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Music Theory Made Simple #45: Inverted 7th Chords

stevel

Member
Messages
15,177
Again, nothing too much new here (see how I told you if you learn the basics the harder stuff just build on it - but you have to have the basics to "make it simple").

7th chords have FOUR chord members (being a Tetrad) but they work the same way as a Triad.

To review:

A Triad is in "Root Position" when it's Root is the lowest sounding note.

When the 3rd of the chord is the lowest sounding note, the Triad is in First Inversion.

When the 5th of the chord is the lowest sounding note, the Triad is in Second Inversion.

Root Position = Root in the Bass (Bass here meaning lowest sounding)
1st Inv. = 3rd in the Bass
2nd Inv. = 5th in the Bass

Guess what? Same for 7th chords:

Root Position = Root in the Bass (Bass here meaning lowest sounding)
1st Inv. = 3rd in the Bass
2nd Inv. = 5th in the Bass

But since there's one more chord member in a 7th chord, it too can be in the Bass. In that case:

3rd Inversion = 7th in the Bass.

So:


Root Position = Root in the Bass (Bass here meaning lowest sounding)
1st Inv. = 3rd in the Bass
2nd Inv. = 5th in the Bass
3rd Inv. = 7th in the Bass

For a chord like an E7 which consists of E G# B D, this would mean:

E7 = Root
E7/G# = 1st Inv.
E7/B = 2nd Inv.
E7/D = 3rd Inv.

Note: when the 7th is in the Bass, in slash notation it will appear after the slash so some people don't always write the "7" on the letter before the slash because the "7" is the Bass note. So you may see E/D or E7/D. There can be subtle distinctions intended between the two but for most intents and purposes, they are both 7th chords.

Like Triads (gee, see how easy everything is because you mastered these concepts with Triads!), you can have Open and Close position 7th chords.

Again, for the purposes of calculation, we "compact" everything to Close position to figure them out.

So let's say you get a chord with 4 different notes:

F# D# B A (lowest to highest, left to right)

What chord is this?

Well, first off, we need to figure out if it's a 7th chord or not. If you know your orders, you can find it quickly. If not, you have to use trial and error to stack it into 3rds (because 7th chords are still Tertian chords). Short answer, it's:

B D# F# A

This is in Tertian order and Close Position (no other B, F# or A can fit between B and D#, etc.)

So it's "some type of B7 chord".

What type?

Well, what kind of Triad is at the bottom? What's the interval up to the 7th? Answer these and you have it. Otherwise, what's the interval structure of the 3rds - if you know that (and you should) you can get it that way.

Happens to be a B Major Triad (B D# F#) and a m7 (B up to A). Mm7 = Dominant 7, or "just 7", so the name of this chord is:

B7.

But wait, the original had an F# in the Bass. Ok, no problem:

B7/F#

But what Inversion is that? F# is the 5th of the chord, so it's in 2nd Inversion. It is:

B7 in Second Inversion

What's the iii7 in 1st inversion in the key of F Major?


Holy Crap Steve, what do you think I am, a Rocket Scientist?

Let's work it out.

F Major. Key Sig, one flat, which is Bb. So the notes in the key are:

F G A Bb C D E (F)

"iii" is the chord on the 3rd scale degree. That's A.

"iii7" tells you it's a m7 chord, but we can also assume I'm talking Diatonic here (becuase you already know the Diatonic Mediant 7th chord in a Major Key would be a iii7, correct?) so we know it's going to be an Am7 chord.

Alternatively, you could just take every other letter of the Key (Scale) starting on A:

F G A Bb C D E F G A Bb C D E F

So it's A-C-E-G.

That's iii7. But we want it in First Inversion, which means the 3rd of the chord is going to be in the Bass. That's the note C.

So the answer is:

Am7/C

What's the Supertonic 7th chord in Eb Major?


Supertonic means "II" of some sort. It's 7th. In Major Keys, the "II7" is a Minor 7th chord, so it's "ii7".

What's the 2nd note of Eb? Well, you can work out the scale, but remember the 2nd note of a Key (Major or Minor in fact) is always a Whole Step above the Tonic. E-F is a Half Step in the Natural Notes. So Eb-Fb is also a Half Step. Eb-F is one Semitone larger, so it's a Tone or Whole Step. That's what we want. So F is in fact the "2" in Eb Major.

So it's going to be an Fm7 chord.

That's all that was asked, so there's your answer.

What's the 7th of the Supertonic Seventh in Eb Major?


Either write out the notes in the Key and pick every other note up to the 7th above F (the Supertonic degree)

Eb F G Ab Bb C D Eb F G Ab...

Answer: Eb.

