Why is the submediant chord in a D Dorian mode a Bm7b5? I thought a Dorian mode has only flatted 3 and 7 compared with a major scale. I am trying to learn about harmonizing church modes and need to learn how to harmonize the other church modes. Are there any rules I did not read? Pretty confused.
I find it easier to relate back to what I call the 'parent scale or key' with modes. So here, we have D Dorian mode, translating back to parent key C major.
That gives this mode all the 'white keys' on a piano - naturals - no # or b. Thus the 4 notes using B as a bass/base are B, D, F, A. This is Bm7b5.
The confusion comes, I think, from the fact that Dorian does have a b3 and b7 in comparison to the major scale notes, but that's a red herring. This chord is based on B, not D, and if it's built up in thirds, there is a minor third (B-D), then another m3 (D-F). Putting two m3s together produces a b5 (B-F). The 7th part is going to be B-A.
Harmonising any mode is so much clearer when it's taken back to parent key. Because the harmonies produced there have probably been met many times previously. Why re-learn something we already know?
The notes in D Dorian are D E F G A B C. If you build a 'pile of 3rds' on the 6th note in that list, you get B D F A. Which can be called Bm7b5.
Now, be sure to keep your head in modal mode, lest you're tempted to follow it with E7, Am7, D7, G7, C :-)
Perhaps I've misunderstood the question, because it seems a little bit obvious to me. The fifth tone of the submediant is the third tone of the tonic, and you've already pointed out that the third tone of the tonic is flatted. So, yes, the fifth tone of the submediant would also be flatted because it's the same note!
Please tell me what I've misunderstood in your question so I can give a better answer!
This might not be the most scientific answer, but to make this easier, when I get confused with modes, I try to think in terms of scales. D Dorian would be the ii in the C major scale. The B chord in this scale is Bm7b5 (B D F A).
Or else, I would see the notes that are in the D Dorian scale: D E F G A B C. To form a chord on B using these notes, you'd get the Bm7b5.
Also, you seem a bit confused about the Dorian scale. You mentioned
a Dorian scale is only flatted 3 and 7. This is true. Just start from D: D, E, F(b3), G, A, B, C(b7), D. Νοw again, if you use these notes to build a chord on B, you'll get the Bm7b5 chord. Τhe flatted 3rd and 7th apply only in relation with the root (in this case D); they don't apply to each note of the scale.