12 ms·

I really don't understand all the hate in the comments for this article. This seems like a really fine introduction to a lot of the concepts. I had to scour the

I really don't understand all the hate in the comments for this article. This seems like a really fine introduction to a lot of the concepts. I had to scour the web a long time before understanding that the scales were constructed because of the simple/reduced ratio of root note to the others, which is clearly spelled out in this article. Music theory is, in my experience, typically taught as a list of facts to remember. Deriving it from first principles, insofar as it can be, is not common. This article is attempting to start that process. Some commentators are saying that the article doesn't address why we have 12 notes but I wonder if they even know why (one answer is because it's a good compromise between number of notes and that have simple/reduce ratios to each other [0]). I'm also skeptical of music theorists that can't even attempt an answer to basic questions about note length frequency, why some chords are "sad" or "happy" and other basic questions. It's difficult because music theory is a hodge podge of theory that's attempting to describe what's effectively an evolved language (with different music evolution for different regions), but there are some basic tenets that probably apply. I don't claim to have deep knowledge but there are a few key facts about music and music theory that are really obscure unless you know where to look. Any attempt at coming to music theory from a more rigorous foundation should be encouraged. [0] "Measures of Consonances in a Goodness-of-fit Model for Equal-tempered Scales" by Aline Honigh (https://github.com/abetusk/papers/blob/release/Music/measures-consonances_honingh.pdf https://github.com/abetusk/papers/blob/release/Music/measure...) EDIT: corrected spelling (thanks for the comments pointing it out)