Or, if you know F is scale degree 2, and a m7 is the Diatonic Supertonic 7th, you'll know the 7th of that chord MUST be in the key, so it's GOT to be the Eb 7 steps higher!!!

Wow. That's so easy it drives me crazy. It used to drive me crazy when I taught theory because students couldn't get this. It was because they missed something along the way, like the fact that a "ii7" HAD to be Diatonic, so it HAD to use notes from the Key, so there didn't have to be all this figuring out the chord by interval - it MUST be the Eb in the Key that's the 7th above the F.

But if you don't know your Key Signatures, or you didn't learn how to count Intervals (generic Intervals no less), etc. You can't do it.

Give me an Eo7 chord in 3rd Inversion in the Key of Bb Major.

A HA! You're trying to trick me, because I know that fully diminished chords are viio7 in Minor. So you're asking me for a non-Diatonic chord.

So?

I can do that. You'll find them in music.

So there are a couple of ways to do this:

1. Figure out the notes the chord would have by interval, regardless of any key.

2. Figure out the notes of the chord based on the Key it would have most likely come from (in this example E is the L.T. in Fm, so you'd use the Key Sig of Fm to work it out)

Let's do #1.

We know it's Eo7.

It's built on E.

So it's going to contain:

E - G - B - D

A o7 was the one that's all m3 - sometimes that's easier to figure than a Dim Triad + a Dim 7, so let's try it intervallically:

E-G = m3. Check (if you don't understand why, go back!)
G-B = M3. We need m3. Can't adjust the G becuase that will change the distance between it and the E, which is already the m3 we need. So we must lower the B to Bb making it one Semitone closer to the G (and thus making the distance one smaller) turning a M3 into a m3.

E-G = m3
G-Bb - m3

check

Now, Bb - D - what's that? M3 again. So we've got to lower the D for the same reasons and by the same method as above.

Bb-Db = m3

E-G = m3
G-Bb = m3
Bb-Db = m3

or

E-G-Bb-Db

That's Eo7.

We need to put it in 3rd inversion, so the 7th has to be on the bottom. You could "rotate" the notes, putting the Db at the beginning and move everything else to the right one slot:

Db-E-G-Bb (that keeps it Close position)

And of course the symbol would be:

Eo7/Db

Now, the original question asked for this in the Key of Bb (Major).

Bb Major has a Bb and Eb in it, so if you were writing this out you'd need to put a NATURAL sign on the E (so it's E and not Eb as the Key Signature makes it) and add a FLAT to the D note to make it Db (since it's just a plain D in the Key Sig).

In text, we would usually still just write:

Db-E-G-Bb but sometimes you might see:

Db-En-G-Bb to clarify (and note, even though the Bb is flat in the key signature, we still include the flat sign in text and should do it in conversation!)

But Eo7/Db is proper for the name, becuase we don't call it "E-natural diminished 7".

Now let's do it the 2nd way - by figuring out the notes from the key it would have come from Diatonically.

Again, the viio7 appears naturally on the raised 7 of a Minor Key (Leading Tone) so you have to ask yourself, what Minor key is E (because we want Eo7) the Leading Tone in. Since the LT is a half step below the Tonic, you can also simply ask yourself, what note is a half step above E?

Answer, F.

So F minor. Eo7 comes from the Key of Fm. BUT remember that the viio7 is one of the two chords created by using the HARMONIC MINOR form of the scale (i.e. using #7 instead of the natural 7 of the Key). So let's write out F Minor.

I'm waiting....

Ok, 4 flats, Bb, Eb, Ab, and Db, meaning:

F G Ab Bb C Db Eb (F)

BUT, we're using Harmonic Minor, so:

F G Ab Bb C Db E F G Ab Bb C Db E F

And let's do every other letter starting on the E:

F G Ab Bb C Db E F G Ab Bb C Db E F

See, E (natural) - G - Bb - Db

And of course, since it's 3rd Inversion, the 7th of the chord, Db, goes in the Bass:

Db - E(n) - G - Bb

And in the key of Bb, the E would need the Natural sign and the D would need a flat sign.

What's the 7th of the IVM7 in C# Major?


This is easier than you think.

But I'll come back to the easy version and do the way people who didn't pay attention to their early lessons would do it, not knowing any better ;-)

Key of C# Major. That's 7 sharps. 7 notes in a key, so they're ALL sharp:

C# D# E# F# G# A# B# C# D# E# F# G# A# B#

We want IV, so we start on 4 and pick every other letter:

C# D# E# F# G# A# B# C# D# E# F# G# A# B#

There are the notes. The 7th of the chord - well, that's on the 1st fret of the high E string. So that's an F.

WRONG.


It's an E#. Forget enharmonics.

