Modulation into the Minor Subdominant

Can anyone tell me any examples of or anything about modulation into the minor subdominant? Is this common? Uncommon? Does it sound nice?

Modulating from a major key to its minor subdominant (for example G-major to C-minor) is basically equivalent to going from a (major) dominant to a minor tonic (again G-major to C-minor) and the latter, consisting of V-i, is of course one of the most common progressions of all. So yes, it's common and sounds perfectly "nice", although the latter is, as always, a purely subjective question. It is also a very easy modulation to achieve, since by just adding a minor 7th to your tonic chord (in our example turning G-maj into a G7) you have already reached the a clear dominant chord of your new tonic. Modulating from a -minor- key to its minor subdominant is similar, just that if you want to approach it with its dominant, you'll also have to raise your old tonic's third (i.e. to go from G-minor to C-minor via a dominant, you'd have to turn G-minor into G-major and possibly add a 7th). But that's no big deal either. (Of course there are also tons of other ways to modulate without going via the dominant so directly, but that's just the "easiest", most direct way.)

If you want a more complete cadence before arriving at your new tonic (your old subdominant), you might want to use a diminished (seventh) chord before turning your old tonic into your new dominant, which serves as a ii(7) chord in your new tonic (i.e. a subdominantic chord) and may serve as a number of functions in your old key (since diminished 7th chords have the property of being interpretable as a lot of things in any key, if you approach their enharmonic spelling freely). In our example of G-major/minor to C-minor we could use the chord B-D-F-Ab (a vii-dim7/IV in G-major/minor, a normal vii7 in our final C-minor, or, respelt as Cb-D-F-Ab a diminished ii2 in C-minor) followed by B-D-F-G (a V56 in C-minor) followed by a C-minor chord (I).

Thank you, that was REALLY helpful!

It's not quite a V-i. It's a I-iv. It is not common and neither is the I - IV(generally thought to be anti-climactic but I actually like it). Of course one can properly turn this into a V-i without much issue but there is a technical distinction. Also, in minor one generally modulates to the mediant(Am to C) rather than to the dominant(Am to E) and it is more common. The reason is that the change of mode from minor to major gives the variety of a modulation and is much closer than that of the dominant(which is technically somewhat more distant(the key, not the chord)).

e.g., Am to C is more "natural" than Am to E because E the key of E is further way than that of C to Am.

C to G is very close and because the major quality stays the same it is more natural than C to Am(has to do with the nature of the overtone series).

In the case of, say, C to Fm we are going from C to the submediant of Ab. This is a relatively distant change but because C is the dominant of Fm it is not too abrupt.

What sounds nice about a modulation is not what you modulate to but if it is in the proper context. If it sounds good then it is good regardless if it is common or not(common != good). For example, one can setup the expectation of to modulate to any key and if it is fulfilled it will sound natural. To make it sounds good depends on the music. Also, just about any modulation can be made smooth by bridging it. C to Fm can easily be accomplished using the circle of 5ths and it will sound very smooth.

Is C to Fm common? No. But C to F is and you can use modal interchange to get Fm. It is just not as common as C to G(again, most likely since the modulation to the subdominant is generally anti-climatic).

While I have not explored such modulations to any degree it's obvious that they can work. It all depends on the context. The most common modulation is tonic to dominant and dominant to tonic in major(since almost always we return to the tonic). The second is tonic to subdominant in minor and vice versa(Since minor pieces are less common than major).

Most other modulations are far less common(thanks to must of early music which extensively used such modulations and made them so common).

Since the subdominant region and the tonic are closely related, on one hand, and parallel keys (minor and major with the same tonic) are also closely related through the dominant, therefore the minor subdominant is also not distant, therefore this modulation isn't (that) uncommon, unless you mean it is less common than modulation to the dominant, for example.

I never claimed I-iv was the same as V-i. I said that their respective translations to key relationships is equivalent, which is quite a difference: In a harmonic progression between scale degrees/functions, the main tonic always stays the reference point. In a modulation between keys however, this isn't necessarily the case - what was once the tonic may even be totally forgotten at some point by the listener.

