The Order of Chord Inversions?

[Garrett Smith]

Please describe the pattern-based, contrapuntal voiceleading "order of inversions."

For four part chords, there are three "orders of inversions" the third being subdivided. They are:

1. Root, 3rd, 2nd 1st
2. Root, 1st, 2nd, 3rd
3. Root, 2nd | 1st, 3rd

E.g.
Chord Quality: Maj7
Interval: b3
Voicing: drop 3
Start: Amaj7, root pos

1.
Amaj7, root: A G# C# E
Cmaj7 3rd: B G C E
Ebmaj7 2nd: Bb G D Eb
F#Maj7 1st: A# F# C# E#

2.
Amaj7, root: A G# C# E
Cmaj7 1st: E C G B
Ebmaj7 2nd: Bb G D Eb
F#Maj7 3rd: E# C# F# A#

3.
I.
Amaj7, root: A G# C# E
Cmaj7, 2nd: G E B C

II.
Amaj7, 1st: C# A E G#
Cmaj7, 3rd: B G C E

What do you call the pattern-based contrapuntal voiceleading "order of inversions" listed above as 1. 2. 3. I. & II?

And if there is no term, I will continue to call it "order of inversions". This type of concept should have a more succinct or more descriptive name.

Thank you.

[JonR]

I've no idea, and I'm not sure I even understand your examples.
Eg your Amaj7 (first 3 examples) is not "root position", it's 3rd inversion drop 3 (G# A C# E with the A dropped an octave).
The last one (C# A E G#) is root position drop 3.

[Guitarzen]

Hey Garret, you will always find interesting patterns in music because there is a heavy mathematical thing going on. But in your examples, there is no relationship between the chords whatsoever as far as functional harmony goes, and therefore the pattern you are seeing is not really very useful, in my opinion. I think this is just a case of over analyzing. But feel free to prove me wrong by writing a composition where this pattern becomes important. Good luck.

your Amaj7 (first 3 examples) is not "root position", it's 3rd inversion drop 3 (G# A C# E with the A dropped an octave). The last one (C# A E G#) is root position drop 3

.

Jon, root position just means the root of the chord is the lowest note in the chord. So [A G# C# E] is most definitely root position. [C# A E G#] is most definitely 1st inversion. I'm not sure where you got that from. In determining inversions, it's purely a matter of what note is in the lowest voice in the end result. The order of the remaining pitches of the chord have no bearing at all on the inversion.

[JonR]

Jon, root position just means the root of the chord is the lowest note in the chord. So [A G# C# E] is most definitely root position. [C# A E G#] is most definitely 1st inversion. I'm not sure where you got that from. In determining inversions, it's purely a matter of what note is in the lowest voice in the end result. The order of the remaining pitches of the chord have no bearing at all on the inversion.

My understanding was always that you started with a particular inversion and then created a drop voicing. IOW, in this case, "root position drop 3" means you begin with A C#E G#, then lower the C# by an octave - ie the name defines the derivation of the chord, not the inversion that results.

However, I hope you're right, because IMO it makes more sense - at least for practical purposes - to name the inversion that's the end result, not the inversion you start from.

I've been looking for internet support for my understanding, and there's a surprising lack of confirmation either way. Most info on drop voicings talks about the method, not about how you name the chord inversion-wise, either before or after.

This one mentions inversion names prior to the drop, without actually naming the resulting inversion:

Drop 2 Chords - Chord Chart, Theory & Exercises

[Guitarzen]

Well I can 100% assure you that is how I was taught in my music theory class. I also verified it by looking it up in the harvard dictionary of music, before I put up the previous post. I can quote it for you later when I have time. Inversion naming has nothing to do with how they lay out on guitar or what adjustments we need to make to get all the notes we need etc...It only has to do with how the notes lay on the staff, and consequently what our ear hears in the lowest voice.

[randalljazz]

the bass note determines the inversion. the order of the other voices is immaterial, as is how that order was selected.

[BigDaddyLoveHandles]

the bass note determines the inversion. the order of the other voices is immaterial, as is how that order was selected.

