Paradigms: The useful version!

     When we last left our Valiant Heroes they were learning of chord Paradigms, specific Progression templates, in a sense, that could be fiddled with.
     Now we talked about the most common in terms of overall music, but there are some progressions and paradigms that are just absolutely necessary to be known, and even have their own names(The I-V-vi-iii-IV-I-IV-V kind of bridges this gap a little, being the Pachabel's Cannon progression, as well as being in such songs as Green day's "Time of your life").  Today we're going to learn about two incredibly common Paradigms, with their variations.
     The first thing we're going to learn about is the Twelve bar Blues.  The classic version of this is very simple, and amazingly famous.  In it's most basic form, it is as follows:
(I'm not sure I covered anything in this fashion before, so here's a brief breakdown on the new notation system I'll be using some of the time.  Basically I use vertical dashes: |, to indicate a bar line.  I use horizontal dashes: - to indicate beats, if there needs to be differentiation.  For instance, if a bar only contains a V chord, it will be written thus: | V |  If it contains a V chord on beat one and a IV chord on beat three, it will be written thus: | V IV |.  If it contains a V chord on beat one and a IV chord on beat two, it will be written thus: | V IV - - |  If there are no dashes, it is assumed that the chords are spaced evenly in the measure)
Twelve bar blues:
I7 | I7 | I7 | I7 | IV7 | IV7 | I7 | I7 | V7 | IV7 | I7 | I7  :|   <-(This last bar has a colon indicating a repeat)
     It's really as simple as that!  It's a little repetitious, yes, but it works.  Now, how would we add variations to this progression?
     Well the first possible variation is what's known as a Tritone Substitution.  This is a huge, huge, huge, huge concept in jazz and related styles.  It's also one that is barely ever actually used on the fly, but it's still a big concept.  In order to understand the tritone substitution, let's first look at a typical dominant 7th chord.  For an example, let's imagine a G7 chord.  What are the notes in it?  G - B - D - F.  Now, between B and F, there's a tritone, which I believe we touched on before.  A tritone is an augmented 4th, or a diminished 5th.  It is also the interval at the beginning of "Maria" from West Side Story.
     Speaking of tritones, let's look at a C#7 chord, a chord with root one tritone away from a G7.  In the C#7 chord we have notes: C# - E#(F) - G# - B.  This chord, like all Dominant 7th chords, has a tritone in it as well.  In fact, while notated differently, it has the same tritone in it as the G7 chord.  It stands to reason if you think about it that this would happen.  A tritone is exactly 6 half steps in size.  An octave contains 12 half steps.  Therefore, a tritone is the middle point of the octave.  If there is a tritone in a chord, and you move by a tritone, the tritone in the chord will remain the same.  So what a Tritone Substitution actually is is swapping out any Dominant 7th chord with the chord with root one tritone away.  This gives us some opportunities for some fun with the substitutions.
     My next post is going to be a bit of a physics and math talk to explain what I'm about to say, but I want to take a moment to mention that for the most part, the 5th of chords without a modified 5th is the least important note of a chord.  Especially with a major third, the 5th is implied through the other notes, and if it's not altered, especially if there's no inversion, the 5th doesn't really add anything to the chord.  I mention this now because I'm going to be ignoring the 5th sometimes and I wanted to explain why it's ok.
    Now with this in mind, I'm going to demonstrate use of a Tritone substitution in between the I7 and the V7, in G.  So we've had 4 measures of G7.  Then C7 | C7 | G7 | Now let's say we want a substitution here to lead a little more into the D7 chord.  The tritone from G is C#.  We're going to throw out the 5th of the C#7 chord for now, so we're dealing with notes C#, F, B.  Without the 5th in, we're only altering one note, the 5th of the G7 - D, to the root of the Substitution F#7 - C#.  This gives us the same feel as a G7, but with a little more leading.
     This is just one example of the uses of Tritone substitution, however.  They won't always work, but they can provide a nice sound when they're used right.  This is also a really, really easy way to alter the 12-bar blues phrase.
     Another way to alter the Twelve bar blues is with passing chromatics.  For instance, when going from the V to the IV, we can pass through, either syncopated or not, with a #IV7 chord.
     Another very, very simple way to alter the Twelve bar blues is to add a turnaround to the last measure, often ending on a V chord.