The easier way to do this is if you know that C# is the same as C just with sharps on everything all you have to do is take the sharps OFF everything to figure. IOW, figure out in C, then add the sharps back in. IV in C is F-A-C-E - 7th is E, so add your sharp back in, answer is E#.

Oh, you of course knew from the git go that IVM7 is the Subdominant Diatonic 7th in a Major Key yes? So you knew the notes would be in the Key? Yes? Good.

Let's do a harder one. F# is the 5th of a m7b5. What's the chord?

OK, if F# is the 5th, just put the Thirds in place:

1 3 F# 7

The 7 has to be some sort of A

1 3 F# A

the 1 and 3 you can figure backwards:

B D F# A (and again, if you know your 4 letter Tertian groups, this would have come instantaneously).

So it's "some type of B" 7th chord.

A m7b5 is a Diminished Triad+m7, or the Interval content is m3-m3-M3.

We can't change the F# because that's given, so let's work from there.

F#-A needs to be a M3. Is it? No. Has to be F#-A#

B-D-F#-A#

NOw, D-F# needs to be a m3. It's not. D-F# is a M3. We can't move the F#, so the D has to get closer (to decrease the distance) so it has to go up a Semitone to D#:

B-D#-F#-A#

Finally, B-D# needs to be a m3 as well, and you can't move the now correct D#, so B has to move up a half step:

B#-D#-F#-A#

There's your answer. F# is the 5th of a B#m7b5 chord.

Darn, if I had only known that the Natural notes B-D-F-A formed a m7b5 and that applying a sharp to ALL of them would keep the quality the same and give me the F# I needed...

See, you can "cheat" learning to play guitar with "patterns" - you can do it with Theory too! I don't think you should use them as a "crutch" in either pursuit, but by all means, that doesn't mean you shouldn't use them to your advantage!!!

By the way, chord above - isn't that a Cm7b5? No. No Enahrmonics. Get over it. Move on. Learn it the right way. We'll deal with Enharmonics properly in the future.

Links will appear yadda yadda yadda

Steve
 

Beto

Silver Supporting Member
Messages
4,186
I had slipped out of this subject - when it comes to practice; I already knew the theory involved because I had read a bit about it - a few times because I always felt overwhelmed by the amount of different chord shapes that comes with this topic.

Fortunately, my guitar teacher finally figured an efficient way to push me into this: some exercises over a ii7 V7 I7M progression, often applying some sort of modal interchange - e.g. we've been mixing chords to intermittently evoke a minor key feeling (chords containing tones from the 'melodic minor' scale), in the form of progressions like IV7M iv7 iiim7, ii7 ii7(b5) I7M, vii7(b5) viiº7 I7M. Such progressions work with subtle changes in inverted chords which are very helpful to learn all those shapes - and the most important is that they are very musical and gorgeous.

I know this is going to take a good while, but it's very fun to play with once you got started.
 

m_b

Member
Messages
197
I haven't read all your chapters yet so forgive me if you've already mentioned the following, but there's a little mnemonic trick from the Eddie Lang guitar method which I've found surprisingly useful to reduce the mental math involved in finding the key if for instance, as per your example, you needed to find the key for a F# that is a flat 5. The trick is as follows.

In the C major scale three major triads (1,3,5) have no sharps:
CGE
FAC
GBD

Three have one sharp:
AC#E
DF#A
EG#B

One has two sharps:
BD#F#

Those have to be memorized like formulas so as to enable automatic recall (one week of light mental work on the commute worked for me), any other combination is simple deduction (e.g., to find the Bb major triad, move everything back 1/2 step, i.e. BbDF, or to find Emaj7, add one note a half step down from the root, i.e. EG#BD#). In your example, knowing F# to be the 5 of B, you would also know instantly F# to be the flat5 of B#.
 

stevel

Member
Messages
15,177
In the C major scale three major triads (1,3,5) have no sharps:
CGE
FAC
GBD

Three have one sharp:
AC#E
DF#A
EG#B

One has two sharps:
BD#F#
Actually, I've never noticed that before. But it is similar to some other related concepts. Nifty!
 
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Motterpaul

Tone is in the Ears
Messages
13,414
I haven't read all your chapters yet so forgive me if you've already mentioned the following, but there's a little mnemonic trick from the Eddie Lang guitar method which I've found surprisingly useful to reduce the mental math involved in finding the key if for instance, as per your example, you needed to find the key for a F# that is a flat 5. The trick is as follows.

