Thursday, November 29, 2007

A Scale! Ahava Rabbah!

http://en.wikipedia.org/wiki/Ahava_Rabbah

I'm a Jewish atheist, or Humanist, or Pastafarian, or whatever. I don't believe in gods, but I'm Jewish. Figure it out if you feel so inclined (Wikipedia can help). But the Ahava Rabbah scale is one of my favorite scales (mentioned in the last post as well), also known, according to the article linked above, as the Spanish phrygian, Jewish scale, Hungarian scale, or phrygian dominant. I'll stick with Ahava Rabbah, at least for now, but it really is a phrygian with raised 3rd.

I love this scale. I suppose the augmented second sounds "mystical", which in today's postpostmodern age is quite the cliche, but to me it really does. Listening to liturgical music that uses it makes me feel, well, elevated, which I'm sure the religious would interpret as "closer to Hashem". (This is because the religious can't write "Adonai", as that is using the name of God in vain -- instead, they use "Hashem", meaning "the name", in writing and singing, and they use "Adonai", "Lord", in actual prayer. They will sometimes use "Adoshem" when emphasis on pronunciation is necessary, and "Elokeinu" for "Eloheinu". Now you know.) The point is that I love this scale, and modulating to it is an interesting touch, much like that major chord in a minor piece that is like sunlight.

The typical cadences in Ahava Rabbah are not V-I as might be expected, since the 5 chord is actually vo rather than the v that you can change into a V. Instead, the cadences are bII-I and bvii-I (the convention is confusing and I can't be bothered to follow it; hopefully this is clearly referring to the chords on the 2 and 7 of this scale). bvii is especially nice, because since the important half step occurs between 3 and 4, an improvisatory-style melody would tend to hover around there, and the 7th degree would be a refreshing note to signal the cadence. In some chanting schemes this is actually done. A nice melodic cadence using bvii-I would be, in C: Bb' F E Db C; the Shabbat prayer Shalom Aleichem uses this, though the position of the tonal center makes this a half cadence instead. In fact, this is just the conventional phrygian cadence of Western tonal music, iv6-V, but with the function of an authentic cadence (and since this is used in mostly monophonic liturgical music anyway, with no attention to inversion numbers).

But yeah, Ahava Rabah, awesome scale.

Sunday, November 18, 2007

Scales, Harmonic and Melodic

There are two similar but somewhat different things we call "scales", and sometimes those two things are different and sometimes the same. There is the harmonic scale and there is the melodic scale, and they are each sets of pitches from which one draws harmony and melody, respectively. The melodic scale is an ORDERED set of pitches, and the harmonic scale is not -- this is one of the main distinctions between them. This is important when we consider what the silly "common practice" people call the minor key.

It took me a while to realize that the three minor "scales", natural, harmonic, and melodic (and I don't mean the jazz melodic scale, I mean the CP one), were not all meant to be played. My first encounter with scales, as such, was in beginning band in sixth grade, or maybe in my piano computer program in fifth grade, and they were major. I knew what the minor keys were, but I never had to play minor scales. When I saw "harmonic minor" and "melodic minor" in a book from the school media center in sixth grade, or maybe someplace else, I saw them as curiosities, and I liked the sound of the harmonic minor scale, and I wondered at this melodic scale thing that goes up and down differently.

Eventually, in college, while taking a music theory course, I realized several things. First, the augmented second in the harmonic minor is essentially wrong. Second, the leading tone HAS to be a half step below the tonic, which is why the 7th is raised. Therefore, the 6th needs to be raised as well if you're moving to the raised 7th from below. So the minor key, with a flatted 7th and 6th, needs to be modified. The V chord has a leading tone when it goes to i, so it has to be V rather than v. Everything else still works, so the scale with this modification is the harmonic scale. The b6 and b7 still want to be used, but they can't be used if the tonic is approached by step from below. So if you're going to PLAY the scale, you have to raise the 6th and 7th on the way up, but going down you can keep the minor key feeling.

Personally, I find this all very silly, and enough other people find it silly, so we play just one minor scale: the melodic minor. When we play scales, which are a useful exercise for instrumental technique, the melodic minor should be played (if we are practicing for CP music), since those are the note patterns that we are likely to see. There is no reason to practice playing the harmonic minor scale -- this is because the harmonic minor scale was never meant to be played! The harmonic minor is the set of notes from which we draw the harmony. There are really only five chords, i, ii0, iv, V, VI, in the minor key (though with melodic minor melodic materials, you can include also ii and IV, but these are essentially chromatic alterations). III and VII don't really have functions so much, and even VI is a little iffy, so we can essentially limit ourselves to using the notes from the harmonic scale. The melody, conceived entirely separately and heard entirely separately (this is not true, but let's consider it as such), uses a different set of notes, and given the rules of CP, they are different going up from going down.

