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Basic Music Theory in ~200 Lines of Python (mvanga.com)
451 points by mvanga 65 days ago | hide | past | favorite | 188 comments

As a primer for music theory, this post doesn't teach much. It's using Python to derive various sets of notes in scales and modes, which is already easily available via google search, and in a more learnable format than Python code.

The most basic aspect of Western music theory overlooked here is the relationship between tonic and dominant. If you know the "home" chord aka "the I" aka "tonic" is C major, the dominant will be G major, aka the V chord. Add just the F major chord, and you'll know 1-4-5 in a "basic" key: C major. 1-4-5 is the simplest chord progression, you can play amazing grace, you are my sunshine, even The Beatles, you'll be rocking with 1-4-5.

Next level, if you add in the minor 6 (a minor) and minor 2 (d minor), you realistically know 95% of the chords you'll ever hear in C major pieces. And on the piano, this is ALL white notes, so even someone with zero musical knowledge can "solo" over your chords by just plunking any white notes while you play these chords (kids LOVE LOVE this btw, highly recommend trying with a kiddo).

I wouldn't consider double-sharps and double-flats "basic" music theory. They really aren't needed for beginners, since they're relegated to keys like C# major where you'll occasionally sharpen a note like E# (aka F) into E## (aka F#). I didn't run into these until around 5 years into my piano training, playing Chopin's F# major nocturne Op 15 No 2, there's a bunch of double sharps in that piece.

In any case, don't worry about double-flats and double-sharps or the precise notes of various modes and scales. Just learn pieces you enjoy, preferably with a mentor or teacher who can suggest improvements based on their trained ear.

Heh, I understood your first paragraph. I understood literally nothing in the following two paragraphs. Is this what it is like when I talk to people who don’t know anything about programming about my work? Pure gibberish?

Yes, it is! Music and programming both have a lot of notation, syntax, and terminology.

I am not really a programmer, but the thing I always wanted wasn't a "how to program guide" but "what is all this syntax" guide.

It is funny, but when you learn a written language, you spend a lot of time learning grammar and punctuation, but when you go to learn programming it all seems conceptual. there are lots of demonstrations of grammar and punctuation, but I rarely see nice, succinct lists of all the syntax you might encounter.

https://learnxinyminutes.com might be what you're looking for. Concise syntax guides for many languages.

So, this is for a few reasons.

Syntax is a skill floor, but it's not anywhere close to a skill ceiling.

If you want rapid-fire example of the various forms a given language commonly uses, I recommend X in Y minute guides. Those show off the various bits of syntax for a given programming language, though without rigorously defining them as such.

Part of the reason that programming syntax is usually taught by example, rather than by formalism is that the formalisms for programming syntax, well, look like this: (cribbing from wikipedia).

  program = 'PROGRAM', white_space, identifier, white_space, 
            'BEGIN', white_space, 
            { assignment, ";", white_space }, 
            'END.' ;
  identifier = alphabetic_character, { alphabetic_character | digit } ;
  number = [ "-" ], digit, { digit } ;
  string = '"' , { all_characters - '"' }, '"' ;
  assignment = identifier , ":=" , ( number | identifier | string ) ;
  alphabetic_character = "A" | "B" | "C" | "D" | "E" | "F" | "G"
                       | "H" | "I" | "J" | "K" | "L" | "M" | "N"
                       | "O" | "P" | "Q" | "R" | "S" | "T" | "U"
                       | "V" | "W" | "X" | "Y" | "Z" ;
  digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
  white_space = ? white_space characters ? ;
  all_characters = ? all visible characters ? ;
Can you take that grammar and write 10 examples of valid statements from it, with no other context?

vs, if I give you

  MYNUMBER := 123;
That gives you a much better flavor from looking at things.

Ultimately, most programming languages should have defined grammars in their docs somewhere, but most devs use them by intuition, rather than formally.

The other thing, as well, is that it's one you get past grammar as a primary concern that you gain true fluency. And there are a lot of things that are higher level than grammar that can aid/hurt a program much more than the grammar constructs (like various patterns, know algorithms, schemes of organization for different types of projects, and so on). A mostly human-usable grammar is table-stakes these days.

If you have a specific language you want examples or a grammar on, let me know, and I'll see if I can find it.

(edited for formatting)

> Part of the reason that programming syntax is usually taught by example, rather than by formalism is that the formalisms for programming syntax, well, look like this: (cribbing from wikipedia).

Here's the thing though -- a "what is this syntax" guide does not imply that you need a formalism of the syntax. What the person is asking for, in my opinion, is a linkage between the symbols and the concepts.

For example, when reading mathematics, often the problem was not my conceptual understanding of the material, but merely that I was not sure how to parse the symbols and map them to what it was doing. I could read a formula, but the mapping of each component piece as a shorthand was not there. At the time I did not internalize that "square root" is literally just getting the side of a square (A somewhat silly, obvious-in-retrospect idea! But it gives you a perfect example of the kind of mapping I'm talking about) -- because of this I wasn't able to get an idea of what it was doing!

In such a case, your formalism would not have worked, because it's simply a grammar. I did not need the grammar -- examples can show that, wikipedia can show that, what I needed was enough information about the link between the symbolic, and the conceptual, that I could find reference material. What I found instead was either as you put down, literal grammars, or vast tomes of knowledge that required more vast tomes of knowledge to read and figure out what each one in turn was saying. So I would get lost down this rabbit hole.

What the solution to this is, again IMHO, is a listing of syntax, yes, but with a conceptual mapping on the right.

So not saying things that we already know -- like "this is a number", but having a construction of an IF statement, and then a conceptual mapping on the right in the form of written description of how it works, or a visual description like a flow chart.

The point of writing was to convey knowledge, it is possible to convey intuition, and yet in scientific fields we seem adverse to doing so! It's treated almost like an unspoken thing, it is covered in passing, but almost never explicitly. It's why much of "intermediate programming" is difficult to break into, in my opinion -- and the same for mathematics (3blue1brown is breaking this up, however)

This is the answer that actually explains my problem! I went to the Learn X in Y site that another comment recommended and scrolled to the python guide[1]. It is a list of syntax, but it is (in my mind) insane! It goes right through all the math that is there and then jumps into lists. The first thing it does is show this!

# Add stuff to the end of a list with append li.append(1) # li is now [1]

And this is exactly the kind of stuff that keeps me from getting deeper into programming. I look at that, and wonder, "what the hell is that . doing?" Now, I know enough python to know that it is calling some function on an object called 'li', and that li is a list. or something that can take a .append() command. I also know that append() is some kind of function. But, these guides never give me enough detail on what the . means. Worse, it seems difficult to find answers to this kind of stuff in aggregate. If I google everything I can find stack exchange pages on each piece of syntax and can get to the point, but for fluency and retention I really need that conceptual piece.

I don't write software, but I use python/pandas for basic work with restructuring data. The hurdle to understanding how to slice data frames was incredible for me. I couldn't understand from the examples why the behavior works the way it does. I often feel like I can get working code without any real connection or understanding of why the code works.

You're answer is great, I wish there was a solution for this disconnect since I can't imagine I'm the only one who feels this way.

[1] https://learnxinyminutes.com/docs/python/

I'm just glad there's someone else with the same problem!

I think the best way might be to make something like Albertini's charts for file encodings, but for programming.

An example is here: https://raw.githubusercontent.com/corkami/pics/master/binary...

Of course even within that graph there could be more expansion that it would be nice to see

Also, to add a further point: Because much programming is done by intuition rather than formalism is why there can be so much unintended use of a given program.

I recommend you subscribe to prof Guy Michelmores YouTube channel then.

He is pretty good at explaining music theory without boring you to death. He even has a video on 1-4-5

Scales are the set of notes you can play during the song that will sound ok to the ear.

On a song in C major (or A minor), you can play any white key.

Chords are sections based around a note.

The notes played during a chord give mood and color to the chord (harmonies). The main notes of a chord (that will sound the best) are found by taking every two notes (the note+2+2), e.g. for the C chord it’s C, E and G.

Also the sequence of the notes is the melody.

And also simultaneously the ordering of the chord “drive” the song and also the mood. The 1-4-5 the parent is talking about is a very common chord progression (C major, F major, G major). The numbers here are simply the 1-index of the note in the scale used as the base for the chord.

So while you have three dimensions simultaneously which can feel overwhelming the parent was saying that simply following the 1-4-5 progression and playing randomly white keys will sound ok.

Next step try to hit one the main notes of the chord when it is playing (C E or G for the 1 for example).

I think it depends on who is explaining the complex topic. The main goal for the "explainer" is to implant ideas in someone else's head in a way they can understand and relate to. This is done through a shared vocabulary. If someone knows nothing about a topic, then the entire explanation must be done in the listener's vocabulary (while slowly and deliberately introducing new terms, and clearly defining them), which OP didn't really attempt to do.

Add on top the time signature grid and then you got some real giberrish! ‘The 6th hits on the ah of 3 ok!’


>The most basic aspect of Western music theory overlooked here is the relationship between tonic and dominant. If you know the "home" chord aka "the I" aka "tonic" is C major, the dominant will be G major, aka the V chord. Add just the F major chord, and you'll know 1-4-5 in a "basic" key: C major. 1-4-5 is the simplest chord progression, you can play amazing grace, you are my sunshine, even The Beatles, you'll be rocking with 1-4-5.

Having learned music theory on a guitar rather than a piano, I learned this in a different order. C Major wasn't the focus at first. We started with Am Pentatonic and learned the common 1-4-5 progression and how to build chords and progressions out of that. Then added the rest of the notes of the Am scale in before finally going into root notes and relative scales and learning C major.

It's just my conjecture, but i think Am works better on guitars for learning because it's right in the middle of the guitar starting on fret 5 on the 6th string. Makes it easy, like you say, for someone to solo along with a 1-4-5 progression just by running up and down the scale. As long as you hit the right frets, it'll sound decent, you don't have to stretch too far, you get a nice clear view of the scale's 'pattern' on the frets. Plus, it's the relative minor of Cmajor meaning, you can still play along with someone just hammering white keys on a piano.

