[MUSIC] A melody, as we have said, is a coherent collection of pitches animated by a rhythm and usually supported by a harmony. We can simply remember a melody or, in the western tradition, we may wanna write it down, capture it, preserve it, using musical notation. Written notation of melodies in the west, again, goes back to the ninth century. We talked this a little bit last time. Here are a few images showing how pitch notation developed for western music. So on the screen to the left side you see an early manuscript with neumes up above, just squiggles, and with some letters representing both pitch indication and the Latin text of this particular chant. On the right we have the text of the chant and then the neumes, the prototypes of our musical notes. As you can see on the next slide, here we begin to get horizontal lines to help us with pitch indicators, a grid of some sort, that allows us to specify particular pitches, and you can see off to the left hand side there the letters C and F, indicating where the pitch C and F appear. On the right side we begin to see these neumes become increasingly separated, and now, as mentioned last time, with a different symbols to indicate the rhythms that are involved. In the next slide, we see that system of a grid supporting pitches being confirmed in four red lines there. And on the right we see it progressing to what we have today, five lines on the stand, again with pitch indicators out there to the left to signify what those particular pitches are supposed to be. Moving on to the next slide, here again we see more signs for clefs indicating what those lines on which the notes sit are meant to be. On the left, we have a very deluxe manuscript from my own Yale University rare book library. And on the right a sort of, we'll call it, a more middle level volume for an average music consumer of the 16th century. But again, we have a time signature there, we have pitch indicators and the notes sitting on a grid. Finally, we're going to come to an example of some printed music. A volume here, actually by Martin Luther on the left, with his famous hymn tune [FOREIGN] there, and you can see Martin Luther's name actually on the printed copy. And this is the soprano part, and we see that same music on the right now with all four parts set one on top of the other and the music ending up towards the bottom right there. [MUSIC] So that's the way our notation developed, and at the very end as you heard again. [MUSIC] What Martin Luther is doing there is simply coming down the scale. Right down the scale. So let's talk about scales for a moment. Scale in music is simply a pattern of adjacent pitches going up or down the keyboard. Different cultures have different scales. Much of Chinese music is written in a five note scale, so called pentatonic scale. [MUSIC] That sort of sound. Indian Ragas sometimes use a six note scale. [MUSIC] That's a six note scale used by Ravi Shankar in a piece called [FOREIGN]. Melodies in western music, however, are written not in patterns of five or six pitches, but in scales of seven pitches. Did you ever wonder why we in the west have seven pitches in our scale? And why there's an irregularity in the western keyboard? Why there is no key at two spots on the keyboard. If you look here on the screen you can see that we're missing an effective black key between B and C, and E and F. How did this come about? It has to do with the way the ancient Greeks back in the time of Plato and Aristotle set up their melodies. They privileged mathematics above all else, and as a result, we end up with seven pitches in our scale. A class video will explain how this happened. Okay, so we have this whole idea of octave duplication, sometimes six notes, sometimes five notes. We in the west have settled on a seven note scale. Why did that happen? Well, we had this idea of a seven note major [MUSIC] and seven note minor. [MUSIC] Why seven notes? Well for the answer to that we have to go back to ancient Greek music theory, and you read about this, it's really turgid stuff. But believe it or not, I teach a course on this at the graduate level. We have to read and poor Linda has to take this kind of stuff. We're reading Aristoxenus and things like this. So what we're dealing here with is a situation where the ancient Greeks were very much into mathematics as a way of explaining the world and explaining music in particular. And they thought these ratios were primary, so they had the ratio of two to one, which gave them the octave, and three to two, which gave them the fifth, and four to three, which gave them the fourth. They also, because the system worked out better for their purposes, then jumped to nine to eight, which gave them the whole tone. So they started out there and let's say they're working down here. They filled in the octave up above, and then they filled in the fifth, and then they filled in the fourth, and then they came down a whole step. Then they went up a fourth from that whole step and then up a fourth from that, and they were filing in, in this fashion. Interestingly enough, and you ever wonder this? Sometimes someone wandered by a keyboard, said that's odd. What's the great oddity about the keyboard? What's strange about this keyboard? It's very asymmetrical, right? Marcus? Yeah it's missing some notes in there. It's missing something in here. Well what these are were the cracks. After the Greeks laid out their fifths and fourths and whole steps they had these little leftovers. They called them lainmas, and they had these little leftovers in there, and that's why we end up with these small distances between B and C. [MUSIC] That's a big step. [MUSIC] That's a small step there. So the scale is actually not equal. A to B is one distance, which is a large one, and B to C is only half that distance, and that's because of the way the Greeks laid this thing out with their two to one ratios, three to one ratios and so on. But in any event, we end up with this. Now, the Greeks had a whole series of patterns, and they called them myxolydian and hypomyxolydian and Phrygian and hypophrygian and stuff like this. A lot of different patterns, but in the course of history, we settled, beginning in the 16th and 17th Century down into just two patterns. What we call the major pattern and the minor pattern. So, let's talk about that just for a moment, and before we do it I should add one other thing. How, then, do we get these other notes up here? Well, what we know call the black notes, although historically keyboards could be either way. You could have these added notes, black or white and then these underneath would be black. So we fill these out. Sort of in the 14th century all of this got filled in. These between B and C and E and F didn't get filled in because they were already just the smallest amount that they wanted to deal with, just half steps. So we end up here within an octave, we end up with 12 equal pitches. But we still use this term of seven note scale, cuz we have seven notes within the scale of the major scale and seven notes within the scale of the minor scale.
