The algorithm makes several false assumptions AND misses some crucial points about harmony that affect chord naming. One of each below:

- Chords are definitely not always built on thirds. Mainly the traditional western sounds are.

- Even more importantly, chords are never named in isolation, they are named with respect to their musical context. An Am7 could more correctly be called a C/A depending on the overall harmonic picture - the melody, the chords before and after and even the emphasis created by the performing musicians. Voicings are basically ignored but could be said to come under this point.

When I teach harmony to students I always point out the key thing to understand is how the harmony is changing, and to look at it dynamically not statically. It's more about the relative motion of notes comprising chords than names although names are obviously a useful construct.

I agree with you but I wonder if this algorithm could be reworked to be an important part of a system of that considers context.

Roughly, what if we consider x_i the sequence of latent chords, and y_i the observed notes. If we reframe the accidental-based sorting this uses to act like a likelihood function e.g. P(y_i | x_i) ~= 1/exp(# accidentals), then we "only" need a transition function P(x_i | x_i-1) which describes what chords typically follow which preceding chords, and then we have an HMM system for which we can do inference easily. You can also imagine extending the order (number of preceding chords regarded as context), or training some higher order latent state z which might carry information about mood or genre and what chord sequences are appropriate in context e.g. P(y) = P(z_0) \Product P(z_i | x_i-1, z_i-1) P(x_i|z_i) P(y_i|x_i)

> My hunch is that any algorithm that analyzes chords in isolation (and not in the context of other chords in the song)

You can at least get much further by naming a key (what a key is, is not etched in stone either, but there are some useful enough definitions for most cases). That would be a bare minimum for a useful algorithm though. Especially if your input is just a set of notes.

Sometimes the context even includes the genre. A F/G might be written G9sus4 on a jazz lead sheet or G11 for a pop song. The latter is somewhat incorrect, since the 3rd is pretty important in a G11 voicing.

Without other context I would say that you can probably label G/C as Cmaj9 or even Cadd9, even though the E was not in the original label, but to be sure you do need to check whether the E is indeed okay instead of or in addition to the B.

Yes.[1] In particular your point about analyzing chords in isolation is spot on.

In “An Introduction to Musical Analysis”[2], Nicholas Cook says something that I have always considered very profound and applies widely, not just in music, which is

   > All notation is analysis

So when you write Cma7 for a jazzer, that’s an instruction that you are generally in the major tonal area and they may well play a Cma9 or a Cma7#11 for example. This is why my functional harmony teacher used to get annoyed by people writing the “Crosstown Traffic”/“Purple Haze” Hendrix chord as E7#9 (which you see a lot). He would say it is E7b10 because that g natural is coming from the minor modes so it’s actually the fourth degree which has been flattened. If you call it a #9 you’re telling players the wrong scale for improvisation (pretty much everyone else in the whole world calls it E7#9 though).

Likewise going back to your point about slash chords, a lot of people learning this stuff get hung up on “what is this slash chord really?” (Eg if I’ve got B/C or whatever what actually is that) whereas when I’ve talked to really serious musicians in that world who play that kind of intense modal music they really are thinking about what the slash chords are in terms of where they come from and what they are leading to. Because that gives a sense for what the underlying tonality is. You can’t get it just from the notes of the chord vertically in that one instant.

If you look at baroque music and earlier, if you just do a vertical chord analysis (eg something like Gesualdo if you really want an extreme example) the chords make absolutely no sense in many cases but that’s because they work in terms of voice leading (ie context) rather than vertical relationships. Analysts used to call that feature “vertical false relations” because they found the vertical chord analysis troubling.

[1] ex-professional musician with a degree and postgrad in jazz, contemporary and popular music here. Wife is a professional musician who teaches at a couple of conservatoires and mostly plays baroque and early music with some 20th and 21st C music thrown in for good measure. Lots of pro musician friends. Not trying to argue purely from authority but I do talk music a lot with people who know a lot, and this topic comes up a lot.

[2] Which stands out as a great book in a field with lots of terrible books btw.

I'm going out a limb here and saying "your ears interpret them in terms of their relationship to thirds and everything else is a fiction"

Although:

a) I have only given this a moment's thought and...

b) The term "fiction" here is relative as all music theory is a fiction to some degree.

c) "Ears" here is short hand for a weird mixture of maths, physics, brain structure and learned cultural expectations.

I'm kinda clutching at a valid idea here though - despite the above flakiness.

Zappa used 2nds a lot, for his improvs. Allows a lot of freedom to both major or minor or both.

The thing is though you can get to every note by stacking enough thirds - I don’t think it’s a particularly bad perspective

And don’t forget the barbershop 7th!

For what it is worth it’s not wrong to say that the triad where E is the root would be Em#5. The inversions you point out still have the same root (C) even if the bass is different. But I agree you’ve identified the fundamental problem: we cannot infer the root note and, therefore the name (enharmonics aside), from just a set of notes and attempting to is a fool’s errand. Even with a root note, it's going to be difficult many times to have a sensible answer

The key problem with this implementation in addition to not simply taking the root note as input (or a key or scale), appears to be the chord database is pretty spartan, since it doesn't appear it would identify C-E-G as anything other than CMaj. If you want figured bass/slash notation then you'll need to specify that as well (bass note).

A number of chord namers take these as additional inputs.

Interesting.

