[MUSIC] Welcome back. In the last lecture I talked about meter signatures, which show how many notes each measure contains, and how notes, usually eighth notes, are grouped. I said that the bottom number of the meter signature indicates the reference note, quarter note, eighth note or half note, usually. And the top number indicates how many of those reference notes fit into each measure. So four-four means four quarter notes in a measure, 12-16 would mean 12 16th notes in a measure, and so on. Most important, the meter signature indicates whether or not there will be a level grouped into threes. If the top number is 3, 6, 9, or 12, there will be a triple level, usually the eighth note level. If the top number is not divisible by 3, there will be no triple level. If the top number is larger than 3, that is 6, 9, or 12, there are multiple groups of three in a measure, so the meter is called compound. When the bottom note is eight, the beat is the dotted quarter note, equal to three eighth notes. When the bottom number is 16, the beat is the dotted eighth note, equal to three sixteenth notes. So 3-8 means three eighth notes in a measure grouped by threes, with the dotted quarter note getting the beat. One, two, three, one, two, three. 6-8 means six eighth notes grouped in two groups of three. One, two, three, four, five, six, one, two, three, four, five, six. 9-8 means nine eighth notes grouped in three groups of three. One, two, three, two, two, three, three, two, three. 12-16 means 12 16th notes grouped in four groups of three 16th notes. The four meters look like this. Notice that we show the grouping, by beaming eighth notes, or sixteenth notes, together. This beaming is strictly for the benefit of the performer. Beaming does not change the way the music sounds. When a measure doesn't contain all eighth notes, we choose note values that show this grouping by three, as clearly as possible. So for example, this rhythm of quarter, eighth, eighth, eighth, eighth, is best beamed like this, with the first eighth note unbeamed in order to show the triple grouping of the remaining eighth notes. Here are the beats. So the rhythm is bah, bah, bah, bah, bah. Notice that the meter beat in 6-8 is usually the dotted quarter note. Which equals three eighth notes. So this notation also helps make that clear. Here is another one. This one is a mix of eighth notes and 16th notes. The beaming always tries to show where the three eighth notes end. So, the dotted eighth, 16th, 16th, 16th adds up to three eighth notes, or one dotted quarter note. Notice that if the dotted quarter notes are the beat, this shows clearly where the beats fall. [MUSIC] Here it is again. [MUSIC] Where I'm snapping the dotted quarter notes. Here are the beats that I was snapping. You may have noticed that we have two meter signatures that seem to add up to the same thing math wise. 3-4 and 6-8 both dictate six eighth notes in a measure. 3-4 means three quarter notes in a measure, so six eighth notes. And 6-8 means six eighth notes in a measure. So why have two different meter signatures for the same number of notes in a measure? It's because the implied different beats and different eighth note grouping. By our definition of meter signatures, we know that one of these meter signatures suggest grouping eighth notes by three, namely 6-8. The measure with eighth notes group by twos is best shown with a meter signature of 3-4. We feel different meter beats in 6-8 and 3-4. In 6-8 we're likely to feel one, two, three, four, five, six. In other words each beat contains three eighth notes, which equals a dotted quarter note. So to complete our definition, 6-8 means there are six eighth notes in every measure. The eighth notes are grouped by threes, and the meter beat, the beat we tap along with, is likely to be the dotted quarter note. The traditional definition of 6-8, six beats in a measure and the eighth note gets the beat, is mostly not correct. It's not impossible, but it would mean that 6-8 was being played unnaturally slowly. In 6-8, the beat we’re most likely to move to is usually the dotted quarter note. The meter beat in 3-4 is likely to be the quarter note. One, two, and three and, [SOUND] that’s the top line shown here. Let's look at some examples of music in 3-4 and 6-8 to see the difference. Here's a fugue in e minor from The Well-Tempered Clavier. We see that the sixteenth notes are grouped in fours. Which means the eighth notes are grouped in twos, three groups per measure. The implied beat is quarter notes. Let's listen. [MUSIC] One, two, three, one, two, three, one, two, three. [MUSIC] This is another fugue, from The Well-Tempered Clavier, this time, in G major. All the notation is showing the grouping of three eighth notes per beat. In the second measure, for example, the first three eighth notes are beamed together, but not the fourth one. That's because the fourth one belongs to beat two. Let's listen to this one. [MUSIC] One, two, one, two, one, two. [MUSIC] So I was counting along with a dotted quarter-note beat. Here's one more. Lets listen to it first. This is the tune Beautiful Dreamer by the American composer Stephen Foster. See if you can figure out all the metric levels. [MUSIC] There is obviously a triple level in there. 1 2 3, 1 2 3, 1 2 3, 1 2 3, 1 2 3, 1 2 3. But if we try to feel the next slower metric level, it gets tricky. One two three, two two three, one two three, two two three. That doesn't work. How about this one? One two three, two two three, three two three, one two three, two two three, three two three, one, two, three. Three, one, two, three. This one is that this is a relatively unusual compound triple, a meter with two triple levels. The most likely meter for this, is 9-8, which is in fact what the notated meter is. So, you can see. 1 2 3 4 5 6 7 8 9, 1 2 3 4 5 6 7 8 9. The eighth notes are grouped by threes, and there are three groups of them to every measure. So there are two levels of three. One final word about time signatures. You sometimes see these symbols instead of time signature at the beginning of a piece. The c without the line through it stands for "common time," which is short hand way of writing 4-4. The c with the line through it stands for "Cut Time," the short hand way of writing 2-2. By our definition of meter, 2-2 means two half notes in a measure, which is the same quantity of notes as 4-4. Cut Time implies that the meter beat will be the half note, making it faster than 4-4. Obviously, as with all meter beats, it's dependent on tempo. Slow 2-2 sounds exactly like 4-4. But usually, the expectation is that the meter beat will be the half note in cut time. That's enough for now. In this lecture, we talked about the difference between 3-4 and 6-8. 3-4 is a simple triple meter in which there's only one triple level. One two three, one two three. Where I'm counting quarter notes. 6-8 is a compound duple meter with two groups of three eighth notes in every measure. One two three, two two three, one two three, two two three. Where I'm snapping dotted quarter notes. We looked at ways of beaming to show the underlying meter beats. And we saw how 4-4 can be called "common time," represented with a c, and 2-2 can be called "cut time," represented with a c with a line through it. In the next lecture, we'll look at more examples of metric notation. We'll determine meter signatures from notation. And we'll create notation based on meter signatures. [MUSIC]
