Basic Music Theory in ~200 Lines of Python

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?

>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.

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?

> 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.

> 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 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!

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

:-)

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.

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

> 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!

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.

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.

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

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.

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.

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...

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/

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.

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.

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.

Different way of saying the same thing.

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

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

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

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.