## Friday, February 5, 2010

### Lesson 10: Roman Numberal Chordal Theory I: Foundation

Ok, so.  Finally, right?

It took us long enough to get here, but now we're at roman numeral theory.   Roman Numeral theory is great for about a billion reasons, and if you're conversant in it and understand it, it is easy mode for music in so many ways.

You see, we talked before about how specifically to talk about chords, by talking about Co7/Eb or whatever, and that's great, and tells us a bunch, but it is also like, completely in a vacuum in terms of how it relates to anything around it as an intellectual object.  While that's how you'll see specific things written, and you'll be using written out sheet music for, you know, reading sheet music, when discussing music in a theoretical way, we normally don't get that specific, because we're dealing with relationships, not specific things.

You know what, that's sort of a confusing thing to say without explaining first the basics of Roman Numeral theory.

Ok, so we've all heard people saying things like "Yeah, it's just a I-vi-IV-V-I thing" or shit like that, I'm sure, and maybe we even have a basic idea of what all that means, but what does that all mean?

Well, let's look at a basic major scale.  We have 7 unique pitch classes in a line.  To start, let's assign each of those pitch classes a number.  We'll take C major for fun, and so we start saying C is the 1st one, D is the 2nd, etc.  These are scale degrees, and are what we use to talk about notes in any nonspecific scale.  That is to say, the 3rd scale degree in C major is E, but the 3rd scale degree in Gb major is Bb.  So the advantage is that now when we talk about the 7th scale degree, we can know how that relates to the 1st scale degree in every scale we talk about, not just, for instance, how B relates to C

We also have names for scale degrees, because apparently numbers were just a little too simple.  Actually, the names are really useful, because they give us some terminology that is pretty descriptive of the job the notes do instead of remembering, for instance, that scale degree 7 naturally leads to scale degree 1.

These names are:
(Scale degree - - Name)
1 - Tonic
2 - Supertonic
3 - Mediant
4 - Subdominant
5 - Dominant
6 - Submediant

Ok, so the most confusing one there is the Submediant being above the mediant.  Other than that, the supertonic is above the tonic(and sounds awesome), and the subdominant is below the dominant.  So what's the deal with it being the "submediant"?  Well, measure a third up from the tonic and you get the mediant.  Measure a third below and... submediant!  The other way to think about it is that the Mediant is the middle note in a triad with the root of the tonic, and the submediant is the middle note of a triad with the root of the subdominant.

Now, I'm willing to bet that some of you also know the scale degrees by other names, which would be Do(or Ut), Re, Mi, Fa, Sol, La, and Si(or Ti).  I will not be using these, for two reasons.  One reason is that this has no advantage over knowing the scale degree numbers or names in terms of theroy, so it's really just another thing to learn. Another is that Solfege(the system where we call the notes those names) comes in two varieties.  One is "Fixed do" and one is "Movable do".  In fixed do, Do is always C, regardless of where it is in the scale.  In moveable Do, Do is always the tonic, regardless of where it is absolutely.  So essentially, solfege is either an absolute or relative measurement.  There are reasons for using both, but really, I still don't think they really have any advantage over the other absolute or relative measurements we have for Theory.  Now, I will probably be using the fixed do system while hoping to also phrase things in movable do if I cover sight-singing, because solfege is a great tool for that, for a variety of reasons.  But for theoretical purposes?  I really don't see a reason to use them.

Anyways, those are the scale degrees.  Now, let's not alter any notes from the key signature and build chords on each scale degree, and we get 7 chords.  We refer to these by the scale degree they're built on in root position.

So basically that.  We use roman numerals here.... well, because we do.  This makes things easier than using normal numbers actually, since you'll notice that some of the roman numerals are capitol and some aren't.  Well, look at the chord makeups and you might see why.  You know how instead of writing "CMaj" or whatever, you can just write "C" and assume major?  Well it's the same thing with the roman numerals.  I is a Major chord based on the Tonic(Scale degree 1), and i is a minor chord based on the Tonic.

In Major, the chords are as we see in that image.  I is naturally Major, ii is minor, iii - minor, IV - Major, V - Major, vi - minor, viio - diminished.

In minor, things get a little wonky.  In its natural position, also known as the natural minor scale, we have the following:
i - minor
iio - diminished
III - Major
iv - minor
v - minor
VI - Major
VII - Major

Now, the reason things get wonky is because as we'll learn, the V chord is a really, really strong move to I(or i).  Like it is the way to lead back to I(or i).  Even more so if we make it a Dominant 7 chord(I'm sure you've noticed that the Dominant tone of the scale is based on V.  And the Dominant 7 chord is... well, it's called the Dominant 7 chord.  These two are related.  V leads to I, and Dom 7s have the V-I motion).  There's a really nice explanation for this involving the tritone collapsing and all that, and I'll get to chord relations and voice leading with that, but basically all you need to know is that V goes to I(or i).  A reasonable substitute for V or V7 is viio, again, for a reason we'll go over(Actually, this one is a little simpler.  Take a V7 chord in any key... for now let's say C Major to keep things simple, and then take a viio chord.  Look at the notes there.  G7: G, B, D, F.  boB, D, F. Hey look).  Anyways, so they lead super-well to the tonic chord.  Well, in minor, you'll notice that v is naturally minor and VII is naturally Major.  So to compensate for this, in minor it's very common in tonal practice to raise the leading tone to make V major and viio diminished.  Also, having the leading tone raised to give it only a half step away from the tonic makes it really... well, lead as a tone.

Now, this also brings up a slightly confusing thing.  We will find we reuse terminology a lot in this section.  For instance, the Dominant can refer to the scale degree, the Chord built on the scale degree, or the type of 7th chord.  The only real way to figure out which is in context, unfortunately.  It's safe to say that, for instance, if I say "x based on the subdominant", I'm probably talking about the note.  If I say something like "The Dominant-Tonic motion", I'm probably talking about the chords, for reasons we'll get to, and if I say "Dom7" I'm talking about the type of the 7th chord.  That one's easier.

Anyways, I know this is a super-short post, but I just came back from a long-as-fuck night, and I need to go to sleep.  Also, the next thing I'm going to cover is chordal tendencies and holy shit you guys is that post going to be a doozy.  I don't want to mix them up, so for now, just take these basics and make sure you understand them before we move on.

#### 1 comment:

1. Hi man! I just came across your entry, trying to get music theoriy knowledge from everywhere. It's really hard to wrap your mind around as a beginner, but that post is rather nice. Granted, you've lost me a bit after building the scale chords, but it's nevertheless very enlightening. Thanks!

-Mike