Slash chords and notation for A/C (according to Haunschild Book)

Question

I am currently working on a book on music-theory by Haunschild “Die neue Harmonielehre” (the question is not too specific so it might also have some general value for people not working with this book. Nonetheless I will use the table in the book (see photo) as a reference.)

In the table it is stated that the slash chord of the form “A/C” is a C^(7/♭9/13) chord without fifth and seventh (“ohne Quinte und Septime” in the book). It is also stated that B♭/C is a C^(7/9/sus4) chord without fifth and seventh.

The questions:

1. Why is “A/C” given as “C^(7/♭9/13)”? Up to this point in the table all slash chord definitions made sense to me but there is no 7th and still it is added to the chord symbol and then it is stated that there is no 7th afterwards. The chord consists of the notes “C-A-C♯-E” in rising order so to me it would be a C^(6/♭9) chord. Because the sixth is in the same octave (below the C one octave higher) I thought it should be “6” and not “13” added to the chord and more strangely why is a “7” added if it is not in the chord? What am I missing here?

2. In a previous section of the book (this should be a general thing in chord notation too I assume) it is stated that “add9” is used if the seventh of the chord is taken out and “9” if the seventh is either part of the chord or not. Now in the table the slash chord “B♭/C” is given as “C^(7/9/sus4) without fifth and seventh”. Even if the chord in question one is written like it is for some reason this (for my understanding) is clearly the case for which “add9” was conceived. So I would write it as “C^(add9/sus4)”. So same question: what am I missing here?

The only explanation I could come up with was that the notation always includes all stacked thirds up to the highest even if they are not included but it is not stated explicitly in the previous chapters. If this is the case could someone please explain to me why it is done that way (if it is not purely for historical reasons).

I am not a classically trained musician so I assume I got a wrong idea of something I learned from the book previously. It would be great if someone could explain this to me. Thank you in advance.

Answer 1

Why A/C = C13(♭9)

Here's how to think about this chart: the slash chords provide optional ways to "voice" or spell out more formal chords. And it's okay to voice a chord in a way that is incomplete. For example, if you're reading a piece of music that says "Cmin7," you're not strictly required to play C-E♭-G-B♭ every single time the Cmin7 chord appears. The Cmin7 chord will occur repeatedly as we cycle through the form, and so it's okay for the musician merely to hint at the underlying harmony without playing the full chord. For example, it's perfectly fine to voice a Cmin7 chord with: D-E♭-G. This chord voicing doesn't contain the flatted 7th and contains an extra note (the 2nd/9th). But that's not a problem. Not every iteration/voicing of the chord must contain every note. This is particularly true in jazz.

So, while the chord A/C is not a full and complete voicing for C13(♭9), it is still a very good option. If you're reading a piece of music and you suddenly see C13(♭9), you can immediately think "oh, A/C will sound good." The advantage here is that, when you see C13(♭9), it's simpler to replace it with the slash chord A/C. In effect, the goal of this chart is to demystify complex chords like C13(♭9) by translating them (partially or wholly) into simple triads/slash chords.

You might be wondering why A/C only works for C13(♭9) and not CMaj6(♭9). There's no logical reason why a CMaj6(♭9) can't exist--it's just very uncommon. The ♮6th/♮13th and the flat 9th is a very unique combination of alterations and extensions, and that specific combination almost exclusively occurs over a dominant 7th chord and almost never occurs over a major 7th chord. Thus, it's much more useful for the book to list C13(♭9) as the underlying harmony.

B♭/C = C7sus

The book contains a typo here. The chord B♭/C does contain the 7th! The 7th of C7sus is B♭, and B♭ is part of the slash chord B♭/C. So the book is correct that B♭ = C7sus, and it's true that we don't need the text "add9" in this case since the 7th is present. The book states that B♭/C omits the 7th, but this is incorrect.

In general, the book is correct about the fact that, if you see "add9" written on the page, then the underlying harmony must omit the 7th. However, it's fine to voice an add9 chord with a subset of its notes.

Note

I've simplified the chord's notation. Instead of calling it C7/♭9/13, I'm calling it C13(♭9). This is fine because a C13 chord implies a flatted 7th. By contrast, a C6 chord wouldn't imply any 7th. To read more about these conventions, check out this great answer: https://music.stackexchange.com/a/20561/40842.