One way of thinking about music is that it can be divided into horizontal and vertical ways of thinking. If the horizontal metaphor represents one note after another, the vertical image represents the different ways notes can be combined together simultaneously. Of course, before going any further, we should note this metaphor though pretty wildly imperfect, lots of melodies including some we've already examined previously have all sorts of vertical or harmonic implications. We've remember some pitches in a melody more than others, and the way we link them together is very related to a sort of vertical thinking. So, it's really impossible to separate the two. But hey, it's a metaphor, not an exact equivalence, and speaking of metaphors. This is the right time to reintroduce the chair metaphor for learning music theory get this. Trying to teach music theory is like trying to build a chair while you are sitting on it. Everything depends on everything else. Everything is interdependent and rather wobbly. But with love dedication and a firm realization that understanding is never really complete, we can build the chair of music theory while we are sitting on it and wobbling around. So, we're going to talk about one specific thing for a bit. But will also have to reference other things that affect our perception of that one thing we're focusing on. It's a methodology that risks being confusing, but it's absolutely essential. Part of the message of this course is, it really just doesn't work to talk about one thing in complete isolation. Music is made up of many things, we try as best as possible to isolate one thing but each and every isolated thing we talk about is in fact quite dependent on other things we hear. So, let's begin by talking about the vertical way of looking at music. In other words, harmony or notes combining with other notes at the same time or even more precisely, how do we choose which notes to combine with each other? This is a huge topic and it leads smoothly into such things as harmony and harmonic function, and other things like bidder lawsuits about musical plagiarism. But before we define those particular terms, let's just focus in on two very useful words for talking about combining musical notes at the same time, consonance and dissonance. Consonants literally means sounding width or sounding together, and dissonance literally means against to sounding or sounding an opposition or it's almost like from the original Greek, "Hey, you know good kids get off my lawn." Despite this loaded etymology, consonance and dissonance are neither good nor bad in and of themselves. But using them well, has everything to do with the sense of style, taste and aesthetics. So, do understand, dissonance is not bad. Music without dissonance, it's a little bit like Belly without lips. It can be beautiful and pretty. But without graceful jumps, Belly lacks a certain dimensionality. So too, music without dissonance can maybe sometimes lack a certain depth. So, how do we tell which combinations of notes or consonant and which are dissonance? I think there're probably something like four determining factors. First, the physics of it all. Physics is the study of matter and energy in nature, and the physical properties of the sound waves of music determine how clingy or clean different combinations of waves end up sounding. The second way of thinking about it might be just the culture you swim in. Musical customs can define which note combination sound ordinary which some wrong and which sound really special, or the context within any given piece can be a factor. You can even look at each piece as its own little cultural world. It is fascinating to hear how individual pieces of music can customize their own flavors of what pitches sound rates together. Last, the internal functional relationship between consonance and dissonance over time does affect how we hear music. There's a very specific tradition that fashions a wonderful tension and release relationship between dissonance and consonance. It is a system that governed western art music for almost 400 years, and I'm going to explain a few of these factors in the next few lectures.