: How does harmonic analysis work in different modes? I noticed that normal harmonic analysis doesn't seem to work when playing in different modes. For example what is the dominant and sub-dominant chord in the Dorian mode?

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"Dominant", "Subdominant"... are really terms from functional harmony, the kind where keys are major or minor, dominant 7ths resolve to tonics etc.

You could consider D Dorian as C major, with the supertonic being emphasised as "home". But that wouldn't be particularly useful. Neither would considering Am the "dominant" chord of D Dorian, but without the C# that gives it a dominant function.

Let "Dominant", "Subdominant"... go. They're not much use to you in modal music.

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The term dominant simply means "fifth." Thus the dominant is always the fifth above tonic and the subdominant is always the fifth below tonic. (Subdominant does not mean "the one below dominant," which is a common misunderstanding.)

So in the Dorian mode, the subdominant will still be built on the fourth scale degree, and in this case it will be a major IV. The dominant will still be built on the fifth scale degree, but in Dorian it will be a minor chord (v) instead of a major chord.

Indeed, this is one of the aspects that makes music written in modes interesting. The very fact that these chords are "different" from normal major and minor is what gives the modes their flavor; enjoy it!

Edit: I should say that, in modal music, sometimes there are chords that will stand in for the dominant; perhaps this is what you mean? In modal music, the major triad built on the lowered seventh scale degree is often given a type of dominant function. In D Dorian, for instance, this chord would be C Major (VII).

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What Richard said there could be challenged by conceptualizing dominant as function, not a scale degree. Dominant chord V7 has a tritone that largely defines the tonality in major scale at least in contemporary harmony. Tonal harmony functions mostly inside major scale, and dominant functions in such way that it has a tritone that resolves upwards through leading tone to tonic chord's root and down to third.

Tonal harmony in major scale can be applied to other modes though, but it's handwork, as it is with many complex pieces anyway. In this view, dominant is NOT simply a V degree of the scale, it has a function and thus in modal music you can't apply the same analysis to all modes that you apply when you analyze music in any major basing it just on the scale degrees. Any dominant seventh chord can function as dominant chord when it resolves to its tonic, and tonal center is defined by various tensions, leading tones and resolutions pointing towards somewhere, until you "hit home".

F.ex. D dorian is a minor mode with Am7 as v7 chord. It's a minor dominant seventh chord, and weaker resolution to Dm because it doesn't lead to tonic but iii. If you borrow a chord from D mixolydian and make it A7, you get stronger resolution through the III of V leading tone, but not through dominant seventh, because MVII of V points towards a major chord's III. Full cadence resolves to major through leading tone of the scale and then you get cadentic tonicization to tonal center, depending on how you voice it and what you use before and after it. So it's handwork, you have the tools for functional analysis and you're supposed to use them in such way that your reasoning stay sound.

If then you don't mean tonal harmony and it's functions, you really need to be more specific.