     Anyways, there was an introduction to both the Twelve Bar Blues Paradigm and the Tritone Substitution. Since Tritone Substitutions are so complex and required such an explanation, I'm going to lightly brush on this next Paradigm relatively quickly.
     The next paradigm is a very simple base, that can be used in so, so, so many things.
I - vi - ii - V
     On its own it seems pretty innocuous.  It's a cute little progression that is pretty happy.  However, the variation, the very specific variation that builds off of it, is incredibly, incredibly great.  You see, this paradigm is useful in a longer progression which extends it a little:

I vi | ii V | I vi | ii V | I I7 | IV #IVdim | I V | I
Still doesn't quite look like much, does it?  Well there's a song you may have heard of:

Hey that's what that song that's super famous!  In fact, that progression is used in, like, a million songs.  The Flinstones theme even works over it.  Now, there's also the bridge, which is just a Falling fifths paradigm starting on the III chord.  So it's just:

III7 | VI7 | II7 | V7

Simple as that!  The whole song together is AABA, so it's the I-vi-ii-V progression in entirety twice, then the bridge, then the I-vi-ii-V progression again.

Obviously that's just one variation on the I-vi-ii-V, sometimes you don't need any, and there are others.  But that's definitely the most famous and useful progression based on the I-vi-ii-V.  Also, if you play bass or guitar, Rhythm changes are hilariously easy to voice lead.

Anyways, that's all for our first post back, more to come!

What the back?

     And a very good morning/afternoon/evening to all of you!  It's been a while, hasn't it?
     Well I've got some fantastic news:  I'm back!  That's right, I'm(for now) done cruising the high seas, and I certainly won't be gone for very long if I am again.  I've grown a lot as a Musician over these last two years, and I've grown a lot as a person.  I of course remembered all of you lovely people and decided to start up the blog again, and get some Theory all up ins.
     There are going to be a few changes in the writing of this blog as I return, mostly because after my time working on the ships, there is a lot more insight I can give on certain things.  Also, I've received a much more practical education while working, so we're going to have some more practical posts in addition to the hoity-toity book theory that will, of course, continue.


     Anyways, there may be a post up later today with some of the new stuff(I've got a great add-on to paradigms coming your way), but I just wanted to get the word out that I am in fact back, and the blog continues!

Shutting down....kind of

Hey everyone, I know it's been a super long time and I wanted to explain why and get ready for the future.

I've now got a full-time piano gig working on Cruise ships for a while, so my internet is intermittent at best, and while I do have time to write the posts, I don't have any of the references I use to check myself to make sure I'm still doing things right, nor do I have the programs and materials I normally use.  If I can, I'll try to continue to update, but, for instance, audio files, pictures, anything like that I probably won't be able to put up as easily, and there will most likely be a big delay.  Sorry for anyone missing the posts, but the gig just doesn't leave that much time to really work on the blog that much.

Thanks for reading.

Paradigm analysis

Hey readers! It's been a super-long time since I've updated, I know, but with a combination of being ridiculously busy and changing my mind on how best to do this post(and the one after it) as well as now-resolved technical difficulties with my MIDI keyboard, which made putting examples into Finale an exercise in frustration. Anyways, I'm now back-ish. I have an audition in a couple of weeks which will be super-important, so I'll be in and out practicing for that many hours a day, but after that I should be able to keep at least something approaching a regular schedule.

Now, last time I brought up the idea of Paradigms for chord progressions, which are interesting ways of thinking about progressions where you're not nailed down to a specific progression of chords, but rather you have a nice framework that you can play around with a little more. I've got today examples of the first two paradigms I mentioned, as well as a single variation on both. Without further delay, here's the first example, a very short piece for a string quartet.

I-vi-IV-V-I

I'd like to apologize again for the PDF handling.  If anyone can suggest a way to host PDFs, or any multi-page document, that'd be awesome, but for now we have to go through Wuala, which while not awful, I can't just have a hotlink or inline.  Or at least don't know how.

Anyways, that score is great, but since that's sort of useless without the corresponding sound...

Wonderful. Ok, this is fairly straightforwards as a piece, so let's do a quick and dirty analysis. The first thing to do is figure out what key we're in. After that, see if you can get the general idea of what the chord progression is. In this example, all of the chords are in root position, so that makes that part super easy. Also, the title happens to be the Paradigm I'm using, so that makes it even easier.

So we're dealing with a piece in F major, and the progression is I-vi-IV-V-I-vi-IV-I. Now we can notice that it sounds like we have two phrases in here, the I-vi-IV-V, and the I-vi-IV-I. So the first phrase ends with a Half-cadence, and the second ends with a Plagal Cadence.