Of course you're right that modulations to a dominant, or the major parallel of a minor key are more common. But you said yourself "The second is tonic to subdominant in minor and vice versa", so what's your point exactly? The OP didn't even state that the question was going from a major tonic to a minor subdominant, so "tonic to subdominant in minor" is exactly what the question in the OP may fall under. A modulation from a major key to a minor subdominant also gets increasingly more common in the late 19th century (admittedly, pretty much any modulation became "common" by then), especially when used continuously to go through the circle of fifths in order to deliberately let the listener forget where the original tonic was. (Which is exactly why it was much less common in the classical period.)

I also don't quite understand what you mean with "anti-climatic". Going to the dominant classically signifies an increase of tension, whereas a modulation to the subdominant is generally a release of tension. And a climax is usually a release of tension, no?

No, you seem to have a mistaken understanding of modulation and key centers. If we are in the key of C, for example, and we modulate to F, then we are modulating into the subdominant area. If we are in the key of C, modulate to the dominant, then modulate from the dominant back to the tonic, we are not modulating to the subdominant.

i.e., a dominant to tonic modulation is not equivalent to a tonic to subdominant modulation.

For example, suppose you have a song that starts in C and modulates to G. When we modulate from G back to C this is not a I-IV type of progression. If it were we would be in the key of G and we are not, we are in the key of C. If we were in the key of G then it would be anti-climatic.

You seem to think that we can willy nilly replace a dominant to tonic with a tonic to subdominant. e.g., that you can call a G C progression(or modulation) a dominant to tonic or tonic to dominant(V-I or I-IV).

This is very far from the truth. Another possible way to see it, at least using "chords" is that V-I is really a V7-I and a I-IV is really a Imaj7-IV. We can't relabel the V7 with the Imaj7. Just because we leave off the sevenths doesn't automatically make them equivalent(this is where the key comes in in supplying us with the implicit knowledge of the 7ths and why key matters).

Now, I see your confusion, If your in the key of C, modulate to G and if you think your in the key of G then modulating to C is a tonic to subdominant like modulation. But it is equivalent to thinking that if you come in on the middle of a movie and not have seen the plot and the release will make sense. It generally won't depending on the movie except that now days most plots are the same and we can deduce them with great accuracy. Also with 3D graphics and other techniques we can be drawn into to a seemingly anti-climatic section without realizing it. (BTW, anti-climactic is not necessarily bad)

You just have to realize that modulation is not a key change. In C, when we modulate to G we are not changing keys but sort of extending the tonal region of C by emphasizing G. We change some accidentals to conform to the new tonal center(F to F#) because, at least in ccp, we are not dealing with modal music and need be able to have strong cadences and such(the same reason why modes are not used that much in cpp).

Because we change the tonal center from C to G it may seem we have changed the key centers, but if the piece is tonal then we have not. In that case there is only one key and that generally is the first tonal center heard.

I don't wanna write a thesis on it and hopefully I've given enough reasons or at least enough that you sorta understand why dominant to tonic != tonic to subdominant. (this is not to say that they don't have similarities as they obviously do)

Now, to elucidate on why the the tonic to subdominant is anti-climatic. First, I don't mean it is always anti-climatic. Obviously there are many things involved in a climax. But, as you have already said, a dominant to tonic progression is a release of tension. Even if you were correct in you original analysis(forgetting everything I have said above), then a tonic to subdominant is a release of tension... but since we are already at low tension, being in the tonic, we are not releasing any tension(or in a sense releasing too much). Hence it is anti-climatic because we are moving away from the the direction of a climax. More so than just the dominant to tonic. i.e., if we had tension built up from a tonic to dominant modulation then going from the dominant to the tonic would have released the tension so there is no need to go from the tonic to subdominant to release more. If we had no tension to start with then what is the point in releasing it?

This is why it is not common as it serves almost no purpose in tonal dissonance. Now, this does not mean it always serves no purpose or is bad. It just means that it is harder to use properly and hence why it is not used as common. It can be very effective if used right and I personally love even using it just with disregard to tension because I generally like the serene effect it produces when there is no tension to release(it kinda takes you to 0 tension).

