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Here is a problem I have struggled with as long as I've taught.

For years I tried to avoid teaching dominant 7 chords in the simplified inversion usually shown first in beginning books.

For practical reasons, I find them useful, so I do teach first:

C (CEG)
F (CFA)
G7 (BFG)

Now, we all know that BFG is in 2nd inversion, leaves out D, etc.

Uusally when beginners ask me why BGF is G7 chord, I try to evade the question (which I always explain later, or try), although if I see someone with a very logical, mathematical mind, I will show GBDF, explain that this uses 1357, then show how BFG puts the G on top and leaves out one note.

Of course, next comes the question: "If it is note 7, why is it F natural for G7 and Bb for C7".

At that I sigh or gulp, because I'm left with explaining that the dominant 7 chord is based on the 5th of a scale, not the tonic.

These are such basic concepts, anyone who understands basic harmony has absorbed this long ago and finds it self-evident, but no matter how many different ways I approach this, I still find a percentage of my students are just lost, and that's not only the beginners. In includes the people I call "the theory-challenged".

I never had any problems with ideas like this. They immediately made sense to me. Any suggestions from other people who have run into glazed-over eyes from people who find theory hard? (Or harmony, or harmonic analysis, whatever word or term you prefer…)

I find it is best to explain that it is a chord of G (G,B,D) with the 7th added(F). After the chord is understood you can show how using the inversion and leaving out the least important note is a useful way of playing it.

I explain that the F is natural because all three chords (C, F and G7) are within the key of C major.

Gary, as a student I tried to put myself into your students' shoes. Since I'm primarily a violin student I was first mystified by your choice of chords until I saw they were the I IV V progression for C major.

I've taken theory but I'd want to start on the bottom. First I learned what major and minor triads were, and then their inversions. I also learned the names of the degrees: tonic, supertonic etc. So if I hear Dominant 7th, it's easy for me to understand that this chord begins on the 5th degree of the C major scale with G being the root. If I'm a kid maybe I can understand it without using fancy terminology: I'll know the Dominant is the 5th note up, anyway. A triad skips every 2nd note, the last note is 5 up from the root, so obviously the next note is 7 up - voila. Then if I know it's the triad of C major, of course it's F and not F#.

Same as what Chris said, just more wordy.

Your explanation is perfectly logical, and when I work with people who already play well but who are lacking in theory (chord structure knowledge), this is precisely what I do.

I think what has always frustrated me as a teacher is that in all cases I can think of, when letter names are used, any number is the major interval by default. And any minor interval is marked with "m" or "-".

So when letter names are used, I find students who understand major and minor intervals always want to assume that X7 (for instance C7 means CEGB). They logically expect the Arabic number to show a major 7, by default, and they expect the 7 in a dominant 7 (C7) to be marked as minor.

Now, if I have the time and will-power to teach a thorough knowledge of Roman number analysis first, this problem will not be there, because then people realize the absolute connection between G7, IV7 and dominant 7.

If we are thinking in terms of Roman numberals, it's quite logical:

I7 and IV7 chords are major 7 chords
II7, III7 and VI7 are minor chords.

V7 is the dominant 7, and VII7 is a half diminished or Xm7-5

All about as hard for you as 2+2=4.

If I only had more time. (sigh)

The problem is that most of my students run into "pop notation" most of the time, and there letters dominate almost completely. Even fake books with roman numberals are rare. I don't remember seeing any.

The problem I ran into today was a practical one, and honestly, I feel as though I am an absolute idiot when it comes to teaching structure to people who don't think as I do, in a very mathematical way.

I was teaching "Take Me Out to the Ball Game", and it has three dominant 7 chords:

BFG
C#GA
F#CD
We would think of these as V7, V7 of II, and V7 of V (secondary dominance). We would also immediately see circle of 5ths (A7 to D7 to G7 to C).

I don't use the Roman numberal system much, so I hope I didn't mis-type any of the symbols.