Infernal 5y ago
> basic tenants Just in case it’s helpful - “tenets”
chrisweekly 5y ago
+1 / agreed. Also (tangent / tiny nit): "tenants" (inhabitants) -> "tenets" (rules)
criddell 5y ago
You seems to know a lot about the art and science of music so maybe you can answer a question I’ve had lately: what’s the difference between pitch and frequency? When a person talks about middle C on a piano, is that ‘C’ more closely related to pitch or frequency?
- sevagh 5y ago
  Frequency is the repetition rate of the sound wave created by the instrument. 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.
  - criddell 5y ago
    Is the phenomenon you describe in your last paragraph the thing that makes a Shepard scale work? If one were to make a pitch classifier machine, would it always agree with the human ear?
    - sevagh 5y ago
      I don't know much about the Shepard scale. 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.
  - pvarangot 5y ago
    > 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.
ben7799 5y ago
It's only taught as a series of facts to remember if you're not involved in practical application.. AKA actually playing music. 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.
- danShumway 5y ago
  > It's only taught as a series of facts to remember if you're not involved in practical application.. AKA actually playing music. 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.
danShumway 5y ago
Agreed, the pushback on this reminds me ironically of some of the pushback I see towards people who try to break apart math notation to make stuff like science papers more accessible. 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.
gjulianm 5y ago
> Some commentators are saying that the article doesn't address why we have 12 notes but I wonder if they even know why 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".
- abetusk 5y ago
  I'm trying to walk a fine line. On the one hand the 12 note equal tempered scale has almost surely a societal component to it. That is, it was one that won out for weird cultural reasons that don't have a lot to do with some idea of correctness or utility (like why 'qwerty' won out over Dvorak keyboards). 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.
  - scythe 5y ago
    The use of pentatonic scales is extremely cross-cultural, with independent discovery on at least four continents: https://en.wikipedia.org/wiki/Pentatonic_scale#Use_of_pentatonic_scales 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.
john61 5y ago
There are twelve tones because the pitch between them is the smallest one that our ear can differentiate as two distinct tones. Is the pitch smaller, you hear only beats.
- proposicion47 5y ago
  Wait until you learn about live beyond 12TET 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 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
  - tarentel 5y ago
    While you are 100% correct a very simple counter example to the op that a lot of people have likely heard in their life is someone tuning a guitar. It would have saved me a lot of time if people couldn't tell the difference. :D
  - john61 5y ago
    You can test this in the Vienna museum of music. There is a live demonstration with a headphone and with two knobs for the frequency of two separate tones playing together. Also, it visually shows the pitch of those two. If you go below the 12 tone pitch you hear only one tone, near the 12 tone pitch this one tone becomes suddenly to two separate tones.
- dekhn 5y ago
  No. Go look at Ragas in indian music. “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.
twelvechairs 5y ago
Music can be analysed in many different ways. People often respond poorly to an explanation of 'music' that doesnt cover what they see as important or what/how they have learned.
- Kye 5y ago
  Music rage made sense once I understood most people learn One Way, and don't learn there are many convergent cultures and applications that work with the same underlying wiggly airs, and there's often animus between those traditions. Hip-hop has as much potential for exploration in theory as anything else, but a lot of people raised on Western music theory consider it inferior mumbling. 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.
  - bityard 5y ago
    I only dabble in music as a hobby, started later in life, never had any professional instruction whatsoever. So occasionally I find myself on forums populated in part by people who have been taking formal music lessons from strict teachers since the age of three and OH BOY do they get fired up when someone suggests anything that differs even slightly from their training. 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.
TheOtherHobbes 5y ago
There are no first principles in music. The harmonic series is relevant, but you can't start from the harmonic series and find your way to Western classical music. 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.
- abetusk 5y ago
  This type of reply is indicative of precisely why it's so off putting for programmers to get into music. The attitude of "there are no rules!" is espoused while artist after artist that produce music that we like are clearly following some type of ruleset, at least to some extent. 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.
tarentel 5y ago
I'm also skeptical of music theorists that can't even attempt an answer to basic questions about note length frequency, why some chords are "sad" or "happy" and other basic questions. 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.
- abetusk 5y ago
  Not everyone learns the same. Some programmers and math centered folks need a guiding "first principles" approach before being able to move past to higher level understanding. This was the case for me. Without some way to organize knowledge, it's hard to understand which pieces of information are important, which are redundant and which should be applied (and why). 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.
pvarangot 5y ago
The reason some chords or progressions sound "sad" or "happy" for some people is mostly cultural and based on association. And you can rewire your brain to get rid of those associations. It's like saying chocolate taste is happy and lead taste is sad, and complaining chemistry doesn't have an answer as to why. 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.
- andrewzah 5y ago
  Major = happy seems like a lesson for really young kids that somehow got internalized by a lot of people. It’s so bizarre. In a major 7 chord, the 1 to major 7 interval is quite dissonant… Never mind that a major 7 chord has a minor chord in it, and a minor 7 chord has a major chord in it. 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.
gnud 5y ago
It's a fine article, but not a fine introduction. I read more as a list of all the things the author didn't understand (or pretended not to understand), because they couldn't describe them mathematically. 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!
xhevahir 5y ago
> Music theory is, in my experience, typically taught as a list of facts to remember. Yes, but accompanying those facts is a set of phenomena that you're supposed to experience physically.
deleted 5y ago
[deleted]

Infernal 5y ago

> basic tenants Just in case it’s helpful - “tenets”

chrisweekly 5y ago

+1 / agreed. Also (tangent / tiny nit): "tenants" (inhabitants) -> "tenets" (rules)

criddell 5y ago

You seems to know a lot about the art and science of music so maybe you can answer a question I’ve had lately: what’s the difference between pitch and frequency? When a person talks about middle C on a piano, is that ‘C’ more closely related to pitch or frequency?

sevagh 5y ago
Frequency is the repetition rate of the sound wave created by the instrument. 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.
- criddell 5y ago
  Is the phenomenon you describe in your last paragraph the thing that makes a Shepard scale work? If one were to make a pitch classifier machine, would it always agree with the human ear?
  - sevagh 5y ago
    I don't know much about the Shepard scale. 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.
- pvarangot 5y ago
  > 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.

ben7799 5y ago

It's only taught as a series of facts to remember if you're not involved in practical application.. AKA actually playing music. 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.

danShumway 5y ago
> It's only taught as a series of facts to remember if you're not involved in practical application.. AKA actually playing music. 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.

danShumway 5y ago

Agreed, the pushback on this reminds me ironically of some of the pushback I see towards people who try to break apart math notation to make stuff like science papers more accessible. 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.

