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I've been trying to understand the theory behind dominant sevenths and have been reading a lot of articles. There's just one thing I couldn't understand-- the basic relationship of the minor 7th to the 5th.

Wikipedia says:

In music theory, a dominant seventh chord, or major minor seventh chord,[a] is a seventh chord, usually built on the fifth degree of the major scale, and composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad together with a minor seventh, denoted by the letter name of the chord root and a superscript "7".[3] An example is the dominant seventh chord built on G, written as G7, having pitches G–B–D–F:

What do they mean by it being built on the fifth degree of the major scale? I played around on the keyboard trying to figure out a relationship of Bb to G and I couldn't make one out.

Take key of C and the C7. The dominant 7th is root-major 3rd-perfect 5th-minor 7th. That's easy, but what's the relationship of Bb to G? G major triad is just 5-7-9 of the C and Gmaj7 adds an 11. Moreover, since we're talking C, it's guaranteed to be all white keys, yet the minor 7th is black.

It seems like the minor 7th is just injected in there arbitrarily and doesn't seem connected to anything else in the key, which is alright, but I know there's supposed to be a relationship.


I maybe figured it out by playing around but I won't answer my own question because I'm not sure and don't want to spread errors, but here's what I got.

If you think in the key of C only you can't figure out where the minor 7th comes from and therefore what builds C7, but you can figure out what G7 will be and where that minor comes from. The knowledge of the key of C gives you knowledge of G7. It appears to be just 3 degree-stepovers (i.e. 1 to 3 or 2 to 4 is a stepover) of the notes in the key of C, starting at the 5th. I'm trying to be careful not to call them whole steps because that has a different meaning, and it indeed makes the dominant chord sound when played. Since the 5-7-9 of a given key is guaranteed to be a major chord in the 5th position (perfect fifth triad that many know from the I-ii-iii-IV-V-vii-dim model), that gives us the triad base we need. Now all we need is to bring in the 7th, specifically a minor 7th, which if instead of switching keys to the key of the fifth, we confine ourselves to the key that our fifth is the fifth of, the 7th is a natural minor (I thought this had to do with 'relative minor' but now I don't think so). BTW I apologize if I sound both naive and then over the top. I'm learning this all on my own by reading and thinking about it.

So to get the C7 dominant, we have to think backwards and find what C is the perfect 5th of, and that would be F. Now stay in the key of F and take 3 "steps-overs" or hops, from it's 5th ('-') => C-E-G-Bb. There's our Bb, linked to both a 5th and to a tonic. It's linked to the tonic F and C is the fifth of F, so there's a union there, the union of root, fifth and minor 7th note I was looking for. That's the best I've been able to figure it out. Maybe I'm making it overly complex but at least I found this connection.

I'm certain this has everything to do with the circle of fifths but I'm not good at learning or remembering things top down if I haven't build up to it from simpler primitives and working through logic, but basically to find the X7 chord, walk back p steps to key of Y where X is Y(5). Make an ordered set of all the note degrees n of Y (do re mi) and then play the odd degree n of Y 4 times (i.e. to the 7th; 4*2-1=7) starting at Y(5), or in symbols:

for z=0 to z=3: note n = y(tonic) as 0 + 5 + 2*z // returns 5-7-9-11 of F or 1-3-5-7min of C ==> we got our translation

So again, simplified, walking back until you find what C is the fifth of -> F. Then taking the 5-7-9-11 of F (staying in key), is the same as the 1-3-5-7 of perfect 5th (skewed scale of C) or the 1-3-5-min7 of pure C (breaking keys or crossing keys if you look at it from that way, as I did in the beginning)

BTW yes I'm just figuring this out in real time and yes the math notation makes it easier for me to understand. Maybe someone else shares my frame and it helps them. Of course if I'm wrong, correct me and stop the error propagation.

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    The confusion is really an issue with terminology: "the relationship between the 5th and minor 7th" should read "the relationship between scale-degree 5 and the minor 7th," since the dominant seventh is built on scale-degree 5. – Richard Mar 7 at 17:03
  • Here's why. The M7 is a M3+m3+M3. The m7 is a m3+M3+m3. How about the other two combinations? (1) M3+m3+m3. This lets you transition from M3+m3+M3 to m3+M3+m3 ... first, one note changes between M3+m3+M3 and M3+m3+m3 (major7 interval to minor 7), then one note (the third dropping down, changing the chord from major to minor) changes between M3+m3+m3 and m3+M3+m3. In other words the dom7 isn't naturally occurring ...it's a by-design transitional chord built on the 5th because the 5th is harmonically closest to the 1. (Circle of 5ths,,, each key up is a fifth higher, the minimal harmonic diff.) – Randy Zeitman Mar 8 at 1:37
  • @Richard I'm a huge fan of clear language. It's sometimes the only thing that keeps you out of the woods. I'll remember your phrase, the scale-degree 5. So C7 is really F based. F is the power behind the throne setting the tone. I also caught another pattern which is obvious if you think about it or write it down. hopping forward lands you on C(m)7 if you stay in F but taking one step back does as well. And it's the 4th of F (as C was the fifth). I feel like the more angles I hit this the easier to remember. – gcr Mar 8 at 17:04
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Let's take key C. So C is I. The dominant of that is G. So the dominant chord is built off the 5th note of C, which is G. So the dominant seventh will be 1-3-5-7, based on the diatonic notes of key C. They're G B D F. Note that the F is the 7th (from G) but isn't a major 7th note (in key G). It doesn't need to be, as we're in key C, not key G. It just happens to be m3 away from its 5th note. As in G B D >(m3)F.

