Studying Dominant 7th chords, their inversions and position

[geopianoincanada]

I just can't wrap my few remaining brain cells around this stuff.

It's ok to sit at the piano and lay my hands on it, play every other note, that sort of thing and call it sound. But this grade 7 music theory stuff, my professor understands it backwards, forwards, upside down and inside out but when I'm trying to do my theory homework I become completely stumped when trying to figure out what "position" a dominant 7th is.

Does anybody have a recommendation, perhaps one of those 'For dummies" books which were so popular? Because my RCM books and other theory books just leave me frustrated and confused.

My professor says I should be able to grasp this because I have pefect pitch. But my eyes don't have perfect pitch and that's where it just becomes a jumble to me. I can read the notes correctly, I know a sharp from a flat. But this Dominant 7th stuff is all so confusing.

[keypeg]

Can you explain what you mean by "position"?  If you are studying RCM theory material, I might have the book(s) you're using.

The Dom7 is built on the 5th note of your key.  For C major you simply have G B D F (G is the 5th note).  For C minor you also have G B D F, but you'll notice that while the key signature of C minor has a Bb, we have a B.  By "position" do you mean the fact of 5 up (V) or something else?  Let's start there.

[geopianoincanada]

Let me see if I can attach photos of the pages in question. I am using both the RCM 7 theory and this other book "Elementary rudiments of music" by Barbara Warrham. It is in this book where my homework is assigned.

My professor helped me work through some of the problems but now that it's a couple of days later (and I'm a couple of days older) I'm stumped not only in how to answer the unfinished problems but also in trying to comprehend how on earth she coached me to find the answers to the other problems.

[keypeg]

That's page 145 and there is one more set of problems on that page.  If the answers there are due to your teacher helping you with them, but you don't know how you got there, then that is not good enough - I agree.  One unfortunate thing with the book and program is that they don't introduced seven chords until the very last level, and then throw everything out at once, and over only a few pages.  All the chords you learn before that are triads - three note chords.  Then suddenly they throw a four-note chord at you.

Looking at the first exercise:

To be able to do this, you have to know key signatures for the major and relative minor key.  At level 2 I think you know this.
- Identify the two possible major and minor keys.  Your Dom7 will be a 5th (5 notes) above that key.
In the first example, two flats = Bb major (5 up is F, so F7), or G minor (5 up is D, so D7).  Your chord is one of the two.

You don't actually have to consider "major vs. minor" because you have an immediate clue for minor: there will be an accidental since the third of the chord gets raised.  Measure 3, with a single sharp, could be the key of G major or E minor.  We have a D# accidental so right away we know this is E minor.  5 up from E is B, so B7.

In the way they set up the question: root - key - position.  I would actually start with "key" - considering two possible keys (major or minor), always assume major if there's no accidental - then you have your chord.   

Position is a matter of lining up your notes from the root.  R 1 2 3   So for F7  F A C Eb

R = F
1 = A
2 = C
3 = Eb
which of those is on the bottom.  C is, and you correctly wrote "2nd" position.

It's not my favourite way of looking at dom7 chords.

[keypeg]

Your second exercise
You have the same answers as in my old book, except for a careless mistake in the last one.  G# is the root, not G.
To get "position", write out your chord in root position to visualize R 1 2 3 as above and see which it is.
======================
Exercise 7 below that is nuts!  I do have the answers in my book.  I don't know if musicians would ever use this, so if it's at all useful.

"Write the Dominant seventh and inversions of other Dom7s, using E as the lowest note for each."

Root position is easy.  E G# B D

I'd solve the others by first thinking root position as follows:

1st inversion means you have a chord that goes * E * *.
Your dom7 chord always has a major 3rd.  C E is a major third.  So your chord has to be C7.
Now write it with E on the bottom for your 1st inversion.

2nd inversion means you have a chord that goes * * E *
Your dom7 always has a P5 in root position.  A to E = P5.  So your chord has to be A7.

3rd inversion means you have a chord that goes * * * E.
There are two ways of thinking about this.  In a Dom7, the 7th is a whole tone below the root.  (G B D F ... F is a whole tone below the next G, or a m7 above the root).
E is a whole tone below F# --- so F#7.  We can test this: F# A# C# E = F7

After getting your four chords, stick E on the bottom, and stack the remaining notes belonging to the chord.

-------
For the 2nd part, "two keys", the Dom7 always goes to a major and the parallel minor key.  So if it is the Dom7 C major, it is also the Dom7 of C minor.

You might ask your teacher whether the last exercise has any practical uses in music.

[keypeg]

What bothers me 18 years since I did those exercises, is how impractical and intellectual they are.  I was thinking about the last "E" exercise.  Nowadays, F#7 just pops in my head immediately, because a dom7 with E on top just is that, just like F7 has Eb on top.  That's  from working on music, playing chords in inversions and the like.