Now when we modulate to the minor subdominant it is somewhat of a different story and depends on a lot how we get their. If we do as you suggest and go turn I into a V7/V then it simultaneously builds up tension and releases it. How much depends on contexts. Modulating from tonic to dominant, at least in your ordinary music, always increases tonal dissonance. Modulating from the tonic to the subdominant always increases it(because we are moving away from the tonic) but overall tension is generally decreased. Modulating from the tonic to subdominant minor is effectively modulating to a distant key but because of the ambiguity it could be seen as modulating to a near key. Now the tension depends on the strongly on the context as does the tonal dissonance involved. If we modulate by using modal interchange then it is relatively close. If we modulate through the cycle of 5ths then it is relatively distant(but not so much as other methods that could be used).

Again, specifics really depend on the context and the overall tension of a section of music depends on many variables. One can make the tension of a tonic to subdominant modulation larger than that of a tonic to dominant modulation so that it is climactic. But this is not something that can be done at any piece and any moment.

Also, as a piece becomes more atonal these notions of tonal dissonance and tension are pushed into other factors. Obviously for atonal music the concept of key is relatively nil and modulations do not mean the same. Hence one has to adjust the concepts of tension in those types of musical styles.

I've already wrote enough to start a thesis so I'll stop now...

I don't get why you're writing a huge post on the topic why I-IV is not V-I when pointed out in my very first sentence of my last post that I never claimed that. You don't have to convince me there…

Again: I never said I-IV is V-I, so please stop insinuating that I did. It's perfectly clear to me that architecturally, in the scope of a whole piece, they are something completely different. Otherwise I wouldn't have written my whole last post about the difference, would I?

The "basic equivalence" of which I spoke (and yes, it may have been a poor choice of words) is the relationship of two harmonic centers at the point of the modulation (and NOT in regards to the whole piece).

Whether modulation is a key change or not is by itself a huge topic. The problem here is that in English, the term "modulation" is used for a lot of different things and can thus indicate a mere local emphasis on a different region of the original tonality, or a whole key change. The fact that it -can- be a total key change is, as mentioned, shown by the fact that modulations may obscur the original tonality to a degree that the listener forgets where he is in relation to it. The fact that pretty much all classical pieces eventually still modulate back to the original tonic changes little in this respect - it only shows that a superordinate sense of formal balance still mattered for these composers. But really: You can't tell me that in a Wagner opera he isn't modulating between different keys, but is just "extending the tonal region of the original tonic to emphasize some other area". No. He leaves the key. He eventually tends to get back, but that's a different story.

But I think we're beginning to split hairs on terminology here…

Why don't we just agree on: Write whatever sounds good to you.

Calm down... no need to get upset.

Your first sentence:

"Modulating from a major key to its minor subdominant (for example G-major to C-minor) is basically equivalent to going from a (major) dominant to minor tonic (again G-major to C-minor) and the latter".

Now maybe by "basically equivalent" you meant not equivalent but that doesn't seem to be the proper semantics. To me, in that statement, you are implying that one can think of the V-i as a I-iv. You say

"Modulating from a major key to it's minor subdominant", i.e., a I-iv(tonal centers and not chords)

"basically equivalent" =

"major dominant to minor tonic", i.e., V-i.

So you are saying I-iv is "equivalent" to a V-i.

I use the major subdominant rather than the minor but essentially they are the same. i.e., I-IV to V-I.

Regardless the same logic applies to both.

So, while you may or may not know the difference you implied something entirely different with your first response and I simply was correcting that misinformation.

I do realize that the terminology is not completely adequate but generally it serves the purpose. Wagner's music is non-standard for cpp and it can be difficult to analyze because it generally is more complex(relatively speaking). My point is not about specific music because one can almost always find counter examples. For example, if you never firmly establish the key then "changing keys" is entirely possible. It is somewhat ambiguous to say the key has changed when it wasn't strongly defined in the first place. Similarly in atonal music where there is no true key one can't really talk about modulations, at least using the classical definitions.

