Quick explanation of the Dorian mode: if one plays all the white keys beginning on C, one plays the notes C-D-E-F-G-A-B-C: the C major scale, otherwise known as the Ionian mode. If one plays the same notes but beginning on D, the notes are D-E-F-G-A-B-C-D: still the same notes, but the intervals are different. The C major scale has a major third (C-E, four semitones) whereas the scale beginning on D has a minor third (D-F, three semitones). But this is not the D minor scale: in D minor, the subdominant chord (formed from the fourth note in the scale, the sixth and the eighth) is G minor (G-Bb-D). This scale has a subdominant chord G major (G-B-D); this 'sharpened sixth' causes the scale built on the white notes starting on D to be called the Dorian mode.
David plays tunes in the Dorian mode and points out that the typical chord change in Dorian is i-IV, for example Dm to G. Of course, the Dorian mode doesn't have to start on D; it can start on any note, but what is important is the intervals between the notes. If one starts on E, then the notes are E-F#-G-A-B-C# (sharpened sixth)-D-E, etc.
David asked for songs that use the Dorian mode, and I pointed out that 'The Banks of the Nile' by Fotheringay is in E Dorian (whenever a C is sung, it is C#). I was thinking about this the other day when walking the dog and thought that maybe I can break my temporary drought by using the chords of 'Banks' in order to write a new song, using primarily the chords Em, D, A and Bm. I sat at the piano and quickly came a tune based on these chords. The actual sequence is Em-D-A-Bm (twice) A-Bm-Em-D A-Bm-Em-G-F#-Bm: the notes of all these chords are contained within the E Dorian scale (except for the A# in the F# chord; Dorian would have an A chord instead) and so this song - unusually for me - is perfectly scalar, albeit in a mode.
The instrumental/bridge part in the middle is of a different species, what could be called a cycle of fourths: Bb-F-C-G, repeated several times. The move from Bm to Bb might look odd on paper but it sounds correct (I actually heard it in my head before I started playing it). I thought that going back to E Dorian from G would be easy, but because I extended the instrumental with several bars of Bb, I had to transition back via C.
After I finished sequencing (including playing a brief solo on my new mini-keyboard) and having the traditional post-prandial snooze, I took the dog for a walk. Naturally my thoughts turned to this new song (no lyrics yet and I have no idea what they will be about when they get written); it suddenly occurred to be that it might be more accurate to say that this song is written in plain B minor. The notes are exactly the same but start at a different place: B-C#-D-E-F#-G-A-B. So is the song in E Dorian or B minor?
The answer to this (somewhat pointless) question depends on which note sounds like the base note (or tonic, to use the musical name). Is it E or B? Whilst the song might start on an E minor chord, it ends on B minor, and in fact the only place where a perfect cadence (a dominant chord followed by its tonic) appears is at the end: F# > Bm. So however much I might have though that this song is in E Dorian, I have to conclude that it's in B minor. Does this make any difference? Not really.
[Edit from a month later] In order to confuse things even more, I decided to replace the F# chord towards the end of the verse with an A, definitely making the song Dorian. This required a slight change in the tune that actually made it easier to sing. Just to be contrary, I didn't replace the perfect cadence in the final verse.
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