We also learned using a lot of blues music. There's a lot of easy variations you can do on a guitar in an Am blues key that can teach you all those fundamentals.

Modes were also worked in at the same time. This was probably not the best though, cause i really didn't get them at the time and only fairly recently sat down to study them and actually figure them out.

Just a note, it would be less ambiguous to say the chords are a 6 minor and 2 minor since minor 6th and minor 2nd are both intervals that don't relate to those chord qualities, for example the minor 2nd is a semitone above the tonic note, whereas a 2 minor chord (or ii, since lowercase represents minor chords in roman numeral chordal analysis) starts a whole tone above the tonic. Also, I think you mean the iii chord, since the ii chord is much less common. But by that measure you may as well be teaching the bVII (flat 7 dominant), which shows up all over the place in popular music (https://www.hooktheory.com/theorytab/common-chord-progressio...). That said, I agree chordal analysis is quite useful as a beginning point, but mostly for teaching the instruments that, well... play chords.

> Just a note

This made me smile.

That was (p)unintentional on my part, your pointing it out was instrumental!

Good stuff, but since it seems like there is a lot of pedantic responses to this post I'm going to chip in myself and say that most traditional gospel renditions of amazing Grace also make use of the supertonic. In the key of C that would be DMaj.

Your advice is good and most of the advices stop at this level. Do you have any advices for what to learn next?

Any suggestions about theory learning beyond of what you've described?

Something that would help with composition perhaps? Music phrasing? Some book to read?

Thanks a lot. I am adding your post into my collection of Hacker News wisdom snippets :)

Do you know why these chords are so common? Is it simply cultural or something else?

The notation OP is using is relative to the key of your song. So if your key is C major, the V chord is G. However, if your key is F major, the V chord is Bb. So it's not that there's only a few chords used in popular music, it's that there's a very consonant group of chords for any key your choose.

Also, OP is leaving out lots of ways to modulate these basic chords into more complex ones (adding a seventh step, inversions, power chords, etc.).

Finally, as with a lot of pseudo-Pareto type things, often the few exceptions are what make or break a piece musically.

Any suggestions about theory learning beyond this?

Something that would help with composition perhaps? Music phrasing? Some book to read? Something for self learning? I wish that melodies I am trying to compose would be better in reflecting what I like in music, and I whish to figure out what is missing.

I can improvise with different chords but it is getting boring and once I try to do something more comlex it doesn't reflect what I like.

I think I am missing something basic and simple but since I had no other option but to learn myself mostly it is probable that I simply wasn't exposed to something essential in theory, something that all good composers know very whell, something that allows experimenting but in a productive way.

May be there is a book that is like a bible for all composers and I simply never heard about it?

I don't have any specific recommendations and am quite rusty - but years ago when I was similarly interested I just looked up a decent undergraduate music programs course requirements and got their intro harmony text followed by intro comp text; learned a lot from that.

This is not a bible for composers but does cover some common chord progression for popular music: https://smile.amazon.com/gp/product/0595263844/ref=ppx_yo_dt...

As it was explained to me by my musician aunt (and I've heard it repeated in other places): because Music Execs. Lots of successful pop music is uses the 1-4-5-(6) chord progression, thus, when executives are picking hit songs, they go with what they know will work.

It's like bringing brownies to a potluck. It won't blow anyone's mind, but everyone will happily eat them.

That still doesn't explain why those chord progressions became popular, and they far predate the late 20th century record industry, so it really isn't a very satisfying or informative explanation, even though it's not outright wrong (it's just a restatement of familiarity bias, which generalizes outside music).

A fair bit of early music composition is weighted by what is easily sung, more than anything else.

It can be tricky to deal with the intersection of music and programming. For example:

> The chromatic scale is the easiest scale possible

So far so good-- in both programming and music we're just stepping through the smallest values (half step for music, the integer "1" in programming). So "easy" definitely applies to both domains.

> We can generate a chromatic scale for any given key very easily

For programming, sure-- you just find your offset and go to town.

For music, however, this is a wrong warp. The chromatic scale is a special case of a symmetric scale which cannot be transposed. There's literally only one such scale-- each transposition brings you back to the same exact set of pitch classes.

Figuring out what it means to have a chromatic scale "for a given key" is advanced music theory. In fact, I can only think of a few places where that makes sense:

* studying the complex harmony of late-19th century Romantic music

* studying the choice of accidentals in chromatic passages of Bach, Beethoven, etc. to infer the implied harmony

Those are important things, but they are definitely advanced concepts.

Long story short for programming, the author moves logically from an array to stepping through an array. But in terms of music, they start with the simplest possible scale and then jump to a third year undergrad theory concept.

> Figuring out what it means to have a chromatic scale "for a given key" is advanced music theory

Interesting... Do you have any links for learning more about this - maybe some analyses?

My take on chromatic scales (in the context of this post) is that the very existence of a(n equally tempered 12 tone) chromatic scale is the axiom the OP is using but not stated - hence a comment further up/down about P5s not necessarily being equivalent to d6 in other tunings.

My take on chromatic scales (outside the context of this post) is that there is only one, like there are only two whole-tone scales, etc, and that it wouldn't necessarily make sense to say "the E chromatic scale" - instead you'd say "playing a chromatic scale over an E major harmony" (for example).

However, if there are cases where it's useful to be more specific I'd be really keen to go deeper.

> My take on chromatic scales (in the context of this post) is that the very existence of a(n equally tempered 12 tone) chromatic scale is the axiom the OP is using but not stated - hence a comment further up/down about P5s not necessarily being equivalent to d6 in other tunings.

Ooh, good catch-- I completely left out tuning systems!

But again-- the point of "basic" music theory is to simplify the practice of discussing music. In that context, the fundamental purpose of the chromatic scale is to introduce the complete set of note names, as well as the range of the piano pitches. This gives the student a full set from which to derive all other concepts like scales, keys, triads, and all the other fundaments of the common practice period.

So again, if you start with a chromatic scale and then start talking about the differences in half-step intervals along it-- boom. Huge conceptual warp.

Honestly, I don't know much about the intersection between symmetric scales and alternate tuning systems. Personally, it seems like it would be an incredibly esoteric niche, although I can imagine some funny musical jokes with the idea. :)

> The chromatic scale is a special case of a symmetric scale which cannot be transposed.

I would not agree here. I think you can transpose a chromatic scale, but you end up with the same "set" of pitches. (So you _can_ transpose, but if you only consider the _set of pitches_ you end up with a invariant.

But scales are not just a set of pitches, but also have a root note.

You can establish the key of C and play a chromatic scale from c' up to c'' and there would be the feeling to accept C as the root of the scale.

So the chromatic scale is kind of a _total_ (all 12 pitch names) and _trivial_ example, as you pointed out, very symmetric and usually not so interesting for analysis if you want to detect and describe structure.

In general it depends on the music. If the music is based on diatonics, then a major scale or it's modes will be a fitting primitive for analysis, considering chromatic notes something like side notes.

On the other hand 12-tone music uses a chromatic scale as a basis, negating the structure and hierarchy of diatonic scales.

So I don't see a problem with transposing a chromatic scale, it's useful and necessary for mathematical sound systems (helpful for computation) to define operations, even if there is no direct gain (functionally speaking - identity / mempty etc.) :

1 + 0 = 1

> I would not agree here.

Yeah, I was hasty. Of course you can transpose any segment of intervals, including a chromatic scale. The point is that a chromatic scale is a special case of a symmetric scale which includes all pitch sets (and therefore, all pitches).

That's important, because to a beginner in tonal harmony the combination of "scale" and "key" is like a pedagogical sandbox. The intervallic profile of the scale serves to reinforce the very idea of music being in a key-- it extends to the system of harmony as triads are stacked thirds within that given intervallic profile. So everything has guard rails which serves to reinforce the relationships between tonic/dominant harmonies, cadential formulas, and so forth. Those guard rails are important since the modulo math of starting on different scale degrees to generate church modes can be conceptually confusing-- at least you've still got the lynch pin that the quality of the chords in a I-IV-V progression is unique to the major scale.

It would be a twisted pedagogical move to pair the starting point of "chromatic scale" with "key" because suddenly there are nearly no guardrails. Sure, you've got the placement of the "starting note" at the beginning, and you could give that an agogic and dynamic accent when playing the scale to emphasis "tonic." But there are no other clues for the listener about harmonic or scale-degree hierarchy. You've literally removed everything else.

It'd be like teaching beginners how to dribble a basketball, then moving directly to how to call a time-out before you fall out of bounds. I can imagine how strange that team would be. And I can imagine how weird the music would be from a python programmer who incrementally builds a sophisticated program for the purpose of deploy chromatic scales in various keys. In both cases I certainly want to experience the result, but in neither case would the participants be building on "the basics."

Edit: clarification

I don't think this is really anything to do with music vs programming. The author just used the wrong words... it's pretty clear they meant "generate a chromatic scale starting at any note" ;)

Thanks for bringing up the connection with symmetric scales -- these are really interesting!

If you want to go further down the rabbit hole of symmetrical scales, checkout Olivier Messiaen's modes of limited transposition https://en.wikipedia.org/wiki/Mode_of_limited_transposition. For a given set of pitches within an octave there are a limited number of times those pitches can be transposed before you wind up with the same set of pitches. And the modes in that scale must also be fewer in number than the number of pitches in the scale, meaning at least two modes of the scale must have the same interval spelling. The simplest example is the whole tone scale. Up a half step I get the same set of pitches, another half step and I get the same pitches I started with, so it is 'limited' to one transposition. And there is only one mode of the whole tone scale, since no matter where I start I always have the same set of intervals.

Shtaaap, you’re headed for the Totient Function! Collision immanent, abort, abort!