That how I was taught, but it was so long ago, I think my instructor was a student of J.S.Bach.

[JonR]

Well I can 100% assure you that is how I was taught in my music theory class. I also verified it by looking it up in the harvard dictionary of music, before I put up the previous post. I can quote it for you later when I have time. Inversion naming has nothing to do with how they lay out on guitar or what adjustments we need to make to get all the notes we need etc...It only has to do with how the notes lay on the staff, and consequently what our ear hears in the lowest voice.

Yes I understand that (and I know what randalljazz and BigDaddy are saying).

What I'm assuming is it's a contextual thing: it depends on why we're naming the chord. (The one reply I've had so far on the other sites suggests that.)

Eg, I know G C E B is a 2nd inversion Cmaj7. But can't we also call it a "root position drop 2"? - to describe how we could construct that specific 2nd inversion (as opposed to G B C E, G E B C or G E C B)?

[Toat]

Inversions, while it has it's place in classical theory, is not really a useful concept in jazz theory, and escpecially the guitar, does anyone disagree?

[Garrett Smith]

Inversions, while it has it's place in classical theory, is not really a useful concept in jazz theory, and escpecially the guitar, does anyone disagree?

Inversions, while it has it's place in classical theory, is not really a useful concept in jazz theory, and escpecially the guitar, does anyone disagree?

Why are inversions prevalent in music? Generally this has to do with the way that they sound. Other reasons might be convenience, ease of playing and not being able to recall other voicings and inversions quickly. Any other reasons?

Contrapuntal voiceleading exercises (and this is) serve purposes related to playing.
1. The ability to understand and construct inversions without resorting to chord books.
2. Expand the player's hands-on chord vocabulary, in hands, brain, ears, and ultimately intuition.
3. Drill quick recollection of nearby voicings and intervals and their enharmonic equivalents, while playing.

These exercises achieve this by imposing restraints on the practitioner, focusing on one chord quality at a time and forcing "this voicing next".



Aside: Yesterday, I spent 30 min thinking and typing a reply and it vanished immediately without being posted. I went "Back" but the message was gone and the "Back" navigation was amiss. It appears that the programmer used javascript to post the message via XHR, that failing, and the failure case being handled by dropping the message. I never had this problem with the old UI.

And now I see:

Your submission could not be processed because the token has expired.

Please reload the window.

And reloading and resubmitting results in the same. Trying a different approach now, having saved the message separately...

...

Wow, this is not working.


Trying to re-navigate to the thread to try to reply again....

[Bryan T]

Inversions, while it has it's place in classical theory, is not really a useful concept in jazz theory, and escpecially the guitar, does anyone disagree?

I disagree. I use my knowledge of inversions all the time in composition and improvisation, typically to find parsimonious voice-leading. Of course, I do sometimes think of myself as a pianist trapped in a guitarist's body.

[Guitarzen]

What I'm assuming is it's a contextual thing: it depends on why we're naming the chord. (The one reply I've had so far on the other sites suggests that.)

Eg, I know G C E B is a 2nd inversion Cmaj7. But can't we also call it a "root position drop 2"? - to describe how we could construct that specific 2nd inversion (as opposed to G B C E, G E B C or G E C B)?

Quite simply if you analyze (G C E B) as "root position drop 2" on a theory test, you will get it wrong. Music theory is all analyzed on staff notation, not guitar. Keep in mind there are a lot of people on the web that answer theory questions that don't have formal training and/or make mistakes. So just because someone on the web promotes a theory on the web doesn't make it right in the context of a formal theory exam. I realize people like to create their own personal takes on theory (I do this too!) but it's important to identify a theory as such and not as the common practice. I was taught this in school and I also took the time to verify my answer in the havard music dictionary before I answered you initially. But I didn't need to verify it. I spent four plus years doing nothing but analyzing music scores (and having them graded by music professors) and a huge part of that was identifying inversions. It's all second nature to me. I'll attach a scan from my college theory book, Music In Theory and Practice, Benward & Saker.