Coming from a cover band/local small-time musician, C6 means C-E-G-A. In other words, C with an added 6 on top.

The charts I play from generally don't have any inversion information on them, and I probably play different inversions each time.

Hey I’m guilty of going on unpopular nit-picky language rants, but I’ve learned something over the years after doing more historical language research: there are almost no rants about language abuse that are correct, they are almost always incorrect. And this one is incorrect, I’m sorry to say. The first mistake is assuming a comma has a well defined right and wrong usage. It doesn’t. Your favorite pet use of comma is not the only use of a comma. There are lots of valid uses of comma that have overlap with other punctuation marks, and with lack of punctuation marks too.

Language is extremely fluid and is defined by usage and changing over time. It is not defined by style guides or dictionaries or what we think we learned in school. Personally I think it has become far more fun to be a language pedant once I’ve embraced that fact that there’s rarely ever such thing as wrong usage, and started to look for the interesting uses in the past and the in present to think about how things have changed before and how they might change in the future.

Other examples of incorrect rants include how to use the semicolon (lots of ways), whether to use two spaces or one between sentences (either, who cares), whether using literally figuratively is wrong (it’s not), whether using the word really as an emphatic rhetorical question is acceptable (it is), whether the word myriad can be followed by the word of (it can), etc., etc., etc..

Come join the side of enjoying how weird language is and how many different flavors it comes in, and how as long as someone gets their point across, nothing else matters, though some people make really beautiful language and also communicate well while breaking all the “rules”.

> or a dash or a hyphen

Em-dashes are typically used for separating clauses. Hyphens and en-dashes are used for hyphenating terms and indicating ranges (among a couple of other uses).

Not that this really matters in practice, but the visual cue is useful for reading rapidly and accurately

what?

it's perfectly readable to me, I just read any comma as a short pause. When saying that out loud, you would make a short pause. It's read the same whether there's an ellipsis, semicolon, hyphen, or whatever.

Also, no, it isn't semantically indistinguishable from that latter sentence, what? You literally know this, you said that that's "obviously not what is meant". The order of the sentences, and the pause there, is what conveys semantic information, not whether that pause is a comma or not.

Phew! That wasn't nearly as misguided as I thought it was going to be. It is a mostly decent and sensible guide. And if you're going to do one and only one dialect, a Broadway dialect isn't a terrible choice. I do hope your software has an easy way to override your auto-generated chord symbols though.

Also because when you add diminished chords you get lots of double flats (for example C-E♭-G♭-B♭♭ vs C-E♭-F♯-A)

The problem is not the testing. The problem statement is flawed.

Chord naming is not particularly useful as simply a function mapping a set of undifferentiated notes to a name. The post interestingly gets that the root note is important, but then sort of misses the point in the end. You either have to specify the root, or if the procedure is generating all combinations then one needs to know the implied root in the output (and then this of course leaves the hard bit of identifying what is the correct root to elsewhere). As an example, an input of {A, C, E, G} will spit out C6 and Am7. Which one it is, is the important part. And these are both relatively common chords.

Looking at prior art you will see that chord namers either take something like a key to infer the root, they take the root explicitly, or they treat the notes as an ordered set, some then improperly assume the first element is the root (conflating root and bass). In a GUI that is super misleading.

https://muted.io/chord-identifier/

eg: If you put in E-G-C it identifies as Em#5. Which is a completely false sense of "oneness" and would usually be incorrect. In practice E-G-C played on the keyboard in pop music is more likely a first inversion Cmaj chord, or C/E.

There are better tools out there (https://www.scales-chords.com/), but the example above would be how not to do it. This is not to dunk on it (or the post), but to motivate thinking more about the problem.

In this case the posted algorithm won't identify Em#5, simply because the database doesn't have an those entries. If you scale the algorithm by augmenting the database with more spellings then the output set is going to become larger without being more useful. It will be technically correct, yes that C-E-G might be a Csus4♭4, a C, a Em#5, but what do I do with that.

It’s only so important for “Western” music. Other musical traditions/cultures (including some from the “West”) find other scale patterns more important. Or they don’t even use the 12-tone division of the octave that this is working within.

Because that pattern forms a scale that allows for playing several intervals such that the harmonics line up nicely, so that they're either very similar or very distinct, but not annoyingly almost similar. William Sethares has a good overview here:

https://sethares.engr.wisc.edu/consemi.html

Note how figure 3 shows dissonance minima close to degrees 3, 4, 5, and 6 of the major scale when played against degree 1. Although there are many other possible combinations of notes, combinations with degree 1 are very important because degree 1 provides a kind of "home" that the music often returns to (the "tonic"). But the goal isn't just to maximize consonance, so these notes alone would make for a boring scale. For better musical value, we need some more dissonant intervals to build tension before it can be resolved with the consonant intervals. The obvious place to put them is in the big gaps. Putting degree 2 a single semitone above degree 1 is probably overdoing the dissonance a bit, but putting it two semitones higher gives a useful mild dissonance. Considering only combinations with degree 1, degree 7 could theoretically also go a single semitone above degree 6, which gives the mixolydian scale, but the major scale is more popular. I assume this is because of combinations that don't involve degree 1.

It's pretty much historical, and initially based on the tastes of medieval priests doing Gregorian chant. It started with the handful of intervals they would use and more intervals were added as needed when music grew more complex until we got to similar-ish 12 intervals, which were then actually equally spaced later.