There are maybe three aspects to music theory:

(1) Theory of how things sound like: Tones, melodies, scales, chords, based on the frequencies of individual sounds.

(2) How to name things.

(3) How to handle the mess of naming things in Western music theory, where things have 12 different names, depending on which note you choose as the base.

This post seems to focus on 3.

most disciplines, music included, have theory and practice. how things sound is an element of the latter, whereas why things sound the former. this article as the title atates is about music theory and does a pretty decent job IMO

I would be delighted to see a follow up article that explores frequencies and harmonics while sticking with the code demonstrations and incorporating a simple tone generator for the practice side of things

Here I was expecting you to say:

(1) Melody

(2) Harmony

(3) Rhythm


Really all of these are shorthand for something much more fundamental around ratios and how these are experienced by the human body at different frequencies.

Harmony is shorthand for ratios at audible frequencies (~20-20,000 Hz) as they are quite directly picked up in the ear. Rhythm is shorthand for ratios expressed at much lower frequencies (~0.1-10Hz) which the body interprets with relation to its own functions (heartbeat, walking, dancing, speech). Melody is a combination of harmonic and rhythmic ratios in a way the human body has been trained to hear as a 'voice'.

It would be interesting to go through a modern college level music theory textbook and break it down into which of those 3 things each concept falls into. I can't imagine getting past maybe the first chapter.

> How to handle the mess of naming things in Western music theory, where things have 12 different names, depending on which note you choose as the base.

You are missing the point.

I once listened to a podcast where fourier transforms were used to generate sounds that otherwise don't exist.

Could you maybe share which podcast? Generating “sounds that otherwise don’t exist” does not sound particularly remarkable taken at face value. It’s basically what any synthesizer or audio processor does, and Fourier transforms are also a very commonly used in audio processing.

This podcast. The episode of Joseph Fourier.


What I meant by "sounds that otherwise don’t exist" are sounds that are too complex to be created by physical music instruments its easier to simulate them by computer.

> sounds that otherwise don’t exist.


Why is that mess necessary? Cant a semantically rich notation be devised to avoid that mess?.

To me, that’s like asking “why are inconsistencies in English necessary? can’t we all just learn Esperanto?” There’s hundreds of years worth of written music, hundreds of years worth of pedagogical material, and millions of people who simply will not “un-learn” the current tradition. Just like English, over the centuries, music notation evolves, but only just does that, evolves.

Anyone wanting to take things back a step further to first principles may enjoy this (shameless plug - I wrote it)

Deriving the piano keyboard from biological principles using clustering (Jupyter)


> If you hear a sound of frequency f and others of frequency 2f, 3f, etc then there's a good chance these sounds come from the same object, due to the physical principle of resonance. And so our perception of sound evolved to reflect this...

Wow that's interesting enough to share as a standalone post, so I took the liberty! Thanks for the link!

The quoted sentence seems false to me. Most physical objects do not have naturally harmonic vibration spectra. The vibration modes are not integer multiples ofthe fundamental (except for a vibrating string). Only the finely tuned western instruments do. So this is a somewhat backwards argument.

> Most physical objects do not have naturally harmonic vibration spectra.

What is your basis for saying this?

A large number of physical objects, solids as well as hollow can be approximated as systems of springs, surfaces and tensile elements, which all have some frequency response. It isn't rare at all for a physical system to have a very sharp resonant peak in its frequency response, to the point that you'll often find mechanisms to dampen that response so the structure will survive certain inputs.

Many objects don't have audible vibration modes (infrasonic, ultrasonic, so damped that sounds are too brief and too quiet) but it doesn't mean that they don't vibrate.

what you are describing is a graph. The laplacian spectrum of a graph is arbitrary.

Every rigid object has a fundamental frequency, regardless of whether you put it on a graph.

Sure. But the other frequencies need not be integer multiples of the fundamental.

They don't have to, but usually those integer multiples will be present as well. Whether they are dominant or not is another matter but it is quite hard to design something in such a way that if it has a natural resonance at a certain frequency that integer multiples will not be present in the response spectrum.

A typical object will have multiple modes of resonance as well.

> usually those integer multiples will be present as well

"usually", under what probability model? A random 3d or 2d shape will have zero harmonic partials with probability 1. What is hard to achieve is having even a few harmonic partials. A rectangular wooden piece is painstakingly carved to have a couple of harmonic partials, in order to become a xylophone or marimba bar.

Yes, but shapes are not usually random. Bars, cylinders, cubes, rectangles, squares and circles are everywhere. That does not mean that they will have a string like attenuation curve for those higher harmonics, but they'll be there.

> Yes, but shapes are not usually random. Bars, cylinders, cubes, rectangles, squares and circles are everywhere.

While there are some exceptions, this is skewed in the modern industrial world. If we're making evolutionary scale arguments about sound perception it's a much tougher sell.

Consider one of the only objects that actually matters in this context: vocal cords. Of course it's true that many inert objects don't have audible overtones or resonate at all, but nearly all animal vocalizations do. More complex auditory processing means better ability to distinguish between kin and predators. The fact that non-living objects tend to produce sounds via the same principles is just icing on the cake.

You have the causality backwards though. It isn't saying most objects emit quantized overtones. But if you hear quantized overtones, there's a very good chance they are from the same source.

It's not just strings, either. Drum heads have varying degrees of quantized modes.

The code itself also contradicts that sentence. Notice that the first roughness graph doesn't have any local minima at rational numbers. It's only when the overtones are added to the notes (at integer multiples of the fundamental frequency) that the minima appear.

So the code thinks that human ears don't detect integer multiples specifically, they just detect sounds whose overtones line up with each other.

Good point, but our ears definitely do perceive the 2 to 1 ratio. Maybe that particular phenomenon is better analysed through the usual pschoacoustic approach of "at what point do we stop perceiving one sound and start perceiving two "?

I don't think so. If a sound persists long enough to hear its continuation, then its partials are generally going to be harmonic. Non-resonant frequencies will have a tendency to dissipate very quickly, unless they are explicitly designed to warble between resonances (like a gong or similar).

@harperlee no worries about the share, it's great to see the variety of responses on the other thread

As someone who might use these with kids: I think the problem with both of these is lack of, well, sound.

To get things, people need to hear sounds, not just see note names and pictures.

it could be argued that this is music theory, and therefore sound belongs to the realm of music practice

Things get more fun when we explore musical tunings other than the 12 equal divisions of the octave (EDO) of Western music.

You can define interval structure as a sequence of large L, small s, and optionally medium M steps.

For example, the Major diatonic scale - a 7 note scale from 12 EDO - in Ls notation is:

   LLsLLLs with L: 2  s: 1 (12=2+2+1+2+2+2+1)
A 19 EDO, 7 note scale:

   LLsLLLs with L: 3  s: 2 (19=3+3+2+3+3+3+2)
And here's a 19 EDO scale with 9 notes (Godzilla-9):

   LLsLsLsLsLs with L: 3 s: 1 (19=3+3+1+3+1+3+1+3+1)
You can then explore frequency ratios beyond those available in 12 EDO: https://github.com/robmckinnon/pitfalls/blob/main/lib/ratios...

And chords based on those ratios: https://github.com/robmckinnon/pitfalls/blob/main/lib/chords...

The above links are Lua code files for a monome norns library for exploring microtonal tuning: https://llllllll.co/t/pitfalls/37795

A perfect 5th is not the same as a diminished 6th unless we assume equal temperament tuning. Granted it is the dominant tuning, but it irks me when this is just silently assumed.

Plenty of music around that is recorded using actual perfect intervals, so why muddy the waters?

I think going out of equal temperament into other modes of tuning/intonation would definitely be considered outside of "basic music theory".

It feels like grumping about some inaccuracies/glossing over in elementary school mathematics because of the existence of imaginary numbers.

I firmly disagree. I learned about staying "in tune" with those that I was playing with in an ensemble long before I learned about equal-temperament and its concessions to multi-key harmony.

I'd say removing the beats from your partials is way more fundamental to both music making and music theory than chromaticism. Chromaticism is the next step, beyond basic music theory.

> I learned about staying "in tune" with those that I was playing with in an ensemble long before I learned about equal-temperament and its concessions to multi-key harmony.

I'd consider that a performance technique before a theory aspect, like vibrato speed and control or enharmonic fingerings.

Consider this: If you were in a duet as a beginner and the sheet music had your partner playing a C and you playing an A double-flat, how would you be instructed to play it?

You'd be told it was enharmonic to a G, and play it as a G.

Until you start reaching deep into historical re-enactment or advanced theory, it's very safe to assume equal temperament and leave the ear-adjustment to performance.

I guess my response to this is that basic music theory is roughly equivalent with basic acoustics, has more bearing on generalized musical practice than what you are implying, and that even reading sheet music is an abstraction that requires foundations in a musical culture that has a prerequisite of certain assumptions that may not actually hold.

If you listen to CPE Bach knowing that each note can be bent (as on a guitar, because it is a clavichord), then the written music makes more sense because each note can be tuned to be harmonic with the fundamental. The sheet is just a sketch. The presumed required bend in each note totally changes the expectations of the key it is written in.

Or, if you are listening to a gamelan, then the beating of notes becomes an essential rhythm of the instrument, informing the tempo of the ensemble as a whole.

Music theory is a combination of acoustics and music history, but the acoustic part is more fundamental/basic. Like knowing "Clueless" is based on "The Taming of the Shrew" is informative, but the fundamentals of quality movie making or movie consuming do not require you to know anything about Shakespeare.

Interesting. Do you have some reference or link where I can learn more?

The wikipedia page is pretty good https://en.wikipedia.org/wiki/Equal_temperament#Comparison_w...

A fifth might even sound off key if you're very used to equal temperament (it's about 2 cents below an equal temperament). You know it by there being no or less "wobbling" between the tones.