Now, if you'll just picture this, I circled all three chords in a pink marker but used three shapes for the three 7 chords and pointed out that all of them sound the same, just higher or lower. Instinct to told me to shut my mouth at that point. But then I went a step further, showing how you move from GBDF to BFG (inversion and leaving out a note), and that the other chords sound the same, mentioning that GBDF is 1357.

Then I showed inversions of the G7 chord and pointed out that the inversions all have a 2nd in them, and that the 2nd is a clue to 7 chords. By no means something that works more than some of the time, but a clue. I pointed out the fact that when this occurs, the visual clue is the note that is kicked out to the side.

I'll find out soon if this worked, or if all I did was confuse the student. (I did not spend but a couple minutes, in case it doesn't work.)

I find all this so immensely frustrating because I don't remember a time when I couldn't instantly hear such chords in any key, without knowing how I did it. I'd wager that there are many talented beginners and intermediates in this forum who have that same sense, but most of my students don't have it. No one taught it to me, and that's why I continue to struggle with how to teach it more than just about anything else I try to teach at the piano.

By the way, I teach reading in advance of structure, preferring to use music learned for the purpose of analysis. I've successfully taught advanced students how to break down chord structure and melodic structure. It's just the beginners that I'm unsure with. Mostly I mark things that are the same with colors and shapes, pointing out more what is alike and not alike than giving names to the structures. This seems to make people's reading ability absolutely explode, and my students play well early on, but I remain highly unsure about whether or not introducing more formal concepts sooner might acclerate the process faster.

My exposure to chord structure is really weird. I had nothing but standard classical instruction, which was very easy for me. I always aced any exam in theory.

I had absolutely no experience whatsover "gigging" and wanted no part of it. But in my 20s, I needed money, and my best friend roped me into playing in a small group. At first I was lost without written out arrangements, although I was already able to improvise to some extent from what was written. Over the next few years I learned to play from fake books, of course writing in changes that were correct or better when some awful substitution chord was notated, and at first I felt a total disconnect between the tradional "classical" approach and what I call "pop notation".

If you use this notation, you get very used to seeing letters instead of Roman numberals, and you link both systems together in your mind, so Em7, Am7, Dm7, G7, C is just some kind of III, VI, II, V, I progression in a key. I know that such things as ii and vi are also used, but I forget when and how, because I've only seen them in jazz analyses.

Jazz players seem to love pure numbers, since mastery of this system potentially allows instant transposition of any chord progression and thus the structure of any tune to any key.

On the other hand, I find pop analysis extremely useful for so called "classical music", for instance in highly chromatic Romantic music, or Impressionistic music.

I actually think, using the famous 1st movement of Beethoven's "Moonlight":

C#m, C#m/B, A, D/F#, G#7, C#m/G, G#sus, G#7, C#m (etc.)

Any good jazz player could put that all into Roman numbers with arabic numbers and might or perhaps probably would prefer it that way, but our "classical" pieces do not need to be transposed, so using letters is a bit more like using fixed do, while roman numberals is more like movable do.
<sigh>
If my students would learn all inversions of all major and minor chords in any key, I would faint from surprise, and of course I'd be SO pleased. Again, if you find such things logical and easy, you will never understand how hard other people find learning scales, arpeggios, and so on. A few get them in almost zero time, and then you just smile. Some seem to be unable to grasp it no matter how you explain it. Most people are in between somewhere, but then you run into problems of time. In a perfect world I would have time to teach each interested person a lesson in playing each week, one in writing music, one in listening and transcribing, one in analysis, on in composition. Most of the people I teach can barely affored one half hour lesson per week, and I'm trying to do it all. That's why I keep looking for ways to explain things to those who "don't get it". The ones who do pick up just about anything I explain, because they have a natural bent for it.
You would think that anyone would get what you just said. Seems elementary to me, entirely logical. Just trust me when I tell you that *some* people would say, "What is a triad again?" As a teacher your challenge is communicating with those who seem resistant to any kind of explanation. The others are not the problem.
Not really, because it helps to hear how students explain how they understand these things (or former students explain how they first grasped things). For me, the only problem with your thinking is that you are already so more advanced than my young students. Something I'd like to explore in the future is the link between math and musical structure. My best adult student became a wonderful reader and played well, but she was totally math challenged, her own words, and it took me YEARS to succesfully teach her how to analyze chord structure. She would learn and memorize anything I asked to learn, including scales, arpeggios, cadences, the circle of 5ths, but she was as slow in this area as she was quick in reading. And she played expressively too.

