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These chords occur naturally in the key of C major.
John
Seems kind of dumb to try and cram basic chord function, diatonic triads, 6(13), and 7 chords all into one lesson.
What I would have avoid personally is writing the Dmin6 and the G6 on the chart because in functional harmony these are not really useful.
may be my previous post was a bit too much advanced.
This is the simple, but important take away (until you can press your professor for what he was trying to teach you, lol).
No, those are indeed Dm6 and G6.
Labeling with the "13" presumes that there is a minor seventh in the chord.
Dm6 = D, F, A, B
Dm13 = D, F, A, C, (E), (G), B. The E and G may or may not be in the chord, but there must be a C (minor seventh).
Same with G6 v. G13.
You haven't read or didn't understand my post. These 2 chords don't have a harmonic function in a key. So these two degrees need a 7 to function, not a 6, even if mathematically you can do it.
Please help with this! Trying to learn theory and I'm told by my professor to understand and memorize this chart, but what does it mean??
I am still having trouble understanding, would someone post a link to an Internet lesson/explanation on the subject?
I read your post. I understand 'functional harmony'.
A G6 has no minor seventh interval above the root and is therefor NOT a G13 chord.
Looking at the Professor's worksheet, he's not interested in functional harmony - the chords are labeled CM7, G6, Bø7, etc.
If the Professor was interested in 'functional harmony', he'd be using I7, iim7, V7, etc for chord labels.
First by using 1st,2nd... I'm pretty sure he/she is talking about degrees which is written also on the chart and yes roman numbers should have been used.
About Dmin6 and G6 been wrong imo on the chart here is my explanation:
You can use a x6 or xmin6 chord when you don't have a minor seventh in your stack. In the case of the minor chords built on the major scale ,all of them have a minor 7, so no minor 6th chords can be built from the major scale.
The other reason to prove my point is that the x6 chord is used to avoid the cluster interval in the first inversion when you have a major seventh as the fourth tone and you substitute the major 7th by the 6th. Your example of the end of the Beatles song a good example of the I6 been used to enhance the triad chord into a fourth-part chord without problem. In the case of Dmin6 and G6 you don't have this problem because you have actually acces to the minor 7th interval in the stack that make you use the first inversion without problem in the upper register by having a whole-tone interval instead of the half-tone.
Also by harmonic function and probably melodic function there is little chance that you'll have a C# played over the Dmin and a F# played over the G6 in the key of C. These 2 chords have there own minor 7th in the stack and no 6th should be played without the 7 which make them a 13th instead.
I hope you understand the differences and my point of view ;-)