Chord progressions/intervals

So, I went onto the page with chord progressions on this site and it says that the major triad progression is I,ii,iii,IV,V,vi,vii*. I tried it with root as 'C'. Now, I understand the roman numeral intervals to mean the following:
I - root V* - dim. 5th
ii - minor 2nd V - perfect 5th
II - major 2nd V+ - aug. 5th
iii - minor 3rd vi - minor 6th
III - major 3rd VI - major 6th
IV - perfect 4th vii* - dim. 7th
IV+ - aug. 4th vii - minor 7th
VII - major 7th

In the Cmaj progression, it says that the ii (minor 2nd) is D minor, but the minor 2nd for the Cmaj progression should be C#/Db. Why is it a half step higher? This also applies to the iii, where it says E instead of Eb, and the vi, wher it says A instead of Ab. Could someone explain to me waht's going on? Sorry if what I have said is a little confusing. Many thanks.

I - root V* - dim. 5th
ii - minor 2nd V - perfect 5th
II - major 2nd V+ - aug. 5th
iii - minor 3rd vi - minor 6th
III - major 3rd VI - major 6th
IV - perfect 4th vii* - dim. 7th
IV+ - aug. 4th vii - minor 7th
VII - major 7th

i don't really get what you want to say with this? and what it has to do with the question you're asking

i also don't get how you get to c# and and Ab , explain how you get there ?

maybe someone else gets what you mean :)

i don't i get where you get the c# and d# you think the ii stands for a minor second up and the iii for a minor third up from the root?

well that's not what these roman numerals mean
I stands for first note in the scale(C) , ii for the second note in the scale (D) and it's not capitalized because it's a minor chord

maybe that's not what you mean but i'll await your answer

OK, let me tryit another way. For example, ii means a minor second, whereas II means a major second. 'ii' is a half step above the root, whereas 'II' is a whole step above the root. Is that OK so far?

Yeah, that 'ii' doesn't mean minor seccond, but the 'ii'-chord in any major key. It's the "root-note" on witch you build the ii-chord, In the key of C major this would be a D minor. You are right in so far that the minor seccond in a C scale is a C#/Db, and a major seccond is a D, but if you play in any major key, the common chords you use are; I, ii, iii, IV, V, vi, vii*, I don't know if this is the best explanation, but I couldn't do better :)

the II and ii don't mean minor second or major second , these are not the intervals
II just means it is a major chord and ii means it's a minor chord so in C second note is D (up major second and no minor second) and it's ii (lowercase) so minor , so the roman numerals have nothing to do with the intervals beeing major or minor and they don't even have anything to do with the intervals

I'm sorry mightydave, I can see the mistake I made now, so that's all clear. I understand that II means major chord and ii means minor chord. So when the roman numerals are being used in the context of chords, what you are saying is correct. But if you are talking about scales, for example take a major scale, you have a major third (amongst others) and this would be written as I, II, III, etc because this indicates the distance between each note. whereas if it were a minor scale then it would contain I, II, iii, etc... this would mean that there is a semitone difference between the second and third, but in a major scale it is II, III instead so this means there is a tone difference between the two. That's right isn't it? I think paerdeveygh gets waht I'm going on about. I hope I haven't confused you too much!!

yes i get what you mean but i don't use roman numerals for the intervals i just use w-w-h-w-w-w-h-w so i first didn't really get where you where going to , i hope it's all clear for you now !

and good luck with the guitar !

Talking about intervals, even in the opposite (descening) direction, from C to B, is also called a minor seccond interval, correct me if I'm wrong please.

that's true paerdeveygh, you're right

The uppercase/lowercase Roman Numerals aren't used as indicators of the intervals between the scale degrees. Don't try to interpret them that way. If you were to study Harmony, you would not find the uppercase/lowercase Roman Numerals even being used to indicate what kind of triads are built off the degrees. You have to memorize the intervals and types of triads. It keeps things from getting confusing like they had to you.