I came across this question in my theory workbook, (Master Your Theory Grade 4 by Dulcie Holland). I have to harmonize it in four part vocal style. However, the thing is, I can't seem to be able to get rid of exposed/hidden octaves and fifths. The book doesn't cover this topic, so maybe that's why they always appear. The piece is in C minor, since that is stated in the book. The chords which I'm allowed to use are: i and i6, iv and iv6, V and V6 and VI and VI6.

However, I am ok if chord ii6 is used, if it leads to chord V.

As for doubling, it is preferable if the root in root position chords is doubled. The exception is chord VI, where it is preferable to double the third. As for first inversion chords, it is equally preferable to double the root or the fifth. However, do feel free to try other doubling options, if it allows the problems to be solved.

Here are the vocal ranges of the voices.

Alto: G3 to C5 Tenor: C3 to G4 Bass: F2 to C4

The only cadence point is the two notes at the end. It would a perfect cadence, and as it is a supertonic to tonic ending, the root in chord i must be tripled and the fifth removed.

Could you guys please help me harmonize this piece? Thanks a lot. Feel free to ask any questions needed.

If there is no way to remove the exposed octaves and fifths, are there any situations in which they are allowed?

enter image description here

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    Generally we don't do homework for people here. You can ask us something more specific, but this 'harmonize this melody for me' is bound to get closed . Also, I don't see any point in making someone else solve this for you. How will you learn to solve this kind of things if you don't practice? – Shevliaskovic Dec 20 '15 at 12:30
  • It's not homework, I've been doing this question for like 2 hours. This is the last harmony piece in the book, so I've been doing this sort of stuff a lot. I'm not the sort of person to give up easily unless I'm really stuck. – AgentWin Dec 20 '15 at 12:47
  • The G in the bass in the perfect cadence has to be approached from below to avoid the exposed fifth. This means the bass before it could only be an F, as the only chord that I'm allowed to use which has a F is chord iv. Now that F has to be approached from below as well to avoid the exposed octave. If the F was F2, then an exposed octave cannot be avoided without going outside the range of a bass voice. If the F was F3, then voice overlapping would occur in the perfect cadence. The G would be shared by bass and tenor, and the tenor HAS to drop to the E in chord i, causing the overlap. – AgentWin Dec 20 '15 at 13:10
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    It'd be better to edit the info you provided here at the comments on your question, so as to show your problem, because the question as it is doesn't show that – Shevliaskovic Dec 20 '15 at 13:39
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    @agent5514 Why can't the Ab in m. 3 be harmonized by iv with F in the bass followed by ii6 with F still in the bass? Then you can go to G and C without problems, right? I'm not sure, because your book appears to have far more severe rules than the ones I've taught from… – Pat Muchmore Dec 21 '15 at 3:46

Consider that the cadence might be an authentic cadence, but not a perfect authentic cadence. (I'm not sure which terminology your text is using, but "perfect" is often used as a synonym for the broader category of authentic cadences.)

Let's think about it: to achieve a perfect authentic cadence without exposed direct fifths and/or octaves, the last three notes in the bass would need to be a rising line of F -> G -> C.

So what does the 2nd bass note in the 3rd bar need to be? It could be C (as part of VI6), but that means that you have a falling direct octave between the descant and the bass (A♭/C -> F/F), so that means it must be F.

So what do we need then for the first bass note of the 3rd bar? E♭ (as part of i6) would work, but E♭ below the bass stave is proscribed in this exercise as out of range (as you have stated), and if you hoist everything up an octave to near the top of the stave, you run out of room for the alto and tenor. A♭ might do, but you will have a hidden octave between descant and bass. F then, maybe? In that case the last note of the bass in m.2 must drop to F, forming a direct fifth in the outer voices.

So you have a choice here: trying to figure out the least objectionable direct fifth or octave between the descant and the bass, or using an imperfect authentic cadence. The latter has the advantage of actually suiting the melody, because the "Scotch snap" D -> C at the end of the melody sounds more like an appoggiatura than a cadence - it rather suggests that something should follow the phrase.

So let's look at this:

enter image description here

Example B is a skeletal harmonisation that would fit the exercise. Example A fills out the example with a number of non-harmonic tones (marked "+") that don't really change the way the part writing is handled. I added them because it is always interesting to see if you can get something musical out of an exercise.

Here the cadence is V6-I, and, as you can see, meeting the constraints becomes possible. There is an augmented second in the bass between bars 3 and 4: that's within the idiom, especially as the bass is arpeggiating a diminished triad (as bracketed in the score). I've marked out the direct fifths and octaves with lines. You'll note that none are exposed; all involve at least one of the inner voices. (Direct octaves and fifths are preferable with one voice moving by step, but that is not always possible in a skeletal harmony exercise. That's part of why I added passing notes to the "artistic" version.)

