Chords are built starting with 1, 3, and 5 - the notes of a triad.
Historically, the next extension was to add the 7th. Then 9, 11 and 13, after which you've used all the notes in a 7-note major or minor scale.
Extending the uneven numbers up like that is just a way of being logically orderly in how you construct, or arrive at, a particular formation.
How you *voice* a chord is another matter. You can put the 9th in a lower octave where it may form the interval of a second with the root, for instance. That's sort of what the guitar teacher was getting at, but he didn't understand (or chose to ignore) the distinction between construction and voicing.
Now if you just add a 2nd to a chord (as opposed to a 9th), the distinction is that it feels like an added tone that may set up tension because it's dissonant with the root and the third, and may required resolution to a consonant note to relieve the tension.But if it's part of a 9th chord, even though it's technically dissonant, it's supported by the 7th (which is also technically dissonant) but now it feels like an integrated part of the chord. It may resolve to something consonant when you change to the following chord, but while that chord is playing, it's a full member of the family.
The existence of something like an 11th chord presupposes that you got there by the ladder of thirds and that the same chord has a 7th and a 9th. But in practice, players may omit the "ladder" steps so that you have a chord that may have, for instance, C, E G, D F# A - a #11/13 chord (F# being the #11) even though what it sounds like is a D Major triad plonked on top of a C major triad.
Then you get added color notes as with the so-called major 6th chord such as C E G A. In music school I had theory teachers who insisted that there was no such thing as a C major 6th chord and that it was just an inversion of an A minor 7th chord (A C E G). But the practical fact is that it functions like a C chord with an added 6th. You can give it a structural rationale (f you feel you need one) by saying that its origin is in building up in thirds from an A root, and then inverting it.
Winslow Winslow Yerxa Author, Harmonica For Dummies ISBN 978-0-470-33729-5 Harmonica instructor, The Jazzschool for Music Study and Performance Resident expert, bluesharmonica.com Columnist, harmonicasessions.com
________________________________ From: Elizabeth Hess <TrackHarpL@xxxxxxxxxxxx> To: Harp-L <Harp-L@xxxxxxxxxx> Sent: Fri, December 3, 2010 10:12:20 AM Subject: [Harp-L] Numbers Game
Why are they called 9th chords and 11th chords and not 2nd chords and 4th chords? Is the difference between a Maj6 chord and a 13th chord that in the 13th chord the 7th, 9th, and 11th are in there, too? Or is the difference the octave in which the note-in-question (6th/13th) is played?
A major 6th chord and a minor 7th chord seem to have an awful lot in common: Am7 vs C6, for example. Is one not an inversion of the other? Is there any value in thinking of these as "enharmonic chords"? Is the decision of what to write on the chord sheet dependent on context? Something else?
When can you play a chord in any inversion that's convenient, and when is the inversion played (or written) significant?
These are not burning questions... Just stuff that's rattling around in my brain that won't go away.
Thanks in advance.
Elizabeth (aka "Tin Lizzie")