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Will I even encounter any enharmonic chords? For example would an inverted variation of one chord be equivalent to the root variation of another chord?

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I presume your question is outside the scope of, say Dbdim being enharmonic to C#dim, yes? –  NReilingh Feb 20 at 1:27
    
Right, besides accidentals. –  RyanScottLewis Feb 20 at 1:35
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Well, accidentals are usually what define enharmonics... I might actually put enharmonic in quote marks in your question, just to make that a little bit clear... or not even use the word at all; rather just ask "Are there any chords that can have more than 1 valid name?" –  NReilingh Feb 20 at 1:47
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Agreed with NReilingh here - enharmonic refers to multiple ways a sounding pitch can be notated. The OP appears to be asking whether or not two differently-named chords could contain the same notes. See Dom's answer below. –  jjmusicnotes Feb 20 at 4:16
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What NReilingh and jjmusicnotes said. I'd like to add that chord inversion is yet another, mostly different aspect that is completely separate from enharmonic equivalency. For chord inversion, the following usually holds: 1st inversion (3rd in the bass) is usually harmonically equivalent to the root position chord. The 2nd inversion (5th in the bass) almost always has a different function than the root position chord. It's often treated as a suspension of the chord a fifth above it. So GCE (2nd inversion C major) is heard as a suspension that resolves into GBD (G-major root position) –  Roland Bouman Feb 20 at 12:40
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5 Answers 5

Yes they exist. I don't know all of them of the top of my head, but I'll give you the three that come to mind easily.

The first is a fully diminished chord. Because there are only 12 named notes and a fully diminished chord is made of 4 notes that are a minor 3rd apart from each other (3 semitones) there are only 3 different chords but each can be named 4 different ways. For example, a C fully diminished chord would consist of the notes C-Eb-Gb-Bbb, a Eb fully diminished chord would consist of the notes Eb-Gb-Bbb-Dbb(C), a Gb fully diminished chord would consist of the notes Gb-Bbb-Dbb-Fbb(Eb), and an A (Bbb) fully diminished chord would consist of the notes A(Bbb)-C-Eb-Gb.

The second is an augmented chord and like the fully diminished chord because there are only 12 named notes and an augmented chord chord is made of 3 notes that are a major 3rd apart from each other (4 semitones) there are only 4 different chords but each can be named 3 different ways. For example a C augmented chord would consist of the notes C-E-G#, an E augmented chord would consist of the notes E-G#-B#(C), and a G# augmented chord would consist of the notes G#-B#-Dx(E).

The third example are 7th and 6th chords. Some minor 7th chords contain the same notes as 6th chords. For example a C6 would contain the notes C-E-G-A and an Am7 would contain the notes A-C-E-G.

In all these examples you name the chord based on the context of the key for example if you are in the key of Db minor and you see the notes Eb, C, Gb, and Bbb you would call that a C fully diminished chord because C is the leading tone of Db minor so it makes the most sense in the key.

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To expand on Dom's answer, it is not confined to tertian harmonic practices; you can also include Set Theory and 12-Tone Technique here as well. In set theory, you can not only have different sets containing the same notes (K or Kh relationship) but different sets can also contain the same intervals (Z-complement relationship.) –  jjmusicnotes Feb 20 at 4:19
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There's another pair: Dm6 contains the notes D-F-A-B; Bmin7b5 has the notes B-D-F-A, where F is the flattened fifth. –  No'am Newman Feb 20 at 4:19
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Another good one is the German Augmented 6th chord, which can be enharmonically respelled as a dominant seventh chord. E.g. Gr+6 in c minor is Ab–C–Eb–F#, but could be used as Ab–C–Eb–Gb, or V7 of Db. –  Pat Muchmore Feb 20 at 5:37
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The most likely candidates here will be the symmetrical chords (dim and aug) as all the intervals from note to note are the same. The m7/M6 chords can be called either but in most situations there will be an obvious choice. You will probably never see a chart that has a M6 chord with the 6 in the bass (ie C6/A). Almost anyone analyzing that harmony would call it an A-7. Similarly, most would analyze A-7/C as C6. I actually recall reading in Mark Levine's 'The Jazz Theory Book' that he says there is no such thing as A-7/C, that it is definitively C6, which I would tend to agree with. –  Basstickler Feb 20 at 19:28
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I will avoid the debate in the comments about whether "enharmonic" is the correct word.

