This post is the second in a very occasional series on the old way of learning about sight singing and intervals. I’ve been thinking about this subject again, since I’m teaching a new class based on it at Juilliard. I also am visiting a class at Case Western this week where the students use this method. I think it is a very good thing to explore these older ways of thinking; often the old, discarded ways have their merits. See this recent blog, as well.
Part 1 of this series was a very basic introduction to the topic. In this post, we go a little deeper.
IN the previous post, I described the first six notes, which are all you need to sing the hymn Ut queant laxis. These notes also have letter names, which are somewhat older than the solmization syllables, and the letters and syllables go together like this: C ut D re E mi F fa G sol and A la. Since the really important thing to know about singing these six notes is that the smallest step is between mi and fa, we mark the place of that step with a clef, which means “key.” So far we haven’t done anything different from modern solfège, although the first syllable has a different name.
A drink with jam and bread? • How do we get past six notes? We have to push the scale further, and it is natural to do so with the kinds of steps we have already used: whole steps and half steps. How do we figure out where to put which kind of step? Above A, there is a minor third to C, and we know that we should have that high C in our scale because it seems closely related to the low C that we started on (octave equivalence is a very mysterious topic for another time, but it seems near universal for human cultures). This minor third from A to C seems to have been the strange bit of the medieval pitch system that took some time to sort out. One thing is for sure, we need another half step in the scale around now.
Which will bring us back to . . . fa • Here is where the medieval system parts ways with the modern. Nowadays, we just put a seventh syllable in, and we teach children that there are two half steps in the scale: one between mi and fa, and another one between si and do (or ti and do, depending on where you go to school). In the medieval way, there is more sensitivity to the special importance of the half step. In the old system, half steps are always mi fa, and clefs are always on fa to show us where the half steps are. So we can say that in addition to ut, the higher C must also be fa, with a B mi just below it. This means that the last two notes of our original scale (G sol and A la) must also be G ut and A re in relation to the notes above. In addition, above C fa we must also have D sol and E la.
Solfège at your fingertips • We can visualize this all on the hand. Remember that the lower scale went across the base of the fingers, index-middle-ring-little and then curved up the two joints of the little finger. Now if we start with G ut on the middle joint of the little finger and go up, we have ut re mi all on the little finger followed by fa sol la on the tips of the ring, middle, and index fingers. You can see this in the following diagram:
Doesn’t seem too hard • Not so fast! There is one more detail. Most chant works like this diagram, but sometimes we have to put the half step above A, especially as an upper-neighbor figure. Think of the beginning of the introit Gaudeamus. In this case we use what we moderns call B-flat. The medievals called it B fa, since it is a half step above A. Almost always in chant, you can get by using the syllables from the two scales described above, but occasionally throwing in a B fa.
This system of looking at it has some advantages and some disadvantages. One advantage is that you can teach your children Kyrie XVIII and Agnus I without teaching them any new syllables. The clef is still “fa,” and it shows where that all-important half step is. One apparent disadvantage is that it is not clear how we switch between these two scales. To change in the middle of a piece of music, you need to pivot on one of the notes that belongs to both scales. By convention, we choose to pivot on A, by sing re on the way up on A when changing, and singing la on the way down when changing. This takes some getting used to. The best way to learn to do the thing is to practice. Here are some exercises I use with my class to practice switching between scales.
This can seem a little complicated. There remains a lot to say about this subject, but I will offer two brief thoughts now: musicality and tradition.
First, I have musical reasons for liking this way of thinking. If we can develop that keen awareness of mi and fa and how those two syllables are colored by their placement below and above the semitone respectively, we are richly rewarded with improved melodic sense. Thus the fifth E-B is mi mi, while the fifth F-C is fa fa. This seems somewhat nonsensical from a modern perspective, but from the traditional perspective, those notes all feel quite different from each other precisely because they stand on opposite sides of that half-step divide. The half steps are the most important thing for position finding in the scale, which is a fundamental part of our melodic intuition. The difference between mi and fa seems to have had a real importance for musicians in earlier times.
Secondly, this was the way people thought about intervals and pitch all through the age of renaissance polyphony. In the Catholic parts of Europe, this system seems to have stayed in use into the eighteenth (or even the early nineteenth!) centuries. Why not try our best to think about music the way the composers of renaissance polyphony did? If it was good enough for Palestrina, Victoria, Lassus, and Guerrero, maybe it’s worth looking into.
In future posts (hopefully sooner than eighteen more months from now), I plan to show how this works in an actual piece of chant, talk more about the qualitative differences between mi and fa, and apply this to polyphony as well, where it has some uses for understanding musica ficta. The scale also keeps going in both directions, but these ten notes get you a long way with the Gregorian repertoire, fortunately.