The OP's asked a very simple question, one about generalities, and to re-frame it is not being intellectually honest. I'm not saying you did that but simply that bringing in a few specific counter examples to describe generalities when those counter examples are clearly not representative of the population is a fallacious argument. Again, some of it is due to the ambiguities involved but not all.

Even if I interpreted your statement wrong it does not harm in answering if what I say is correct. At the very least I'm simply duplicating what you have said.

To make it clear, there are many tonal pieces that modulate in such ways to obscure the tonal center. This in no way contradicts what I have said. If we obscure the tonal center so that a true key change is somehow felt then that new key is the new key and a I-IV in that new key is still somewhat anti-climactic even though in the old key it is simply a V-I(But now we changed keys, remember?). It's like having a extremely long movie, so long that you forget the original plot but somehow a new one was introduced. Now everything is in reference to that. You must update your thinking.

One last example,

Suppose you have

I V I

where they are the tonal centers. For whatever reason when we get into V we completely forget that the key was I. Now the V becomes the new key and we really have

I I' IV'

In this case the return to the tonic, i.e., the V-I is really a I-IV and is somewhat anti-climatic. It may look like a V-I but really isn't. We may actually have something like IV I IV. the IV-I being very close to a I-V but the I-IV not being close to a V-I w.r.t. tension/release.

If the piece is somewhat non-tonal, or only slightly tonal, then the lines are blurred and it becomes more ambiguous to discuss and even talking about modulations and key centers is not technically correct.

You may agree with what I have said but the point of the discussion is to make sure there are no misinformation(and hopefully I'm not contributing to it).

You are definitely right on the fact that my original wording may have been somewhat misleading and imprecise. I had admitted that in my last post by saying "it may have been a poor choice of words". I simplified some things in order not to make the answer more lengthy than necessary (because certain people keep making fun of me for doing that :( ). I think the important points have been made by now and there's no need to delve much further into aspects that will probably be of little help to the original poster.

Great ;) I'm glad that is out the way. My intention wasn't to attack you or your intelligence but just to makes sure no confusion would come out of it. Not that what you said was an egregious error cause I even sort of think about it that way(V-I is sorta like a I-IV) but I wanted to make sure it was clear that they are technically two different things and it should always be kept in mind because it can lead one astray.

It's not quite a V-i. It's a I-iv. It is not common and neither is the I - IV(generally thought to be anti-climactic but I actually like it). Of course one can properly turn this into a V-i without much issue but there is a technical distinction. Also, in minor one generally modulates to the mediant(Am to C) rather than to the dominant(Am to E) and it is more common. The reason is that the change of mode from minor to major gives the variety of a modulation and is much closer than that of the dominant(which is technically somewhat more distant(the key, not the chord)).

I - IV is anticlimatic, I agree. I don't agree with your statement that modulating from i or I to IV or iv is uncommon. Lots of musical works feature that modulation. In fact, in sonata allegro form some have even shown that it was common for composers to modulate at the end of the recapitulation at a certain point to the subdominant region. This served to provide a more relaxing contrast as opposed to the dominant itself. Also, in other forms, a modulation to IV generally precedes a modulation to V. So modulating from the subdominant is a very common modulation.

e.g., Am to C is more "natural" than Am to E because E the key of E is further way than that of C to Am.

C to G is very close and because the major quality stays the same it is more natural than C to Am(has to do with the nature of the overtone series).

This really lost me, actually. Yes, the region of C major is closer to A minor (they are relative major and minor). But, this is assuming that you are using a very mundane understanding of harmony in your work. Many composers of the Romantic and Modern era stopped using this sort of modulation for more interesting modulations to remote key regions. Schoenberg devotes significant space in his Functional Structure of Harmony to this even.

What sounds nice about a modulation is not what you modulate to but if it is in the proper context. If it sounds good then it is good regardless if it is common or not(common != good). For example, one can setup the expectation of to modulate to any key and if it is fulfilled it will sound natural. To make it sounds good depends on the music. Also, just about any modulation can be made smooth by bridging it. C to Fm can easily be accomplished using the circle of 5ths and it will sound very smooth.