[Guitarzen]

Inversions, while it has it's place in classical theory, is not really a useful concept in jazz theory, and escpecially the guitar, does anyone disagree?

It's extremely useful no matter what style of music you are playing. It allows us to form good bass lines. Each inversion also has it's own unique sound. Creating music is creating a "sound painting", so why would you not want to intelligently use all the available sounds?

[JonR]

Quite simply if you analyze (G C E B) as "root position drop 2" on a theory test, you will get it wrong. Music theory is all analyzed on staff notation, not guitar.

Of course. I wasn't limiting the question to guitar - although all the results on a google search seem to relate to guitar. (Why are guitarists so obsessed with them?)
Likewise I totally accept what you're saying about the resultant chord.

My only question was trying to clear up the notion of describing where a drop voicing actually comes from.
Ie, if we see a chord built G C E B, obviously it's a 2nd inversion Cmaj7. No argument.
But that particular voicing is a drop 2. Drop 2 from what? Root position, equally obviously. And my question was would it be right (on certain occasions) to refer to it as something like "root position drop"?
I agree (of course) that would be confusing, and that the impression I got from somewhere is mistaken.
Nearest seems to be the possibility of "drop 2 voicing (from root position)" which fits the bill while being quite clear.

[jckoto3]

Jon

In the past 11, 12 years or so of reading, digesting and getting an enormous amount ofvalue out of reading your posts on various websites, I'm a bit amused in that it seems as if your vast knowledge is working a bit against you here! I genuinely mean that with the utmost respect.

I've seen e.g. G C E B as both a "2nd inversion CMaj7" and "Root position Cmaj7, drop 2" being used in print (literally in paper books, not just "some dude's blog"), and not necessarily in guitar-specific literature. I think both are correct but for different reasons: if we consider the lowest note to be the sole criterion for determining a chord's inversion then G C E B would be aptly called "2nd inversion CMaj7" (as would G E C B, G B C E, etc), however if we want to know the specific voicing "Root position Cmaj7, drop 2" is IMO ambiguous but not incorrect -- is it a description of the resultant chord (which would be "C G B E") or is it an instruction on how to derive a chord (C E G B then drop the 2nd voice G = G C E B)? Or ...what? I think even Mick Goodrick himself has used both of those examples at different times..

I'm not sure what pianists think (or even if they do (haha, kidding)), but people who arrange for multiple instruments (like horn sections or whatever) seem to often disagree with people who solely play guitar on the details and definitions of drop voicings. IMO I think using inversion terminology makes more sense for triadic harmony and intervals rather than 7th chord drop voicings since the concept of "drop voicings" itself is a relatively recent invention and not quite so codified. "CMaj7 drop 2 with the 5th in the bass" is pretty clear but literally saying "G C E B" (or "5 1 3 7" if a degree of arbitrariness is warranted) is about as simple as it gets to communicate the point to another musician.

Guitarists in particular seem to be obsessed with both drop voicings and modes, and often seem to lack any substantive understanding of either, eh Er, I mean in general, and not necessarily at this website, in this particular thread.

...too bad ksjazzguitar isn't here for this discussion.

[Guitarzen]

Ie, if we see a chord built G C E B, obviously it's a 2nd inversion Cmaj7. No argument.
But that particular voicing is a drop 2

There are other ways we could derive that chord too. So to say that it must defined as a "drop 2" could be debated. I see the whole drop voicing thing as merely somebody recognized a pattern consistent with chords on the guitar and came up with a system to describe it logically. But that doesn't mean we that we must label it as being derived by the "drop 2" system.

Of course we are all free to use our own methods for memorizing how to play all this stuff on the guitar. I don't think there is any problem with thinking of a chord as "a drop 2 derived from a 2nd inversion chord" or whatever.

