Depending upon where you come from (classical or otherwise) a 6th chord may need some explaining.
If you study music theory in school you'll undoubtedly start with the so-called Common Practice period (roughly the time period from Bach to Brahms). And in this case a 6 chord means a triad in first inversion. It's actually short for 63: i.e. above the note in question a third and a sixth should be added (this comes from the basso continuo practice in Baroque music). So an E with a 6 under it could be read as follows:
The 'could' meaning that how the triad is voiced, the texture, etc is up to the performer. We'll do a post that more fully addresses basso continuo at some point. For now keep in mind that it's diatonic: an F in the key of C (no sharps or flats in the key signature) would produce a D minor triad in first inversion. To depart from diatonic triads symbols were used underneath...
And now in Roman numeral analysis you'll see something like I6, again meaning a triad whose root is built on the 1st scale degree and is in first inversion.
(BTW a triad in second inversion is notated as a 64 -- pronounced six-four -- chord, e.g. in the common progression
I64 - V - I
that is a note with a 4th and 6th above...write it out and you'll see.)
But if you read a chart that contains the symbol C6 it does not mean a first inversion chord. It means that a triad with an added major 6th should be played -- in fact in classical music this is called an added-6th chord:
The only issue that arises (and used to drive me crazy until I realized the convention) is when a minor triad is involved. Cmin6 indicates that a C minor triad is to be played along with the addition of a major 6th. For some reason I had always assumed that the 6th would be minor, too. IT ISN'T! So Cmin6 can be seen as:
One interesting thing about these kinds of sixth chords: context is everything! A C6 contains the same notes as an Amin7. Cmin6 is the same collection of notes as an Amin7b5. (To some extent this subject was broached in the post concerning the open guitar string chord.) So it might be easier for you to play a min7 than a 6...the resulting chord will be the same.
Oh, I should mention that, concerning inversions, the notation on a chart would fall into the category of 'slash chords'. For example C/E (pronounced 'c' over 'e') means a C major triad with an E in the bass (the very same as the first example in this post). Also worth nothing is that while all inversions can be expressed as slash chords not all slash chords represent inversions...more to come on that later on.
OK some future posts based on this subject will include more fully tackling basso continuo realization, Roman numeral analysis and other sixth chords found in classical music: augmented sixths (Italian, French, German) and the Neapolitan sixth, oh and more on slash chords.
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