A Musical Structure
 

We will consider a structure for a collection of chords that will provide a tool for writing abstract music as patterns of notes with few tonal features.

Conditions for a Musical Structure of chords
Here are two examples:
Notice that each structure has 7 chords and 7 notes!
C E G     G B C
B D G G D F
A F G G A E
A D E C E D
B F E D A B
A B C C A F
D F C B F E
Here's how we might use this structure to write a sequence of notes:

Start with two notes: Say DF, so use the first structure to find the third note, namely C. Now choose a note not already used, for example G, so we can determine a fifth note from the chart as the third note in the chord, CGE. to continue, choose a not yet used, for example B, and the 7th note is determined to complete the chord, EBF.

The sequence is now DFCGEBF. Now use the letter A (that has not yet been used) and we look for the chord with F and A to find the next note: G.

The sequence is now DFCGEBFAG. Continuing ,we can choose the next letters when needed from the letters that are used as little as possible and then use the chord structure to determine the next note.

Interesting.... but the question we have is:
Are there any chord stuctures that have more or less than 7 chords made from 7 notes?
That is, is there some special relation between these chord structures and the number 7?