You seem to be describing two difference scenarios, but I can try to explain both and then it may become clearer to you.
I-ii-V-i... Once we land on the i chord, we find what scale uses the notes in the i chord as a ii chord and then play the same functions in the progression in the new scale.
First, it's better to refer to a key or mode rather than a scale. Also, you really should indicate key or mode when giving Roman numerals, especially when asking about modulation.
So, assuming we are talking about major/minor keys let's start on
C: I ii V i shows the tonic chord changes from major
C major) to minor
C minor.) That's a change in mode rather than key.
The simplest way to play the same chord functions in the minor mode are:
Cm: i iio V i. In addition to the change of the tonic chord to minor, the
ii chord becomes diminished
iio and the
V chord stays the same (a major triad.)
It might help to name the chords, like
C Dm D C changes to
Cm Ddim G Cm.
The second scenario is changing from
A#. I assume you mean both keys are major. It's much more sensible to call the second key
A# major or minor are odd key signatures, you normally use
Bb major or
C: I ii V I to
Bb: I ii V I with chord names
C Dm G C to
Bb Cm F Bb.
How do you use these ideas?
For the first scenario, the change of mode, I think you understand. A common use is to darken the mood. You could repeat a phrase and switch from major to minor for the second iteration. Or you could start up a totally new section in the minor. You can play with the endings a bit to emphasize the surprise of the change. Instead of
I ii V I try
I ii V V hold the
V then make the mode change
i iio V i.
The second scenario, the modulation, presents a problem using your example
I ii V I progression. I may have misunderstood you, but I think you mean to repeat the progression transposed to another key. That process is more like a harmonic sequence. It's tricky to describe the distinction briefly, because there are similarities between the two, and a harmonic sequence can be used as the means to modulate.
A harmonic sequence is when a chord progression is repeated but transposed up or down. It's common to use only a two chord progression in sequence. Sequences can be diatonic
C: [ I6 IV ][ viio6 iii ] or chromatic
C: [ I6 IV ][ V6/V V ]. I used brackets to show the sequenced (transposed) pairs of chords. I think you can see why just transposing a progression to another key is like a harmonic sequence.
C: I ii V I to
Bb: I ii V I is like a sequence. But, you might ask if a modulation is a change of key, and that transposition goes to a new key, why isn't it a modulation?
I suppose you could call it some kind of direct modulation, but it's more common to have some common chord between the two keys. More importantly the
I chord doesn't normally start the modulating phrase. Think of it like modulating to a new tonic.
For an example let's start in
C and modulate to
Bb. A common chord between the two keys is
F major. We will have two phrases. The second one will end on a
Bb chord, but not start with it.
| C: I ii V I | Bb: V6/V V6/IV I64 V7 I | with names
| C Dm G C | C/E F Bb/D Eb Bb/F F7 Bb |
It's easier with notation.
The first 2 bar of the modulating sequence could be interpreted in
Bb. That's typical of the common chord area of a modulation.
Modulating down a whole step from major isn't really common in classical style, but I wanted to keep with your example.
Jazz does something like
A: ii V I I | G: ii V I I | F: ii V I I (
Bm7 E7 Amaj7 | Am7 D7 Gmaj7 | Gm7 C7 Fmaj7...) but it's just another application of the modulating by sequence principle: don't start with
I, repeat the pattern sequentially, end with a cadence in the new key.