Last week we looked at music written with two parts. It's a very good exercise to work with just two parts. It lets you isolate and think about very discrete phenomena. With two parts, you can see things very clearly. Everything is plain and explainable. However, there's very little real music that is only in two parts, except Shostakovich. Well, okay, it's a joke, kind of he just gets really bitter sometimes and has these long passages of the entire orchestra playing, extremely austere two-part writing. Did I mention it's bitter? Hey, even Bach, two-part writing actually contains more voices folded up in on themselves. Heck, he wrote a four voice fugue for a solo violin. But anyway, back to it. Musically, music usually has more than three parts. As we go, we'll see why. It's very hard to have functional harmony with any fewer than three parts. In order to approach thinking about harmony, let's look at what happens when we first begin to have three voices. First of all, let's not even worry about harmonic function. Let's still just think a little bit about consonance and dissonance. When writing three parts, the rules of consonance and dissonance most definitely still apply in common practice music, but things do get slightly more complicated. Even so, the following will seem perhaps a little dry. We'll just have to get through it. Maybe have a drink. Put on some relaxing music while I talk about consonance and dissonance over the bass. Because when writing in three parts, the tyranny of the bass begins to emerge. What is the tyranny of the bass? Well, dissonance and consonance are perceived above the bass line more than they are between other voices. Why is this? Because their outer voices, because their dissonance is generally sensed above something, because the overtone series goes up and the lowest voice is the most present overtones? I really don't know. But in any case, composers of the Renaissance, the Baroque, the classical, and the Romantic eras all agree that dissonance seems to be defined primarily as being above the lowest sounding voice in any group of voices. Interestingly, composers of the Middle Ages and the 20th century sometimes emphatically do not agree with that. Actually, that tells you a lot about common practice, and its emergence from the medieval era and its dissipation into the 20th century right there. In this image, these numbers describe two simultaneous intervals over a bass. All the middle voice notes and all the top voice notes are cleanly consonant with the bass. Let me say that one more time. See, all the middle voice notes and all the top voice notes are cleanly consonant with the bass. But, what about the interval between those two top voices? This is where it gets wonky. Fortunately, when combining two consonant intervals above the bass, most of the resulting intervals between the top two voices are consonant themselves or to put it technically, a third plus another third on top of that is a fifth and also a sixth plus a third on top of that is an octave. But you don't need to know that level of technicality. Still, there are a few combinations of consonants as with the bass that are not consonant with each other. In fact, when combining more than two voices, the difference between types of dissonance emerges, seconds and sevenths resulting from the sixth and fifth above the bass at the same time. It's still pretty dissonant either from a cultural or the physical standpoint, and between two upper voices, they still sound pretty funky. Remember, I mean, this doesn't mean funky bad, but rather funky, hey, it's a dissonance treated with special passing neighborly or suspended care. Fourths, however, sound just fine between upper voices. Now, according to the [inaudible] weasel, this may have to do with the fact that the whole reason fourth seemed dissonant in the first place, was not really for physical reason. They are after all perfect fourths, geometrically perfect fourths. Perfect is the proverbial debutante. Rather, they were considered dissonance due to the encroaching triad, the gravity of the third immediately irresolvable down two or maybe it's for other still more easily contextual reasons. In other words, the fourth just has to go somewhere. Unless in three voices, it already is somewhere as in, unless it is already part of a triad and not a fourth from the lowest note, the root. Let me play what I mean. Listened to these three things. Here is a fourth. Now, put yourself back in counterpoint land for one second, I promise it won't be too traumatic. Can you hear this as part of a credential formula? It just wants to resolve down to the third. But now here are the same two notes. Here it wants to resolve. I'm just going to slip a third in below or the note making this a triad. I mean, technically this is a triad, what we call a first inversion, because the lowest note is a third of the chord instead of the root, but don't worry about that for now. What I've just done is that keeping the fourth on top, so you can hear it more clearly and, did you notice that the fourth is suddenly consonant? It doesn't need to resolve. It's already home. Part of that triad. It doesn't need to go anywhere. Now, not every triad makes a fourth a home. Listen to this. If that fourth is actually above the bass, it's still a dissonant because tyranny of the bass. This chord is subtly dissonant. It's still in this fourth wants to resolve down. We'll talk a lot about this particular chord that has a fourth and a sixth step of the bass. It will needs to resolve. It really, really needs to resolve. No, seriously, it's just not stable. Fourths between upper voices are different than fourths above the bass. How cool is that? It is magic. I mean, listen one more time. Dissonant fourth and magic. Presto change-o. It's not dissonant at all.