Now, here we already are starting with playing around a bit. The Paradigm is I-vi-IV-V, right? But while the first phrase does that, the second one careens off the cliff at the end and doesn't go to V, instead opting for a Plagal Cadence. Well, we'd still call that the I-vi-IV-V Paradigm, probably, because the function of the chords is still about the same as though it were, and the first phrase does it exactly. The only difference is that to preserve having the phrases having equal lengths, we just chopped off the V and replaced it with a I.

Ok, now let's look at a slightly changed piece.

Variation

And it sounds like...

Bam. Ok, almost the same, right? In fact, I don't know how many of you are using Foxit Reader, but I've got them both open and can quickly change between them in tabs to see very clearly the difference. All I've done is altered the Viola line in measures 2 and 6 from alternating between F and A to alternating between F and Bb. So what does that mean? Well, a vi chord in F Major is D-F-A, right? A d minor triad. And a Bb chord, Bb-D-F, is a IV chord. Well what I've done is taken out the vi chord and replaced it with a IV6 chord, or a IV chord in 1^st inversion.

Now let's think about that for a second. The vi chord is a minor chord, and was played in root position. This gives it that nice grounded sound of the root position, and it's the only minor chord in the progression, which gives that sort of more “sad” sound to it. Meanwhile, the IV6 chord is in first inversion and is a major chord. This means we have a much, what I would call softer texture to the whole thing. It gives us a nice “happier” sound, it makes the progression have less movement, since we're really now just going I-IV-IV-V in terms of the actual notes played... while we're only changing one note, it really gives a nice different feel to the progression.

However, calling that a I-IV-V progression wouldn't really give us the whole picture, because of the way it's voiced. This is what makes thinking in Paradigms so great. The variation still sounds like I-vi-IV-V, for the most part, but just subtly different. The bass line has the same contour and the same notes, and we could use this progression as we use I-vi-IV-V much more than we could use it as we use something like I-IV-V.

This is also great if we're listening to something, and we hear a I-vi-IV-V run in the bass, and when we play it it just sounds wrong. There's always the chance that they're doing a IV6 or some other variation somewhere that makes it sound a little different.

So, to expand on that, let's take a quick look at a second example, and then I have some tunes I cooked up in Reason that are a little more full, so we have the use of the paradigm in context and not just on paper in tiny examples.

I-ii-IV-V

Great, so here's one for brass, if you couldn't tell. Let's do the quick look here. We have two sharps, which puts us in D major, and the progression.. uh oh. This one is a little busier than the last one, which makes this a bit harder. Well, luckily, again the title is the progression, but also, just take a look at the beginning of each measure. That first beat is a really nice way to figure out where things are, because barring a suspension, it's really common to have things line up there. Also, the first thing I do is just look at the bass line for major changes, which in this case is the Tuba. Sometimes, as we saw in the variation back there, there are inversions, but the bass notes will very, very often be at least in the chord, if not on the root or outlining it entirely. Anyways, the progression is I-ii-IV-V for the first and second phrase, and then the 2^nd page just finishes the whole thing off with I-V-I.

So this is pretty straightforwards again, it's the second paradigm I mentioned in the last post, and there are some more nonharmonic tones, but for the most part, there it is.

So let's fuck with it a bit, because we can.

Variation

Now this one is slightly more changed than the last one, but again it's that second chord that I changed up a bit. This time instead of a ii chord, which in D major is E-G-B, an e minor triad, I substitute in a V in 2^nd inversion, with the notes E-A-C#. Now here's a huge example of how thinking in Paradigms is really, really, really awesome. The progression, were we to ignore inversions, would be I-V-IV-V. I-V-IV-V is another paradigm all together from I-ii-IV-V, and has its own very distinct sound. Even if we just add in the inversion, and say it's a I-V6/4-IV-V, it still would be super-easy to think about a I-V-IV-V thing if that's all we saw. However, having the bass line rise to the second scale degree makes the piece have a very clear sound that is characteristic of the I-ii-IV-V progression. The sound is a little different than I-ii-IV-V, but it's much, much closer to that than I-V-IV-V. So this is a great example of how thinking in terms of these big broad umbrellas that I call Paradigms and then whittling down to specific variations and progressions gives this really nice immediate recognition and classification that just looking at a billion progressions doesn't.  In fact, if someone were to talk to me about I-V-IV-V, the sound I would immediately go to would be Blink182s All the Small things.(There may be an ad with that link, sorry about that).  Now, that's not only a different sound from this Paradigm because of the style, but it just has a completely different harmonic sound in general.  Again, this is why Paradigms are awesome. All the Small Things could be I-iii6-ii6-V and would probably sound a shitton of a lot closer to the original song than doing a variation of I-ii-IV-V. 

