Writing characteristic chord progressions in inversion, & doubling notes other than the root
There are characteristic chord progressions taught in music theory, for example, the cadential 6-4, which is Ic - V - I. Then there's Ib - ii7b - V - I, & so on. I want to know if these cadences have to be written as is, or they can be modified by writing one or more chords in them in an inversion?
Also, from a previous question asked by me (double the third or the fifth of a chord), I learnt that notes other than the root are also doubled. I want to know if this is ok to do in the cadences I mentioned above (& other examples of such characteristic cadences). For example, is it ok to double the third instead of the root in chord Ib of the Ib - ii7b - V - I progression?
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...or they can be modified by writing one or more chords in them in an inversion?
In a nutshell, no.
You can't arbitrarily change a progression to any inversion.
In the case of a cadential 6/4 chord the whole point is the dominant in the bass. Inverting those chords changes the bass and the whole harmonic identity of the progression.
Similarly you couldn't take any progression and then arbitrarily invert it such that lots of second inversion chords are formed. Second inversion gets special handling that wouldn't be a concern with other inversions.
On a certain level you can say some progressions are roughly the same regardless of inversion. You could say generically I IV is the same as I6 IV. Certainly the root movements are the same. But I think you shouldn't indiscriminately treat them as the same. With I IV both chords in root position treats them as sort of equal in terms of stability. It has an evenness. But the inversion in I6 IV sets up a more dynamic progression. With the bass half step motion of MI to FA - analogous to a leading tone to tonic motion - makes IV more of a goal. The two chords are uneven in this sense. Various inversion are not total equal, not the same harmonically.
Regarding doubling of tones in inverted chords I like Walter Piston's rule of thumb: double the tonal degrees for inverted chords. The tonal degrees are ^1 the tonic, ^4 the subdominant, and ^5 the dominant.
Can you deviate from the various norms and rules? Yes. It's art. There is always artistic license. But it depend how closely you want to hew to a particular style. In common practice style harmony is pretty circumscribed so don't deviate too much if you want to get that period sound.
In regard to cadences it's best to stick to their formulas. That's part of the point. The clear formulas signal ending types. When a V I6 cadence is called imperfect and described as an incomplete closing, it's the inversion that makes it incomplete. This makes a good phrase ending to push into a new phrase. Changing the inversion type would then miss the whole point of how phrases are structured by cadence qualities.
In Western classical music theory classes, progression writing is typically focused on the voice-leading principles of Tonality, in the context of four-part vocal writing. So cadences, for example, are voiced to preserve the smooth movement of each voice (pitch) to the next. (Jazz and Pop music are looser in this regard, but tend to follow the same principles.)
You can change the voicing/inversion of any chord, but the subsequent chords would also change to preserve the voice leading. Taking your Ib - ii7b - V - I in the key of C Major, a standard arrangement would be:
But let's say you prefer ii7 to ii7b. If you change only that one voicing, you get this:
To get a "correct" solution, you would have to change, at least, the V chord. For example, Ib - ii7b - Vc - I:
It's okay to double any pitch(es) in the chord, but -- again for "correct" voice-leading -- it's best not to double pitches that have strong movement toward another particular pitch in the next chord. For this reason, you should near always avoid doubling a leading tone (e.g., the third of a dominant chord).
For a (vastly) more detailed description, see Laitz, Steven G. 2008. The Complete Musician. Oxford University Press.
The 'Cadential 6/4' just about has to BE a 6/4 :-) You could divert its resolution to VI or bVI to form an Interrupted cadence rather than a Perfect one.
Your other example, Ib - ii7b - V - I, is characterised by the bass line walking up to the dominant. It would have much the same feel if IV was substituted for ii7b. Or, obviously, if V7 substituted for plain V. And again, it could go interrupted instead of Perfect.
But this is a strange question. Yes, you've quoted a couple of useful musical clichés. Yes, other things are also good. A Cat may sit on the Mat, but so may a Rat. Or a Bat.
(Nice to see the clear, compact Ic, iib etc. notation for inversions. Why write 'ii[6-5]' when 'ii7b' does the same job? We should use it more.)
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