the opposite. The 'rules' (again, this should be understood as patterns, or perhaps rules of thumb) practitioners implicitly rely on are far more complex than most theorists are implicitly comfortable with. This is why bookish music theory was mired for centuries in pointless discussions about acoustics and ratios, or some incredibly weird formalisms for representing meter, whilst practitioners got on simply focusing on what sounded good.

(The 'Rule of the Octave', which is the kind of rule I'm pointing to, was quite exceptional in being explicitly taught in actual published treatises about music - and even that was practically forgotten later on; it's not usually taught in "introductory music theory" classes even though it arguably should be!)

I hit my head... and other people's heads... and tables and walls... until I realized that:

1. Yes, there are "rules"

2. They are far far far more arbitrary than I realized

3. They are far from universally applicable.

Personally, I expected music to be heavily math based, with universal rules.

But my current understanding is that while there IS a lot of math, what sounds good / what people in any given culture like, is all arbitrary. You can use math to describe some of it, but not to derive it.

As well, unfortunately, when people say "Music Theory", they largely mean a variation on one or both of:

1. Note reading - Western music notation, which I don't consider "Music Theory" but rather notation, but many will disagree

2. Western Music Theory, largely though not entirely put down by 18th century old cranky europeans based on what they happened to like at the time

There is FAR less "universalness" in Western Music theory than I thought.

So there is this combination of:

* Huge englightnment and pattern recognition and increased understanding as I learned more music theory

and

* tremendous frustration at inconsistency and arbitrariness, until I realized it wasn't my music teacher who hated me, it's that what they are teaching me is arbitrary

So personally, I think it's important for programmer to accept "there are no rules (in the sense that we think of "rules", boolean logic and math etc), though there are guidelines and recommendations (which are completely arbitrary and cultural-based)"

It turns out "what rhythm / note / combination / frequency is more pleasing" is 99% how you were brought up / what you are used to, rather than some math/physics correlation. Move to another part of the world and throw out your 4/4 and 12-note equal temperament and I-V-vi-IV

You absolutely can, because that's essentially exactly what western classical music (and more or less all other forms of music) already did, just spread out over a very long period of time.

Take Western music. Early music is mostly vocal, and early principles of music theory evolved around what would be possible (and practical) to sing. Different people have different vocal ranges, and the constraints that puts on the music lead to certain constraints in counterpoint. Eventually instrumental music becomes more socially important, and that changes what kinds of music can be made. Mathematics progresses in such a way that new tuning systems (12 tone equal temperament, and its precursors) make it easier to modulate between keys, and more modulation (and chromaticism) becomes common.

Even things like the way the music is structured depend on social practices, they're not spontaneous. The sonata form depends on an audience that listens attentively to music so that they can perceive the way the themes are gradually transformed.

I could go on, but nearly everything in music goes this way--there are principles, but they only have a limited explanatory power, you need to get into historical contingency to really understand why things evolve the way they do.

I certainly agree that historical context has always been central to the way music has developed. It's not for nothing that most of Europe refers to "the church modes" rather than using a more abstract term for a set of interval rotations. But that historical context is only absolutely necessary if you want to try to understand why music evolved in the way that it did. It's not necessary if your goal is to understand the way we understand, compose and perform music today.

Of course, I'm all for more understanding of music, so I'd favor historical context every time. It's just that it's not a necessary feature for understanding where we currently are.

There is no one true "music theory". Music theory as it is typically taught is no more than an elaborate system of nomenclature of the stylistic preferences of European music in the last three centuries. It is a cultural description of a cultural phenomenon.

To get into more specifics, when explaining music theory at an elementary level, you might say that a frequency ratio of 1:2 is called an octave and all the notes with an octave relationship to each other are considered equivalent. That is true, if you are making European-style music. Most other cultures around the world have a name for the interval called the octave, but most of them don't consider all octaves to be the same note. "octave equivalency" is fundamental to Western music, but it's not a universal law, it's a stylistic choice. To imply otherwise by claiming that your explanation of this European convention is essential to music writ large is to do a disservice to the many musical cultures around the world that don't follow that convention.

> The harmonic series is relevant, but you can't start from the harmonic series and find your way to Western classical music.

As big as fan as I am of being aware of non-western musical culture, I was commenting on the specific idea of moving from the harmonic series to a specific musical culture (the western classical one). This is why the chemistry analogy is (roughly) appropriate, because there are in fact a substantial number of (western) music theorists who consider there to be only a single western classic music theory.

I try to almost never use the words "music theory" without prefixing them with a temporal and/or geographic cultural qualifier (though I likely often fail here).

It's not just a "convenient for the players" moment. It's also because changing over to non-transposing instruments would create a generation-long transition period of broken pedagogy. It's the same reason oboe fingerings are so nonsensical. It's backwards compatibility to preserve previous fingerings that makes the new fingerings awkward and arbitrary.

