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I'm confused by the following exercise in the 5th ed. of Piston's Harmony, page 21. "Exercise 7 j: With G# as the soprano note, write in four parts a triad in first inversion, with the subdominant in the bass."

I take this to mean a II triad (II-IV-VI) in the first inversion (IV-VI-II, i.e. subdominant/IV in the bass), with the extra constraint that the triad contains G#.

This gives us 3 potential solutions (illustrated in Root for simplicity):

  • If II is G# then IV=B and VI=D# (i.e. the key of F#), so our first inversion would be B-D#-G#
  • If IV is G# then II=E# and VI=B# (i.e. the key of D# as unlikely as it is) so our first inversion would be G#-B#-E#
  • If VI is G# then II=C# and IV=E (i.e. key of B) so our first inversion would be E-G#-C#

Am I reading this correctly and are these potential solutions? Or have I missed something?

  • @Richard is right, there are many correct answers available with the limited information. It doesn’t even specify major or minor. Are you sure there is no other info provided? – John Belzaguy Jun 8 at 19:12
  • Hi @JohnBelzaguy, that's all the information to go on! And I think it was this lack of info that was leading to my conclusion. Thanks for the comment! – comedydave Jun 8 at 19:42
  • Wow, the possibilities! It doesn’t even specify that the G# has to be a chord tone! – John Belzaguy Jun 8 at 20:21
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    It's interesting to compare this question to this one, which seems to be based on a different edition, and which also leads to a different answer. – Matt L. Jun 9 at 7:55
  • @Matt - yes! It was in fact that question that lead me to SE Music. The subtle difference that "of G# minor" makes to the question is important (and also confused me somewhat!) – comedydave Jun 9 at 13:11
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Yes, this strikes me as an example that willfully invites multiple correct answers.

Your three solutions are correct, but there is one other possibility if we change mode. In addition to your first solution in F♯ major, you could also have one in F♯ minor, which would involve G♯–B–D. This chord is almost always found in first inversion, which would be correct with the subdominant in the bass.

The two other keys don't work in minor: first because D♯ major isn't a real key (it requires two double sharps in its key signature!), and because B minor requires a G♮.

I wondered if perhaps Piston was slyly hiding in a doubling rule here; some books/teachers say that first-inversion chords can't have this or that doubled, but he has made no such claims in this chapter (p. 17: "Doubling of the root is most usual, but the third or the fifth may on occasion be doubled instead."). As such, any of these four options would be correct.

Furthermore, there are multiple realizations for each of these correct answers: as one example, the soprano G♯ can either be on the second line of the staff or above the top line, both of which fall into Piston's suggested soprano range on p. 16 (even if the high G♯ is really pushing it).

Edit: After considering Peter and Matt's comments regarding the use of "mode mixture" chords, I decided to look a bit more closely at the book. At this point the text has only discussed triads in the major mode; triads in minor wait another two chapters. As such, any minor examples were likely not intended answers, and they should probably instead be limited to the B and F♯ major examples in the original question.

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  • Hi @Richard, thanks for this and clearing it up for me! I hadn't thought of the minor option. Regards the doubling it's interesting you make this point as I was thinking about it: I have read one such rule which suggests avoiding doubling the 3rd of a first inversion; if we had G# in the soprano this would preclude the triad where G# is the 3rd as it would have to have G# in the bass and the soprano - this is our D# example and is therefore unlikely anyway. – comedydave Jun 8 at 19:51
  • @comedydave My thoughts exactly. It's clear you're thinking through these questions exactly as you should be. Keep it up, and welcome to Music.SE! – Richard Jun 8 at 19:56
  • @MattL. E major chord in B minor would work as a chord, but E is not in the bass in 1st inversion – Peter Jun 9 at 8:03
  • @Peter: You're right, I meant a C# minor chord, so E-G#-C# in the key of B minor. The other part of my argument remains the same. – Matt L. Jun 9 at 8:12
  • "[...] because B minor requires a G♮". Wouldn't a C# minor chord be perfectly OK in the key of B minor? The required G# is available in melodic minor and in dorian, and it is used anywhere from Bach to Pink Floyd. – Matt L. Jun 9 at 8:13

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