Yes, it all depends on your modulatory passage. If you are going to keys more remote you need to prepare the modulation in some manner. I - iv, is a very close modulation actually. It only requires a chromatic modulation in and of itself. Remotely, it's actually quite close in comparison to other regions.

Is C to Fm common? No. But C to F is and you can use modal interchange to get Fm. It is just not as common as C to G(again, most likely since the modulation to the subdominant is generally anti-climatic).

I think this is, again, a matter of taste to be honest as well as a thorough understanding of many works from the classical period onward. As I said above, this is a very common modulation. And really, to verify that all you have to do is look through the vast repertoire from the last 300 years of classical music.

While I have not explored such modulations to any degree it's obvious that they can work. It all depends on the context. The most common modulation is tonic to dominant and dominant to tonic in major(since almost always we return to the tonic). The second is tonic to subdominant in minor and vice versa(Since minor pieces are less common than major). Most other modulations are far less common(thanks to must of early music which extensively used such modulations and made them so common).

Okay, you just modulating from tonic to subdominant wasn't common... but yet, here you say it is. I'm really confused now. Is it common or not? The reason why V - I is common is because it has a strong sense of closure aurally (at least that is how I was always taught in that regard.) And minor pieces are less common than minor???? What music do you listen to? What period?

I - IV is anticlimatic, I agree. I don't agree with your statement that modulating from i or I to IV or iv is uncommon. Lots of musical works feature that modulation. In fact, in sonata allegro form some have even shown that it was common for composers to modulate at the end of the recapitulation at a certain point to the subdominant region. This served to provide a more relaxing contrast as opposed to the dominant itself. Also, in other forms, a modulation to IV generally precedes a modulation to V. So modulating from the subdominant is a very common modulation.

By common I mean relatively common in cpp music ignoring outliers. Chromatic mediant modulation is extremely uncommon as is a ton of other modulations. But out of the common modulations the dominant is the most common. Because it is so common it it dwarfs almost all other modulations. If you choose a cpp piece of music randomly it will almost surely modulate to the dominant in a major piece(and most pieces are major). Next would be the relative major if minor. In fact in cpp music almost everything else is uncommon.

Now, I am not simply comparing a piece that has a modulation to a subdominant and making it equal to that of the dominant but considering the lengths of the modulations. It wouldn't be fair, IMO, if you made very short modulations comparable to long ones. Also I do not consider tonicizations as modulations.

If you ignore the lengths of modulations then one might start to think that even relatively rare modulations are used fairly often(specially if you include tonicizations).

Also most cpp music(such as all the minuets, trio's, etc...), being rather simple and short do not modulate to anything but the dominant/mediant for major/minor. Since there is a huge collection of these types of pieces they skew the numbers.

If, for example, you only consider the masters then the distribution changes since they tended to be more adventuresome. But overall they represent less than 1millionth of a percent of the total music out there.

Of course I have not look at all the music but it's obvious that there are probably billions of pieces of cpp music and probably 99.9% were created by amateurs and semi-professionals. It is not too hard to guesstimate that the most of them probably were not harmonically varied.

Now maybe I'm considering way to much music and probably should use those from the masters only since this is mainly what we hear. But even the masters have a large collection of simple music.

Now, I could be wrong, but, I would be willing to bet that if you looked at all the pieces in the WTC that the modulation's to the dominant, simply by counting with disregard to length(except no tonicizations), would far outnumber any others. Second would be to the relative major for minor pieces(and in this case it is skewed since half the pieces are minor by design). All others would occupy probably less than 5%.

Now, remember, a modulation that occurs in the dominant to it's dominant is a dominant modulation rather than that of the supertonic. Hence there are very few supertonic modulations since it doesn't occur in minor and is generally a dominant modulation(in the dominant rather than tonic).

While I haven't analyzed every piece in the WTC I can't recall any seeing modulation to the minor subdominant in major. Of course there are many tonicizations of the minor subdominant(although still not that common as others such as the major subdominant).

