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I don’t think that this algorithm can handle slash chords like G/C (G over C) and would instead label it as Gsus4. The former gives a lot of important context to voicing which can by important if you need a particular sort of motion in the bass line.

My hunch is that any algorithm that analyzes chords in isolation (and not in the context of other chords in the song) is going to miss out on overall readability. Good chord notation has a sort of elegance that can highlight the similarities/differences between sequential chords that can make things very intuitive for the musician

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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.

And then the key may be unclear, or musicians may differ as to where they feel, say, modulations occur: "it clearly modulates in measure six" "no, measure six is just a borrowed chord and the real modulation is at the cadence in measure eight" etc.

The way music is written has more to do with tradition and legacy systems than being efficient and correct and musicians like to fight about ultimately meaningless things like time signatures.

Naming a key seems, at the very least, a better way to decide the root note than counting accidentals; but which chords are the preferred, common ones isn't completely clear-cut.

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.

What’s more functionally F[maj7]/G¹ is functionally a G7 chord in that any place you see the one you can substitute the other and the harmonic function remains the same.

⸻

1. This chord and its relatives in other keys is my favorite chord.

Kind of since you don't have the B-F tritone. There is a lot more instability, and the resolution to C is a lot stronger, in G7 than in F/G or similar chords.

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 whenever you write something down in music you are (of course) making some simplifications and you are also doing it for a particular purpose. Usually the purpose is performance. So when you write something you are providing an instruction to the performer.

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.

> 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).

you mean the third degree I think?

at first I thought your teacher seems overly pedantic here, but it does kinda make sense... I'm surprised I've never heard anyone argue that before!

I'm not sure your teacher is right. The notation should be Em7b11.

Ultimately, I think it would depend on whether Hendrix included F or F# in the scales that he used to solo over The Hendrix Chord. If he includes F, E7#9 would be the better notation, since it suggests an altered mode: I, IIdim, IIImi, IVdim(and probably Vdim). (E, F, G, Ab, Bb, C D) . If he includes F#, then you could make a case for E7b10, which I would read as implying a blues scale, although I've never ever seen that notation: I, II, IIImi, IIImaj, IV, V (E, F#, G, G# A B C D). My bet is that Hendrix plays F, not F#, given that he was a jazz musician before he was a rock musician.

The argument for Em7b11 would be that the major third is actually the FOURTH note of an altered scale. . Better still: Em7b9b11. Or I suppose you could be uncontroversial and just write Ealt.

Chords derived from altered scales, and chords based on quartal stacks are both severely broken cases in modern chord notation. Neither seems to have settled chord notations, and the chord notations that do exists vary greatly by dialect.

(Jazz guitarist who very much prefers modern functional chord notation, that implies both scale and chord, to the older Broadway jazz notation style).

Well he would say it's not functioning as a minor chord it's functioning as a dominant, so any kind of Em is off the table. Also if you call the major third the b11 you are turning one of the notes of the main triad into an extension which he would take issue with too.

But you know, obviously do whatever makes sense to you. As Schonberg says in Harmonielehre, "There are no rules of music, only rules of style".

yes. Blame it on lack of sleep.

Also as a sibling to your comment points out it's a blend of major and minor, so also in jazz you'll often see something like E7b9#9b13 written, but that really makes no sense in terms of a scale. The 9th is either flattened or sharpened, can't be both. So the next degree of the scale is the b10, which also makes sense when you think about something like a "diminished" scale which people play over this chord often.

He also used not to like the name diminished for the scale btw, but would refer to it as one of Messiaen's modes of limited transposition. I can't remember Messiaen's nomenclature exactly but the scales which people call the wholetone/semitone diminished and semitone/wholetone diminished are one of his symmetrical system of scales. IIRC there are 3 distinct "diminished" scales and all the other ones are just modes of these three. So you can see that the st/wt diminished starting on D is just a mode of the wt/st diminished starting on C for example.[1]

[1] This is him https://williamkinghorn.org/Biography he was an awesome guy and I learned a lot from him

Yep! It’s far more logical. This chord blends major and minor so the obvious way to indicate this is by adding a flattened 3rd.

> 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.

I'm not at all into music theory and such, but your passage just reminded me of what AlphaPhoenix mentioned in his latest video[1], where he analyzed two frames from an experiment, both with a piece of string stretched horizontally across the screen.

They look identical, but they are not. One is a stationary string and the other in an oscillating string which just happens to be flat at that moment in time, but the pieces of the string still carry momentum.

[1]: https://youtu.be/WCKt405t9V8?t=478

> 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.

I'm guessing you mean Emin7b10.

It's in interesting take, but a bit weird considering you wouldn't stack the chord that way. You want to voice the G# below the G, E G# D G, making a major 7 interval which sounds good. If you instead voice it E G D G#, then the G to G# will form a minor 9th which is pretty clashy, generally avoided, and doesn't sound like the Hendrix chord anymore. Try it out, tab (0 7 6 7 8 x) vs (0 7 5 7 9 x). This is a standard jazz voicing rule of thumb, although I forget the name of it.

All of this makes a lot of sense. But to add; a semi-professional piano player I know once gave me a heuristic that can help sometimes, namely “the lowest fifth contributes the most to what the chord feels like”. But you can still get into discussions about whether something is, say, a Dm/F or F6 (and I see a lot of tabs where I disagree which the author's choice).

(semi-professional piano player here) That's interesting. I've never heard that...not even sure what "lowest fifth" would mean. I would think that the root and the third contribute the most, right? The fifth is sometimes even omitted. I'm very curious how this might work. Do you have any examples?

(Semi pro jazz guitarist here). The heuristic I was taught: the accompanist owns the 3rd and the 7th, which allows the SOLOIST to choose #4, 5th or the #5 as the muse dictates in the moment. The 5th is an semi-avoid note, until I hear the soloist commit to a choice of 5th.

I guess it means in the sound scape as a whole, potentially including multiple instruments. But to keep it to a single piano, e.g. if you play B3 D4 G4, then it won't sound like a B chord (neither minor nor major) because there's no fifth. Instead, you'll hear D5 as an overtone of D4, and G4-D5 will be the lowest fifth that you hear, so it is readily interpreted as G/B. If the third were the most important, then this would have been a Bm, which is pretty clearly isn't unless you add an F# (or there is some other instrument in the mix that provides one).

At least that's how I interpreted him :-)

Allowing that I'm simply not sophisticated enough to understand this, I think he's overthinking things. :-)

I mean, B3 D4 G4 in isolation probably does sound like G/B to western ears, and maybe the overtone explanation is acoustically relevant, but it seems like there are not too many other things that those notes could be, and the spelling clearly spells a Gmaj triad.

It looks like this book is called "A Guide to Musical Analysis" (or does Cook have more than one such book?)

Maybe. Or my edition is old or something. He does have a few books. “music, imagination and culture “ is also excellent

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