But the important point here in regards to labeling inversions is that they are labled purely based on the lowest sounding pitch. Inversions are not even a complicated aspect of theory I just think you got stuck on combining inversions with your drop voicing theory as though they were one in the same? Or something like that. But two seperate things really. I personally have never used the drop voicing system, and yet I know every single one of the drop voicing chords, by memory. The bottom line is to use chords they must be memorized. We have no real use for the theory of how one person derived or explained that chord, when we are comping changes. And I have derived many "drop voicing" chords by simply using my knowledge of chord formulas and my knowledge of the fretboard, i.e. "...Ok I need the notes A,C#,E,G#, what's the easiest way to play those in this position?". I think my way of deriving those chords was just as valid as the "drop voicing" guy's way

And my question was would it be right (on certain occasions) to refer to it as something like "root position drop"?

I don't think there would be any problem with explaining that to another guitarist that you derived the drop chord -GCEB - from a root position chord. But you then must also explain to them by dropping the 2nd highest voice to the bass, you have changed the chord to a 2nd inversion chord And hence, "root position drop" is a bit of a cumbersome way to explain it, IMO, because then you have to essentially cancel out what you just said. Anyways, my apologies to Garret for taking the thread a bit off topic here...But I think we are done now ;oP

[jdaguitar2]

Inversions are very important for chord-melody and comping as well.

[JonR]

There are other ways we could derive that chord too. So to say that it must defined as a "drop 2" could be debated.

Sure.

I see the whole drop voicing thing as merely somebody recognized a pattern consistent with chords on the guitar and came up with a system to describe it logically.

It doesn't come from guitar though. Drop voicings are a standard arranger's tool, for opening out harmonies in various ways. (Eg drop 2 helps a top melody line stand out.)

Of course we are all free to use our own methods for memorizing how to play all this stuff on the guitar.

As I say, playing the guitar is not the issue. I was only wondering about terminology.
In any case, most guitar chord shapes are drop voicings of various kinds, because they have to be. We can't generally play close-voiced 7ths, so something has to give.

I don't think there is any problem with thinking of a chord as "a drop 2 derived from a 2nd inversion chord" or whatever.

Right.

But the important point here in regards to labeling inversions is that they are labled purely based on the lowest sounding pitch. Inversions are not even a complicated aspect of theory

Sure!

I just think you got stuck on combining inversions with your drop voicing theory as though they were one in the same?

Not at all. I just picked up that confusing naming system from somewhere, many years ago (damned if I can remember where).
My whole point (which I guess I didn't express very well ) was that I know G C E B is a 2nd inversion chord. And yet I had this memory in my brain of naming drop voicings using a close-voiced inversion they derive from - which I always thought was kind of crazy.

I personally have never used the drop voicing system, and yet I know every single one of the drop voicing chords, by memory.

Pretty much my experience.

The bottom line is to use chords they must be memorized. We have no real use for the theory of how one person derived or explained that chord, when we are comping changes. And I have derived many "drop voicing" chords by simply using my knowledge of chord formulas and my knowledge of the fretboard, i.e. "...Ok I need the notes A,C#,E,G#, what's the easiest way to play those in this position?".

Right. It's never occurred to me to follow any particular drop voicing principle when comping, or even when playing chord melody. It's just "what notes do I need for this chord, and how can I get them easily?" - combined with "how can I get the best voice-leading to the next chord?". Plus, if playing chord melody: "melody on top, bass line on bottom - and any other useful chord tone(s) between."
Like you, I could name the inversions involved, and (maybe with a little thought) any drop voicings employed, but they're of no concern in how I form my chords.

I don't think there would be any problem with explaining that to another guitarist that you derived the drop chord -GCEB - from a root position chord. But you then must also explain to them by dropping the 2nd highest voice to the bass, you have changed the chord to a 2nd inversion chord

Of course.

And hence, "root position drop" is a bit of a cumbersome way to explain it, IMO, because then you have to essentially cancel out what you just said. Anyways, my apologies to Garret for taking the thread a bit off topic here...But I think we are done now ;oP

We are. Thanks for your clarification, and the opportunity (hopefully) to clarify myself.

I'm still intrigued about Garrett's question, as I don't fully understand it...