This really lost me, actually. Yes, the region of C major is closer to A minor (they are relative major and minor). But, this is assuming that you are using a very mundane understanding of harmony in your work. Many composers of the Romantic and Modern era stopped using this sort of modulation for more interesting modulations to remote key regions. Schoenberg devotes significant space in his Functional Structure of Harmony to this even.

I'm not really into "modern" music that attempts to banish tonality. The only modern music I listen to is rock/pop/country. I'm more into cpp music and generally discuss theory in those terms(since it is the most well-founded and the theories we use today were all derived from it). I assume if the discussion isn't clearly geared towards a specific genre that it defaults to cpp.

Yes, it all depends on your modulatory passage. If you are going to keys more remote you need to prepare the modulation in some manner. I - iv, is a very close modulation actually. It only requires a chromatic modulation in and of itself. Remotely, it's actually quite close in comparison to other regions.

It depends. It is close and far. Which means context matters. If the I-iv is hear as a simple modal interchange of I-IV then it will work... but this is harder to do because it is a modulation unless the modulation somehow sets this up. And generally if it sets it up then it is not a I-iv modulation but a I-IV-iv modulation which is really a modulation to the major subdominant then to the parallel minor(this being completely different than a I-iv modulation)).

Now we can setup the I-iv to work as a modulation to the iv through context but it is not easy(which is why it is not common).

Suppose you take a simple piece of music that modulates from I to V. Now you transpose the V part to IV. When you listen to this you'll hear a I-IV modulation. But suppose you now change the mode to minor so you get I-iv. Now you'll year it not as a mode mixture but a distant modulation(but it actually isn't far as some as you have pointed out). Unless, of course, the context somehow makes it work. The more abrupt the modulation the more it will sound distant.

If you emphasize the subdominant region in the first section and setup a modulation to the subdominant but present the minor subdominant then your ear may except it as a modulation to the minor subdominant. If you don't set it up properly then your ear will hear it as a distant modulation.

With the dominant, there is no confusion(well, I suppose it is possible but much much unlikely).

I think this is, again, a matter of taste to be honest as well as a thorough understanding of many works from the classical period onward. As I said above, this is a very common modulation. And really, to verify that all you have to do is look through the vast repertoire from the last 300 years of classical music.

Well, of course. We really need to define what we mean by common. If we include all music then who really knows(I will still bet that the dominant is the leader by far). We also have to define how to include the modulations(do we take into account the length?). etc... etc...

Okay, you just modulating from tonic to subdominant wasn't common... but yet, here you say it is. I'm really confused now. Is it common or not? The reason why V - I is common is because it has a strong sense of closure aurally (at least that is how I was always taught in that regard.) And minor pieces are less common than minor???? What music do you listen to? What period?

No, I said tonic to subdominant in minor... i.e., i-iv. This is different than I-iv.

By common I mean relatively common in cpp music ignoring outliers. Chromatic mediant modulation is extremely uncommon as is a ton of other modulations. But out of the common modulations the dominant is the most common. Because it is so common it it dwarfs almost all other modulations. If you choose a cpp piece of music randomly it will almost surely modulate to the dominant in a major piece(and most pieces are major). Next would be the relative major if minor. In fact in cpp music almost everything else is uncommon.

Extremely uncommon??? Since when? Chromatic mediant modulation has been in use since the days of Haydn and Mozart. By the time of Beethoven, it was in regular use! In fact, there are tons and tons and tons of treatises on this:

Chromatic mediant relations are, of course, not exclusive to nineteenth-century music. Their presence in Renaissance music is familiar. In Baroque style they often occur at the boundaries between large sections of pieces, as a half cadence resolving to an unexpected new tonic. Similarly in the music of Haydn and Mozart, they appear most often as major-third mediants at the boundaries between sections in a minuet or scherzo. Between or within phrases, though, they are exceptional. In Beethoven's and Schubert's music, chromatic mediants began to appear with greater regularity and to find their way into more local harmonic contexts. As their presence grew and their profile became more familiar, chromatic third relations gradually became an accepted and much-exploited aspect of nineteenth-century harmonic practice. It is this normative practice which will be examined throughout the following chapters. - Chromatic Transformations in Nineteenth - Century Music by David Kopp, University of Washington.