If I had to pick one reason that I'm spending so much time on this subject, that would probably be it. Being able to look at a piece and just sort of give a nice broad classification, and understand how those broad classifications fit together will make doing any sort of deep, particular analysis faster and easier, and being able to hear in those giant brush strokes and then pick out the finer detail is also incredibly useful if you're trying to play by ear. Note that I've always said “think about” in terms of Paradigms, and not “analyze”. That's because if we were to write down the paradigm instead of the progression in an analysis... yeah that would be wrong. But if we recognize and think in the paradigm, and then whittle down into the progression, we'll be adding a tool to help us easily understand the larger picture.  I know personally if I'm sightreading, or improvising over a line, I think in terms of the paradigm a lot more than the progression.  In general, thinking in Paradigms is the practical way to go about things.  "Close enough" is, well, close enough 90% of the time.

Anyways, I know that we've basically just covered two pieces with variations, but I'm working on some more fun examples of the things we covered today, it'll be an enjoyable experience.  Also, I have super-awesome news, which is that Tindeck seems to have added an embedded player, which I'll probably start switching over to soon.

Lesson 13: Paradigms

Hey everyone.  It's been a long time, hasn't it?  Updates may end up being a touch.... sporadic for a while, but I swear I haven't forgotten about this.

So way back when, when I last posted, we had talked about single chord on chord tendencies, which is, as you'll recall, less hot than it sounds.  Now, that's great for songwriting and composition, and pretty ok for performance.  But it's pretty small and self-contained too, unfortunately.  When we start stringing them together a little more, before we get to, say, a whole song, we deal with Chord Paradigms.  Paradigms are.... ok, this is a really patronizing metaphor and I apologize, but think of them like combos in a fighting game.  You've got normal punches and kicks to be strung together, and that kind of works, but if you use certain combinations you launch a badass fireball at the audience.  Ok, it's also not a perfect metaphor.  Anyways, basically they're small, sort of self-contained, loose chord progressions.

I've only heard them referred to as Paradigms when I was at Oberlin, so this may be a very strange way of thinking about it, but I actually really like this way of doing it, because it gives a nice intermediate step that most people arrive at anyways formality and a name.  For instance, if you talk to a Jazz musician, they'll know what "Rhythm changes" means without needing to say "Ok, we'll go I-vi-ii-V twice and then we'll do a I-V7/IV-IV-vii^o/V-I-V-I.  Awesome everyone remember that and let's jam"  They'll be able to easily solo over that, they'll know good voicings, they'll understand how it sounds and how it feels just by saying "Rhythm changes".  Paradigms give you that freedom but in a more structured classical setting.  So for instance, if you learn what I-vi-IV-V sounds like and how to voice those chords, your workload is cut down from playing around with each chord in that line and its tendencies, and you can play around a little more with the specifics involved.

Now, unfortunately for me, a lot of this is not so much just learning from a book or blog like some of the other things I've gone over, but a lot of it depends on just listening to, noticing, and hearing all of these paradigms in use.  To that end, my next post is going to be a bunch of examples written in a variety of styles that sort of goes over these ideas, so you all can get practice in reading and hearing these.

But for now, let's take a glance at the most common paradigms:

I-vi-IV-V
This is used all the time.  All the fucking time.  It's the "Heart and soul" paradigm.  There are some common substitutions in here too, such as I-IV6-IV-V, which makes it a little more stagnant in my opinion, but also has a more uplifting sound to it.  Sort of.

I-ii-IV-V
I-iii-IV-V
I group these together because they're relatively similar, they're both ascending bass motion to V.  Again, some of these all I can do 'till I have examples is sort of list them, and you'll be able to hear them more when you actually see them in use.

 I-V-vi-
You'll notice this one is only three chords and doesn't immediately lead back to I.  That's because while this is a common opener, sometimes it completes the Pachabel paradigm and continues the general motion(iii-IV-I-IV-V), or sometimes it just goes IV-V after that.... it's a common opening paradigm that has a lot of variation, one major one is practically it's own paradigm:

I-V6-vi-V
Descending bass line paradigm.  This happens everywhere, and again, is pretty much a variation on the I-V-vi

Now, as with the last one, some of these paradigms have common names.  "Descending bass" will tell you a lot, and sometimes it's just to V, sometimes we take it all the way to ii, then V, then I, but it's still all under the "Descending bass" paradigm umbrella.