gjulianm 5y ago

> Some commentators are saying that the article doesn't address why we have 12 notes but I wonder if they even know why 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".

abetusk 5y ago
I'm trying to walk a fine line. On the one hand the 12 note equal tempered scale has almost surely a societal component to it. That is, it was one that won out for weird cultural reasons that don't have a lot to do with some idea of correctness or utility (like why 'qwerty' won out over Dvorak keyboards). 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.
- scythe 5y ago
  The use of pentatonic scales is extremely cross-cultural, with independent discovery on at least four continents: https://en.wikipedia.org/wiki/Pentatonic_scale#Use_of_pentatonic_scales 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.

john61 5y ago

There are twelve tones because the pitch between them is the smallest one that our ear can differentiate as two distinct tones. Is the pitch smaller, you hear only beats.

proposicion47 5y ago
Wait until you learn about live beyond 12TET 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 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
- tarentel 5y ago
  While you are 100% correct a very simple counter example to the op that a lot of people have likely heard in their life is someone tuning a guitar. It would have saved me a lot of time if people couldn't tell the difference. :D
- john61 5y ago
  You can test this in the Vienna museum of music. There is a live demonstration with a headphone and with two knobs for the frequency of two separate tones playing together. Also, it visually shows the pitch of those two. If you go below the 12 tone pitch you hear only one tone, near the 12 tone pitch this one tone becomes suddenly to two separate tones.
dekhn 5y ago
No. Go look at Ragas in indian music. “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.

twelvechairs 5y ago

Music can be analysed in many different ways. People often respond poorly to an explanation of 'music' that doesnt cover what they see as important or what/how they have learned.

Kye 5y ago
Music rage made sense once I understood most people learn One Way, and don't learn there are many convergent cultures and applications that work with the same underlying wiggly airs, and there's often animus between those traditions. Hip-hop has as much potential for exploration in theory as anything else, but a lot of people raised on Western music theory consider it inferior mumbling. 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.
- bityard 5y ago
  I only dabble in music as a hobby, started later in life, never had any professional instruction whatsoever. So occasionally I find myself on forums populated in part by people who have been taking formal music lessons from strict teachers since the age of three and OH BOY do they get fired up when someone suggests anything that differs even slightly from their training. 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.

TheOtherHobbes 5y ago

There are no first principles in music. The harmonic series is relevant, but you can't start from the harmonic series and find your way to Western classical music. 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.

abetusk 5y ago
This type of reply is indicative of precisely why it's so off putting for programmers to get into music. The attitude of "there are no rules!" is espoused while artist after artist that produce music that we like are clearly following some type of ruleset, at least to some extent. 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.

tarentel 5y ago

I'm also skeptical of music theorists that can't even attempt an answer to basic questions about note length frequency, why some chords are "sad" or "happy" and other basic questions. 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.

abetusk 5y ago
Not everyone learns the same. Some programmers and math centered folks need a guiding "first principles" approach before being able to move past to higher level understanding. This was the case for me. Without some way to organize knowledge, it's hard to understand which pieces of information are important, which are redundant and which should be applied (and why). 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.

pvarangot 5y ago

The reason some chords or progressions sound "sad" or "happy" for some people is mostly cultural and based on association. And you can rewire your brain to get rid of those associations. It's like saying chocolate taste is happy and lead taste is sad, and complaining chemistry doesn't have an answer as to why. 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.

andrewzah 5y ago
Major = happy seems like a lesson for really young kids that somehow got internalized by a lot of people. It’s so bizarre. In a major 7 chord, the 1 to major 7 interval is quite dissonant… Never mind that a major 7 chord has a minor chord in it, and a minor 7 chord has a major chord in it. 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.

gnud 5y ago

It's a fine article, but not a fine introduction. I read more as a list of all the things the author didn't understand (or pretended not to understand), because they couldn't describe them mathematically. 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!

xhevahir 5y ago

> Music theory is, in my experience, typically taught as a list of facts to remember. Yes, but accompanying those facts is a set of phenomena that you're supposed to experience physically.

deleted 5y ago

[deleted]