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.
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?
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.