Sunday, August 4, 2013

Keys, Modes and Scales

Prompted by some comments on one of my Beethoven posts I think it might be useful to talk about these mysterious things: keys, modes and scales.

To get the obvious out of the way: "keys" are those regions that are defined by "common practice" tonality. But what does that mean? Not so terribly easy to explain. Here, have a look at the Wikipedia article. They have difficulty defining the meaning of "key" as well.

"Key" is a fundamental concept in traditional harmony. In order to write a piece of music, the first thing you have to do is decide what key it will be in. You also have to decide what time signature, tempo and instruments you are going to use. Maybe pick a title. But all these are secondary to deciding on the key. Here is a bare bones piece in C major:

Here is the "same" piece in a different key, E flat major:

I just used the music software's transposition utility to move the music up a minor third, putting it into E flat. The "key" of a piece of music in traditional harmony is the name of the tonic, the "home base", where the music begins and ends. It is defined harmonically with a perfect authentic cadence, as in both the examples. A C major or E flat major triad on its own does not define anything. To create the sense of a key, you need a cadence. A lot of so-called "tonal" music written nowadays does not have cadences so is only loosely tonal. In the Baroque and Classical periods, every piece and every significant section of every piece HAD to end with a perfect authentic cadence. The only exceptions are the "church keys" found in 17th and some 18th century music where the key signature appears to be missing an accidental and where the composition appears to end not on the tonic, but the dominant. There are lots of examples in Corelli and there is even a Bach prelude in D minor that ends on an A major chord. The reason for this is that this is a holdover from the older modal system. As soon as tonal harmony fully established itself in the first half of the 18th century, these anomalies disappeared.

There are twelve major and twelve minor keys. Ah yes, there are two kinds of keys: major, as shown above, and minor, which share the same key signature but start in a different place. Here is the key of A minor, which has the same key signature as C major, no sharps or flats:

What is that sharp doing there? The problem with minor keys is that they don't have a leading tone, so we have to insert one. The leading tone is the note one semitone below the tonic which leads to the tonic: B leads to C and G# leads to A. G natural is a whole tone below and does not lead to A. The major and minor keys are a very useful relic from the modal system as they derive, respectively, from the Ionian and Aeolian modes.

So that is a rough and ready introduction to the idea of "key". And I've also slipped in the idea of "mode". There is a Wikipedia article on modes as well. Modes have a very long and obscure history that goes right back to the ancient Greeks. They had different kinds of musical structures that they named after different tribes (Dorians) and regions (Lydia). In order to talk about modes and, indeed, to complete the notion of key, I'm going to have to talk about scales.

If you go back and look at my little example in C major, you will discover that it uses all the notes from C to D: C D E F G A B C. This sequence of notes, placed in order, is called a "scale". To write in C major, you use the C scale and to write in E flat major, you use the E flat scale. These are major scales and they all have the same interval structure: tone, tone, semitone, tone, tone, tone, semitone. There are also minor scales that are different because they have a different interval structure. The minor scale is all those notes from A to A: A B C D E F G A. The structure is tone, semitone, tone, tone, semitone, tone, tone. But we can't use exactly this structure because of the lack of a leading tone, so we always have to raise the G to G# in a cadence. The rules about when to raise the leading tone (and sometimes the note before, the F, as well) are complex.

What complicates things even further is that the Greek modes fell completely out of use. In the middle ages, when the monks were developing chant, they also developed a set of modes and they used the Greek names. But the so-called "church modes" have nothing musically to do with the Greek modes, they just use the same names. See the Wikipedia article for more confusing details! The church modes, which include the Ionian and Aeolian, source of our major and minor scales, also include several other kinds of interval structures. Here are the eight church modes with their modern names:

Click to enlarge

That little "f" indicates the finalis or note to end on. The modes on the second line, with the prefix "hypo" all end on a middle, not bottom, note. To take just one example, the Dorian mode shares qualities of both the major and minor scales. There is a minor third above the "tonic" so it sounds minor, but the sixth note of the scale is a major, not minor sixth. So it sounds a bit major as well. The Phrygian mode sounds most unusual because it has a leading tone from above--F to E--instead of from below. A lot of the harmonic color of Spanish music comes from using the Phrygian mode.

One way of looking at the relationship between key, mode and scale is to see key and mode as the theoretical structures behind the music, while the scales are what you hear used in the music.

Before leaving this complicated and confusing subject, I should mention that there are scales that lie outside the whole key and modal systems. For example, one scale that was used quite a bit by Debussy is the whole-tone scale, so-called because it consists only of whole tones. No cadences are possible because there are no leading tones. Also, all the chords are augmented chords. Here is what that scale looks like:

Debussy used this in a prelude for piano called "Voiles" that I talked about here.

But there are other scales as well. Russian music often uses the octatonic scale which has eight notes. They are typically organized alternating tones and semitones like this:

But this does not exhaust the possibilities as there are many other possible scales (or modes). Russian theorists have postulated quite a few interesting modes to describe the music of Shostakovich and based them on traditional Russian concepts of mode. As an example here is what the theorist Alexander Naumovich Dolzhansky calls an "Aeolian double-lowered melodic" mode:

And there are a whole bunch of others!

I think that I will stop here before things get any more complicated. Let's end with a piece of music that Dolzhansky used to illustrate his theories of mode in Shostakovich: the Sonata No. 2 in B minor, op. 61. Here are the first two movements played by Valentina Lisitsa:


Rickard Dahl said...

