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Theory of Harmony, page 100

Hello, the current topic is minor mode. Why can only II degree follow major IV in minor scale? Can't quite figure this one out.

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    He keeps saying "at present." I wonder if there are some voice-leading concerns he hasn't addressed yet? IV might not be able to go directly to V so as to prevent parallel perfect fifths, maybe?
    – Richard
    Dec 19, 2022 at 14:31
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    @Richard all of the chords in the example are in root position, so it may be that inversions are not allowed. But whatever it is, it's clearly some limitation that exists in the context of the rules and techniques that have already been covered in the book, so only someone who knows the book or has access to it will be able to answer.
    – phoog
    Dec 19, 2022 at 16:10
  • Are you able to get hold of the German original? That might shed more light on what exactly he was bringing up there.
    – leftaroundabout
    Dec 19, 2022 at 19:38
  • @leftaroundabout Quote: "... Dagegen geht die Verbindung mit der IV. Stufe ganz gut, nur ist sie an eine bestimmte Fortsetzung gebunden, da nach der IV. Stufe vorläufig keine andere wird folgen können, als die II. erhöhte. Glatt erfolgt die Verbindung mit der V. erhöhten, dagegen ist die mit der VI. erhöhten vorläufig unbrauchbar, denn die VI. ist ein verminderter Dreiklang, müßte also durch den Quartensprung des Fundaments aufgelöst werden; das fis des Basses muß aber nach gis gehen (zweiter Wendepunkt), kann also nicht wegspringen."
    – Lazy
    Dec 19, 2022 at 20:55

1 Answer 1

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Schönberg is treating the minor scale here with the options to raise the sixth or the seventh scale tone, forming a rising and a falling scale. A few pages before this Schönberg postulates four "turning point laws" for the minor scale, which try to keep the tonal character of the minor scale clear. These are:

  • Erster Wendepunkt gis: gis muß nach a gehen, denn gis ist nur wegen des Leittonschrittes zu nehmen. Keinesfalls darf g oder f gebracht werden, ebensowenig fis (wenigstens vorläufig)
  • Zweiter Wendepunkt fis: fis muß nach gis, denn es wurde nur wegen des gis gebracht. Keineswegs darf g oder gar f folgen. Aber auch (mindestens vorläufig) nicht e, d, a usw.
  • Dritter Wendepunkt g: g muß nach f, denn es gehört der fallenden Skala an. Keinesfalls dürfen fis oder gar gis folgen.
  • Vierter Wendepunkt f: f muß nach e, denn es gehört der fallenden Skala an. Keinesfalls darf fis folgen.

Trans:

  • First TP g#: g# has to go to a, for g# is only used because of the leading tone interval. In no case may g or f be used, nor f# (at least for now)
  • Second TP f#: f# has to go to g#, because we only use it for the g#. By no means may g or even f follow. But also not (at least for now) e, d, a &c.
  • Third TP g: g has to go to f, because it belongs to the falling scale. In no case may f# or even g# follow.
  • Fourth TP f: f has to go to e, because it belongs to the falling scale. In no case may f# follow.

So keeping by these rules we see that the f# of the IV# chord may only rise into a g# (or remain on f#).

Furthermore at this point Schönberg is only considering chord changes that share at least one note in common, which he calls harmonisches Band (harmonic bond) (so at this point Schönberg does not consider changes like IV-V. But IV# - V# will actually cause a problem, as f# → g# would require parallel shift of the chord).

But thus the IV# in question has only a limited amount of options:

  1. D → B minor (IV - II)
  2. D → G major (IV - VII)
  3. D → B dim (IV -II)
  4. D → F# dim (IV - VI#)
  5. D → F major (IV - VI)
  6. D → A minor (IV - I)

But if we consider the TP rules (f# may only be followed by g#) only the first options remains:

  1. f# → g is not allowed
  2. f# → g is not allowed
  3. f# → f# would be allowed, but as the last clipped sentence on your pictures says this diminished chord would need to be resolved by a 4th upwards (cf. the early section about the 7th scale degree in major), f# would need to go into b, which is not allowed, as f# → g#.
  4. f# → f is not allowed
  5. f# → e is not allowed

Thus only the given chord change is possible.

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  • I started to edit this answer because "by no means" requires subject-verb inversion in the clause it introduces (yes, this does happen in English, contrary to popular belief; it needs to be "by no means may one follow x with y"). But then I noticed that the translation changed the subject from the pitches themselves to the impersonal "one," so I decided to change it back.
    – phoog
    Dec 19, 2022 at 22:16
  • Thank you man. I had the pivot rules written down but apparently could not use them correctly, your answer is very clear. Be well.
    – Ledy Buzna
    Dec 20, 2022 at 10:36

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