My experience with being taught music theory lines up with your experience, and I spent a lot of time learning both piano and instrumental music leading up to college, to the point where I considered myself to be a fairly decent-ish musician. I was not taught why anything exists I was taught rules: rules that I constantly saw being broken around me, and that I was constantly told, "well, it's OK for them to break the rules once they understand them." It was not until I started to think of music-theory as a grammar based on conventions and social norms that any of it clicked for me, before that point I hated music theory. Certainly it was rare for people to try and break things down to first principles or to describe why things were the way they were.

What happens as an early musician (in my experience) is that over time you just kind of get used to the social conventions and it becomes intuitive because you've spent a lot of time on it. I learned about stuff like ratios once I started getting into intermediate jazz on the saxophone; it was not an early concept taught to me in piano lessons.

And then people look at articles like this and say, "well, that's all super-basic stuff, and it's not completely right, and she's doing a bad job of explaining..." Nonsense, she's doing fine. Even if there are a few inaccuracies, this is a good article: it's written in a way that's sympathetic to people who know nothing about music theory, it gets across the immediate points that musicians might not even realize are problems (why is a C a C, why is B# C), it is a (mostly successful) attempt to tie music theory to something that readers might already understand. It's helping bridge this gap of "repeat this rule until it becomes intuitive", and that's a good thing to do.

Even with really simple concepts, people forget how big the barrier of entry is around notation. It's extremely common for me to run into people who say they would read more scientific papers or statistical research if the math notation didn't throw them off. Music is the same, there is a common language that is very efficient and nice for people who know it, and is indecipherable for everyone else. Anything that helps lower that gap is good, and looking at this article as someone who knows the notation already my immediate reaction is that it seems pretty helpful and a lot of "intro" music courses won't explain these concepts, they'll expect you to tough it out and just memorize the rules.

An electronic musician working in a DAW needs to understand notes as ratios and frequencies lest they produce a mix that sounds like goop on club speakers, but a pianist can get away with not having any idea. Put them in a room and ask them to explain the difference between a mode and a scale, and you'll need a hazmat crew.

Realizing all this led to a handy heuristic: the best musicians to know and work with are those who can navigate those different conceptions and traditions without fear or judgement. There's no reason an orchestral composer can't learn from riddim without tripping over triplets.

There is definitely some subset of musicians that cannot conceive the notion that someone somewhere on the planet might be learning music just for fun and don't WANT to take it uber-seriously.

Just in case it’s helpful - “tenets”

Is there an actual reason or are all of these post-hoc explanations? Depending on the culture you'll have different scales and ways of organizing the sound. From what I understand it always comes down to "some people thought it sounded good and from there they made music and people got used to it and it snowballed".

But there is an explanation that does try and get at it a bit more analytically and that's in the paper I linked to. With the above caveats about the cultural momentum, the 12 not equal tempered scale provides a happy compromise between the number of notes to provide a basic building block for music (characters or digits would be an analogy to notes in an octave) vs the number of "good" note pair combinations (where "good" is if the frequencies have a small/simple fraction approximation).

Some of it is hand-waivey, to be sure, but at least it provides a potential reason and a starting point.

https://en.wikipedia.org/wiki/Pentatonic_scale#Use_of_pentat...

As far as I can tell, 12 ET is the smallest equal temperament that acceptably encodes the common variants of pentatonic scale. Meanwhile, the pentatonic scale probably appears because (3/2)^5 ≈ 8.

I assume it's written partly tongue-in-cheek, to show how arbitrary a lot of music tradition is, and how it creates a barrier to entry.

And the article didn't even mention different clefs or transposing instruments!

Also (tangent / tiny nit): "tenants" (inhabitants) -> "tenets" (rules)

Frequency is a physical measurement of a periodic waveform.

Generally, a tone is composed of harmonics, which have frequencies that are integer multiples of a fundamental frequency. The pitch physically corresponds to the fundamental frequency of harmonic sound (or a sound that is mostly harmonic). But the relationship is complicated, as we can perceive two tones as having the same pitch (and fundamental frequency) even if the actual spectrum of one of them does not actually contain a component at the fundamental frequency (see https://en.wikipedia.org/wiki/Missing_fundamental).

This is because our brain will fill in the fundamental frequency if a tone has most of its harmonics. This is why you can hear bass notes of a song even if the speaker you're listening to doesn't have the frequency response to actually reproduce the fundamental frequency.

I hope some of this nuance is making this make sense.

There's also a concept of "pitch class", which is the idea of what you might call "C-ness" of every C note on the piano. In other words, octave equivalance, or the fact that you can substitute nearby C for each other without ruining harmony. Pitch, in some ways, is the intersection of pitch class and a specific fundamental frequency.