-----------
Back when I did the exam, "positions" is where I sometimes made mistakes, and there's a reason for it.  We see four notes in a row.  I naturally see "1st, 2nd, 3rd, 4th" note but of course it's "Root, 1st, 2nd, 3rd" position - so I'd sometimes be off by one.  It's a thing that my later teacher and I discussed a few times.  We'd also discuss the advantages of the "jazz notation" style where you don't have "F#7 in 3rd position".  You have F#7/E which tells us that E is on the bottom of a Dom7 chord.  Much more straightforward!

[keypeg]

I am using both the RCM 7 theory and this other book "Elementary rudiments of music" by Barbara Warrham.

I'm not familiar with the "RCM 7 theory" btw.  I exclusively used Barbara Wharram at the time.  I wrote the level 1 and level 2 exam.  That was close to 20 years ago.

[geopianoincanada]

That's page 145 and there is one more set of problems on that page.  If the answers there are due to your teacher helping you with them, but you don't know how you got there, then that is not good enough - I agree.  One unfortunate thing with the book and program is that they don't introduced seven chords until the very last level, and then throw everything out at once, and over only a few pages.  All the chords you learn before that are triads - three note chords.  Then suddenly they throw a four-note chord at you.

Looking at the first exercise:

To be able to do this, you have to know key signatures for the major and relative minor key.  At level 2 I think you know this.
- Identify the two possible major and minor keys.  Your Dom7 will be a 5th (5 notes) above that key.
In the first example, two flats = Bb major (5 up is F, so F7), or G minor (5 up is D, so D7).  Your chord is one of the two.

You don't actually have to consider "major vs. minor" because you have an immediate clue for minor: there will be an accidental since the third of the chord gets raised.  Measure 3, with a single sharp, could be the key of G major or E minor.  We have a D# accidental so right away we know this is E minor.  5 up from E is B, so B7.

In the way they set up the question: root - key - position.  I would actually start with "key" - considering two possible keys (major or minor), always assume major if there's no accidental - then you have your chord.   

Position is a matter of lining up your notes from the root.  R 1 2 3   So for F7  F A C Eb

R = F
1 = A
2 = C
3 = Eb
which of those is on the bottom.  C is, and you correctly wrote "2nd" position.

It's not my favourite way of looking at dom7 chords.

Yea it's still as clear as mud to me.

[essence]

Sounds too much like maths! in maths, you have to accept it is a struggle, and just be patient and work through it. By doing lots of exercises it can start to click.

Also, maths teachers can find it too easy, and they can be very bad at explaining in a painstaking way.

If I was going to answer the last question, I would play all dominant 7ths, one by one, in root position, going up a semi tone each time, and see if they contain the note E. Then I would invert so that the lowest note is an E. Then document.

Very mathematical approach, totally useless for improvising!

[keypeg]

Very mathematical approach, totally useless for improvising!

The whole system is horrid for improvising.  When I met my teacher umpteen years ago and he wanted to see what kind of things I had studied in theory, he was aghast at a lot of it.  That said, it seems that the RCM was better two decades ago than it is now.  I got Google Chat to get me up to date on this "grade 7 theory" and it has become a mishmash.

Regarding your approach.... First there is no reason in real music why you would want so suddenly find a Dominant 7 chord that has an E somewhere in it.  But if you're used to playing you'd probably pull one out of your hat from your experience in chords.  The F#7/E is super easy now because E is the 7 of F#7 .... it just is.  Just like of Bb was on the bottom you'd immediately think C7 .... F, everyone would catch G7.

The exercise is designed to have you use all the knowledge you gained in the system, sort of like a puzzle.  It's very intellectual and impractical.  The worst is, for that question, they have you write it into tenor clef!  Just to make it disorienting.

[keypeg]

Yea it's still as clear as mud to me.

I asked AI about the system you're studying now, and it seems to have made it worse.  When I studied, we had only the Barbara Wharram book, "rudiments".  When all three levels were done, we started harmony theory - which is where those chords start being applied in (a limited) context.  It seems that now they are mixing rudiments and harmony together.

I once translated the internship training of a dental assistant  overseas.  Her first level was to memorize the name and appearance of all dental instruments, and how they are placed on the tray.  The next level was to be able to hand an instrument to the dentist when he asked for it.  She could only do that if she recognized the instruments by name, and that was the first training.  The "rudiments" were like that first training.  You didn't try to simultaneously start trying to use them according to (antiquated, limited) harmony theory rules.

For your present understanding, I'd go way back, and also simplify.  You need to be able to
i) recognize a Dom7 in root position
ii) know your major and minor key signatures
iii)  understand the V relationship to the key signature

These are the things supporting everything else you do.  Do you have these things?