For listening tips, look for vocalist groups where there's "One Voice Per Part" (OVPP). Voces8, Vox Luminis, etc. When there's only one voice, you don't get the inherent wobbling happening when two instruments/voices play in unison.

Not all genres are possible to have just (jazz chord colors would sound rubbish).

You basically can look up just intonation versus equal temperament for the basics. https://pages.mtu.edu/~suits/scales.html gives the mathematical answer but doesn't get into the history.

A clause that says "assuming twelve-tone equal temperament" would be sufficient here, but you can really go down the rabbit hole if you start digging into scales (see microtonal), and your page is meant to be more basic.

Here's some good background on equal temperament as explain by Howard Goodall on a BBC series about music:


This is great but if we could go back in time and influence the naming conventions so that the 12 semitones were called A-L or just numbered 1 to 12, and if the intervals were named after the actual semitone distance (a 'fifth' is actually seven semitones) the whole thing would be soooo much less jargonny. With all that bumf removed, the patterns of the 'scales' and 'chords' would be foregrounded and thats the actually interesting bit IMHO (the bit defined as 'formulas = {..}' in the article)

People have had this idea before but I've never seen a version of it that is better than our existing notation systems. Most of our music is diatonic, and we named the notes in our scale A B C D E F G. Seven notes in the scale, seven letters. Seven positions on the staff.

Our harmonies are built on stacked thirds, and the stacked thirds line up perfectly on a staff. Line, line, line; or space, space, space. Three dots stacked neatly on top of each other. Easy peasy. Easy to read all the common intervals at a glance, once you get past an octave it starts getting a bit harder.

If you had chromatic notation, you'd allocate a bunch of extra space and names for things that you spend most of your time not using. An octave would have eleven spaces in the middle, which is practically unreadable.

I think in the long-run chromatic notation is just hostile. Go ahead and use chromatic solfege, that's super useful, but chromatic notation is usually not.

Most often I hear the criticsm from people who are not musicians or do not know how to read music. It's often smart people with an analytical mind, but people who don't have much experience with music. Just speaking from my own experience, it's much harder to read a chord from a piano roll than to read a chord from traditional notation.

In some parts of the world, it's A H C D E F G, with B being what you'd call B flat.

Because of that, it took me way too long to figure out that there was any sense in the note names.

I appreciate most of your points and I appreciate the conciseness of the stave notation for example. But ...

A B C D E F G. Seven notes in the scale, seven letters. Seven positions on the staff.

Thats fine as long as you're in C Major. As soon as you depart from C Major it all starts going wonky. Why is C Major baked into the notation as if you'd never want to use anything else?

> Thats fine as long as you're in C Major. As soon as you depart from C Major it all starts going wonky. Why is C Major baked into the notation as if you'd never want to use anything else?

Actually, it works for every major scale and natural minor scale!

What are the notes in E major? E F# G# A B C# D# E.

It's still the same letters, E F G A B C D. Now, you may think that this is CHEATING because I've added sharps. But when you write it out on staff paper, the sharps get shoved off to the side on the far left in the key signature, and you basically forget that they are there. You really still just care about seven notes, so you still have seven letters, and seven spaces on the staff, they're just a different seven notes from the C major scale.

You have to know which key the song is in... but you have to do that anyway.

When I say that you basically forget that they are there... I mean it. This does not even require an especially advanced level of musical skill. People with even a passing interest in music theory should be able to breeze past it.

So if you pretend that the sharps arent there and that they dont make any difference to anything then its all simple?

I'm saying that our music is largely diatonic, and it's better to base our notation and terminology on the diatonic rather than the chromatic scale.

The idea that you can number semitones 1-12 has some mathematical elegance to it, but it's a terrible system in practice. It turns out that mathematical elegance doesn't count for much, and domain knowledge is important here.

You have to pick something as your starting point.

The sharps and flats diatonic system is way easier to read because you just mentally parse "key of D" instead of "start on D but also sharp the F and C". It takes time but your brain just starts to grok shapes.

"Piano roll" notation, like in DAWs/midi editors, is actually in certain ways a lot hard to read than staff notation, due to the lower density and lack of reference frame. It _is_ easier to see chord shapes transposed up and down as the same. But I'd argue that's an anti-feature, because of said lack of reference points. The symmetry /sameness makes it a lot easier to start on the wrong note.

> Thats fine as long as you're in C Major.

C major, yes, but also A minor - where it actually starts from A :)

There probably is a better or more general notation system, but specifically for western music it is actually pretty efficient and logical once you start working with it a bit. Just don't put too much weight on the names and think in intervals. You have a scale made up of 7 notes/intervals with the "fifth" simply being the fifth note in the scale. Same with third, etc. The specific flavor (major/minor) of e.g. the third you're playing usually depends on the mode, but it is still a "third" and serves the same-ish function. Extending the names i think would actually be more confusing. I'd argue it already puts the patterns of scales and chords in the foreground.

I'm too excited not to comment on here specifically, although I have another comment in this thread already. I made a proposal for this in my book which isn't out yet but basically I'm using only consonants for these.. so that I can link a vowel for a separate encoding.. so in order of notes where their set notation is 0 1 2 3 4 5 6 7 8 9 10 11, B D F G J K L M N P R S.

It's an idea, and possibly somewhat arbitrary, but it's a proposal at least and it will connect to other things well due to uniformity. Then there's my python code which takes a scale.. and writes nonsense with shakespeare verse using words beginning with the letters that spell them. Then words can be used to learn melodies.

But what I was really thinking about more is like depending on the vowel after that letter you will form different chord qualities.. The first most important being the unison, or 'a'.. so to play a major scale with single notes you would say Ba Fa Ja Ka Ma Pa Sa.

But to say the seventh chords that the major scale implies you'd say: BatEk FabEt JabEt KaTEk MatEt PabEt Sabat, which would be a a way of saying: DMa7 Emi7 F♯mi7 GMa7 A7 Bmi7 C♯⌀ - but way less syllables

⌀ is pronounced "half diminished" or "half diminished seventh" which is a mi7(♭5) which would be pronounced "minor seven flat five" for those who don't know.

The insanity of modern music theory is the superimposition of the number 7 (A B C D E F G) onto the number 12 (the number of notes).. everything in the system is skewed by this fundamental wonky shape. But I'll remind everyone that 12/2=6 and 12/3=4 and from these facts more logical systems can be envisioned, as opposed what's 12 notes with 7 names. 12/7=? A number that seems not to have relevance to the comprehension of music patterns.. BESIDE the fact we are forced to think like that with things that conform to 12/7 like sheet music, note names, or piano key locations...

But nature and even a guitar fretboard has less concept of the obsession with the number 7 by design.

I've been working on a fixed chromatic solfege system (MaNePu) for a while as well. It uses a repeating vowel pattern which I find produces some really interesting effects. In MaNePu, the chromatic scale is ma - ne - pu - qa - re - su - ta - ve - wu - xa - ye - zu. In other words, consonants starting with M til the end of the alphabet, and rotating through the vowel sounds "ah", "ee", and "ooh". What's neat about this is that the pattern repeats every minor third, so that means every diminished scale internally rhymes! Similarly, transposing any melody by a minor third will also result in a melody that rhymes with the former. Likewise, either whole tone scale will result in a reversal of the vowel pattern. There are other fixed chromatic solfege systems that use an alternating vowel pattern, but MaNePu is the only one that uses a minor third rotation (the others I've seen typically alternate by whole tone), and I think it opens up some interesting avenues for music education.

I like your shortened chord quality convention, though MaNePu takes a different tack. Instead, it favors what I call "descriptive chord naming". Instead of being prescriptive about the quality, a chord is simply described by appending the notes contained within it. This is great because it also removes ambiguity in the cases where a chord might include certain notes or exclude certain notes implicitly. So Dmaj7 would be PuTaXaNe ("Xa" is pronounced like a "j"/"sh" sound sort of like in Pinyin). It also typically reduces the number of syllables spoken, like your system.

The superimposition of 7 on 12 as you put it, is indeed a problem, but there's also an issue with intervallic favoritism (of half and whole tones). After all, there are 7 note scales with minor third intervals, and so on—imagine a world where one of those scales was the basis for diatonicism. Representing that on a keyboard, and the subsequent accidentals would be a nightmare.

Notation is the big unsolved problem, I think, but I'm aware of some work being done in the area if you're interested. As far as the public facing projects I'm aware of, Dodeka is likely the most promising.

Your MaNePu system sounds very cool! It's interesting that you speak of the symmetry vis a vis the number 3. My "way of word" has a similar property. It's based on trigrams from the I-Ching and all of that follows the diminished (3) geometry.

Regarding spelling chords as the iteration over their notes like MaReVe for a major chord, my system can do this as well, by using an -a ending for each letter. In this case a major chord would be BaJaMa. Or even just B' J' M', as in "B'eatles J'amming M'usic" et al. I think this would be used melodically rather than chordally in my system.

Let's say that the first measure of the melody to Ode To Joy is (in MaNePu, Jazz, Word notes):

Ja Ja Ka Ma Ma Ka Ja Fa Ba Ba Fa Ja Ja Fa Fa

3 3 4 5 5 4 3 2 1 1 2 3 3 2 2

Re Re Su Ve Ve Su Re Pu Ma Ma Pu Re Re Pu Pu

It's great to see that. I immediately notice we're both using consonants only for the first character. I can describe to you the trigram lines being referred to in MaNePu as a bottom line if ending in a, middle if e, and top if u. But the glyphs didn't work here so find the trigrams. I notice you didn't demote the letter 'u' out of your system. I personally am much more partial to the letter 'o'. ;)

We can write this passage with the bass accompaniment as well. Bassline just plays 1/Ja/Ma and 5/Ma/Ve. Weird to look at here because Ma=root for you and Ma=fifth for me! Obviously our layperson reader might not also know that Ma is a standard way to notate a major chord in music, as well.. which kind of also has nothing to do with the first two Ma's we were discussing. And we're not going to bring your mom into it either ;) Anyway here it is. Maybe mistakes (?) cause I'm handwriting here, and I just learned your system:

Bat BAt BAk BApEp Map MApAt MApAb MapEp Bap Bap BIp BAt Bat BIp Map

3/1 3 4 5 5/5 4 3 2/5 1 1 2 3 3/1 2 2/5

ReMa Re Su VeMa Ve Su Re PuVe Ma Ma Pu Re ReMa Pu PuVe

As a critique of your system if I was fluent and you read that out to me, I'd be unsure of when the root actually changes.. because when I read ReMa out I think of playing F# then D. As opposed to F#/D (at the same time).

