Reading a Parallel Mode Table Vertically

When writing a primer on learning and understanding modes (using Roy G. Biv), I discovered some interesting curiosities about modes that I had never seen or read about. I wanted to share them, but that article was getting pretty long, and these things aren't particularly useful or practical, just interesting, so I made two separate pages to share them, this one, and this one on modes, the order of sharps and flats, and the "circles" of fourths and fifths.

This article can also be read in conjunction with Modes Quiz / Flashcards and Mode Calculator and Mode Chart.

Below is a table listing all the modes of the major scale in a parallel fashion (all begining with C). The top row features the notes of the mode in C and the bottom row shows the scale degrees and their alterations from their parallel major. It starts with ionian and follows the order of the modes in relation to the order in which they appear in a major scale (i.e. 1,2,3,4,5,6,7). This is perhaps the most common method of showing the modes.

C ionian	C 1	D 2	E 3	F 4	G 5	A 6	B 7
C dorian	C 1	D 2	Eb b3	F 4	G 5	A 6	Bb b7
C phrygian	C 1	Db b2	Eb b3	F 4	G 5	Ab b6	Bb b7
C lydian	C 1	D 2	E 3	F# #4	G 5	A 6	B 7
C mixolydian	C 1	D 2	E 3	F 4	G 5	A 6	Bb b7
C aeolian	C 1	D 2	Eb b3	F 4	G 5	Ab b6	Bb b7
C locrian	C 1	Db b2	Eb b3	F 4	Gb b5	Ab b6	Bb b7

This is a common visualization of the modes, and it's obviously meant to be read horizontally. But, when I was writing that article I thought "there must be some sort of vertical pattern, right?" and after a few seconds I had a Eurkea moment (I was even in a bathtub at the time...).

Here's What I "Discovered"

Reading vertically, the first column is "C C C C C C C," nothing interesting (except for the 7 C/Sea's thing, but that's not what I'm here to write about). The second column is "D D Db D D D Db" -- nothing interesting there either... or is there? I nearly jumped out of the bath when I looked over the second column again and realized that the Dbs occured in the same spots as they should for a dorian scale -- on the 7th and 3rd! Look at that column again and mentally replace all the "D"s (keep the flats) with scale degrees. You end up with "1 2 b3 4 5 6 b7." Whoa, dorian! Try the same for the next column and you get "1 b2 b3 4 5 b6 b7," phrygian! That seemed pretty exciting in the moment, especially because this little phenomenon holds true for each column, and in the "correct" order: ionian at column 1, dorian at column 2, phrygian at column 3, lydian, at column 4, and so on.

Here's the table again but with a header-row and just (horizontal) scale degrees.

Parallel Modes	Ionian	Dorian	Phrygian	Lydian	Mixolydian	Aeolian	Locrian
Ionion	1	2	3	4	5	6	7
Dorian	1	2	b3	4	5	6	b7
Phrygian	1	b2	b3	4	5	b6	b7
Lydian	1	2	3	#4	5	6	7
Mixolydian	1	2	3	4	5	6	b7
Aeolian	1	2	b3	4	5	b6	b7
Locrian	1	b2	b3	4	b5	b6	b7