After that we'd go to inversions (the "positions") for recognizing them and naming them.  How are you with i) ii) and iii)?

[essence]

Maybe you have a melody with an E at the top, and you want to modulate, so you have to think of a dominant 7th with a top E in it? but surely that is now how composition or improvisation works?

I was hopeless at improvising, and really struggled with harmonising a choral melody in style of Bach.

[keypeg]

Maybe you have a melody with an E at the top, and you want to modulate, so you have to think of a dominant 7th with a top E in it? but surely that is now how composition or improvisation works?

I was hopeless at improvising, and really struggled with harmonising a choral melody in style of Bach.

It's an intellectually combobulated exercise.  I just woke up from a lovely nap outdoors and got a picture about this.

Let's take a new note (D) - same question - Four Dom7 chords etc.  What is really being asked is: What Dom7 chords have D in them as Root, as M3, as P5, as m7 (i.e. the 7th)?

If I go to the piano, and play D, immediately have D7.
I play D again and imagine that D is M3 above something.  Immediately I see Bb.  Bb7
I play D again and picture that D as P5 - in other words, the top of a major or minor chord in root position.  Immediately I see G.  G7
I play D again. This time it's a whole tone below a note = E.  E7

In seconds, with my hands and ears I see D7, Bb7, G7, E7.
For the inversions having D on the bottom that gives me:
D7, Bb7/D, G7/D, E7/D

Ok, great, I can do the exercise by getting outside of the formal paper learning.  When would I ever need this?  That question isn't necessarily rhetorical btw.

[geopianoincanada]

I agree, this seems to be very much high theory and not really practical study. I did ask my teacher to guide me through what is needed to eventually be able to write and pass an exam. For just regular playing I don't see any practical use for it.

I'll keep struggling with it. I meet my teacher once a week on Friday so if I still have issues then she will be able to help me.

Thanks for your help!

[lelle]

When solving an exercise like this, first

1. Make a stack of thirds.

Take the four notes and rearrange them so you have a neat stack of thirds on the staff. i e, all the notes should either be on lines next to each other or spaces next to each other.

Example, exercise 6, first item, you have, starting from the bottom:

C A F Eb

Rearranged into a stack of thirds:

F A C Eb

Since I have been eating theory like my breakfast porridge for 20+ years, it's automatic for me at this point, but you can just use the staff and try to place the notes until you get it right.

You will use this to extract all the other information you need.

2. Finding the root

The lowest note in the stack of thirds is the root, so in this case, F.

3. Finding the inversion

Now, look at the actual arrangement of notes in the original configuration:

C A F Eb

What's the lowest note? Answer: C

Look at the stack of thirds you made before again:

F A C Eb

Where is C in the stack of thirds? Not the lowest, not the 2nd note, but the 3rd note in the stack. What's the 3rd note in a triad? It's the fifth of the chord.

A chord that has the fifth instead of its root note at the bottom is in 2nd inversion.

Had it been the 2nd note of the stack of thirds, i e the chord's third, it would have been called 1st inversion.

To summarize a chord that has its
Root as the bottom note - is in root position
Third as the bottom note - is in 1st inversion
Fifth as the bottom note - is in 2nd inversion



This is true regardless if you have a simple triad like in the example above, or have added a 7th like in your example. (print the image above and add a B flat above the G in every inversion if you want to see it in action)

[quantum]

This book is good for reference, but not the best thing for an introduction to the topic.  It succeeds when a teacher is there to walk you through the thinking.  It will also make a lot more sense when you start to study functional harmony.  To use an analogy, you are learning how to build a car engine, before you know what the car looks like, and before you know how to drive.  Some students excel with this style of thinking, others are heavily disadvantaged. 

It's similar to solving math equations.  We don't really think like this when playing real music, or composing. 

Suggestions: solve at the piano and draw a keyboard on your worksheet, don't just rely on letter names.  Learn what these chords sound like, not just how they look on paper.  Observe the shape of your hand when you play the chord. 

Simplify, if the written chord has you stumped, condense it within one octave, keeping the bass pitch class the same. 

Take the pitch classes of the written chord.  What 7th chord is it?

Is this it the dominant 7 of the major or relative minor?  In other words, which tonic does it pair with?

What is the bass note?  Is it Root, 3rd degree, 5th degree, or flat-7th degree.  This defines the inversion. 

Bonus, now resolve it on the piano to the Tonic chord.  Listen. Does this sound like a V7 - I cadence? 

***

This is really an exercise in filtering out unneeded information in order to reach the solution.  Eg: once you determine major or minor of the tonic, you just eliminated half of the possible solutions from contention. 

***

Worked example:
Page 92, first one.

Given information:
Key signature: one sharp
Pitches from bottom to top:  A, C, F#, D

What keys have one sharp for key signature:
G major, E minor.