I use an idea more analogous to the jazz chord symbol system where one specifies the root and the harmony as a compound symbol.. Like 1ma7 or b5mi7. There are actually two separate systems at work in chord symbols like this, and my system is the same as that concept. So you can go either way with "word". That is, using notes (horizontal) vs. using harmonies (vertical). I want to point out that when my system uses less letters it's because the last letters are "A" or "p" meaning no notes in this quarter. That's why some are only one syllable instead of my mentioning two. In another way if a chord is over the root we could omit the B at the beginning because it would be assumed. In this second example I included all the B's and M's (1 and 5. D and A in "normal" notes). This way the melody is seperate on top and the root motion is still specified.

My site is rudimentary but all one needs to name every chord by this method is in a small chart. I threw it in a little html file because posting a table in HN is not going to work well. https://edrihan.neocities.org/ngramcharts.html

I should actually have an explanation on the site which I will add at some point.. but basically you pick a letter for each trigram (quarter scale/chord). So there are four. If they are the first/third it's the vowel, and second/fourth is a consonant. That makes up your quality. Then you combine that with a root-letter of mine. Because those are consonants.. and my word starts with a vowel.. your five-letter word is pronounceable.

You mentioned the pinyin which I intuited on as soon as I saw the "x". You'll see pinyin on my link. Fundamentally related to way of word by its connection to the I-Ching, but not in the sense that I am using it as a sound in my system, like you are.

I like reduction of syllables for these systems. I tried to maximise this property insomuch as all 49152 expressible root-harmonies can be expressed in two syllables. I also like the descriptive property. It just so happens I designed it to be pronounceable and so seem prescriptive as well. I guess the prescriptive version here (which is also derivably descriptive) would be to use the trigram/tetragran/hexagram names. So for our major chord example.. it would be respectively,

Lightning Water Water Earth = = atEp (for some reason HN seems to censor trigram glyphs, on my system at least)

Law Increase Response = 𝌭𝌒𝌮

Sprouting Leader = ䷂䷆ = (atEp)

The trigrams and hexagrams map to this system.. but not the tetragrams. In this trigrammatic way our systems are analogous.

The 7/12 problem is one of the biggest problems with music, I feel as an artist. People have explored a small fraction of tonal possibility.

I will check out Dodeka.. Feel free to check out my material, mostly as we approach the future. I've been hoarding my work for a few years now but am unleashing things. So I guess you heard it here first cause atm I basically do not exist on the internet. But ya I wrote thousands of lines of code to get to this point.

For notation systems I like the circle geometry.. the way of word.. or simply instrument diagrams (mostly only possible with strings and keyboard instruments though, where one can visualise multiple notes simultaneously). I also like the idea of colours.

I think one thing that needs to happen in the education is for people to start learning movable-root systems like yours, mine, the jazz system, or the set system, rather than learning in static keys. People then learn 12 times as much data per neuron (-ish). I thought of a keyboard with 6+6 keys instead of the standard 5+7. Then you'd learn shapes on the instrument 6 times faster by reduction.

Ok there's stuff to meditate on.

Actually my chord naming system is "descriptive" as well but admittedly uses a slightly more compressed encoding.

Thanks for sharing all this, I'll definitely dig deeper into your site! Exciting time for new theories of music.

My pleasure! Thanks for sharing your ideas as well. I read back my post and realised it's a discombobulated mess. I'm glad you were able to parse something out of that. Writing clear explanations is definitely on my todo list.

Agreed. The patterns are the most interesting bits. Actually, just the fact that there exist patterns is pretty amazing. It's unfortunately hard to see them through the notation and that made it very unintuitive for me for the longest time.

Unfortunately the momentum that Western music notation has, with a few centuries of tradition behind it, means one has to work within that system.

There was an interesting discussion I came across on Stack Exchange while writing the article: https://music.stackexchange.com/questions/67730/why-have-sha...

re: the patterns, see discussion here https://news.ycombinator.com/item?id=26860627

and my comment here https://news.ycombinator.com/item?id=26861415

>Actually, just the fact that there exist patterns is pretty amazing.

How so? If patterns didn't exist, it would just be random choices.

Any non-random music making (and thus theory) requires patterns.

I disagree, because with the way of writing it down we have a homomorphism, e.g. transpositions preserve relations between letters, e.g. (A D E) -> (Ab Db Eb), or (G C D) -> (G# C# D#).

Of course, for every rule there are exceptions, e.g. we have things like (F Bb C) -> (F# B C#)

Agreed. I whinge about this all the time. The C-based system is convenient for piano players but it's a mess for guitar players, violinists, and other instruments where there are no

There have been many attempts at a chromatic music notation, but nothing has caught on so far [1].

Things are a little better with solfege -- there is "chromatic fixed do" solfege, where every note has its own name, rather than only having a name for the "white notes," which leaves you to mentally calculate the sharps and flats.

It's a minority thing--maybe 5-10% in Europe? Even regular fixed "do" is rare in English-speaking countries, so I would assume the chromatic fixed "do" is almost unheard of in the US, Britain, etc.

At any rate, there're are at least seeds of hope for a chromatic fixed-do solfege to catch on more. I use it for my own learning.

[1] http://musicnotation.org/

I find the paino-roll notation on DAWs to be a lot more intuitive. Not much good for perfomers of course, but it helped me understand things better. Each semitone is given the same amount of space.

Here's that one weird tip that you were looking for all your life but didn't realize it: pretend the front part of the piano keyboard isn't there, and just look at the part closest to the fingerboard. Presto: chromatic keyboard.

I find piano roll a lot easier to write/produce but a lot harder to sight-read.

I actually find hooktheory's system, where it's diatonic and accidentals are based on the active chord, not the current key, to be the easiest to understand relationships, but also hardest to translate into concrete notes to play.

I find piano roll very hard to work with. The notes are just too far apart vertically.

> Modes are essentially left-rotations of a scale.

While true, I find this interpretation harmful to the understanding of modes. It didn't provide me with any insight and instead it seemed irregular to the other theoretical constructs we have and thus deterred and misled me in the beginning.

To me, it all clicked when I took all the modes, except Lydian, and constructed them by putting down the augmentations to the major scale in a circle-of-fifths sorted way:

Mixolydian: b7, Dorian: b7 b3, Aeolian: b7 b3 b6, ...

You can see that the modes appear walking left on the circle of fifths or walking along fourths (or going "darker", as some prefer to say). Try this out when starting at e.g. C and you see the pattern immediately.

Then take Lydian: #4

That's going right on the circle of fifths or going in fifths going "brighter".

Also, tangential comment: My music and my life has changed profoundly when I found out how to use the Lydian mode. I can't explain it, but it is just exciting.

One way to make that ordering work with Lydian is to start with Lydian and flatten one note each time. So say we start in C. C lydian, flatten the F# we have C Ionian, flatten the b we have C mixolydian, flatten the e we have C dorian, flatten the A we have C aeolian, flatten the d we have C phrygian, flatten the g we have C locrian

Now we flatten the C (after all this is the next note in the cycle of fifths) and we have.... B lydian. And the whole thing starts again.

In this way you can understand how all the modes and keys relate. You can do a similar thing with the other 3 similar modes of limited transposition in this order (melodic minor, harmonic minor and harmonic major).

Have fun.

What made it click for me analyzing music, in particular rock songs like 'Gloria.' That song very strongly identifies E major as the tonic, but the D and A chords are not in E, they are diatonic to A major. To say it is in A major would mean the song's tonic would be A, but since it is E major it is more correct to say the song is in E Mixolydian.

Adam Neely recently did a great analysis of 'Hey Joe' that goes pretty deep into this stuff https://youtu.be/DVvmALPu5TU

Oddly, for me it was the opposite!

I used to be confused on why modes required modifying certain notes from a major scale until I tried deriving them in the way shown in the article.

Of course, once you understand that, the way you go about memorizing and practicing is probably easier the way you described; that is, deriving modes in any given key by modifying notes of the major scale using the circle of fifths.

> modes required modifying certain notes from a major scale

But why though? If you're improvising on a dominant (e.g. a G7 in the key of C Major) with a G Mixolydian scale, you're actually not playing a Mixolydian sound, but Ionian, since your tonal center is C Ionian. It is true, it is indeed a G Mixolydian scale and it is using the tonal contents of our key C Ionian. But our frame is Ionian, so what is the purpose of adding Mixolydian other than ease of construction of the scale?

Does any programmer suffer with music theory as well, just based on the fact that an exact thing could be called in many different ways, depends on its position, function..etc?

my brain kind of cannot accept this fact and I struggle with it

I've been programming for 40 years and playing music for 50. My original background was classical and I play jazz today. I'm a fluent reader.

I think that historically, people were already familiar with "standard" notation and terminology before they learned theory, so it wasn't a major hurdle. Not only do theory students (i.e., at the college level) know how to read, but they are also required to learn keyboard. I've heard people say: Don't try to learn theory without a keyboard in front of you.

Music instrumentation and notation are technologies and as such they are replete with historical baggage. I have an unorthodox view, which is that if someone is not already usefully reading standard music notation by adulthood, then they have no reason to learn it. Explanation of theory for non readers would be better served by using an invented notation that sidesteps the historical naming problems.

One such notation is the Nashville number system. It's not nearly universal, but for the purposes of just enjoying a wide swath of popular and folk music, it actually works. It's fun to see how many different songs boil down to a few basic patterns.

