Simple question: many have noticed that the A minor 7th chord is the an inversion of the C major 6th chord. However, the more interesting this is why they have different quality (as minor and major) despite consisting of the same notes: A - C - E - G. In contrast, C major in different inversions doesn't sound that different, so I guess that the root doesn't play that much of a role.
C Major (C-E-G) doesn't have much "contradiction". The least consonant interval, in any inversion, is a minor 3rd; a more consonant, familiar, and compatible interval (III, IV, or V) will always be present and is perceived most strongly.
On the other hand, the VII interval is extremely dissonant and stands out. At a 15:8 frequency ratio, it's very different from a VI (5:3) and adds to the "minorness" of the iii. This is unlike how nicely the minor and major third combine (6:5 and 5:4). The VI matches well with the IV and V (5:4 and 4:3) and is overall much more consonant. In short, both the intervals themselves and their interactions with the other intervals result in very different amounts of harmony.
I'm over-simplifying things, but I hope you get the idea. It's quite difficult to be precise or objective when it comes to perception — there are undoubtedly people who do not find A-C-E-G much more distinct from C-E-G-A than C-E-G is from E-G-C or G-C-E.
It is only the root that makes the difference. Just play any inversion of C6 (including A-C-E-G) and play a low C below the 4 notes. In all cases it will sound like a C6 chord, i.e. with a major quality. The same is true for Am7. If you play the inversion C-E-G-A (i.e. actually C6) but with an additional low A in the bass, it will sound like a minor 7 chord.
Note that this is true for many chords, e.g. Am7/b5 and Cm6 share the same notes too. Even better, you can play an Am7/b5 over an F as a root and it will sound like a dominant seven chord (F9), and not like a half-diminished chord. There are many more such possibilities and they are used a lot in a band context where you have a bass player playing the root, so you need to play only 3 or 4 note chords to imply a 5 or 6 part harmony.
I don't find the accepted answer explains much, especially how chords and harmony typically work.
Harmony and tonality is very much about the succession of chords. Looking at single chords in isolation doesn't tell us much about how we will perceive their qualities or functions.
In the absence of other chords it is reasonable to say this chord's bass tone
C is the chord root...
A is an added sixth above a
C E G major triad. With jazz symbols we would call it
Similarly, without any other chords to define the tonality, this chord's bass note
A can be the chord root...
G is an added seventh above a
A C E minor triad, and the jazz symbol would be
Both of these interpretations are reasonable. The fact that both basses/roots (
A) support triads help justify the claim that the bass tones are the roots. Those base triads then give the modal sense of major and minor respectively for the two chords.
But music doesn't work by just presenting a single chord.
Let's see how the identity of these two chords can be changed when placed into musical context with other chords.
If we precede either of the chords in question with an
E dominant-seventh chord we get...
In both settings the second chord is heard as
Am7 because it is preceded by the dominant-seventh chord of
Am. Even in the second example where the
Am7/C looks like
C6 the harmonic context (preceding the chord with its dominant) makes the chord clearly an inverted
We can re-interpret that
Am7/C as a
C6 by preceding it with
C6's dominant-seventh chord...
This underscores the importance of how harmonic context - especially nearby dominant-seventh chords - is determining chord identities and functions in tonal music.
In the examples above I opted for jazz symbol analysis, because resolving to a tonic chord with an added
7 is a jazz thing not found in common practice classical style.
We can end with one example from classical style which shows a very common use of the chord in question. In classical style the chord is normally regarded as a minor-seventh chord. But unlike jazz this minor-seventh chord would not be a tonic. Technically it is called a sueprtonic chord and using the Roman numerals of classical analysis it gets labelled
...this progression would be
ii6/5 V4/2 I6.
...the more interesting [question] is why they have different qualit[ies]...despite consisting of the same notes: A - C - E - G
I gave lots of examples to show the quality and perception of the chord really depends on the surrounding harmonic context.
Chords are built up from their root - the clue's in the name. Thus C6 nominally has a C as its starting note, Am7 has an A. Of course, with 4 notes, there will be 4 different closed versions to play, and humans have a tendency to hear the highest and lowest notes more easily when there are several played. In root position, C6 has C at the bottom, and this somehow makes it sound as a major, having a C-E major 3rd, whereas Am7 in root will have A underneath, making it sound more like a minor chord, having A-C.
With an E or a G at the bottom, we perceive it as not so definitive, and this is maybe where the distinctive line gets blurred. For some, that blend of notes can only be C6; others, Am7, but as I said earlier, the root note determines the chord, as a rule.
Yes, I know that C6 has a min3 interval, and Am7 has a maj3. Never really got my head around that phenomenon.Could someone enlighten me, please ?
Mahler's Das Lied ends with a C6 and not an Am7. The gesture is very distinct; the A sounds like a sort of lazy longing, smothered by time and age. It becomes clear that the C6 plays on C-G-D-A, quintal harmony, at least implicitly. When built off the tonic, those four notes themselves sound very homely; changing the D to an E is just another step to the C tonic.
Note also that a C major is much stronger than an Am, as the Major 3rd interval distinctly belongs to C major except when in the root inversion of the Am7. As others have said, anywhere else, the C-E interval sounds major. The bass note also holds significant influence on the chord quality, so of course Am7 sounds minor and C6 sounds major.
As a thought experiment, consider the chord Am9/C, where C is in the bass alone, and G is omitted so the top three notes are A-E-B ascending. The presence of the B can't quite shatter the Am quality, though it comes close in reference to C7. But if the G was voiced, the C triad would isntantly become obvious.