Now, I am not simply comparing a piece that has a modulation to a subdominant and making it equal to that of the dominant but considering the lengths of the modulations. It wouldn't be fair, IMO, if you made very short modulations comparable to long ones. Also I do not consider tonicizations as modulations.

If you ignore the lengths of modulations then one might start to think that even relatively rare modulations are used fairly often(specially if you include tonicizations).

Also most cpp music(such as all the minuets, trio's, etc...), being rather simple and short do not modulate to anything but the dominant/mediant for major/minor. Since there is a huge collection of these types of pieces they skew the numbers.

What?

If, for example, you only consider the masters then the distribution changes since they tended to be more adventuresome. But overall they represent less than 1millionth of a percent of the total music out there.

Of course I have not look at all the music but it's obvious that there are probably billions of pieces of cpp music and probably 99.9% were created by amateurs and semi-professionals. It is not too hard to guesstimate that the most of them probably were not harmonically varied.

Now maybe I'm considering way to much music and probably should use those from the masters only since this is mainly what we hear. But even the masters have a large collection of simple music.

Yes, you are definitely looking way into this. Yes, there have been tons of pieces written. I highly doubt, however, that that number is in the billions.

Now, I could be wrong, but, I would be willing to bet that if you looked at all the pieces in the WTC that the modulation's to the dominant, simply by counting with disregard to length(except no tonicizations), would far outnumber any others. Second would be to the relative major for minor pieces(and in this case it is skewed since half the pieces are minor by design). All others would occupy probably less than 5%.

Considering that Bach was a composer from era that is now about 400 years ago (roughly), I would definitely understand fully that Bach didn't use anything besides what you stated above. However, to blindly just state that the modulations Bach used should be the standard AFTER so much harmonic development in the 400 years since is tantamount to saying we should develop all our computers using the Abacus as a model! This isn't the Romantic anymore, even that era is now 200 years old.

I'm not really into "modern" music that attempts to banish tonality. The only modern music I listen to is rock/pop/country. I'm more into cpp music and generally discuss theory in those terms(since it is the most well-founded and the theories we use today were all derived from it). I assume if the discussion isn't clearly geared towards a specific genre that it defaults to cpp.

So, umm... let me get this right here, your biased against modern music because you personally find it to be inferior to cpp? Also, even with your rather small view on CPP music, you are mainly looking at a window from about 1600 - 1800 as far as harmony goes - as after 1800, you started to see a very liberal and rapid evolution harmonically. Each 10 years or so, saw very new and (what Bach would consider, painful) harmonies were used extensively. By mid 19th century, this type of progression was very, very common.

It depends. It is close and far. Which means context matters. If the I-iv is hear as a simple modal interchange of I-IV then it will work... but this is harder to do because it is a modulation unless the modulation somehow sets this up. And generally if it sets it up then it is not a I-iv modulation but a I-IV-iv modulation which is really a modulation to the major subdominant then to the parallel minor(this being completely different than a I-iv modulation)).

Considering that I - IV - V - I is a very common modulation from that period (1600 - 1750), I'm not exactly sure why your saying this would be a hard thing to head towards.

Suppose you take a simple piece of music that modulates from I to V. Now you transpose the V part to IV. When you listen to this you'll hear a I-IV modulation. But suppose you now change the mode to minor so you get I-iv. Now you'll year it not as a mode mixture but a distant modulation(but it actually isn't far as some as you have pointed out). Unless, of course, the context somehow makes it work. The more abrupt the modulation the more it will sound distant.

Again, it depends on what period of music you are going from. If you're looking at it from a purely baroque to early classical.. than yes, this type of modulation would be rather abrupt. However, if you look at it from 1780 (roughly) onwards, it wasn't abrupt at all but instead was just a beautiful color.

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All in all, I see where you are coming from with this. Your not looking at it with the knowledge of the 1800s - today. That's again, like looking at a computer and not liking it because it's not based on an abacus. Just because music has evolved past this tonal organization, doesn't mean that good music isn't being written. Perhaps, if you opened your ear just a little more, you will join us in the 21st century instead of remaining in the 18th.