Some of these are "Falling" or "Rising" paradigms.  For instance, Falling fourths would be I-V-ii-vi-iii-vii^o-IV-and then we could break to V-I, or we could break after the vii^o

You can sort of do this with any falling or rising interval.  Also you can go into or out of falling or rising intervalic paradigms, which is why I'm not just listing a few.  So for instance, if you get to ii some how, and are looking to get out of it, just fall by fifths and you get ii-V-I, which is a super common way to cadence.

Anyways, I need to do a lot of preparation before I'm ready with examples, but I wanted to get the primer out of the way now instead of trying to combine the posts and having a giant massive post.  Nest update we'll look more in depth at paradigms and how they interact with each other and how they sound and work in the real world.
 

Lesson 12: Roman Numeral Theory 3: Chordal Tendencies 1: USC 23

Hey everyone, sorry this took so long, but I actually wrote this post in entirety, saved it, closed the window, and when I went to edit it, to give it a last once-over and publish it, it had regressed to the save before I wrote it.

Ok, so finally let's talk about chordal tendencies.

We already learned about cadences, and that's a good starting point to think about this.  You'll notice that all cadences with the exception of the Plagal, which is a lot weaker than the others, and is normally used as sort of an after-cadence flourish, they all involve V in some way.  And while one ends in V(Half Cadence), we'll note that the V-anything other than I cadence is referred to as the deceptive cadence.  That's because the V-I motion is so strong in tonal music that V-not I is all "HOLY SHIT WHAT THE FUCK IS GOING ON", or rather, it used to be.  Now we're sort of used to it and it's no big deal, but it used to be like, whack as shit.

So the basics of this are actually really simple.  Each diatonic chord has "natural" progressions from it(and therefore to it as well).  They are as follows:

I   -  goes to - Anywhere
ii   -  goes to - iii, IV, V
iii  -  goes to - IV, vi
IV - goes to - ii, V
V  - goes to - I, vi
vi  - goes to - ii, IV, V
vii^o - goes to - I

Ok, that's pretty simple, right?  Now, it's also pretty damn restrictive, and in fact, you can go from really pretty much any diatonic chord to any diatonic chord without it sounding too jarring(The exception being V7 and vii^o, because of the collapsing tritone(Yeah, I know, I'll get to it.  Maybe not this lesson, but soon)), but these are the ones that work the best and pretty much will always work.

For minor, we get the following:

i     - goes to - Anywhere
ii^o  - goes to - III
III  - goes to - iv, V, VI
iv   - goes to - V, VI
V   - goes to - i
VI  - goes to - iv, III, V
vii^o - goes to - i

I'm a little more shaky on those, and can't find my theory book that mentioned those, but I'm pretty sure that's right.  Also, you'll notice, as I mentioned before, that V and vii^o are altered in minor for voice leading purposes.  We raise the leading tone(Harmonic minor scale) when playing these because we get the strong.... well we get the strong leading tone.

Ok, so that's the basics, and not as big as I kept building it up.

But hey.... like I said, it's pretty restrictive, right?  For that matter.... hey wait, nothing leads to vii^o.  Well, it's time to learn about substitutions, which are the first level of added complexity to basics of tendencies.

Let's look at a V7 chord in C major.  It has the notes G-B-D-F.  Now let's look at a vii^o in C major.  It has the notes B-D-F.

What we can do is essentially use a vii^o in place of a V7, or substitute the vii^o.  By doing this, we can treat the vii^o entirely as though it were a V chord, so we can approach it from ii, IV, or vi, and it can go to I(and vii^o is one of the few substitutions where leaving it is a little different than the V chord.  The vii^o really doesn't go well into the vi chord, which is why evne though nothing leads to it, it still has its own place in the list of tendencies) While in this case, the vii^o simply omits a single note, there are other substitutions I want to look at that change things up a little, and can be used more fully.

The first one I want to look at is the use of inversions as substitutions.  As an example, instead of the strings I used for the last example, here's a brass band:
Click here to listen to iii v I6.mp3
Now, this basically is the exact same figure twice, right?  Except that third chord sounds different.  Just a little, and it still works, but it sounds happier and move conducive to upwards motion in the second time.

