Saturday, February 24, 2007

Modes & Scales

Modes, Scales and Temperments

Hopefully, not more than you wanted to know.

To the novice there are few things about traditional folk music more confusing than the "modes". Of course to a lot of us the whole idea of formal, written music is a bit forbidding; but one system, with its keys and tonics and dominants and things like that, is bad enough without having two, or maybe more, systems. Even to people who know enough about the theory of music to read scores the modes are soinewhat mysterious.
They do, however, make a kind of sense, and I am going to try to articulate that sense in this little essay. I don't guarantee that it will tell you all there is to know, or even feel entirely comfortable with them; but I hope it will leave you able to face the words like "mixolydian" without flinching.

There is a deceptively easy way to explain the modes by reference to a piano keyboard. First of all you ignore all the black keys---the sharps and flats. We'll get back to them, but for now we don't need them. Now sound a scale by starting at "C" and going up the keyboard hitting every key till you reach the "C" an octave above.

In ordinary notation that is called the "major" scale. In modal notation it is called the "ionian" mode. Now do the same thing, except start on the "A". That scale is called the "minor" scale, and it is also called the "aeolian" mode.

In ordinary notation those are the only scales that are given specific names, while in modal notation there are several other scales, each with its own name. Thus we can say that ordinary musical notation has developed by taking only two of the modes and building on those.

This would indicate that ordinary notation is less flexible than modal notation, except that we have been ignoring the black keys. Ordinary notation has the possibility of using the sharps and flats that are entirely outside the major and minor scales, and that gives it a tremendous flexibility.

But folkmusic generally doesn't need that kind of flexibility. Most folksongs don't use more notes than are in the wholenote scales (those that can be played on the white keys). Instead they get their flexibility by using different wholenote scales.

For instance, if you sounded a scale like we did before, but started on "G" instead of "C" or "A", you would get the scale of the ''mixolydian'' mode. If you started with "D" you would get the "dorian" mode. The effect of choosing these different scales is like that of going from major to minor; in fact the tuning of the banjo that is convenient for playing in the dorian mode is often called the "mountain minor."

The mixolydian mode feels a little more minor than the major scale (or ionian mode); and the dorian mode is still more minor in feeling, but not as minor as the aeolian, which is the minor scale. Choosing between these different scales one can find tunes that are appropriate for different modes. That gives a reason why the modes should exist, but it doesn't explain why they have those weird names.

As it happens, that is something of a mistake. The creator of a folksong doesn't say "I think I'll write this one in the dorian mode"; he just remembers (or creatively misremembers) a tune that sounds right for the thing he wants to say. Tunes and scales are given names by music theorists; and the modes were named in the middle ages.

The medieval theorists invented modes as such, but in those days it was important to refer everything to ancient authorities. Theg thus said, and maybe even thought, they were rediscovering the musical system of the ancient greeks; so they gave the modes ancient greek names. There are lots more, because you can get a different mode every time you sound a scale starting on a different key; but most folksongs ae in the four modes mentioned, ionian, mixolydian, dorian and aeolian, so we'll ignore the rest.

That is a simple explanation but, as I said, deceptively simple. It ignores the question of why a wholenote scale starting on "C" should sound different than one starting on "G". Or, conversely, What do you do if you want to play a mixolydian tune in the key of "C"?

That there is any difficulty here comes about because some wholenotes are stparated by two semitones and some only by one. if we look at the piano keyboard again, but this time look at both the white and black keys, we see that some white keys are separated by a black key and others aren't. There isn't any key between "E" and "F" that would sound E-sharp, or F-flat, anid there isn't any key between "B" and "C" either. These short intervals are called "gaps" and the modes can also be characterized by where in the scale the gaps fall.

In the ionian mode the gaps fall between the third and fourth notes and the seventh and eighth notes; while in the dorian mode they fall between the second and third notes and the sixth and seventh notes. (Why this should make one tune sound "sadder' than the other I simply do not know. It may be that we just expect it to.)

If, therefore, you want to play a Dorian tune in key of C you substitute an E-flat for an E and a B-flat for a B and you have a dorian scale.

One of the things that makes the appalachian dulcimer an interesting instrument is that it automatically plays in modes. It is [traditionally] fretted in wholetones and the positions of the short intervals or gaps is such that you get a mixolydian scale when you start with the open string. But the dulcimer is not restricted to the mixolydian mode, because any fret can be chosen as the basic, or tonic, note of the tune; and the drone strings can be tuned to the same note (or an octave lower) and an appropriate harmonic interval such as a fourth or fifth.

