Before we develop the common practice rules of consonance and dissonance, let's do a three minute history of medieval music. Why? Well, it's just to give a cultural context. To show that these rules we're about to study, they weren't received from on high, but they were rather eased into. These rules are, after all, human creations. Ready? Most of the European medieval music that remains today is religious music. The reason is the people who wrote down that music were close to being the only people who could in fact write at that time. There was lots of other kinds of music. We just don't know how it went with the same specificity that we know about the music made by people who knew how to write it down, and possibly that in turn actually helped the music evolve. So religious music. First, there was plainchant, just one note at a time. Much like the very first melody we saw in this course, the setting of Psalm 148 from the Liber Usualis. This Christian tradition started probably around 400 in the Common Era and began to be written down in the 900s. These were the melodies of the many, many religious services that made up each of the different days of the year. They sang a lot. Now, at some point, people clearly wanted to ornament these melodies by adding another voice. In adding another voice, they had to choose which intervals should be consonant. So the first thing they added were perfect fifths, fourths, and then octaves. Let's start by looking at an example. Here is an anonymous piece written sometime around the year 900 probably. The bottom voice is the original chant. The numbers I put in the score, there are just to make it easier for you to discern the intervals between the two voices. In order to really understand this, I urge you to play this example a few times on a keyboard and sing along with the bottom voice, then the top voice, then back and forth until you can really hear for yourself the relationship between the two voices. If you can't play it, don't worry. I'll play it for you, and sing it along as I sing with it. So let's get to know the chant excerpt first. Here it is. Here's the original chant, just the bottom line, and sing along really. Here it is. Now, let's play the bottom voice but sing along with the top voice. By far, the most common interval is the fourth. That is the sound of the piece. It's the most consonant interval after the unison that begins and ends the piece. But what about those seconds and thirds? Notice that as long as you're not on a perfect interval with the other voice, if you're a second and a third, you have to be moving by step or passing. In other words, here's the fourth that you get to. But if you want to start here, you can work your way up by step, passing up to the fourth. This allows you to make a linear melodies, to make a melody that is in fact just slightly independent of the original voice. Here is another anonymous example, from about a 100-ish years later. Again, there is an original chant, and on top of that, they added an ornamental line to make the whole experience more beautiful. Here's the original chant, and here's the upper voice that gets added on top of that. Listen and sing along enough times so that you have a feel for it, enough times for you to feel less passive about the soundworld, be an active listener. Before I talk about it, pause and maybe make a few notes as to what you think of the system this piece creates. This is a great practice for that kind of active listening that will help deepen your approach to all kinds of music. It will actually help you understand other people's analysis of music if you practice formulating your own. So do it. Here are some things I noticed about our second example. First of all, absolutely, all the intervals are perfect, Pythagorean, simple number ratios. Look at the numbers: fives, fours, octaves. I think this creates a unique soundworld you can actually perceive. Go back and listen to it again. See if you can hear not only the presence of that clean intervallic definition of consonants, but see if you can also hear the absence of the softer consonances and the absence of any physically harsh dissonances. We'll come back to this concept quite a bit. When you choose to limit yourself to a certain set of choices, melodically, intervallically, harmonically, that choice and that exclusion can create a whole soundworld. What else? Well, the voices now move in opposite directions. In the first example, the upper voice was very dependent on the lower voice for its direction. It would rise above it, but then parallel exactly, and then sink back into it. In this second example, the voice is usually, actually moving the opposite direction with just enough movement in the same direction to make it not so machine-like or so automatic. This makes the upper voice seem even more independent. Now, there are fancy music theory terms for this phenomenon: conjunct motion, moving together, and disjunct motion, moving apart. A lot of conjunct motion, moving together, makes the voices seem much more dependent. A healthy mixed with a lot of disjunct motion makes the two voices seem way more independent of each other. What else? Well, notice the added upper voice here seems to leap around itself quite a bit, and remember from our very first unit that we perceive leaps fundamentally differently than we perceive steps. Why is the top voice so leapy? I think there's a real reason. It's because the vertical intervallic choices themselves are so very leapy. Unless you have completely parallel motion all the time, you are virtually forced under this system to leap, to find a perfect consonants in the opposite direction. Why is this in turn important? Perhaps because it's an early example of something we will also run into a lot. The phenomenon of creating limited rules in one direction or parameter effects other kinds of rules in different directions or parameters. Choosing the wonderful and pure limited vertical sound of perfect consonances had an actual effect on the melodic values that composer was forced to use for the top voice. The two were related here, a great example of the ways different rules and aesthetics push back against each other. When we get to more traditional harmony, we'll see the same trade-off operate. An austere vertical harmonic sensibility definitely pushes back against smooth horizontal voice leading. It's great to be conscious of both axes. Finally, here's yet a third example from about 1,100 in the Common Era, yet another 100-ish years later. Notice this time how much freer it is. That bottom voice is still the original chant, but now the top voice stretches out the time, allowing the top voice to have a number of different intervallic relationships with it. This constant change gives a flowing undulating sense of the piece. Those waves are helped by the largely step-wise motion of the counter-melody. The intervals include almost everything available within the mode. In other words, this time, shape and horizontal line seem to be more important than vertical rigor. There are some rules. Let's see. You can just see visually perfect fifths and unisons. Those seems to predominate at important starts and stops. But other than that, the rules are very relaxed. It's very worthwhile to notice how changing rules offer a wonderful and changing opportunities for musical beauty. That principle is relevant across centuries. It's relevant across different cultures. But enough talking about this piece, let's actually play it, and see if you can hear the things I was talking about. Let's sing the bottom chant. Here it is. Now, see if you can notice what we mentioned about the upper voice. It's freer. There's more intervals. Everything seems to be changing. It's very beautiful. By the way, about those changing rules and changing wonderful opportunities for beauty, to really understand and appreciate and use that principle, you have to actually learn the rules you want to change. There just aren't many shortcuts. This is what is meant by paying your dues and blues idioms. This is what is meant by assimilate, imitate, and then innovate in jazz. This, dear friends, is what is meant by music theory class. Learn the rules that you want to change. Even more so, learn the logic and reasoning and aesthetic choices behind the rules you want to change. That is what we're trying to do here. Hey, if you like this music, and you want to linger on any one particular era, or if you would like a much more detailed chronological progression through these musical developments, you'll find some great links and sources in the resources below.