Sorting Scales and Chords by Similarity

I tried a number of different sorts to find to the sales and chords which are similar to each other. Similarity is a vague term, so a number of options are available.

Groups can be similar because  of one note being added. For example, The 7 chord (R,3,5,7) is similar to the ninth chord (R,3,5,7,9 or R,2,3,5,7).
I refer to this type of similarity as Pedigree, since the 9 chord can be seen as a parent of the 7 chord.

Chart of all possible Parent/Child combinations

More exploration of Pedigree

Groups can be similar because they differ by one note. For example, the Major scale (R,2,3,4,5,6,7) is similar to Mixolydian (R,2,3,4,5,6,b7).

Chart of all possible scales/chords with one note different by one half step

Scales can differ by more than one note. A complete chart would be impractical, but here are charts for major and minor showing differences of more than one note.

Seven-note scale similarity to major

Seven-note scale similarity to minor

Between combinations the possibilities, constructing a chart with all possible similarities is impractical. Instead, I have composed a number of sorts of the All Possible Scales/Chords charts to group similar items together. Since scales and chords match each other (a Major pentatonic scale has the same notes as a 69 chord, R,2,3,5,6), creating two sets is not necessary.

Sorting by mathematical similarity is not difficult. The best results come after converting the scale degrees into binary (known as Rahn prime) and then sorting.

Sort by mathematical prime

Sort by mathematical prime and then grouped by number of notes

These give a good sort of groups that are similar to each other.

I made a number of attempts to sort using more musical properties, either stressing the importance of pedigree or more common musical intervals. None is the magic bullet I was searching for, but these four seem to be best.

Other sorts found different similarities, so I included them in the table below. The links toward the left of the table are tweaked to make sense musically, and the ones toward the right are most mathematically pure.