This seems to be the other side of "talent", those who can mimic, read and even interpret well but who don't want any part of analysis, and those people do exist, even on the graduate level.

I knew a fine player with a doctorate who could never grasp that two even 8th notes in swing or a dotted 8th + 16th are both played the same way. But he wrote a good thesis, I guess. Strange world we live in.

Gary, it does sound like you might be over complicating things. For a kid playing 'Take me out to the ball game' is it really worth trying to analyse all the 7th chords? All the ones you mentioned are dominant 7ths but to really understand them you have to look at how they resolve in various keys. It sounds like they are not ready for that yet.

I guess it depends on the situation. Are they playing from a lead sheet with chord symbols?

For me, the only 7th chord I would introduce at first (in a theory way) would be the dominant 7th. I wouldn't use the term 'dominant' and I would not use Roman numerals. I start by teaching the use of the G7 chord in the key of C major. All the other chords would just be root position triads to start with. Only after applying this in other keys would I venture into the use of other 7th chords.

Gary:

It sounds like you're trying to teach advanced theory to kids in method books!

I follow the Syllabus published by our state's MTA. We don't get into V7 chords until Level 4, or the 5th year of piano instruction. By then, students are expected to play Clementi Sonatinas, Tchaikovsky Album for the Young, and Burgmuller Op. 100. Usually my students are playing stuff much harder than that before they start learning the V7 chords.

By then, it is easy to find concrete examples in their music for V7 chords, the omitted fifths, and all the inversions. So far, teaching dominant seventh chords has not been a problem for me.

I too wait until they are playing intermediate material before talking about 7th chords. They begin with the basics of I IV V I progressions, then we work with inversions. By the time we hit the dominant 7th chords, then I just say we add a minor 7th interval to the root of the V chord to make it a stronger cadence. I also point out that when you play the root, 3rd, 5th and 7th in a dom 7th, you don't really need to hear that 5th, and so it's easy to leave out. Then I talk about using 2nd inversion for that chord to make it easy to go from a I or IV chord to the V7. We stick with dominant 7ths for a long time unless we are trying to add jazz or blue to their repertoire.

It could be that Gary is teaching jazzy repertoire with the chord symbols printed on the score. I imagine that adult students in particular might ask questions about them. I don't teach many adults but the ones I do ask far too many questions. I like questions but they can eat up lesson time, especially when it involves a complicated theory type answer.

First of all, in the last few weeks I've had a 55 year-old and a 70 year-old learn it, so I'm not only talking about kids.

And no, I probably will not ever get into the kind of analysis I think you have in mind. Yes, it would be too complicated, and it would be premature.

However, I did circle all three 7 chords with the same color but different shapes, which is mostly what I do with structure in the beginning. Rather than spending a lot of time saying what things are, I concentrate on saying that "this thing and that thing are the same—do you see the pattern?" In other words, I'm teaching people to see what is the same and what is different, and also to play any portion of any piece, either hand if necessary, isolated.

I use colors and shapes much more than terms in the beginning.

A few people will hear that the three 7 chords have the same sound, and that they are just transpositions of one "thing". I did when I was young. Others may not hear it but may see the similarity in form. Some will want to know what the names of these three chords are, and why they have a particular name. My answer will vary according to what I sense they will be able to assimilate quickly.

I have one very intelligent 7 year-old who may also be gifted in music. I've only taught him about one month, so I'm still learning more about what he can do.

He is playing When the Saints Go Marching In. I showed him how the C and F chords sound the same and have the same colors (all white) and the same sound. He got that immediately.

