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I am very new to even the basic concepts of music theory so there might be something inherently wrong in my question but here it is,

There are some common chords progressions which are denoted by the Roman numerals , for e.g. I IV V , which for C Major scale is C Major,F Major and V Major

What I understand from this notation is that for a particular scale, a chord progression whose root notes are based on the 1st , 4th and 5th notes of the scale would sound good together. But my question is that it could be a minor or a major scale depending on the intervals between the root note, the 3rd note from the root and the 5th note from the root, but it seems to me that it is presumed that the chords would be major always. Why is it so?

The chords would be major in the case of a major scale because there the interval difference is in that manner. But they could easily be a minor chords or mix of both for a particular scale. Another pattern that points this out is the I–V–vi–IV pattern in which it is implied (as far as I understand ) that the chord based on the 6th note of the scale would be a minor one. But this can't be said universally for all scales , the intervals won't always in this manner. Is there smoother meaning to using upper and lower case numerals ?

Thanks

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The chord types do change and there is an important distinction to make between modes and minor keys.

As you already said, in a major scale our primary chords will be:

I IV V

And if we switch the mode we get different qualities for those primary chord:

Mixolydian: I IV v note the lower case minor 'v.'

`Dorian: i IV v'

...and so on for other modes.

However, watch out for equating the Aeolian mode and minor keys.

Let's use A minor as an example. In terms of mode that will be the Aeolian mode. In terms of scales the basic minor scale will be the natural minor scale.

If we list our Roman numerals for the Aeolian mode/natural minor scale we get:

i iv v note that everything is lower case, all chords are minor triads.

The critical part to understand is that for minor key music alterations are made to the scale and chords. The essential part is that the chord of the fifth degree will get altered from minor 'v' to major 'V' (the ^7 scale degree - the third of the chord - will get raised from G natural to G sharp in A minor.) This will make the five chord a true dominant. This is the essential harmonic definition of a minor key: a minor tonic i chord and a dominant V chord.

The ^6 scale degree can also be raised, but I won't get into that now as it isn't absolutely essential for defining a minor key.

So we can they say our Roman numerals for a minor key - at a minimum - are:

i iv V

Note that none of the diatonic modes will produce that specific set of chord qualities with a minor tonic and major dominant. It's a chromatic alteration. So, Aeolian mode/natural minor is not minor key.

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Firstly, Roman Numerals representing chords have only two functions: upper case (capitals) for major and lower case for minor.

In the very common diatonic major scale, by 'stacking thirds', there are indeed three major and three minor triads. The one built from the seventh degree is diminished, but since there's a minor third between its root and the next higher note, it gets written as viio - lower case, but also 'o' for diminished.

Let's take minors. If we're talking about the natural minor notes, they are exactly the same as those found in the relative major scale, thus all chords will be the same although the root will now be called 'i'.

Looking at the harmonic and melodic minors, with changes of notes 7 and 6, there will be slightly different mixes of notes, with augmented creeping in, but all triads found in them by stacking thirds will still be either major or minor.

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I think the concept you are looking for is “diatonic.”

The chords for each key are based off of building triads from each scale degree. So it is true that in a major key, no mater which key, the 1st, 4th, and 5th will always be major and the 2, 3, and 6th will always be minor chords I, ii, iii, IV, V, vi. And in a natural minor key the 1, 4, and 5 will always be minor and the 3, 6, and 7 chords will be major. i, ii°, III, iv, v, VI, VII

Understanding Roman numerals is as simple as knowing upper case is major and lower case is minor there is no other meaning

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"Irrespective of mode".

One does not typically attribute the roman numerals to each and every mode. It has been mentioned but I'll say it again. The chords are built by stacking 3rds. So the triads (and extended chords, 7ths, 9th etc) that naturally fit on each degree come out of the major scale. I, IV and V are major, ii, iii, vi are minor, and vii is dim.

If I understand your question, and I'm not really understanding all of it, you seem to either want to change the mode that plays over the changes or fit these changes over a new mode or key. If you were in the key of C maj and are playing a C --> F --> G --> F type riff that would not work (in theory) over C minor or dorian, etc. If you translated the progression to A min, A --> D --> E --> D that would also not be "appropriate" in theory. The natural A minor progression would come from the C major chords (they are relative keys, Amin rel to Cmaj), so you have Amin-->Dmin-->Emin-->Dmin, which people have used in tunes.

When you are in a minor key it is customary to use the harmonic or melodic minor scales to create the leading tone movement needed for resolutions. If you apply the stacking 3rds formula you will discover the chords that work with minor keys (harmonic etc). For example the chord occurring on the 5th degree of the minor scale becomes a V7 (with a major 3rd), rather than a V minor.

You can do this with all the modes but you will not discover anything new. You will generate the same sequence as the Major scale but shifted (just like the modes are just shifted versions of the major scale).

On another note (pun) sometimes minor modes or scales work over major chords but creating dissonance. Examples are the minor pentatonic and Blues scale. One typically uses them over I-->IV-->V superimposing the minor third over the major third in the chord. It works.

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