What do those scales have in common?

So we've got 84 different 8-note scales. For any given scale, though, what does it have in common with the rest of the pack?

• common roots: It shares its root with 6 other scales. That is, there are 12 sets of 7 scales that have the same root, but different interval patterns and different notes
  
• common intervals: It shares its "mode" with 11 other scales. That is, there are 7 sets of 12 scales that each have the same interval pattern, but different roots and different notes
  
• common notes: This is a fun one. For each scale, there are 6 others that each use a different interval pattern and start with a different root, but they share the same 8 notes

So what does that mean? It's all about convenience and character. Each mode / interval pattern provides its own unique character to a song. Interval patterns are also what you actually play on your instrument - start at the 6th string first fret, then up 2 frets, then over 1 string and up 2 frets, etc. Often certain interval patterns are more convenient to play than others in a particular situation. Finally, the choice of root can impact how easy a song is to sing, or dictate a certain interval pattern that's easier or harder than others for a given song. For example, a guitar player might be able to clip on a capo to automatically change keys, while a piano player may have to learn entirely new fingerings.

Knowing the above relationships lets you switch scales easily when it's more convenient to do so, or to obtain a different character from the same song. That last category though, scales with common notes, is particularly interesting because it can let you change interval patterns, if that's convenient, without changing either the key or the character of the song.