So I suppose it depends on how broadly or strictly your particular textbook is defining "perfect cadence". Exercises like this often do involve trade-offs, finding the least bad solutions to tricky problems. To my mind, the imperfect cadence is the best solution.

EDIT: Well then, there's nothing for it but to accept an exposed octave or fifth, and also the last tenor note passing below the penultimate bass note, because you probably won't get in the third of the tonic chord any other way. What might be acceptable here is an exposed falling octave in the final cadence, because such do see use in the real world, the falling fifth in the bass being a topos (traditional gesture) of the perfect cadence, thus you get the following possibilities:

enter image description here

I prefer the high bass and accept a bass G higher than the tenor E♭ because dropping F -> G an octave pretty much guarantees either a parallel fifth or a hidden octave between the outer voices, and in a place where such is not traditional. This gives a couple of possibilities for the bass in m.3:

  • As per example C, the low F rises an octave, with tenor F moving the third of the subdominant. This is fairly clean.
  • As per example D, the bass rises in an arpeggio to F. This creates an additional direct octave and a direct fifth with the alto C (as marked), and causes the bass F on the last beat of m.3 to pass above the E♭ in the tenor on the second beat - a messier solution, but one that might be acceptable in real use for motivic reasons (the bass and tenor having something of a pattern).

Example D also has a tierce de Picardie. That's because I won't be writing any more examples: it's a final cadence.

  • I wish this was possible, however we're not allowed first inversion chords directly in a cadence. – AgentWin Dec 21 '15 at 2:56
  • Well, that's a Godawful mess. See my edit when it's done. – user16935 Dec 21 '15 at 6:31

I'm not sure as to why the question would ask you to harmonize the given voice and then tell you what chords to use. One of the more important parts of harmonizing melodies is recognizing the chord progressions. That being that lets see what we have.

In the first bar it seems like you either have the tonic or the dominant for the first beat. I would probably go for a I-V6(or 6/5) and then into a tonic in root.

In bar two I see what looks like a cadence. Probably ii - V (Imperfect cadence). Probably want the super tonic in first inversion.

Bar 3 looks like vi - ii and then for the third beat of the third bar it seems like the ii chord repeats in an other position.

In bar 4 it looks like a regular old Perfect cadence (V - i)

  • Beginner exercises tell you what chords to use to help you a wee bit. In bar 2, I though ii- V as well, but the exercise doesn't want ii – Shevliaskovic Dec 20 '15 at 14:17
  • We aren't really supposed to use chord ii in minor keys at this stage, except maybe in the first inversion. Also, the only cadence is the perfect at the end, there isn't an imperfect cadence in the middle. (there was just a long phrase mark.) I'm just worried about the exposed octaves and fifths and feel that this question doesn't allow the option of avoiding them. – AgentWin Dec 20 '15 at 14:30

Ok, I just came up with a solution to the question just now.

enter image description here

I know that it's bad to have four root position chords in a row, but other chords won't really work. If the C in bar 3 was chord VI6, then there would be three C's, with no room for both an A flat or an E flat. If it was chord iv6, then there would be a consecutive fifth with chord V before it. It can't be chord i as we're not allowed to have V-i in the middle of a piece. It can't be chord i6 as it would create a leap of a 6th and 7th in the bass. So I guess the only option is for it to be chord VI.

  • Hidden octave between the outer voices in m.3: A♭ - > F. – user16935 Dec 21 '15 at 7:39
  • @Patrx2 I don't think it is a hidden octave, since the F in the bass is staying still, creating oblique motion with the soprano instead of similar motion. – AgentWin Dec 21 '15 at 7:56
  • I'd be very surprised if oblique motion into an octave is considered bad. Every book I've ever taught from requires similar motion to be an error. – Pat Muchmore Dec 21 '15 at 11:17
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    Being required to use every note as a chord tone does not mean each one has to be a tone of a different chord as long as both tones belong to the same chord. I think that was @Patrx2 's point. – Pat Muchmore Dec 22 '15 at 1:10
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    All I can say is that I urge you to check into that; it sounds highly unlikely to me that they wouldn't want you to recognize the possibility of a harmonic rhythm slower than the melody. That certainly isn't remotely consistent with common practice. However, I don't know anything about new rules the AMEB might arbitrarily add to the mix. – Pat Muchmore Dec 22 '15 at 1:51

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