#2 Two tetrachords? I think not.

Why do we think of 7 note scales as 2 tetrachords? There are only 7 notes, so why would we think of the scale as piling 2 tetrachords (4+4=8) and include the top octave?
Let's see what happens if we think of it as 123,4567 - in other words, a trichord, then a tetrachord. Let's use the 7 modes of major (in intervallic order of "widest" to "most compressed"):

Lydian - major 1 2 3. 4567 belong to a phygian tetrachord
Major - major 1 2 3. 4567 belong to a lydian tetrachord
Mixolydian - major 1 2 3. 4567 belong to a major tetrachord
Dorian - minor 1 2 3. 4567 belong to a major tetrachord
Minor - minor 1 2 3. 4567 belong to a minor tetrachord
Phrygian - phrygian 1 2 3. 4567 belong to a minor tetrachord
Locrian - phrygian 1 2 3. 4567 belong to a phrygian tetrachord

What's interesting to note is "modes within modes," such as the lydian tetrachord in major, and the fact that Lydian and Locrian both have phrygian tetrachords, though they start on different notes.

This particular way of thinking seems to undermine the fact that major, dorian, and phrygian have dual tetrachord symmetry, which is pretty cool.

I think what this all comes down to is "tetrachordal" thinking...if you have 4 scalar notes in a row, it's some sort of tetrachord. I guess you can hack a scale into whatever bits you like, to expose particular mode pieces within a scale.