Music Theory can be made into a complex subject as this post well shows. In my experiences (undergrad in Guitar Performace and Masters in Music Theory) there has never been a better example of people letting theory get in the way of understanding in music.
In effort to keep this short I will only choose a few quotes to address.
Equator
Neopolitan minor Formula...[1-b2-b3-4-5-b6-b7]
This is not correct. The formula is [1-b2-b3-4-5-b6-7]. Otherwise you would call it E phrygian.
Jolly....
Please consult me before you post in the theory forum. It would be best for your reputation in this section if you didn't say things like that.
I would rather not preserve my reputation if it means limiting my personal views on "music theory." It must be pointed out that we are discussing "theory" of sound and not physics. I have studied and read enough to know that in essence C major and A minor are the same collective and I have taught enough at the University level to say that to many guitarist can not work with their connection.
Yes if you want to be a picky bastard, they do have different sequence of intervals. The largest part of their sound is due to the harmony they are played with.
For example....
"If I were composing in Cmajor, and I decided to write the melody A-B-C-D-E" and end it like that, you would notice something funny about my composition, probably that it sounded like it was in A minor. No, you don't always start on the first note of the scale, but that IS your root note.
The character of your melody will be determined by what chords you choose to accompany it. If you play those notes while I play Cmaj7 G7 Cmaj7 then the enitre character changes. No longer does it sound like an A minor melody.
*The guitar Grimoire-Scales & Modes.(page 12)
This is quite possiblly the worst guitar information book ever printed. It is ripe with errors and contains tons of misleading information. The last time I looked in one was at a store with several other professionals. We used the book as the butt of a few jokes. That is how many errors it contains.
Let me repeat, that the link shows a G6, but there you can see, the chord structure of the Major 6 chord. which is, again: (1,3,5,6)
Now if He wanted to make an accurate comparison, he shoulded say.
The C6 no fifth, or like some people say a C6 shell chord.
There are lots of ways to play a chord with the 6th in it.
Let's not limit the situation. Everyone knows that the 5th of a chord can be omitted without theoritical consequence. That dates back to the 1500's or 1600's.
The chords I refer to (in open position) look like this.
E:0
B:1
G:2
D:2
A:3
E:X
Now.... is this C6 or Amin/C?
If you want to complain about it not being a real C6 due to it's lack of 5th....
E:3
B:1
G:2
D:2
A:3
E:X
C or Amin7/C ?
So, it is not correct to compare the two chords. C6=...............(C,E,G,A)
Am/C=...........(A.C,E,)/C
You have totally missed the point. Quit thinking of it on paper and play above chords on a guitar.