Pitch is the perceptual (i.e., human auditory perception) correlate of frequency. Pitch is what your brain/auditory system interprets that it hears from the sound wave at that frequency.

For a piano chord, there is likely the fundamental frequency (or f0, the lowest frequency), and its upper harmonics (integer multiples of the fundamental). That's why musical instruments (like the piano) sound richer than simple sine waves: their physical bodies create richer, more complex waveforms from the harmonics, giving it a unique timbre.

There are some subtle differences. For example, (very oversimplified), if you were made to listen to a waveform containing the frequencies of 60 Hz and 90 Hz, your auditory system would "hear" a pitch corresponding to a fundamental frequency of 30 Hz, since 60 Hz and 90 Hz are integer multiples of 30 Hz.

Eh, so if you add 60hz and 90hz you get a wave that repeats every 33ish milliseconds. You don't "hear a 30hz sine wave" that your brain is inventing, that's a very common misconception. You just hear a 30hz "thing" that is not a sine wave because there's a 30hz thing that is not a sine wave playing. Just try adding an actual 30hz sine wave to the 60+90 thing and you'll see it sounds very different to what you hear when you add those two sine waves. If you keep on adding waves spaced 30hz adding the 30hz or 15hz one wouldn't make much of a difference because what you are listening to is something very similar to a low pass filtered 30hz pulse wave.

> your auditory system would "hear" a pitch corresponding to a fundamental frequency of 30 Hz

If one were to make a pitch classifier machine, would it always agree with the human ear?

Regarding a pitch classifier machine, typically algorithms for pitch classification/tracking/detection focus only on the fundamental frequency (or f0) of the input sound wave. So, _technically_ pitch and f0 are used interchangeably where they shouldn't be.

I have yet to see a pitch classifier machine that tries to implement the special workings of the human auditory system.

Periodic sounds above about 20 Hz are perceived is being `pitched'. Our perception of pitch is logarithmic. I.e. if you keep multiplying the frequency of a sound by the same number we perceive the pitch as going up in equal steps.

For example, to go up (an equally-tempered) semitone (aka half step or half tone) — which is usually the smallest pitch distance used in music — you multiply the frequency by 2^(1/12) (roughly 1.059463).

To go up an octave in pitch, you multiply the frequency by 2. But going from the pitch A3 (220 Hz) to the note an octave higher, A4 (440 Hz), sounds like the same `size' of increase in pitch as going up an octave from A4 (440 Hz) to A5 (880 Hz), even though you are now going up 440 Hz instead of 220 Hz for the previous octave.

Yes, but accompanying those facts is a set of phenomena that you're supposed to experience physically.

In short: no you're factually wrong. Human ear can discern smaller pitch changes and there actually music composed on smaller subdivisions than 12

For instance https://en.wikipedia.org/wiki/19_equal_temperament

You can check done pieces on YouTube.

Yes it sounds unusual. Yes it sounds strange. But thats just because you've been conditioned to listen 12 tet all your life.

But saying 12 notes because we can't perceive smaller changes is, again, wrong and there's actual counterexamples of music done with smaller changes

“Ragas are precise melody forms. A raga is not a mere scale nor is it a mode. Each Raga has it’s own ascending and descending movement. And those subtle touches and uses of micro tones and stresses on particular notes like this…”

Microtones are less than the difference between two adjacent pitches in western scales and are discernable, even to people like me who have a hard time telling adjacent pitches apart.

For example, lots of the notes in the vocal of the Beatles `Come Together' are clearly (often very) flat — wonderfully so, subversively so, even, in our pitch-corrected age!

A very small gap gives a subtle chorus effect, a little wider takes one into honky-tonk piano territory, and wider still perhaps more like a bell, but still sounding like one note.

But, as you say this doesn't negate the audibility of microtonal inflections in a melodic line.

However, pitch steps smaller that those of 12tet can still provide new chords. For example, in 24tet the triad with a third half-way between minor and major is a distinct and interesting sound. But yes, in 24tet two consecutive pitches sounded together sounds more like a single note with an interesting timbre.

There are systems that have more than 12 notes.

Plenty of instruments hit these "microtones". E.g. string instruments with frets can bend strings, and string instruments without frets can just play those notes.

Genres of music like the blues frequently utilize these microtones.

12TET is just the custom in western music, but we can absolutely discern smaller intervals.

http://terpstrakeyboard.com/web-app/keys.htm

I'm sure at some point those tones will converge into a single note to human ears, but the fact that a 53-note keyboard exists shows that people can absolutely hear smaller divisions than just the 12 standard notes.

https://www.sciencedirect.com/topics/medicine-and-dentistry/...