Well, that's because we use an inversion of the I6 chord in the example.  While the I chord can go anywhere it wants anyways, the ii chord does not lead to the I chord.  However, since the I6 chord is only one note away from the iii chord(That is to say, they share the 3rd and 5th scale degree and only differ as the Tonic is in the I chord and the leading tone replaces it in the iii chord).  Now, the first inversion of chords tends to have a very "pretty" sort of sound, they sound nice and open, and they tend a little upwards.  Second inversions tend to sound a little unbalanced and unstable, and in certain cases can sound like a suspension of a different chord(for instance, in the cadential 6-4 from last lesson, even though it's a I6-4, it sounds like a V chord that just has the 6-4 above it that then resolves down)  Personally, I love first inversions and sub-ing in first inversion chords, I just love the sound, and having them in open voicing I always think just sounds awesome and is a really useful tool.

So with substitutions, we open up those restrictive tendencies a lot, because now, for instance, if instead of a iii chord we want to use a I6 chord?  Well we can.  So now anything that leads into iii can also lead into I6.

Now, not all substitutions of inversions will work, and they won't work 100% of the time, but here are the most common substitutions:

chord - substitution
iii - I6
vi - IV6
V - vii^o


Ok, pretty simple still.

You'll all notice though, that we're still just dealing with groupings of two chords.  x -> y is fine, but that's only a small part of progressions.  Well, we can theoretically tie them together any way we want, but there are a few groupings of chords that are very common in music and have very recognizable sounds and uses.  We're going to refer to these as Chord Paradigms, and they're going to be what the rest of this general unit is about, because they're pretty heavy.  Essentially though, they're simple progressions that are fairly common.

I'm going to end this lesson here, even though it's fairly short, and start on Paradigms next lesson, with the most common ones and their sounds.  We might have a bit of a delay again between these as well, because I'm pretty busy, I'm going on tour the week after next, and I have a lot of examples to prepare sound files for.

Lesson 11: Roman Numeral Chordal Theory 2: Simple Analysis

 Note: This lesson will use PDFs as examples, so you'll need to be able to read PDFs.  I'd use JPGs like normal, but I have multi-page print-outs that I'm using, and PDF seemed the best for it.  Sorry if this is an inconvenience to anyone.  Also, I'll be linking in both Wuala and Wikiupload.  I haven't found a place to host that has direct linking without having the files expire.  With Wuala, you can just download directly without getting the Wuala application, even though the page gives the Wuala application as the first big link at the top.

Ok, I know I said I'd get to chordal tendencies this post, but I'm going to split off a bit to give us some practice in reading and recognizing Roman numeral theory.  Also, I'm going to introduce a new concept known as Tonicization, which is essentially playing pretend in a new key.  I know, this will feel eerily like homework, but getting practice in this is important, and it'll help cement these ideas.  Also, I'll be referencing this example while talking about chord tendencies, since it was originally written just to reinforce that, and then I realized hey, why not get more use out of it.

So, to start, I've written a nice simple, short piece for String Quartet in the key of C Major.



And there it is.

Now, let's a take a look at this piece, since just hearing it doesn't give us too much information:

PDF
(Alt Link)   

Ok.... eh.  That's a little more useful, but that's a bunch of notes in there.  If only we just had the chords laid out a little more simply.

PDF 
(Alt Link) 

Ok, there we go.  Now, for fun, see if you can figure out the Chords written as absolute notation there(e.g. C, C/E, etc)

Side note:  Holy shit, I never taught you guys how to read Alto clef.  Fuck, let's do(it live) that now.

So, those examples have that weird-as-fuck clef thing, don't they?

 Yeah, that one.
Well, as that image shows, C is right in the middle of the clef.  It says C¹ but it's middle C in there.  So that's the equivalent of the C one ledger line below the treble clef, and one ledger line above the Bass clef.  Why do we use it?  Well, you'll notice that the line in those examples pretty much stays in the staff the entire time with that clef.  That wouldn't be the case if we were in treble or bass, so we use Alto to make it easier to read.  I know, it's sort of a bitch to figure out at first, but if you get used to it, it becomes easier.  One thing I like to do to make it easier is to remember that the top line is G, and the bottom line is F.  That way, you only have to count from the nearest known note to get to the note, instead of always from C.

Ok, now let's try to figure out the chords in that example.  There are suspensions and whatnot, but let's not worry about those, and just focus on the main consonant chord.

It should look something like this(Chords given above the staffs)

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Note:  So I fucked up one of the chords.  Anyone spot it?  Measure 18, the third measure of the second page.  That's actually fucked up in two ways.  The first is that I've called it an E chord, which would insinuate E Major, and it's clearly not EMaj.  The second is that while in measure 2 we have the same general thing with a C/E chord, in 18 we've got that B in the top line.  I wasn't going to give an intro to 7th chords in roman numerals just yet, but hell, looks like I did.  So for now, let's say that's a CMaj7/E.  Because that's pretty much what it is right now.