The melody and harmony, let me stress, use DIFFERENT SETS OF NOTES. There are plenty of examples, of course.

First, the blues scale. Mark Levine's Jazz Theory Book claims that nobody understands how it manages to work, but I claim that I do. (: In the key of C, the blues scale is C Eb F F#/Gb G Bb C. The twelve bar blues progression is C7 C7 C7 C7 F7 F7 C7 C7 G7 F7 C7 C7. Now, let's consider ripping the nonfuctional dominant 7ths out first, so we have C C C C F F C C G7 F C C. This uses the harmonic scale C D E F G A B, so we have that as a harmonic scale and C Eb F F#/Gb G Bb C as the melodic scale. The only common notes here are the tonic, subdominant, and dominant, the roots of the chords! We have here an extremely inflexible system, since this blues scale depends in a way on the fact that we're not using it freely but over a progression that essentially works like the traditional 12-bar blues. We can't really modulate in the scale; the scale has no symmetries! Of course, that's also true of the normal major scale; we have to introduce new notes to modulate. In this case, though, the tendency to the tonic is very strong from the Eb and the Bb. The Gb also tends very strongly down in a way that leads to the tonic. NONE OF THOSE THREE NOTES NEEDS TO BE IN TUNE. They aren't in the harmonic scale, and they form no harmonies. They can be wildly flat and they'll work just as well! (If C7 and F7 are used, though, the 7ths in those chords should probably be the same as the ones in the melody, since those are essentially melodic tones added to the chords rather than harmonic/functional ones).

The blues scale is essentially a harmony that works with bitonality over the C major harmonies in the progression. Let's see how the notes match up, ignoring common tones. Over a C chord, we have the Eb clashing with the E. The Eb has a strong melodic pull to the tonic, so you can hear it as an appoggiatura, essentially. The F clashes with the E as well, but that pulls to the Eb which pulls to the tonic. The Gb clashes with the G, but that pulls to the F which pulls to the Eb which pulls to the tonic. The F# pulls to the G, which is stable. The Bb pulls to the tonic or the fifth, but it doesn't actually clash with anything. The tonic essentially remains a pedal through the other chords, and the blues scale is essentially an elaboration of the tonic pedal. You can use the same logic to consider the notes over the other chords. Over F, then, you have C being stable as the fifth, Eb pulling down to it, F being stable as the tonic, Gb pulling down to it, F# not really working, G being the fifth of the pedal C blues scale, and Bb pulling the same as over the C chord in the tonic pedal scale. Over G7, C is the pedal, Eb tends to C in the pedal, F if the seventh, G is the root, F# tends to it, Gb tends down to the F, and the Bb tends either way in the pedal. So the clashes aren't really clashes because the harmony and the melody are heard separately.

Another example are the modes of the harmonic minor scale, taken melodically. The interesting ones in Jewish music are phrygian #3, dorian #4, and aeolian #7 (the original harmonic minor); they have names in Hebrew that I don't remember. The others (locrian #6, ionian #5, lydian #2, and, uh, mixolydian #1 which is really weird) don't have very useful corresponding harmonic scales, that is, the melody notes can't really be used to form harmonies very easily. You could make a doubly "harmonic" scale as well by taking a phrygian #3#7 or an aeolian #4#7. In these cases, the augmented second is a characteristic interval, though it doesn't have to be -- it might well be treated as a leap rather than a step.

The phrygian #3 scale in particular is a MAJOR scale. The tonic chord is major! The harmonic scale for it is certainly phrygian #3, but the melodic scale isn't, if you don't like augmented seconds. It's just as well to raise the 2nd going up and lower the 3rd coming down if it makes sense in the music when stepwise motion is called for. Of course, a solution is to avoid stepwise motion in that direction, never going lower than the raised 3rd in a scalar passage or higher than the 2nd, and leaping across the gap when necessary. An example from Fiddler on the Roof, "If I were a rich man", in C: G F G F E, C. E F G F G F E F G A Bb A Bb A G. This is a somewhat bad example because it isn't really in this mode, but see how it just avoids the Db or D altogether? This is actually mixolydian (which is another Jewish mode as well), of course. A better example, still from Fiddler on the Roof (it's really the easiest source for this, even though it's not particularly authentic), is the fathers' theme in "Tradition", also here in C: C CDE F GF#GAbG E FEFGF Db ED#EFE G C CDE F GF#GAbG EFEFGF Db C. In this case the majorness and the Db are very clear. There is one occasion of Db going to E, but it's certainly as a leap rather than a scale. When E has to be approached by step from below, the passing tone is D, not Db, but when the harmony is a bII Db chord (or a bvii Bbm chord), the Db is necessary. This way you can have music in the mode that still has smooth voice leading.

And so it is that harmonic and melodic scales are not only different notes but different things altogether. Comments?