Then I showed him how the F chord we are using takes the C off the top and puts it on the bottom. I usually call this "scrambling the chord" before I use the word "inversion". He got that too.

Finally I pushed down FG, together, and showed him that when you "flip" those notes, they are 7 aparts. I had him play BFG, and I pushed down the missing D, pushed down the G below, then showed him how I could take his G away. Then he tried to play GDDF, which he could do. (He is tall and his good hands.) He immediately saw the 1357 pattern. He's very good in math.

My primary concern is still reading, and he has a very good start, but he got what I explained and seemed interested. I covered all this in no more than five minutes (the chords). By the way, I taught him how to play the piece before I said one word about structure.
No. I won't teach any music that is not in standard notation, grand staff, unless I have someone who is very advanced and already reads very well.
I don't either.
The only thing I differ with you about is that if a student understands that BFG is a "scrambled G7" with a note left out, I see no reason to not mention that the same thing is equally true for C#GA or F#CD. Now, if I get a blank look, I'll immediately let it go until later.

I have an agreement with all my students. As long as they cooperate with me and learn most of the music that I consider important, to get across the concepts I want to cover, they are free to bring any music that is written in a standard score into a lesson, but they have to be capable of almost learning it without my help. If they can do that, then I will bend over backwards to do the rest, including any kind of analysis (chorad and structure), very careful suggestions about fingering, and help with any other unusual problems.

Again, they have to be able to do most of it on their own, otherwise it takes too much time and encourages slo-mo learning involved too much memorization at the expences of reading.

I have an adult (over 50) who is more interested in blues than anything else, and I told him I would concentrate on this if he worked hard to get the fundamentals necessary. I've also written at least three blues tunes for him to illustrate things that I think are extremely important for where he is now.

I showed these tunes to several of my children, and they all wanted to learn them too.

I try to hook people by helping them play things they really like and have no rules about style, but I won't teach anything to any student that I think will be damaging in the long run to technique or other fundamentals that I believe important. That's it.
Yes. Adults are much more likely to hit me with an avalanche of theoretical questions, and I reserve the right not to answer them if I am sure they are coming too soon (for them).
So true!

I have beginners, as young as four, play V7 chords. I refer to the three note chord and call it a V7 chord... thus they know it as a V7 chord. They also know I, IV's and V's. They know these chords at first by learning it in there repertoire that they learn by ear and demonstration.

Later they learn to read and they then learn their scales, arpeggios, inversions and basic I IV I V V7 I progression.

By this time I do explain (since they now understand and have played inversions) that a V7 chord is really a four note chord and I show it to them in root position, I show how you can either leave out the third or fifth note and it will still be a V7 chord, which is seen in music quite a bit. I also explain that a V7 is a V chord with a minor third on top and that there are other types of seventh chords that we will learn later.

I talk about this often throughout their year of lessons so *eventually* it is absorbed and understood.

Eventually they will learn V7 chords (the full four note chord) in all positions.

When they are really young, and if a child asks, which usually does not happen, I just would say that is the name of it, and we'll learn more about it later; unless it is an unsually inquisitive bright child, then I may even explain it to them, but would keep it brief.

I think anyone who has the patience to teach children under five is a saint!

I have one five-year old girl who began taking lessons almost exactly on her birthday. I teach the wee ones along with a parent, and I start teaching them to read immediately, if they are capable of it (the way I teach). I use a keyboard chart. At such a young age, it is the parent who immediately catches on to the correspondence between the placement on the page and the picture of the notes, on my chart. I don't start out with any ear training, and I don't start out with any writing. This will probably immediately get me stoned by other forum members.