What 7th chord is it?
D7

What tonic does it pair with?
D7 is the dominant 7th chord of G major

What is the bass note?
A

What position in the chord does this bass note take?
A is the 5th of the D7 chord.

What position (inversion) is it:
2nd inversion

Root: D
Key: G major
position: 2nd inversion

Checks:

Does the key we arrived at align with the possible keys for key signature using one sharp?
Yes

At the piano, play chords D7 - G.  Does  this sound like a V7 - I cadence (a perfect cadence)?
Yes

[essence]

And do this in 1/10 second when improvising.

My failure in transposing or improvising is that I treat it like a mathematical puzzle. When transposing, I transpose individual notes, I can't seem to understand it harmonically.

What I wonder is how to make this kind of process intuitive. By spending months doing it laboriously? Of course, to pass an exam, the laborious way is OK.

[dizzyfingers]

Suggestions:
What keys have one sharp for key signature:
What 7th chord is it?
What tonic does it pair with?
What is the bass note?
What position in the chord does this bass note take?
What position (inversion) is it:

I think it was kind of you to go through these steps for the OP.
I'm not sure why some people find these steps difficult - or can't think of them.

[essence]

The steps should be, for absolute clarity:

What two keys (major and minor) have the given key signature:
What is the tonic and dominant of those two keys?
What is the dominant 7th chord of those two keys?
Which of those two dominant 7th chords corresponds to the given chord?
What is the bass note of the given chord?
What position in the dominant 7th chord does this bass note take?
What position (inversion) is it?

An alternative approach:

For the given chord, which notes are a tone apart (apart from octaves)?
The upper of the two notes is then the dominant, the lower is the 7th.
Find the tonic (a fourth above the dominant).
Does the tonic correspond to the time signature?
What position in the dominant 7th does this bass note take?
What position (inversion) is it?

I think either are fool proof, but need checking. It's not the way a trained musician would do it, but it will get you 100% in an exam.

Corrections please!

[geopianoincanada]

I think it was kind of you to go through these steps for the OP.
I'm not sure why some people find these steps difficult - or can't think of them.

I've never been a book musician. I've always played and learned by ear. According to both my first teacher and now my present teacher I do have very well developed hearing. Over the last few years I realied I want to try to train to be able to teach music. I do have two young students already and teaching them the basics has been wonderful!

Placing all of these alien written terms, shifting notes about, stacking them up, shifting them to the side, etc.... it really is confusing for someone who has been taking music in one form or another by ear for the vast majority of my life. It's like trying to understand written Martian language when I only speak, read and write English.

[dizzyfingers]

That comment was to Quantum, but I guess it makes sense you would pick up on it.

The reason I'm baffled by people (you're not the only one, of course) who are challenged by theory is because I was taught theory when I was 12 over a few short lessons, and it made perfect sense, and once you get the basics you just build the rest up on your own by analyzing the harmony in the score.

If you've only learned music by ear your whole life, what are you teaching your "young students"?

[geopianoincanada]

That comment was to Quantum, but I guess it makes sense you would pick up on it.

The reason I'm baffled by people (you're not the only one, of course) who are challenged by theory is because I was taught theory when I was 12 over a few short lessons, and it made perfect sense, and once you get the basics you just build the rest up on your own by analyzing the harmony in the score.

If you've only learned music by ear your whole life, what are you teaching your "young students"?

Introductory, beginner and basic piano. Major and minor scales. Fingering positions. I've beem involved in my lessons now for 8 years since 2018, this level 7 stuff is extremely challenging because it's all book learning away from an instrument.

My teacher says I'm capable of teaching beginners level piano. And it is enjoyable. So I'm working hard to try to learn more advanced theory so eventually I can write and pass an exam just to add legitimacy.

[dizzyfingers]

... this level 7 stuff is extremely challenging because it's all book learning away from an instrument.

I don't want to quibble but - - it's not just Book learning, maybe this mindset is partly blocking you.
You can build a major scale from any of the 12 notes by knowing the sequence of whole and half steps.  Same with minor.  Same with all the modes.  This is something you figure out at the keyboard, looking at the keys.

A composition with nothing but root position chords is going to sound - - er, a certain way (not a very interesting way).  Try it!

If you listen to Brahms, the harmonies are not that adventurous, but he makes them sound different and keeps the music flowing by using a lot of 2nd inversions (built on the 3rd note of the root chord).

[geopianoincanada]

I’ve got nothing against book learning when it makes sense. I’m a retired electronics engineer.

But music I feel should be approached by the ears, not solely by lesson books. This is why I always try to make audible sense out of the book lessons when I can.

These are very challenging lessons however and I admit to having a lot of difficulty understanding the theory side of music.

[keypeg]

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