But yes there are loads of examples of chords with the same notes in them.

Example 1

C D G = Csus2

G C D = Gsus4

Example 2

A C E G = Am7

C E G A = C6

Example 3,4

The full diminished and augmented chords where any one of the notes can be considered a root without even changing the type of harmony:

B D F Ab/G# (full diminished)

C E ab/G# (augmented)

Example in use and conclusion

The best name depends on context, that is what chord it precedes and follows, more than it does on the inversion used.

The following (rather overused) chord progression I heard recently in a local band's song springs to mind:

C Am F G

At the end of the song it went uptempo and the chord progression changed to the following:

C6 Am7 F G

But the C6 and Am7 were exactly the SAME CHORD, completely blurred together.

EDIT: John Lennon's Happy Christmas (War is Over)

Just occured to me this is a good example of why you need different names for the same chord. If we look at the chord progression over the first half of the verse, it's easy even for a non musician to appreciate the symmetry and realise why this song is so popular. The fast change through chord type (3rd, sus2, sus4 and back to 3rd) combined with the slow change through chord root (A B E A) make this song both energising and soothing at the same time.

A Asus2 Asus4 A

Bm Bsus2 Bsus4 Bm

E Esus2 Esus4 E

A Asus2 Asus4 A

Now, Esus4 and Asus2 contain the same notes. If I wanted to standardise the name of this chord I could pick Asus2. Applying this rigorously I get

A Asus2 Dsus2 A

Bm Bsus2 Esus2 Bm

E Esus2 Asus2 E

A Asus2 Dsus2 A

Which is totally confusing and completely misses the point of the chord progression.

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The example from Happy Christmas (War is Over) is excellent! –  David Conrad Feb 20 at 18:29
    
C+D+G don't make a 9th chord.Generally it'll need a maj/min 3 and a 7/b7.It may pass as a cadd9. –  Tim Feb 20 at 18:39
    
@tim I checked and you are right, I didn't realise stacked thirds were applied so rigorously. I taught myself theory with a good head for maths, but nomenclature sometimes escapes me. I've seen guitar books that call this chord a 9, so I have been misled. I have changed it to a sus2 which is definitely right. Cadd9 would need an E as well, so unless I call it C5add9 that's not right either. (C5 is a way of saying "no third" that is widely accepted in rock but I don't know if it's accepted in classical.) By the way, what's the correct name for the chord I call "full diminished?" –  steve verrill Feb 20 at 21:28
    
@steveverrill, half-diminished and fully-diminished are terms in common use, so the chord you call 'fully diminished' is, fact, fully diminished. Most folks would just say 'diminished,' though, and would only qualify a half-diminished (aka minor 7b5) chord. –  kiprainey Feb 21 at 2:04
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There are chords that function in different ways in different contexts. Take for example the chord C-E-G-A. This is the tonic chord of the key of C major with an additional note. It is called an "added-sixth" chord. It has a very pleasing sound and is often used as an ending chord in jazz and in the music of Olivier Messiaen.

Now play C-E-G-A on your keyboard, but follow it with C-D-F#-A and then B-D-G. As if by magic the chord has become the first inversion of the ii7 of G major; the "dominant seventh of the dominant seventh". Same notes, but what was a restful ending chord is now a chord that has to move in order to resolve.

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I realize that this is in some sense the dual to what you asked, but here's one of the most famous chords in music history, the Tristan Chord. 150 years after it was first played, still nobody can agree on how to interpret (and thus name) that chord.

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I don't think there are nor have I ever encountered any. It is mainly because when the notes in a chord are being played, no matter in what order, they all give the same feel as if they are being played together (due to the delay of the previous notes in your head). There are "enharmonic scales" though, for example harmonic minor scale (1 2 b3 4 5 b6 7) and phrygian dominant scale (5 b6 7 1 2 b3 4) both consist of the same notes.

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yes there are enharmonic chords. A 6 chord is usually the same as the inversion of another chord: for example CM6 (C, E, A) is the same as the first inversion of Am. –  Chochos Feb 20 at 7:17
    
Major and minor 6th chords usually contain 1 - 3 - 5 and 6. –  Tim Feb 20 at 17:43
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