To me the things you wrote in this post seem a little strange. Yes I know about the major keys and minor keys (that the 7th and sometimes the 6th are usually raised) and that the modes at least in the beginning contained these two variations (ending on tonic or on the fifth) and so on. But, you're saying that a leading tone to the tonic is always needed to have a key and that a V-I or V-i cadence is needed to end a piece of music and that it's the only type of cadence. By that way of thinking ionian and lydian are the only western church modes that can have keys and that not even an unmodified aeolian can be considered a key. But there are many different types of cadences, for instance the not too uncommon plagal (IV-I) cadence or the very common half cadence (I-V). Other less common (or maybe modal would be a better word) examples are v-i in aeolian or dorian, II-I in lydian, II-i in phrygian and so on. I don't see why the V-I or V-i cadence is needed a end a piece properly, a piece can sound finished in many ways (speaking from my own experience when improvising), such as one of the many types of cadences (some obviously without a leading tone to the tonic).

The book "Modal Music Composition" by Stephen M. Cormier describes all those things in detail (mostly how to approach harmony for the western church modes but also other things to consider when writing western modal music).

Bryan Townsend said...

Very possibly! My blog is not a textbook on music, it is a personal take on things. I often go out of my way to point out things that are unusual. The crucial part of the post is this:


In traditional harmony or "common practice" harmony, the ONLY thing that can end a piece is a perfect authentic cadence. If you don't believe me, then I invite you to look at all the music by Haydn, Mozart and Beethoven. If you can find ONE piece that does not end with a perfect authentic cadence, I'll eat my hat.

Rickard Dahl said...

Yes but why stick to only traditional tonal harmony?

Bryan Townsend said...

Oh, one correction, I did NOT say that V - 1 (or i) is the only type of cadence. I said it was the only cadence that could end a piece and that properly defined a key.

Cadences are what make tonal music, music in a "key", different from modal music.

I was sticking to traditional tonal harmony because that is what I was talking about.

I did NOT say that modal music requires perfect authentic cadences--in most modes you can't even do them. Just that tonal music does.

Rickard Dahl said...

Alright, sorry for the misunderstanding about the V-I cadence. Personally I prefer to think outside traditional harmony in the sense that I like using modes instead of sticking to the major & minor scales (using modes pretty much automatically goes outside traditional harmony when it comes to organisation (for example the principle of major chords on the fifth scale degree leading back to the tonic chord) as the scale and chord structure differs in each mode). I'm not saying that tradition should be dismissed (in fact there is alot of things I think I will use when composing (as I've mentioned in another comment I've recently started to compose) such as common forms (I especially like the idea of composing baroque dance form pieces)) just that things can be approached differently, for example in terms of modes (and thus harmony).

Bryan Townsend said...

Oh, no worries! When I am composing, I can't use traditional cadences because they no longer sound 'right'. So I am forced to find other ways of concluding pieces and sections. I don't use the regular modes either! Don't ask me what I do, because I invent something new for each context.

So what I was trying to do in the post was mainly try and lay out what is the fundamental nature of the traditional meaning of 'key' and add some remarks on modes and scales. I think it fascinating that the music from the Classical composers is so highly structured. There was no accepted 'rule' about it, it was just that a piece in C HAD to end in a certain way.

Nathan Shirley said...

On the subject of modes-

When my kids were both very young I was away from the piano a lot in order to keep an eye on them. In order to stay musically active I bought a tiny plastic fife in C major. Since it couldn't really play chromatically, I started inventing little modal tunes on it, and decided to come up with one for each of the seven modes as a nice exercise. Later I arranged them for piano. If interested here are the results-

Bryan Townsend said...

That's very nice, Nathan!! It reminds me just a tad of Bartok and of some pieces by Komitas that Sokolov plays in that DVD filmed at the Champs-Elysee.

Craig said...

The other commenters on this post understand these matters much better than I do. I have no training in music theory, and I've only picked up things here and there. I can remember cornering a pianist friend of mine a few years ago and asking her questions along these lines:

"What makes a piece of music to be in particular key?"

"Well, you look at the sharps and flat written at the beginning..."

"Yes, I know that, but why does a particular set of sharps and flats make the music to be in a particular key?"

"That's the definition of each key. It defines the scale for that key."

"OK, so if I am playing in a particular key, does that mean I can only play the notes in that key's scale?"



Only later did I slowly come to understand that keys are really defined by the relationships between the notes. I still don't understand it very well. I keep looking for a good explanation that is geared to a physicist or mathematician (which is what I am), but I haven't found one yet.

As you can imagine, I really struggled through the music theory bits in Taruskin!

In any case, I found this post helpful.

Bryan Townsend said...

If you really want to experience severe cognitive dissonance, ask a drummer what a paradiddle is!

But I think I can help you with this a bit. All major keys have the same interval structure. In C major, you just play the white notes on the piano from C to C. Now, it turns out that if you want to reproduce that same interval structure starting on a different note, you have to use one or more black keys. For example, say you want to be in G major instead of C major. It turns out that you will have to use one black key, F sharp instead of F in order to reproduce the same series of intervals that you had from C to C. If you want to start on E flat, you will have to use three black keys, and so on. The same applies to minor keys: all minor keys have the same interval structure, etc. etc.

I'll bet you will understand some books on 20th century music theory better than I, though! EX: Alan Forte, The Structure of Atonal Music. It's all about interval vectors and stuff.