Can you construct chords for all musical modes?
One way I'm aware of to find the chords in a given key are to generate triads 1,3,5 for each note in the major scale. E.g. In C major you get CEG (C), DFA (Dm), etc leading to the typical I ii iii IV V vi dim7 chords.
Applying the same to a minor scale E.g. Am, it works too.
Since major and minor are just two musical modes I wondered if this is a general principle and would apply to all 7 modes as a way to generate sets of chords?
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It's definitely done, if not altogether common.
For example, there are plenty of tunes in Dorian that do just this, with the obvious highlight being the minor tonic with major subdominant. In Mixolydian, you have that great major fVII. In Lydian, it's the major supertonic chord that makes it clear.
This principle applies to all modes, it's just most common in Ionian and Aeolian, least common in something like Phrygian and Locrian.
Edit: Note that occasional chromatic pitches will alter these; you might for instance here a major dominant in Dorian. If this seems strange, realize that it's no different than having a major dominant in minor!
Since the modes are derivatives of standard scales ( or possibly the other way round), then yes. Take the chords produced from C major. C, Dm, Em, F, G, Am, Bo. All based on 'stacked thirds' - not exactly true, but for our purposes...Of course, another 'stacked third can be, and is often put on top, and maybe this is where your dilemma starts, as each third can be maj or min, BUT without care, the chord notes go out of diatonia.
The same notes appear, in the same order, in D Dorian, E Phrigian, F Lydian, G Mixolydian, et al. So, keeping the 'stacked thirds' idea, in D Dorian, the same chords appear. They have to. It's just that now, as in any Dorian melody, the home is based on the root, in this case, D. So the home chord has to be Dm. In G Mixolydian, obviously G maj appears, and quite often in G Mix. tunes, F maj also appears.
The minors present a slightly different arrangement, with the possibility of raised 6th and 7th notes, or not as the minor case may be. However, all chords used in minor modes will be made in the same way - 'stacked thirds'. So there are more options of slightly different chords in the modes of minor keys. Simple example, in A Aeolian, there are two E chord - E min and E maj.
You can generate all 7 modes from each other. I mean they are using same pattern with different starts.
For example intervals in Ionian pattern is like this:
I (W) II (W) III (H) IV (W) V (W) VI (W) VII (H) VIII
(W means 1 step and H means half step(semitone))
We can build chords on Ionian degrees :
Major - minor - minor - Major - Major - minor - dim
So if we have C Ionian as our mode , we have these chords :
C - Dm - Em - F - G - Am - Bdim
If you start from second degree in Ionian and keep the pattern(keep intervals) you will have Dorian.
II (W) III (H) IV (W) V (W) VI (W) VII (H) VIII (W) I
So you just changed the order of degrees. Chords are the same and just order of them is changed.
Dm - Em - F - G - Am - Bdim - C
Of course that is not the only difference between modes. It's a simple example for your question. We know modes are very different from each other , from which chord should be used in one mode and which are important chords in each mode and etc.
This question can be very deep.
The Western music started to be dominated by third-superposition chords (like C4-E4-G4).
This is because the 1:5 ratio (2 octaves plus 1 third) has been accepted and treasured, and the pleasant sound gained popularity.
But other culture need not. For example, ancient Chinese culture has a different scale, which I do not admire much.
The present day "Chinese music" often apply ancient tunes, but Western chords, which seems very odd to me.
In 20th century, composers started to seek non-third-superposition chords, and finding rules of their own.
So, no, there is no all-encompassing rule to cover all chords. Except, of course, if you list them by mathematical combination; there will have been a lot, but certainly be finite.
But what is the use? A chord is not only a set of frequencies, but including a living usage and context.
You may liken this situation to all possible syllables English phonology supports. A quick guess convinces me that's way more than 1 billion.
But this is trivial, since a dictionary is not merely a list of such words.
It is a list and explanation of all actually-used words, and how they are used.
The compilation of a dictionary can hardly be automated by machine even by now, since it involves human culture.
The usage of chords is also a always-changing culture, and a complete list tells little.
(Not entirely a good simile, but you get my point.)
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