[JonR]

Jon

In the past 11, 12 years or so of reading, digesting and getting an enormous amount ofvalue out of reading your posts on various websites, I'm a bit amused in that it seems as if your vast knowledge is working a bit against you here! I genuinely mean that with the utmost respect.

I've seen e.g. G C E B as both a "2nd inversion CMaj7" and "Root position Cmaj7, drop 2" being used in print (literally in paper books, not just "some dude's blog"), and not necessarily in guitar-specific literature. I think both are correct but for different reasons:

Thanks! That's really all I was trying to say, I just couldn't find clear references to the latter, and was beginning to think my understanding was flakey (because I'm cool with everything Guitarzen was saying). Which books have you seen the latter terminology in?

if we consider the lowest note to be the sole criterion for determining a chord's inversion then G C E B would be aptly called "2nd inversion CMaj7" (as would G E C B, G B C E, etc), however if we want to know the specific voicing "Root position Cmaj7, drop 2" is IMO ambiguous but not incorrect -- is it a description of the resultant chord (which would be "C G B E") or is it an instruction on how to derive a chord (C E G B then drop the 2nd voice G = G C E B)? Or ...what? I think even Mick Goodrick himself has used both of those examples at different times..

Well, Goodrick would be a good source if you can quote the reference.

Guitarists in particular seem to be obsessed with both drop voicings and modes, and often seem to lack any substantive understanding of either, eh Er, I mean in general, and not necessarily at this website, in this particular thread.

Too right...

...too bad ksjazzguitar isn't here for this discussion.

Hey I'd forgotten about him! I used to love his tone of sarcastic frustration with us lesser mortals...

[Toat]

So what I'm getting is that thinking in terms of "inversions" isn't useful, but knowing a variety of chord voicings is important, of course.

So I'm back to, instead of getting caught up on inversions, here are possible tones of a chord, how do you want to arrange them on the guitar? Experiment with voicings, but I still don't believe thinking in terms of inversions is useful in jazz.

[bako]

Jon,

Although I know now all the drop chord terminology (and somewhat dislike it) I arrived at the voicings in what I believed is a simpler way.

Start with each 7th chord interval from the root

1 3
1 5
1 7

Each one has two remaining notes and two possible orders

1 3 5 7
1 3 7 5

1 5 7 3
1 5 3 7

1 7 3 5
1 7 5 3

Each of these 6 root voicings has 4 inversions

1 3 5 7
3 5 7 1
5 7 1 3
7 1 3 5

1 3 7 5
3 5 1 7
5 7 3 1
7 1 5 3

1 5 7 3
3 7 1 5
5 1 3 7
7 3 5 1

1 5 3 7
3 7 5 1
5 1 7 3
7 3 1 5

1 7 3 5
3 1 5 7
5 3 7 1
7 5 1 3

1 7 5 3
3 1 7 5
5 3 1 7
7 5 3 1

That covers all 24 orders leaving only octave displacement, doublings, note omissions, note omission + doubling.
Much simpler to me anyway.
I believe the drop system came out of arrangers more than guitarists.
----------------------------------------------------------------------------------------------------------

Garrett,

I didn't follow your example.
Why did you choose

Amaj7, root: A G# C# E
Cmaj7 3rd: B G C E
Ebmaj7 2nd: Bb G D Eb
F#Maj7 1st: A# F# C# E#

as a starting point?
Is it the m3 interval, A-C-Eb-F#?

[JonR]

Jon,

Although I know now all the drop chord terminology (and somewhat dislike it) I arrived at the voicings in what I believed is a simpler way.
...

Pretty much how I'd do it myself, or at least how I'd think of the options.

I believe the drop system came out of arrangers more than guitarists.

Indeed, that was always my understanding.

[Garrett Smith]

Why did you choose

Amaj7, root: A G# C# E
Cmaj7 3rd: B G C E
Ebmaj7 2nd: Bb G D Eb
F#Maj7 1st: A# F# C# E#

as a starting point?
Is it the m3 interval, A-C-Eb-F#?

