# Exercise from second chapter of Harmony by Walter Piston

Exercise 7, j. : With G sharp as the soprano note, write in four parts a triad in first inversion, with the subdominant of G sharp minor in the bass. It seemed to me that such a chord does not exist. The book does not have answers to its exercises. Edit: Added a photo of the page!

• Shouldn't C# be in the bass? I updated the post with a picture of the page. Aug 1, 2019 at 10:58
• I have an earlier edition, which simply reads "with subdominant in the bass." Looks like a typo introduced by later editors. Aug 2, 2019 at 1:10

The subdominant of G♯ minor is C♯ minor. The C♯ minor chord is C♯-E-G♯. The first inversion of that chord is E-G♯-C♯. So that would mean that E should be the bass note.

But the question is a bit badly worded in that it asks you to put the subdominant of G♯ minor in the bass which could make you think that C♯ should be in the bass. But then it would be root position and not first inversion.

In the fifth edition of the book (1987), the exercise reads:

a triad in first inversion, with the subdominant in the bass.

So,

• Our bass note is scale degree 4 of some major or minor scale.
• We're in first inversion, so there will be a third and a sixth above the bass note. In other words, scale degrees 6 and 2. Put another way, we're looking at the ii or iio triad of some major or minor key.
• In a triad, any of scale degrees 2, 4, or 6 may be doubled.
• Since there's no restriction of doubling, the G# in the soprano could be scale degree 2, 4, or 6. Specifically, G# could be in both the bass and soprano.
• Scale degrees 2 and 4 will be the same regardless whether the key is major or minor, but scale degree 6 could be raised (i.e., from major) or lowered (i.e., from minor).

Thus, we're left with the following possible scales/keys:

• G# is 2: F# major or F# minor
• G# is 4: D# major or D# minor
• G# is 6: B major or B# minor

This in turn leaves us with the following possible solution triads for the exercise (given here in root position):

* F# major: G# B  D#
* F# minor: G# B  D
* D# major: E# G# B#
* D# minor: E# G# B
* B  major: C# E  G#
* B# minor: Cx E# G#

The final step is to arrange one of these chords in first inversion and with G# in the soprano voice.