A computerized tutorial could show both notations. There is a lot of instructional material for guitar, that shows conventional notation in parallel with a notation based on a diagram of the fingerboard.

Programming would be just as bad if we were stuck with a 400 year old language. Fortunately we develop new languages, but that's because old programs just get thrown away, and it's easy to teach a computer to read a new language. We also teach programmers not only how to read, but how to create better notation themselves.

This is the first time I heard of the Nashville number system - what's the difference to Roman Numeral Analysis? Is it essentially the same concept, but with Arabic numerals instead?

My take: It's a communication issue.

If you tell me you're going to make my life easier by teaching me "Roman numeral Analysis", I'm gonna run away. That sounds scary and vaguely reminds me of Latin class.

"Nashville number system" sounds easy to master. It's country, and country has a well-known self-imposed reputation as simple. (In truth, country can be just as complicated as anything else. But I'm talking about first impressions.)

I used to be a part of a congregation whose band spoke in 5ths and 7ths and I had no idea what they were going on about. And then I learned that part of joining the band was learning the Nashville system. It's just the simplest way to get everyone on the same page, and when you say "Nashville" musicians immediately relate to what you're saying.

Pretty much the same, adapted to the specific purposes. For instance, Nashville charts also include some notations for the form of a song, such as Intro, Verse, Chorus, etc.

A reason for the usefulness was how recorded music was made. The recording musicians had to be able to choose a key that accommodated the singer's range, on the spot. So a transpose-able format was ideal.

I think the industry in New York had a different scheme, which was to write for a "standard" male tenor voice, and rely on the musicians to handle exceptions.

Yes, but we have similar issues in programming. Is a list a hash? Is a hash a dictionary? Are these all arrays? Are arrays collections?

Of course, there is a right answer, and depending on the language, all of the above can be VERY different things. But they're also similar enough to be completely unintuitive... their distinctions take practice to master.

Likewise, in music there is a right time to call a note a flat, a right time to call it a sharp, and a right time to talk about intervals instead. They can all technically refer to the same thing, yet there is a proper word to be used in any given context.

It's all very confusing, until you start using those terms in their proper contexts on a regular basis. Just like in programming.

Some other examples:

"=" vs. "==" vs. "===" vs. ":" vs. "=>" vs. "~>"

"function_name first_parameter" vs. "function_name(first_parameter)" vs. "hash_name[key]" vs. "object.property_or_method"

"MethodName" vs. "methodName" vs. "method_name"

"function" vs. "method"

...none of these are intuitive. But we use them, we get used to them, and then they seem obvious and we wonder how we could have ever written these things differently.

I think the same goes for musical notations. I struggle with them heavily, but I'm far too casual of a guitar player to take the time and learn the language properly. It's tempting to say the problem is the complicated and confusing language of music, but I know the problem is my own unwillingness to put in the time.

It's all about thinking in thirds. If you want an A chord it has to be A, C, E, in thirds. A major would be A, C#, E not A, Db, E because that breaks the rule of thirds.

Also, and most importantly, if you're playing an instrument like violin, C# and Db are not actually the same note. Since they happen in different contexts, and have different positions in whatever key they're in, they have different psychological roles and are actually played differently by the player.

If I'm not mistaken, a C# would be played slightly sharper, and a Db slightly flatter to fit the particular key.

A fun idea for a function to implement: the negative harmony mapping, which is a note-by-note transformation that preserves some character of the note:

  R ⟷ 5 (stable)
  2 ⟷ 4 (unstable)
  3 ⟷ ♭3 (modal)
  7 ⟷ ♭6 (leading)
  6 ⟷♭7 (hollow)
  ♭2 ⟷ ♯4 (uncanny)

 [1] https://www.youtube.com/watch?v=et3CMn2oCsA
 [2] https://www.youtube.com/watch?v=SF8CdxcdJgw

> For historical reasons, there are no sharps or flats between the notes B/C, and E/F.

Come on, that is not for "historical reasons", that is because those notes are only one semitone apart!

Different way of saying the same thing.

"For historical reasons the notes B/C and E/F are one semitone apart."

But that is not for historical reasons, that is due to the universal mathematical properties of the intervals.

The names of the notes and scales are due to historical reasons, but a major third and a fourth is one semitone apart due to math, not history.

What the article means is: we dont have 12 notes (A B C D E F G H I J K L). Instead, for historical reasons (the choice of CMaj/Amin as a reference due to the notation evolution from heptatonic scales) we have A B C D E F G and we annotate with accidentals but, since those are not evenly spaced, there are some missing "black keys" there.

Also, what devnonymous says, which I agree with too (but that's another story...)

The idea of a semitone in Western classical music is historical not (just) tonal.

True, but that does not mean you can just space notes in a scale randomly.

Hmm, I guess someone should tell those people, like Like Tolgahan Çoğulu who are writing music in microtonal scales with 19, 24 or 31 notes in a scale, that their notes spacing is random.




The spacings are not random, they are still based on ratios. They just include more intervals in (what we call) the octave.

The linked article actually explains the math pretty well.

Ah alright, I finally understand you. What you meant to say is the reason why Western classical music is built on the 12 note chromatic scale is because the musicians used the math! It has nothing to do with history. Sound about right?

Although I agree with you... didn't Pythagoras derive the pythagorean tuning of diatonic doing the math with the 3:2 ratio?

I know near zero music history, but I was under the impression that that's the evolution from diatonic scales and eventually into our western music system.

Yes, intervals are just ratios of numbers, corresponding to frequency ratios. 2:1 is an octave, 3:2 is a fifth, 4:3 a fourth and so on. I didn't even know this was controversial.

Of course a lot of other stuff in music and music theory is due to history and tradition. For example the names of the intervals (octave, fourth, fifth etc.) presumes a 7-note scale. Using 7 as reference is tradition, e.g. the pentatonic scale has 5 notes.

> Using 7 as reference is tradition, e.g. the pentatonic scale has 5.

That's our point.

Ok, but that is kind of orthogonal to the point I was making. I was just stating that it follows from the math that the notes in a 7-note scale are not evenly spaced. The same is true for a pentatonic scale, for the same reason: The intervals corresponds to the simplest ratios (2:3, 3:4 etc.) but these do not in turn correspond to divide the octave evenly.

Not exactly, although I think I understand what you are getting at.

What I meant was that the interval between a major third and fourth in a 12-tone chromatic scale has to be a semitone due to math, not due to some historical accident or decision.

It might be an accident of history that we use a 12-step scale in the first place though, since you can have arbitrary many intervals in an octave - but you can't just divide the octave in arbitrarily places and get music out of it. The intervals still have to be ratios.

(Well I'm sure some avant-garde composer have tried making music with intervals that are not ratios just to be clever, but I hope you get my point!)

“ For historical reasons, there are no sharps or flats between the notes B/C, and E/F.”

Mmmm yes, and that’s also a bit confusing because it dodges around why the scale was and is 7 notes to begin with.

Coincidentally there are no commonly used scales or modes with two consecutive semitones. The semitone gaps are always spaced out. With 11 notes (excluding the octave), that only leaves 4 possibilities for a 7 note scale if you remove rotations. These correspond to major, harmonic minor, melodic minor and harmonic major. It’s easy to prove with pencil and paper concentrating on c to c

> Coincidentally there are no commonly used scales or modes with two consecutive semitones.

It's common in Bebop to add a passing tone to otherwise heptatonic scales. Consecutive semitones are also a common feature in blues.

That’s true but in those cases they are passing tones. For examples in a bebop scale you don’t tend to arpeggiate using both the consecutive tones.

> That’s true but in those cases they are passing tones.

That may well be their main function, especially in bebop (it's not so certain in blues), but they're still considered as part of the scale.

> For examples in a bebop scale you don’t tend to arpeggiate using both the consecutive tones.

That's true for any non-chord tones. The intervals are still very common (in bebop you commonly simply walk the whole scale up and/or down in straight 8ths or 16ths, playing adding the passing tone for the chord tones to end up on the downbeats).

As a kid I dismissed the piano because nobody explained to me why the keyboard was so stupid looking, laid out so irregularly. WbWbWWbWbWW. Wot? Only some self-education (much later) revealed that 12 tones per octave deliver some excellent harmonies, not 11 or 13 or 20 or 36 or whatever. Twelve. But the harmonies come only on odd steps. So we have 5 semitones to a perfect fourth (4:3 harmony), then two semitones to a perfect fifth (3:2 harmony), then 5 semitones to the octave. And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW. If only someone had explained all this in grade school.

I didn't really understand your explanation so I might be restating your ideas, but just in case:

> And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW. If only someone had explained all this in grade school.

We don't arbitrarily split them! It was very much made on purpose to match the diatonic scales, which are very natural due to being a chain of fifths. E.g. from F ascending 5ths: F-C-G-D-A-E-B-¡F!

It's not arbitrary that we based modern keyboards around heptatonic scales! Then we added some black notes so we can transpose, which is pretty convenient on 12-TET.

I'm not sure what you're saying. B to F is not a fifth. A fifth up from B is F#.

Huh, I copypasted that from wikipedia but botched the text when trying to highlight the part where sharps start and left it half-written.

I'll just link the relevant wikipedia article:


B to F is a fifth; that interval is called a diminished fifth (one semitone less than a perfect fifth like B to F#).

Yes, this is true, but it's not how the circle of fifths works (which is what the comment I was responding to seemed to be alluding to).

He's right though, that's not what I was trying to write (not a 3:2 ratio).

I found this very helpful! As a self-taught musician, it filled some gaps in my music theory knowledge - especially being able to visualize computing scales, modes, and intervals as algorithms. I can now better evaluate these in my head when I encounter a key/scale that I haven't seen before! Thank you!

I have some similar notes here: https://calebmadrigal.com/music-theory-notes/. It's all about the ratios.