Yes. It starts and ends on the same chord, same inversion, passing through no other inversions of that chord. This is because the root goes up a second while the third and seventh each go down a minor second. The cancellation effect is regardless of chord quality. Try it with dom7.

Amaj7  root: A G# C# E
Cmaj7  3rd:  B G C E
Ebmaj7 2nd:  Bb G D Eb
F#Maj7 1st:  A# F# C# E#
Amaj7  root: A G# C# E

With major 3rd, other inversions of the start chord are passed through.

[timscarey]

Please describe the pattern-based, contrapuntal voiceleading "order of inversions."

For four part chords, there are three "orders of inversions" the third being subdivided. They are:

What do you call the pattern-based contrapuntal voiceleading "order of inversions" listed above as 1. 2. 3. I. & II?

And if there is no term, I will continue to call it "order of inversions". This type of concept should have a more succinct or more descriptive name.

Thank you.

personally, I'm a little confused as to why this would have a specific name. It seems to be a great method for practicing different inversions/voicings, which is cool, but at the same time has little relevance outside of a practice tool. This is due to the absence of this kind of chord progression in most music.

Most harmonic concepts are given names because they occur in music. I would also like to point out that your "order of inversions" is not complete. Why must we always start on a root position chord? Or not repeat the same inversion more than once?

As far as the "drop 2" thing... I think the terms "inversion" and "voicing" are being either confused or equated somehow in this thread. I've always thought that the term "inversion" refers only to the lowest note in the chord, while "voicing" refers to how the pitches are distributed across the staff(s), which pitches are doubled, added, etc...

In my mind, the term "Drop 2" or "Drop 3" simply means (loosely)... "two intervals > a 3rd and one < or equal to a 3rd" in a 4 note voicing. of course, by dropping the alto voice of a closed position voicing, you will arrive at a "drop 2" but who is to say that we need to start with a closed position voicing at all?

[Garrett Smith]

personally, I'm a little confused as to why this would have a specific name. It seems to be a great method for practicing different inversions/voicings, which is cool, but at the same time has little relevance outside of a practice tool. This is due to the absence of this kind of chord progression in most music.

Hi, Tim. The reason for naming it is for communication. If it doesn't have name, then call it "Cycling Inversions."

Modern music has every conceivable chord change. There is no new relationship between any two given seventh chords. Try to come up with something outlandish, such as Amaj7B5 to Ebmin7b5. Unfortunately, good voiceleading quickly "ruined" my bizarro example, making it sound almost pretty.

Amaj7B5  ... Eb A  C#  G#
Ebmin7b5 ...Eb  A  C#  F#

However, trying to guess up weird voicings that will sound bad together is missing the point.

A better use of time is recognizing the voicings that don't get practiced often enough and work on those so that they can be recalled quickly, out of harmonic context.

Dominant seventh and minor sevenths are good to start with. When these exercises are incorporated into the practice routine, play a blues progression and you will probably find that the exercise does help with chord recognition, both by ear and by hand.

Jazz Blues Chord Progressions - Shapes & Comping Examples

Most harmonic concepts are given names because they occur in music. I would also like to point out that your "order of inversions" is not complete. Why must we always start on a root position chord? Or not repeat the same inversion more than once?

Cycle b3 of any chord quality does not pass through other inversions of the chord it was begun on. This has to do with the simple math of it. It's not my rule. Complain to god if you don't like it! At your bequest:

. The inversions are: A7 root, C7 3rd, Eb7 2nd, F#7 1st, A7 root -- back to the A7 in root position!

See how cycle b3 works now?

Other cycles will do different things. But there is another cycle that repeats without passing through other inversions of the starting chord. Try to figure out which one it is.

The orders of inversions listed above is repetitive and so complete for seventh chords. Start on different inversions to keep your practice fresh. Again, the options are forwards, backwards, and staggered. Staggered is alternating between two inversions, either root and 2nd or 1st and 3rd.

The other variables to the exercise are in my first post.

Regards,

Garrett