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I know in both major (Ionian) and minor (Aeolian) the 1 4 5 chords are the primary chords. as they seem to come up more often than other chords. https://en.wikipedia.org/wiki/Primary_triad

In Aeolian (natural minor) the v is usually turned into a V in order to make it resolve better to the I.

But I'm wondering if this is the case in other modes too like Dorian, Phrygian, Lydian, Mixolydian, Locrian. Are the 1,4,5 considered the primary chords (most used chords) as well in those modes?

note: I am saying 1,4,5 in order to not have to capitalize and lowercase roman numerals.

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Of course I-IV-V are the primary chords for the major/minor system.

You could permute those chords for the modes like i-iv-v in Aeolian.

But some of those permutations will hit the diminished triad like Phrygian i-iv-v°. That isn't a problem necessarily, but it might not provide "most used" progressions.

You might consider the bVII - the sub-tonic triad as a kind of primary modal chord. It would be pretty common in Dorian, Aoelian, and Mixolydian as bVII-i.

I would also think it reasonable to call relative major/minor pairs as a kind of primary modal harmony - like i-III in Dorian and Aeolian.

Personally, I like the sound of i-bII in Phrygian and certainly the flat second degree is very characteristic of Phrygian. That might be a kind of primary progression.

These comments aren't "rules" or supported by statistical studies. Just some observations about what seems like "most used" from my experience.

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In Ionian, the primary triads are [I], [IV], and [V] - just like you've mentioned.

In Dorian, the ^6 degree brings out the Dorian flavor so the [IV] clearly stands out, and I've gone through [i]-[IV]-[VII]-[i] chord progressions in the mode quite often - so in Dorian, I would say the primary triads are [i], [IV], and [VII].

In Phrygian, notice the minor [iv] chord exists. The [II] is usually "substituted" for [vo], and as I read JdJazz's answer on Harmony in Phrygian : What chords are tonic, subdominant, and dominant?, I'd go with [i], [iv], and [II].

In Lydian, I could think of [I]-[II]-[V]-[I] progressions very strongly, so in this view, it would be [I], [II], and [V].

In Mixolydian, we have a major [IV] chord, and because of the minor [v], the [VII] chord is often "substituted" as a dominant, resulting in [I], [IV], and [VII].

In Aeolian, as Michael Curtis had mentioned, we can permute the [1], [4], and [5] chords here. So it's obviously [i], [iv], and [v].

In Locrian, User16935 had mentioned about truncating the tonic chord to just root and third on Locrian Harmony. Due to the flattened [V] chord, I would say the [iii] acts often like a dominant "substitute", and we also got a minor [iv] chord - So I'd go with [i(no5)], [iv], and [iii].

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In major keys (Ionian modes) the presence of a leading note a semitone away from the root is probably the most noted part. It produces a resolution that is acceptable to the listener, found mostly in the perfect cadence. It's so convincing, that in Aeolian mode, where it's missing, often a note is altered in the V chord to provide that leading note.

The only other mode which contains that scenario is the Lydian. In F Lydian, for example, it's the E>F. So in Lydian, there is that same cadence capability.

Dorian, Phrygian, Mixolydian have a whole tone between 7th note and root - not so convincing, but that's actually one of the factors that makes those modes sound as they do. Dorian and Mixolydian can use 1,4 and 7 as well as 1,4 and 5.

Locrian - not going there..!

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I, IV and V belong to the world of functional harmony. The world of pre-dominants, dominants and tonics. The world of harmony built around the tritone - the fourth and seventh note of the major scale which provide most of the tension in a dominant 7th chord. We can graft this sort of thinking onto modal music. Most of the modes we use still have a dominant note, a perfect 5th above the tonic. We can have a V - I bass line, even if the chords above it lack the other features of a tonal dominant chord. Or we can reach home another way.

Also, see the final part of my answer to the 'When we play the C Mixolydian mode...' question. In real music, everything mixes up! As I've said before, 'theory' may help you describe what people do, but it's not going to give you a set of permissions as to what YOU may do!

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In Dorian mode (D dorian is D E F G A B C), the 5 chord appears as ACE, not AC#E, which one might expect. In E Phrygian (E F G A B C D), the 5 chord would be BDF (B diminished), not even Bm and certainly not B Major.

In other words, the normal final cadence 5 > 1 doesn't appear very much in strictly modal music. In Dorian, the final cadence is normally 7 > 1 (e.g. C Dm), whereas Phrygian tends to have 2 > 1 (e.g. F Em) or 7 > 1 (Dm Em).

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