It would be awesome to add short audio clips. I mean, the examples are correct and all, but it's like discussing painting or photography without a single picture.

As a musician, I’d say no. Sure, you don’t get the significance of “what is this Dorian thing” unless Scarborough Fair is playing, but nothing in the article really applies to hearing music.

> As a musician, I’d say no. Sure, you don’t get the significance of “what is this Dorian thing” unless Scarborough Fair is playing, but nothing in the article really applies to hearing music.

I don't know what's with the current flagging/downvoting trends on HN, comments get dead before I can reply.

That said, your view seems rather extreme. What would be the downside of illustrating at least some of the samples with audio clips?

This is a fun read but IMO it falls into the common trap of trying to formalize concepts in music theory based on a representation too close to traditional music notation. A notable consequence of this trap is that the author has to do a lot of distracting work to handle enharmonics, and yet still has arbitrary limits on number of flats and sharps. In other words, he has to do a lot of distracting work, and still all that work doesn't yield a general system.

In my opinion (and experience) it is better to do a little work "up front" and "in the back" to convert to the line-of-fifths representation since that is more friendly to formalization. In other words you can take input in traditional musical notation and give output in traditional musical notation, but "in the middle," formalization should be done in the line-of-fifths representation.

Above I have used "formalize" to mean something like "mathematicize" (if that's a word) or "be precise" or "be able to compute" or "be able to express in a programming language (like Python)". For example, I consider the line-of-fifths representation to be a good one in which to formalize music theory because in line-of-fifths representation, transposition can simply be formalized as integer addition, and integer addition needs no further explanation or formalization, i.e. it can be taken as sort of axiomatic.

Here's another way of putting it: if you wanted to be able to add Roman numeral strings, would you write code that directly operated on the Roman numeral strings, or would you first convert to a compute-friendly representation like integers, and then do your adding from there? No doubt there are tradeoffs involved, but I tend to think that it is usually worth it to move to a compute-friendly representation, both with Roman numerals and music notation.

An added benefit of line-of-fifths representation is it provides a good basis to formalize many important historical European tuning systems.

Unreadable code,considering the subject should have been written in either in c, c#, d, f or f#.

Interesting that there are no languages with "flat" names. I can think of two reasons: - the word "sharp" has more positive connotations - if you're limited to the keys on a usual keyboard "flat" would be denoted by "b".

I think it is just due to C# being a play on C++ (the # could be seen as ++ just rearranged to overlap). No doubt the positive connotations of "sharp" also played a role. Cb or C-flat neither looks or sound cool! That said, MS did have en experimental language called C-flat, but it was not intended for general purpose use (if I remember correctly), so the name might have been chosen as a joke.

F# is in turn named after C#, as it is the functional equivalent to C# in the framework.

Jazz musicians (and brass players) generally prefer playing in flat keys (because of transposition making the reading easier) so while "sharp" has a more positive connotation in normal use, if you asked a tenor saxophone player to play something in F# or C# they would generally not be pleased :-)

I didn't think of that. My musical experience is on piano and voice (neither of which has a preference for sharp or flat keys) and I've played around with guitar a bit (which prefers sharp keys in standard tuning) so I tend to forget that some people like flat keys.

I haven't found an introduction to music theory that makes sense to me.

I vaguely understand that complications arise because we want nice harmonics, ie frequencies whose ratio is a "nice" rational number, such as 2/3 or 3/5 or so.

But our chosen notes should be invariant under doubling of frequencies ("shifting by an octave"), because that's basically the same note.

The problem then is that roots of 2 are irrational, that is, one cannot find (p/q)^2 = 2, or (p/q)^n = 2, or even (p/q)^n = 2^m. Therefore, one cannot find a "nice" interval that, applied several times, wraps around to an octave (or multiple octaves).

However, in a neat coincidence, (3/2)^12 = 129.7463378906... which is close to 2^7 = 128. So, based on that ("Pythagorean comma"), something something something, and we end up with 12 half notes that are basically of frequency f_i = f_0 * 2^(i/12), which are all horribly irrational, but apparently sound "nice" enough, largely (because they are close enough to some "nice" fractions), but only if we pick out some specific 7 of them.

And then the question becomes, which 7 of the 12 do we pick, approximately uniformly distributed. (Why not 6? Every second? I don't know.)

And then, you can transpose them somehow (ie multiply frequencies by 2^(j/12) for some j, but then you change the names for some reason, and everything gets complicated and tonic and Mixolidian double-sharp.

Also, instead of frequencies of the form f_i = f_0 * 2^(i/12) (which, clearly, have the advantage that any multiplication by a power of 2^(1/12) is just a shifting of the index i), you could also use non-equal tuning, with the powers of the 12th root of 2 replaced by some "nice" fraction, which means that any shifting then subtly changes the character of everything, I assume.

This is complicated, admittedly, but for me the nomenclature obscures, rather than elucidates, the issue.

ETA: I sympathise with what irrational wrote: "Is this what it is like when I talk to people who don’t know anything about programming about my work? Pure gibberish?"

If you're trying to learn music theory by thinking about the mathematical relationship between frequencies, you are severely overcomplicating things for yourself. I have a tendency to do the same thing.

What question are you trying to answer with what you just wrote?

I guess you're right. I was trying to understand why it's so complicated, and how one could express it in a simpler manner (that refers to the underlying reality, namely frequencies).

Something I wish was more clear in music theory is just how much overlap exists between the various concepts. I think it suffers from having so many names for everything, the learning curve seems much steeper than it really is. Even in this article, much time is spent on the duplicate names of notes and intervals. As a fairly proficient self-taught guitarist, this intimidating perception of theory delayed my learning of it for easily 5-8 years.

For example, you may spend a while learning the major scale, and what can be done with it. Then you learn the minor scale, and it seems like a totally separate scale that sounds completely different. And after that you learn that there are five other scales (modes) to learn about! (Dorian, Phrygian, Lydian, Mixolydian, and Lochrian!). It can seem extremely overwhelming until you learn that they're all the same scale with different relative starting positions. Where major is [1,2,3,4,5,6,7], minor is [6,7,1,2,3,4,5], and the other modes are all the other permutations of starting positions.

My other gripe is that learning theory on piano puts a lot of bias on the notes themselves rather than the intervals. For example, the B major scale has 5 sharp notes (black keys) to remember whereas C major scale has none. These are pretty different shapes to remember. Learning these on guitar means taking the same exact shape and shifting it up a fret (so if you know one major scale, you know them all!). Not to say that guitar is the perfect instrument for learning this - folks will often learn scales as close to the 0th fret as possible, causing you to start on different strings and have slightly different patterns.

That being said, I wish there was a purely linear instrument (a piano with the black keys flattened?) for learning theory. The real magic comes from identifying the shapes and patterns, and how they're similar to each other. Like how major and mixolydian are identical except for one note, so it's very easy to modulate between them, or make a listener think they're in one mode when they're in another. Same with minor and phrygian. Being able to drop the baggage of "the second note of the B major scale is C# which is this black key here" and just focus on a floating set of intervals seems like it would make this all easier and less intimidating.

That all said, I still feel reasonably early in my theory journey. So maybe this is just my bias coming from guitar.

Notation wise and officially it is a loop. But the tuning is a compromise. Hence some sounds are not harmonised that way using the current scale. There is a reason why well-tempered clavier tuning is still a bit of debate. You may have to tune fir some songs differently in those days. Hence assume all flat and sharp are equal is a bit too pure that might not exist n the real world.

Hi there - was wondering if you had come across my Pentatonic scale github repo by any chance? :) It's a very similar type of study, where I attempted to generate all possible pentatonic scales (within reason).


Overtone is a music toolkit in Clojure. One of its source modules similarly captures music theory:


We need more "Explain things like I'm a programmer" explanations.

I've tried to grok music theory several times. I've never understood the scale/notes, notations. The 2nd array (with sharps and flats) and couple paragraphs made it "click" instantly. Because it was in a language and presentation I understand.

Not a musician here but are scales really necessary? Why not just play any frequency I want?

I'm a musician. For me, a great deal of the pleasure of being a musician is making fairly sophisticated, coherent music, with other musicians, in front of an audience.

Scales are not strictly necessary, but are part of an apparatus of making music work in the way that I enjoy it. They are a technology.

> Why not just play any frequency I want? reply

You're more than welcome to. If you try to discover what intervals between these random frequencies tend to be pleasing, or displeasing, you'll rediscover some of the intervals and scales covered above

You may enjoy looking up micro-tones. Where western scales are made up of whole-tones and semi-tones, other cultures don't necessarily use the 12 semi-tone based scale system. Notably, Toxic by Britany Spears samples some Bollywood music, where the backing singing uses a bit of micro-tonality. You can often find different satisfying intervals, although they won't necessarily have the same cultural context/baggage associated with the sounds and therefore won't convey the same strong connotations that a diminished chord might.

Musician here—strictly speaking, music itself isn't necessary. Armed with that knowledge, you should produce any combinations of sounds that please you.

Scales and Chords are broadly speaking just a way of neatly-ish categorizing sounds and moods. This is true of both most classical music and jazz, for example, but Jazz in particular has a very practical relationship with scales.

One of the personality tests of an improviser is how you think about the music - do you think vertically (in the chord), horizontally (in the mode), for example.

Most composers were musicians before that and a lot of instruments adhere to scales such as fretted instruments or percussive instruments like the piano.

Using scales gives people a familiar territory in which to compose music and a western audience will already be culturally attuned to those sensibilities.

I wonder if there is a scripting environment where I describe a chord progression in one thread, a lead voice in another and run them simultaneously, written entirely in code as a single file (or 2 files for parts + 1 for importing those).