Now, let's look at the chord C7. That's not from key C! It's from key F. That's why it has B♭ in it, and not B♮. C E G B♭. True, C7 does get used a lot in key C, but most times it leads to chord F - no surprise now, I hope. By understanding the circle of fourths/fifths, you'll see a pattern emerge which makes dominants - tonics clear.

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    Put another way, a V chord is made up of scale degrees 5-7-2-4 of the home key. – Aaron Mar 7 at 16:57
  • @Aaron - or even 5-7-9-11 of the home key. – Tim Mar 7 at 17:01
  • Oh yeah the famous circle of fifths! Some day I will unlock its secrets. So high level I understand but I want a quicker understand and I decided that you have two options for deriving a dominant chord if you start on C. You can move up five and return the G7. Or you can go back 5 degrees and get the C7. If you want the Dom chord itself, go back. If you want its 5th degree's dom, go forward. I don't know how they work with this in the real world but that's how I model it. – gcr Mar 8 at 17:12
  • 5 forward or 4 back, it's the same answer! And really, it's worth knowing the circle, bit like times tables, musos need the circle.It's only 12 bits, so not too onerous, and you'll see a couple of patterns repeat within it. You won't regret learning it. Honest. – Tim Mar 8 at 17:58
  • In the real world, a song has a key, a major (or relative minor) that will be our static reference point for a certain part of a piece (for standard music). So we can go up from Cmaj (as the I) to find G7 as our 5th, or we can go down from G (as the I) 4 steps to find C7 (note, same as going 5 degrees up from the G, we get to a C7). The pattern is not symmetrical, but in general we would chose one or the other as our key, and for a time in a piece the only relationships we would have to worry about would be the ones relating to one particular starting point. – OwenM Mar 8 at 23:31
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You start out from C. You pick the 5th scale degree

G

Then add the major third of that

B

and the perfect fifth

D

and the minor seventh

F

All notes are part of the C-ionian scale. No B♭ anywhere.

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  • Yes but that's G7, right? You have to step back to get the correct name. Naive (what I was and am) would be to think that starting on C gets you C7. No no no. That was the trap and my error. You have to know how to back step somehow. Maybe there's a heuristic or algorithm or maybe rote memorization. Out of three options- stay on the tonic of the named Dom chort (nope), check out the key of the perfect fifth forward, i.e. G (nope, my second error). Only the third way, backing up to make C the 5th is the way forward. Back is the way forward. – gcr Mar 8 at 17:08
  • @gcr what do you mean by "correct name"? – phoog Mar 8 at 17:53
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You seem to be confused by the fact that "dominant" means two different things here. Originally, "dominant" meant the fifth degree of the scale.* Eventually, it came to denote chords built on that pitch (and even the related key based on that pitch).

One of the chords built on the dominant scale degree is derived from the major triad by adding the seventh. Because the diatonic seventh above the fifth scale degree is a minor seventh, this chord comprises a major third, a perfect fifth, and a minor seventh. Because this chord came into being as a chord built on the dominant, it came to be called the "dominant seventh." Eventually, however, this term came to denote the shape of the chord independent of any key, regardless of what scale degree it is built on.

So, the dominant seventh chord of the key of C is G7 (G-B-D-F), but a C dominant seventh chord, C7, is C-E-G-B♭. The C7 chord is not, as Tim notes, one of the chords of C major, though pieces in C major may "borrow" it from the related key of F major.

In the first instance, "dominant" means "the seventh chord built on C major's dominant scale degree, which is G." In the second instance, it means "the chord with the shape of a dominant seventh built on the note C," without regard to which key we're in, or even whether we're in a key at all.

At least, that's how classical theory would see it. But during the 20th century, as jazz and also classical harmony expanded the notion of consonance, the idea that C7 would have to imply movement toward F became weaker and weaker. For example, in a C blues, you are very likely to hear C7 as the tonic chord. Still, we retain from traditional theory the name "dominant seventh" to describe its shape even though it no longer has a dominant function.


* Actually, in the middle ages, it meant something subtly different, but with the development of harmonic music it came to denote the fifth degree of the scale.

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