# How do I determine the key of this given only an E7 secondary dominant chord

How am I supposed to determine the key with the only given E7 chord, which is used as an extended dominant in this case .

• In NNS, the arrows could mean pushed chords, but the rest isn't NNS. Do you mean secondary dominant? If it's sub dominant, the key's B. – Tim Nov 19 '20 at 10:58
• E is the sub-dominant note/chord (4th) in key B. But I don't think that's the answer they want. Key sig. says C/Am. But E7 usually, not always, moves up a 4th to A. – Tim Nov 19 '20 at 11:05
• No, I didn't think so too. If it really was C/Am, the appropriate key would have to be C/Am. – Tim Nov 19 '20 at 11:14
• I honestly think the question as it stands is too vague, with too many spurious characters. – Tim Nov 19 '20 at 11:19
• Yikes, there isn't even always an arrow between V7 and the I-based chord immediately after it. – Dekkadeci Nov 19 '20 at 12:01

The arrows indicate secondary dominant chords, as evident in mm3-4 where V7/ii leads to ii, and in mm7-8 where V7/IV leads to IV.

Given that, we have:

E7 = V7/V, because of the arrow leading to a V7 chord. E7 is the dominant chord of A, so the chord following E7 is A7.

Similarly, since A7 is indicated as a V chord, and a I(maj7) chord follows, the latter chord is Dmaj7. The excerpt is in D Major

By the same logic, we know that E7 is the target of an applied dominant chord, which would be B7. Thus, the chord immediately preceding the E7 is B7.

Extending this across the entire chord sequence, we have:

```F#7   B7    | E7    A7 | Dmaj7 B7    | E-7  A7 |
V7/VI V7/II | V7/V  V7 | Imaj7 V7/II | II-7 V7 |

Dmaj7 B7    | E7   A7 | F#-7  D7    | Gmaj7  A7 | Dmaj7 ||
Imaj7 V7/II | V7/V V7 | III-7 V7/IV | IVmaj7 V7 | I     ||

Note 1: My interpretation of the exercise is that the first chord,
for example, is V7/VI. However, it also could be called V7/V7/V7/V.

Note 2: That we're in D major and not D minor is confirmed
by the qualities of the II-7, III-7, and IVmaj7 chords.

Note 3: The (3) above the first chord is indicating that
the chord is built on the 3rd scale degree of the home key.
```
• Seems like it's a good answer, but where did an arrow signifying sec. dom. chords come from? And the (3)? Not standard notation, I believe. – Tim Nov 20 '20 at 12:29
• @Tim I would guess that this was made clear in the parts of the book that the OP has not shared with us – Judy N. Nov 20 '20 at 12:49
• @Tim The arrow notation I first encountered in a music theory class, but the (3) I only figure out after completing the rest of the exercise. – Aaron Nov 20 '20 at 13:11

This quiz probably is from a book chapter where the chapter surely must make clear what the point of the quiz is.

But just looking at the root movements, almost everything is roots by descending fifth: `V7/II II-7 V7 Imaj7` and harmonic sequence `V7/IV IVmaj7`, `V7 I`.

So `E7 V7 Imaj7` treated as all descending fifths would be `V7/V V7 Imaj7` or `E7 A7 Dmaj7`.

fill in the remainder of the chord symbols.

But something worth mentioning is another aspect about harmony, root progressions, and the clues the quiz gives. In measure 2 beat 1 you have the `E7` which we will say is in `D` and labeled `V7/V`, but then later in measure 4 beat 1 have have `II-7` which assuming no key change will be `Emin7`. The quality of the chord changes from a dominant seventh to a minor seventh, but the root progression didn't change. It's easier to see the unchanged roots using letters: mm. 2-3 `E A D` and mm. 3-4 `E A D`. That kind of treatment of chord quality in a descending fifth progression is common. You can choose chord qualities pretty feely.

So, the chord at m.6 beat 1 is a toss up. It could be `II-7` or `V7/V`. Same goes for the opening two measures. You could choose either dominant sevenths or minor sevenths. IMO, either would be justified with the given treatment of of root `E` as either `V7/V` or `II-7`.