You might want to try Sonic Pi, which pairs Ruby with the SuperCollider synthesizer engine: https://sonic-pi.net/

It will work in Sonic Pi, but I’m looking at ways to make the voice leading of chords more intelligent. At the moment it will voice chords in root position unless you specify otherwise. I’m also looking at writing a parser so the chord symbols can be written naturally as a string

Edit: I’m on the Sonic Pi core team. I mean that I’m looking to add these features to sonic pi soon

There are no simple algorithms, because solutions are style dependent, covering the range from parallel transposition of house chords to a full Baroque counterpoint solver, via pop, rock, and jazz theory.

The question isn't can you do it - because you can, with varying degrees of difficulty.

The question is what specific user problem you're trying to solve.


I don’t think this has “execution”/synthesis features, but it could at least provide the basis for this environment.

Love this article, i really enjoyed reading the code and now i want to reproduce it.

I thought this is very cute. Playing these as chords or arpeggios, then adding other features to put them together to form a melody or chord progression, then hearing the effects would be super cool.

Perhaps related:

Haskell School of Music http://www.euterpea.com/haskell-school-of-music/

I've worked on music theory coding for a while. I originally used a dict-lookup style like you have done, but found a simpler way (for me). The problem with that approach is you have to maintain values for enharmonics of note names. It's hardwired. Also what if you gave it something like ♭♭♭♭♭♭44? Why shouldn't it "theoretically" be able to handle that. It is "theory" after all. I use something like this to convert things basically to an int (if we want to for some other function):

  # Assuming note values are of Jazz style.. i.e,  '1', 'b3', '#5', or '♭3' with unicode-sub after
  jazzAllFlats = ['1','b2','2','b3','3','4','b5','5','b6','6','b7','7']
  sharpStrs = ['#','♯']
  flatStrs = ['b','♭']
  accidentalStrs = sharpStrs + flatStrs
  def stripAccidentals(note:str) -> str:
      return ''.join([c for c in note if not c in accidentalStrs])
  def jazzToDist(jazz:str) -> int:
      dist = 0
      degree = int(stripAccidentals(jazz))
      while degree > 7:
          dist += 12
          degree -= 7
      dist += jazzAllFlats.index(str(degree))
      for c in jazz:
          if c in sharpStrs:
              dist += 1
          elif c in flatStrs:
              dist -= 1
          #Here you could add support for double sharps and double flats if you want.. although unlikely as font support for these glyphs is horrible overall.
      return dist
  print(jazzToDist('bb3')) # returns 2
  print(jazzToDist('1')) # returns 0
  print(jazzToDist('♭♭♭♭♭♭44')) # returns 68
  print(jazzToDist('2')) # This one is strange as it's the   only one where input == output
I started making stuff more like this as it just saves a lot of trouble in the long run. Once you have things made generic like these it's easier to think about going into ways that are not Jazz/Dist (which is semitone distance, or set notation), like Keys for example.. because it turns out the logic for that is really similar to what is in the jazz.

The shape of the jazz system is the same shape as a change in the key of C. You would just separate the accidental part of the note's name like I did and look up let's say the index in all keys, giving you distance from C instead of what I showed there which is like distance from what is called 1 in Jazz.

So yes I prefer to make helper functions like this that actually kind of "get it" about what the languages/ways like Jazz or note names are actually saying.. then you can go one to another, or different keys really easily. If interested in more of my "Way Of Change" algorithms I can share.

I think your article is cool and I could comment more.. maybe if you want you could read my repo I could pm it to you. But it's long. In the meantime I have a new website using some of this type of logic. unfortunately js instead of python (where my bigger codebase resides).

Google thinks this site is a security threat and I literally posted it two days ago but it's got all scales/chords etc, and other stuff. Still in prototype phase. https://edrihan.neocities.org/wayofchange%20v14.html

From your link, I followed to the music of Lotus Helix:


Wow, I'm very captivated by it, such high musical weirdness! Excellent stuff.

Thank you very much. I guess because I have not succeeded yet at some externalities in this lifetime the album isn't even properly distributed.. something to do with the cover and my procrastination at registering with SOCAN.. and my preoccupation with my music-coding project for several years. And lack of internet chops and social stuff and neuroatypicality perhaps.

But every once in a while I'll throw it on and be truly weirded out (in a weird/good[?] way). The album is kinda like getting your brain hit by a truck in space. In the future I would like to make stuff that is slightly less dense. And also more focused.

But ya I recorded, composed, produced, played most of the instruments on that piece and am hypothetically available for musical services. Of course peeps can use the wonders of the www and just get weirded out whenever, wow! For free! I guess that's why people like me get minimum wage jobs in kitchens!

Ya that album will always be a personal memento and all round strange banger. I'm glad you enjoyed it!

Most of the stuff on my youtube honestly borderline sucks. Different phase of idea.. more improv and raw.. but there's like 2 or 3 good ones. Then I quit youtubing like 6 months ago cause I had to go frame houses to pay my rent which put my hand out of commission for a while. If you like Lotus Helix maybe check out a more solo-project one I did last year on the youtube.

It's about where I was born, outside among trees and stuff. I was actually born in the middle of a place called Riverdale.. but not like the tv show but the real one by the river. The tune is called Edrihan - The Riverdalian. https://www.youtube.com/watch?v=E-XZx1DUGhM

Very nice! I like your way much better than the one in my writeup :-) I'll refactor things over the weekend to use this approach if that's OK with you.

That would be very cool! Maybe just give me a mention if that is cool, you can use the code verbatim (or changed) if you want. My name is Édrihan Lévesque. My book on music theory which isn't out is called Way Of Change.. which is what I refer to these algorithms by.

You might just realise how this approach goes back into keys.. like Ab, C#, F.. it's almost exactly the same, but you have to account for the accidentals being on the right side of the string as opposed the the left, as it is in Jazz.

And ya! - I actually originally wrote almost exactly what you wrote.. but I kept adding enharmonics of things.. like ['3','##2','b4','bbb5'] # and so on..

So I got to a point where it's like.. yeah this should just understand it. I'll give you another hint for the keys.. Use the scale degree to get your root note name. Get rid of the accidentals (do it after). Once you know that Major in dist == [0,2,4,5,7,9,11] you can use the list that contains all 12 notes in one spelling to find it. That's why I'm getting rid of accidentals. That way if you're looking for C# but you wrote as I did with all flat-spellings, it throws away the "#", finds the 'C', counts from there, and finally adds the sharp back if necessary. Just kinda paying attention to adding a flat to a note with a sharp.. they cancel out etc. Usually that's why it makes sense to keep the degree part separate from the accidentals part in some way. At the end you reconcile a difference between distance and degree-distance. Really easy to do double sharps or flats that way cause you know that all valid note names will work.. don't have to worry about giving it a particular format.

Not only can you use any names notes may have, but you can specify an odd rule.. like for example the difference between looking at the scale in "Western" vs. "Indian". Let's say a scale like Mela Vanaspati/Raga Bhanumati/Zaptian (number 1129 on my site). If it's Zaptian, then let's say we're Western. I'd say it's spelled like the first line following this. If it's a Raga or Mela and we're looking at it that way then even in Jazz we can correctly see it how it's originally stated as the second spelling.

1 b2 2 4 5 6 b7

1 b2 bb3 4 5 6 b7

For me in this case the Indian numbers make sense as you are just counting up integers.. albeit with the "ugly" double flat. And yes it's ugly unless you were using a system that doesn't express it as uglily. Here I'm just comparing the first three notes in a few ways. Let's say for a bb3 a system that would express that less ugly than some would be in the key of C#.. as in [1 b2 bb3] == [C# D Eb] == [Db Ebb Fbb]. Of course all these can be described as [S R1 G1]. This is how it's notated in Indian.. but equivilent to Jazz in that there is a part that talks of which nth note of the change and a part that talks about how far from where it usually is. Obviously C# is better for this change than Db. Even if you use the Western Jazz to derive it it's not good unless in C#. Of course the Western jazz statement to me is more ugly because it doesn't count up in degrees sensibly from 1 through 7. The ugliness of the jazz numbers is equal to the ugliness of putting it in the key of C, like I said before. On other changes Jazz wins because Indian won't let you use #4 or b5.

I'm glad you'll use my codes too. Eventually once you have it working you can do a scale in the key of like... let's say Abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.. which is actually also known as C or even B#.. ok stay sharp out there in code land. ;) Music theory is an obsession of mine and fun with codes. There are always many options. There's more than one correct answer. And there are ones that make less sense than others.

And P.S. to anyone just dropping in.. we're lazy so we type b instead of ♭, and # instead of ♯. The former is pronounced flat, is equal to the number -1 and is pronounced double-flat if there are two. The latter is pronounced sharp, is equal to +1 and same rule applies about not pronouncing something like "sharp sharp" in music ever. This way I can pronounce C septuple-sharp, which I made up. That particular strange way to describe a note is equivalent to G because music is weird like that. Also if something has six sharps then you could just as easily say it has six flats. So B♭♭♭♭♭♭ is the same note as B♯♯♯♯♯♯. And yes those are the very sexy-sounding sextuple type words ;)

Is there a (really) accessible book on music theory that anyone would recommend?

I've been finding Signal Music Studio[1] to be doing a good job of conveying theory with minimal notation and practical examples. E.g. less labeling of things and more "here's what folks like to use this construct for". Not quite a book, and maybe not as comprehensive as you're hoping.

[1] https://www.youtube.com/playlist?list=PLTR7Cy9Sv285kV3pohsMt...

I'm going to go in a slightly different direction and recommend starting with a book on music history. There will probably be enough theory in there, as it's needed to explain many developments. And then, don't try to study it, but start out by just reading it as a narrative.

Modern college textbook writers are doing a decent enough job of not focusing strictly on classical music. You could find out what your local university uses.

I've been working on an IDE for music composition and I like to think that I nailed the UI.

Launching soon http://ngrid.io.

I love this!

Apropos, some years ago I had written this blog post and Python program:

Play the piano on your computer with Python:


The post got some interesting comments with info about Western music theory, which I knew nothing about. And suggestions on how to improve the program to make calculation of note frequencies more accurate.


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