If, for instance, you want to play an aeolian tune in the key of "C" you retune the melody string to sound a "C" when the dulcimer is fretted on the first fret after the nut and tune the drones harmoniously. For a guitar player this sounds inconvenient, but obviously when the frets have some large spacing and some short, making a gapped scale, you can't use afiything like a capo.

But that raises the question of why you can use a capo on a guitar?
This brings in the question of the temperament of a scale and that is quite interesting. It is also a bit difficult, so bear with me.

Let's think about a very simple instrument, the monochord, which has just one string. The basic note that it makes is that produced when the open string is plucked. If the string is fretted or stopped at other lengths it will produce other notes, and some of these have a definite harmonic relation to the basic open notes.

If the string is stopped at its midpoint, the note sounded will be an octave higher than the open note. This is because the pitch (or frequency of vibration) of a plucked string is inversely proportional to its length (all else equal) and the octave is a note that is in a 2:1 ration of pitch to the basic note. Similar things happen when the string is stopped at three-quarters and four-fifths of its length. The next simplest ration to the octave, that with a 3:2 ratio of pitch, is identified with the fifth step of the scale on which the octave is the eighth step.

The musical scale can be built out of this 3:2 ratio alone. If, for instance, one starts with C, the note a fifth higher is G, a fifth higher than that is D, and continuing in like manner gets A, E, B, F-sharp, C-sharp, G-sharp, D-sharp, A-sharp, E-sharp, B-sharp, F-doublesharp, C-doublesharp, etc.

Going down from C in fifths one gets F, B-flat, E-flat, A-flat, D-flat, G-flat, C-flat, F-flat, B-doubleflat, E-doubleflat, etc. The octaves are considered to be musically identical, so we can consider all these notes to be within the same octave. Then we have a problem.

If we look at the vicinity of the interval between B and C, which we know is a short interval of one semitone, corresponding to one fret-spacing on a guitar, we see that we have seven different notes: A-doublesharp, B, C-flat, B-sharp, C and D-doubleflat. In this system they are all distinct notes. Obviously a guitar with seven times the number of frets, or a piano or organ with seven times the number of keys, isn't really very practical. What we do is to compromise, and the way we compromise is called the "temperament" of the scale. The first compromise is to cut down the number of frets on the guitar or keys on the piano by lumping the notes that are close enough into one note. We say, for instance, that A-doublesharp, B and C-flat are all the same note. That gives us twelve semitone intervals in each octave; but we still have the freedom to make any of these semitones a little bigger or smaller than the rest. This would make it inconvenient for the makers of fretted instruments, and it would prevent us from using the capo, so guitarmakers prefer to make all the semitone intervals the same.
In other words each fret-spacing decreases the string length in the same proportion. This is the ''even'' or "equaltone" temperament. In the piano, or harp, or organ, where each note is tuned separately, all lemperaments are equally convenient. and there are some others that can be used.

In what we can call the ''Pythagorean'' temperment we preserve the intervals of octave and fifth in perfect harmony; but this makes the interval of a third, which is important to modern harmony, sound a bit discordant. In "meantone" temperament we preserve the perfect harmony of octave, fifth and third in the key of C; but keys with sharps and flats in them sound more and more discordant as they go farther from C.

In general all modern instruments are tuned to the guitarmakers' compromise, the equaltone temperament. In this temperament neither the fifth nor the third is in perfect harmony in any key, but the degree of discordance differs in each key. This difference is what makes classically trained musicians say that the same series of intervals has a different "feeling" when played in C or, say, in E-flat; so that the key in which music is composed has signifIcance.

This variation, together with the freedom to use all twelve intervals in composition, made the modes superfluous in classical music and they disappeared from the music textbooks.

The voice, however, is a more flexible instrument than one that is keyed, or fretted, or stopped like a flute. This makes it possible for an unaccompanied singer (or the player of a fiddle tune) to shade notes up or down within the tune if that ''feels right". This amounts to a change in the temperament of the scale he is using, so that the key he is singing or fiddling in is less important than something which indicates the general mood of the piece. This, in turn, means that the modes, which represent intervals of gradation of mood, make a very sensible way to characterize a folktune.

The demonstration of this is Bertrand Bronson's massive compilation of The Traditional Tunes of the Child Ballads (Princeton, Princeton University Press, 1959- ) which uses the modes as the basis of a system of classification. The discussion of modes in the introduction of Volume II of the series is recommended to anyone interested in pursuing this subject any farther than this elementary discussion.

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