In the C major scale three major triads (1,3,5) have no sharps:
CGE
FAC
GBD

Three have one sharp:
AC#E
DF#A
EG#B

One has two sharps:
BD#F#

Those have to be memorized like formulas so as to enable automatic recall (one week of light mental work on the commute worked for me), any other combination is simple deduction (e.g., to find the Bb major triad, move everything back 1/2 step, i.e. BbDF, or to find Emaj7, add one note a half step down from the root, i.e. EG#BD#). In your example, knowing F# to be the 5 of B, you would also know instantly F# to be the flat5 of B#.
Honest question - how is this nugget of information applicable to my playing? (or reading, or whatever).
 

m_b

Member
Messages
197
Honest question - how is this nugget of information applicable to my playing? (or reading, or whatever).
It's just a trick to memorize triads and chords rapidly in all keys. As to its usefulness, that kind of knowledge is comparable to a compass (or GPS) to me.
 

Motterpaul

Tone is in the Ears
Messages
13,414
Steve - question - in traditional harmony a first inversion chord is known as a "6" chord - because the root is the 6th intervallic note above what is in the bass, and a chord with the 5th in the bass is called a

6
4

chord, because the root is the note 4 intervallic steps above the bass and the third is the 6th intervallic note above the bass.

So, what is the traditional theory nomenclature for a chord with the 7th in the bass? Is there such a thing?
 

willyboy

Member
Messages
3,404
Steve - question - in traditional harmony a first inversion chord is known as a "6" chord - because the root is the 6th intervallic note above what is in the bass, and a chord with the 5th in the bass is called a

6
4

chord, because the root is the note 4 intervallic steps above the bass and the third is the 6th intervallic note above the bass.

So, what is the traditional theory nomenclature for a chord with the 7th in the bass? Is there such a thing?
3rd inversion 7th chords are:
4
2

2nd inversion 7th chords are:
4
3
 

Motterpaul

Tone is in the Ears
Messages
13,414
Never mind - because your naming convention only shows two characters I was assuming the chord is a triad - three notes (which is what most traditional harmony has), so that one note was eliminated. But I did google the answer and it shows 4-note chords.

Shown below is the I 4/3. In each case the notes that are named includes the root and the seventh. I assume this is just the naming convention. You add 4|2. That assumes the 7th is in the bass, which is the same as the simple 2 (last chord shown below) with the seventh on the bass

Here is the site where I got this: http://www.musictheory.net/lessons/49


Here is a site that explains how these are abbreviated: (note, these are G chords while the above are in C)
https://www.ars-nova.com/Theory Q&A/Q25.html

 
Last edited:

willyboy

Member
Messages
3,404
The 2 for 3rd inversion is new to me. My classical harmony courses taught me 4 2 for that one.
 

stevel

Member
Messages
15,177
The 2 for 3rd inversion is new to me. My classical harmony courses taught me 4 2 for that one.
Sorry I didn't see all this earlier @Motterpaul but it looks like you and @willyboy sussed it all out.

Yes, I too learned "4 2" for 3rd inversion.

IIRC, maybe Walter Piston's text only uses the 2, and maybe some earlier ones like Schoenberg. To me it's "old-fashioned".

Still some people like it because the inversion symbols go:

6
5

4
3

2

that way. Better mnemonic!

So I should add though, since you mentioned the omitted 5th - in classical music, for "inversional symbols", we don't care. A 7th chord may have all 4 members, and omitted 5th, or a little less commonly, an omitted 3rd.

But we use the "full abbreviation" for naming them. Thus Bb - C - G and Bb - C - E are both "4 2". The "6 4 2" is inferred in both cases.

In actual "Figured Bass" (from whence these inversional symbol numerals are derived) it's more common to specify actual voicing - so "6 2" could be a possibility. But for inversional symbols, in essence "4 2" would mean, 7th in the bass, remaining chord members or duplicates above, in any voicing, and possibly with omissions of the 3rd, or 5th, or even, possibly the 3rd AND 5th!
 

willyboy

Member
Messages
3,404
Yes stevel thanks for elaborating. And funny I'd never considered that would be a much better mnemonic device for memorizing those inversion symbols!
 

cubistguitar

Member
Messages
6,069
Nice thread, I know jazz shorthand ( which is sometimes not short or entirely accurate) better than figured bass, which I did learn many years ago. Terrific to see how accurate and quick figured bass can be. Don't know if I will ever use to communicate with my pool of musical friends, but it all gets stored in the noggin somewhere.

Maybe Stevel can do some drop2 and drop3 lessons sometimes, since they are very guitarry and involve inverting 7th chords. Still this is great thread as is.
 

Motterpaul

Tone is in the Ears
Messages
13,414
Stevel - you are right that I should have remembered the "name" remains the same regardless of the positions of the voices where inversions are concerned, but it's been a long time since analyzed figured bass chords. I notice you leave out "7" though, which has the root in the bass but contains a 7 interval. Is there a standard naming convention for this (a chord containing a 7th) in classical figured bass analysis?

and BTW, you get 2, 3|4, 5|6 and 7
 






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