Now, let's try to do some Roman numeral analysis shall we?  This is pretty simple, right?  Take the root of the chord and phrase the number as a roman numeral, so that C chord is a I chord, C/E is.... fuck.  I?  iii?  I/iii?  Eh, skip it for now, F is IV, C/G is.... fuck.  I?  V?  I/V?  Well goddamn, for writing such a simple example I sure fucked that one up, we can't analyze it!  I suck at this music thing.

Note, before I go on, it's important to note that you will often see roman numerals with slashes, such as "I/V".  It's very important to note that those are in fact not inversions, but rather a concept I'll get to called "Secondary Dominants"

We introduce two new things here.  The first is inversions, the second is a specific type of inversion known as the "Cadential 6-4".  So, when we have different bass notes in roman numeral analysis, we phrase them by the intervals in the chord.  Technically, a I chord in root position, for instance, is a I5-3 chord.  We write them as a fraction(sot of) when we actually write them out, after the number.  I can't really explain it better than that here, but you'll see in the example what I mean.  This is pretty easy to understand for triads, and a little more confusing with 7th chords.

Triads though, so root position is 5-3, because above the bottom note, we have a fifth and a third.  When we go to first inversion(Third in the bass.... That lesson was a while back), then above the  bottom note we have a 6th and a 3rd.  So we technically would say it's a 6-3 chord.  With both of these, though, we don't mention the thirds or the 5ths, because those are... well, they're assumed.  Similar to how we don't have to write out "Major" after Major chords, we can just write out "I" and we assume it's in root, or 5-3 position.  Now, for second inversion, we do write out everything, which makes it a 6-4 chord.

So with what I've just said, the C/E is a I6, and C/G would theoretically be a I6-4 Chord, right?  Well, almost.  The C/E is a I6, which is nice and easy, but that C/G is wonky.  First, let's cover 7th chords, then we'll go over why we don't in a very specific instance such as the one in the example, call that C/G a I6-4.

So, 7th chord inversions are trickier, because we have three intervals, and three possible inversions.  Root is still pretty easy, we just write it as the chord, though it's technically 7-5-3.  Now... 1st inversion, let's look at that, 'cause this is where we get stupid.  in 1st inversion, we have a 6th, a 5th, and a 3rd.  Here, we do write the 5 out.  Don't ask me why, but 1st inversion of a 7th chord is 6-5.  2nd Inversion, we have a 6th, 4th, and 3rd.  But we just write out the 4th and the 3rd, so 2nd inversion of a 7th chord is 4-3.  And finally, Third inversion, with the 7th as the bottom note, We have here a 6th, 4th, and 2nd.  We just write out the 4th and 2nd, so it's a 4-2.  I've seen something like I2 be written before, but I learned it as I4-2.

For a nice example, look at this site  It makes things nice and clear.

Now, I know you're all curious about the C/G, but I know there are probably questions about what I'm going to talk about next, too.  So.  Look at that example on that site.  It's written as I7.  But it's a Major 7th chord.  So.... what?  Well, it's time for another "Fuck Theory" moment.  In Roman numeral notation, we assume the unaltered, diatonic form of chords, instead of having different meanings for different 7 writings.  So I7 is a Major 7th chord, but V7 is a dominant chord.  Confusing?  Kind of.  Just assume no chromatic alterations unless clearly specified or specific instances in Roman numeral notation.  The one obvious exception to this is V in minor, since... well, V has to be modified to be V instead of v in minor.

Ok, and what about that fucking C/G that I've now delayed talking about for so long?  Well... this is an example of a specific notation in roman numeral analysis, which we'll see some more of(for instance, It6 chords and the like.  Those are assholes too).  This is what's known as the Cadential 6-4.  It's called that because it's used in a "Cadence"(did I talk about these?  Looks like a no.  Well shit.  Get ready for a long ride)

And what is a cadence, before we explain more the cadential 6-4?  Basically, it's the period on the end of a musical sentence.  Cadences typically come in 4 main forms, with a bit of sub-forms thown in.

The first is an Authentic Cadence, which is any cadence with a V-I movement.  These come in two main sub-forms.
The Perfect Authentic Cadence, which is also the strongest, is V-I in root position, where the highest voice is also the tonic in the final chord.
The Imperfect Authentic Cadence is basically all other Authentic Cadences, including those using a vii^o or Tritone Substitution in place of a V chord(I know, I know... Tritone subs are waaaay off though, sorry)

The second is the Half Cadence, which is any cadence that ends on V.  It's called a half cadence because it's a cadence, but sounds unfinished.  It's usually used as part of a repeated or semi-repeated section to indicate the end of the first part, and then replaced with an authentic cadence in the repetition.  Mozart fucking loved doing that shit, by the way.