Instead, I point from the notes on the page (all my own materials done in Finale and printed out page by page) to the picture on the chart lined up with the correct key. I'm still mostly teaching the parent. Then I get the parent to point in the same way, and in this manner I have the student playing five notes in the LH and RH, separately, but using the grand staff. No single staves, no letter names are ever allowed to be written in the music. If a parent does that, I tactfully remove the page and replace it with another copy that has no such clues. I move from there to a few simple tunes, then to "The Snake Dance", which uses CG in the bass every measure. There is an Eb, but each flat is notated. No key signature. Then "The Spider Song", because it is still in a five finger position but has different intervals. I circle the different intervals in different colors and teach the places where the hands come together by calling out the color and the RH note. But in each piece after that, the colors are used for different skills, so they can't permanently link a color to any note, interval or chord.

Immediately after that, I have a series of pages for only RH or only LH that will start a five finger position on any note, and I won't tell them which note that is. They have to find it, but once they get the first note, the other four will either go up stepwise or down the same way, starting with thumb or five.

And then, still using different hand positions in the RH and still not labeling them (because I want them to find the notes, not memorize them), I give them a page with only the C chord and the F chord (2nd inversion) or the C and G7, which you mentioned. I teach these chords before I give them any name. Immediately after that, I teach four chords, three which have already been covered, for LH only. CEG, DFG, BFG and CFA. These are labeled chords 1, 2, 3 and 4. No names.

Then I go to the Saints Go Marching In, circling all the C chords in pink, the F chords in orange and G7 chords in green. Age 7 up is a snap, and age 6 usually works almost as well, but I test more carefully. Age 5 takes all my patience, but the 5-year old is already finding and matching moving five finger positions, as I said with no label as to beginning note.

I'm an absolute fanatic about developing reading skills and have the greatest success in teaching reading. I'm also very careful with fingering, which is always tricky, since too much fingering ruins reading, but too little can ruin a good technical foundation.

Again and again the parents of my students report to me that while other kids the same age are coloring notes and circling things but can't yet play anything, their kids are zooming ahead. My drive to teach reading is for two reasons: first, I was always a fast reader myself, and I believe most of that was because my first teacher just let me play and play and play. I hated workbooks, coloring, anything like that, and I hated everything to do with writing music while it was just about practicing the skills and suddenly started writing music, on my own, when I wanted to actually write down my own musical ideas.

So maybe I'm just an oddball who doesn't think the way most of you do, although I seem to attract students who are also mavericks. Or perhaps, without knowing it, we all attract people who have similar goals to ours. I really don't know.
Here we do almost the same thing, although the time when I introduce these concepts may be different. I don't like to talk about anything that my students can't already play. The only big difference I see is that I like to explain intervals USING chords, rather than to explain chords by talking about intervals. For instance, I want those who are ready to learn intervals to know that half steps and steps, minor and major 2nds, are the basis of all major scales, but that a major chord is a minor 3rd on top of a major 3rd, and I like to show that the 3rds reverse themselves when the middle note is lowered for a minor chord. If I talked about adding a minor 3rd for a 7 chord, I'd emphasize that you have two in a row over the major 3rd.

But I've taught these things so many times in so many ways, I'm convinced it is not so much how we explain them as feeling instinctively how each student thinks. For adults, I've taught major 7 and 7 chords this way, in any key, but using C as an example:

CECG, simple C chord with the root doubled
CEGB, "one short", move the top note down one key or 1/2 step to form CMaj7
CEGBb, "two short", move the top note down two keys or 1 step to form C7

Now, I may add any other concept to the above ideas, or I may approach it other ways. Most people tend to think of a chord such as the FMaj7 as "modern", but there is one right in the middle of 1st Prelude in C, WTC, which alternately could be called a IV7.

Please don't think that I'm so stupid as to be talking about how to introduce such things to five year olds, or complete beginners. And as much as I'm wandering here, I talk about these things VERY quickly and stop the moment I feel I'm hitting a limit. Often I return to the same idea every few weeks, each time trying a slightly different approach, if it's really important to me to get a concept across.

The point, if there is any point, is that there is no explanation that works for everyone, but having many different ways to approach an idea is a bit like throwing dart after dart at a target. Even if you don't aim very well, sooner or later you're going to hit a bull's eye.
Of course.
There we are in complete agreement!