The third is the Plagal Cadence, or Amen Cadence.  It's any cadence with a IV-I motion, and it's called the Amen cadence because anytime anyone ever sings an "Amen" in choral music, it'll be a Plagal Cadence unless the composer is a douchebag.

The final is a Deceptive Cadence, which is any cadence that goes from V to something not I.  The most common is the V-vi deceptive cadence.  Seriously, you see it everywhere.

So.  Those are cadences.  Now, to the Cadential 6-4.  This happens pretty much always over the V chord when it happens(in fact, I'm not sure it could be anything other than over a V chord), and it's a I6-4 chord resolving to a V chord.  When writing this, we ignore the fact that technically the I chord is spelled out with notes, and write it as V6-4 going to V5-3.  And yes, we write out the 5-3.  Sometimes there's a 4-3 suspension in there, so we have to write the 4-3 resolution after the 6-5 resolution, though the 6-4 are written simultaneously.  Also sometimes if the composer is feeling super-hamfisted they'll add a 7th after a 6-4 resolution with a 4-3 suspension, and we write that out too.  Then we shake our heads and mutter "Hack" under our breath.

Ok, so armed with that information, we can continue looking at the chords as roman numerals in the example, which gets us all the way up to measure 8 before we have another concept I have to introduce.  It's almost like this example was written to introduce as many of these concepts as possible in a really clear way.

Anyways, that gets us something that looks a bit like this(Chords above, Roman numerals below):
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And if we look past that.... well it starts getting weird.  F makes sense, that's just a IV chord, and then... I6?  then... ii...V(Major? there's no Bb or natural to tell)....I, well ok that makes sense, but then that leads back to IV?  I doesn't feel compelled to go to IV normally.  These chords kind of fit in C major, but let's ignore what happened before, and imagine for these 8 measures that we're in F.  Now we've got I - V6 - vi - ii - V  I - V6 - vi - ii.... II7?  Ok, now it stops making sense.

Well, this is a judgment call really.  It does sort of make sense in C, but I think it makes more sense in F, because the Descending bass line is a fuck of a lot more common than a descending IV thing.  And for this example, let's play pretend we're in F for a few measures.

Well, what we have is basically a tonicization.  A Tonicization is really pretending for a small amount of time that we're in a different key, sort of like a key change but without a full key change.  The reason we do this is because while it works in both keys in this example, if that gm had a Bb like it should've if I was being smart, then this would've been reeeeeeeally confusing in C, and a lot of times there are chords that are just stupid as hell in the original key that if you think in terms of a different tonic work wonderfully.

Now, when writing out tonicizations, we normally have a pivot chord, which is a chord that works in both keys.  In this case, it's that I chord in measure 8, which is V in F.  So we add a second line to the analysis that shows us in the new key and continue from there, 'till we get back to the first key.  And to go back to the first key, we basically do the same thing, bring back the first line in C on the pivot.

Basically, finishing up the analysis we get the following:
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Also, you'll notice at the end there I've written "PAC".  When we do analysis we like to identify the cadences when they happen, especially at the end.  Were I being super-thorough I'd identify all cadences, which would put an HC in measure 4, IAC in 8, PAC in 12, PAC in 16, HC in 20, PAC in 25, and the PAC at the end.  And if you're wondering what's with the letters, we basically just abbreviate the names of the cadences.  PAC- Perfect Authentic Cadence.  HC - Half Cadence, and so on(IAC - Imperfect Authentic Cadence.

Also, were we being super strict about things, we would label all nonharmonics.  To give an example, I've done a full-out analysis on the piece, to show what it looks like when you do everything.

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You'll notice that that's incredible amounts of overkill.  We rarely need to go that in depth, but technically we do for a full analysis.  The reason we don't is because that's like, useless amounts of information.  It's good practice, but that's about it.  It's also good to embarass yourself when you write an example for a theory blog originally just for chord analysis and then realize that it's really shittily written in accordance with the rules of voice leading you supposedly know enough about to explain.  There are a lot of awful Nonharmonics there that aren't resolved right so.... don't write like that.

Anyways, I think that's enough for this post.  Next post, unless I realize there's something else I need to cover before going on will be Chordal tendencies.