Bach, whose harmonizations are widely available for study. Your guide in this as in much of life is J.S. While following the rules of good counterpoint you can add "in between" notes to fill in between chords, and you can introduce dissonances that resolve to a note of the requested chord. The next thing you need to know about realizing Roman numeral harmony is that you are not limited to just the tones specified by the numerals. So 10 less than 100, that's 90.If one of these numbers has a flat or sharp by it that means the pitch corresponding to that number is to be raised or lowered from what it would normally be in the key signature. So how do you do 90? You will look at this number, 100, and then subtract N from it. ![]() Once you get the answer, look at what I'm doing. (chuckling softly) I should stop doing this. So what must I do then? And I'm again saying 10 minus 50, what I really mean is 50 What about 40 right now? So instead of thinking of 40Īs four 10s and writing XXXX, what we do is that we We can just take theįour, nine, 40, and 90. And in fact, you can forget 400 and 900, they're two big numbers. You're asking me, "Don't we use this kind In fact, the only specialĬases are four and nine. So where is the subtractive notation used? So you can see that it's And then let's look at where the subtractive notation is used. So I'm gonna fill in forįour and nine over here. Now, the most important thing to know about this subtractive notation That when we're writing it here in this way, we're actually Now this name is not that important, it's just for you to realize And when we do this, this is called the subtractive notation. So we had an IV for four and IX for nine. Minus one, which is four." The same thing goes for nine. You see this happening, "think of it as not one You're seeing a smaller number come before a larger number. Was one less than five." So I can put an I, and then So what is a shorter way to write four? They thought of four as, "Hey, I can write it Where there's not much space, we want a shorter way to write four. Which in fact, people used toĭo back in the Roman times, and then they stopped doing it because it just took too much space. Of four as four ones where we write IIII. So what is it about four and nine? How do we write four and nine? So instead of thinking So we said these two areĬontroversial, right. So whenever we're writing usual numbers it comes in this format, the bigger one first and Over here we can see that VĬomes first and then the I. And you can see that in all these cases the bigger number is what we write first and then the smaller numbers. So that's exactly the backward process that I would have used. How would I have read it? I'll have read it by And as you can see, if I had been given this number and asked, "What is this number?" I'll ask, "Three, where is three between?" It's between one and five. So now what about this three? I treat this as a fresh problem, as if I'm starting all over again. And this 20 has alreadyīeen written over here. So I've taken 23, and I've made it, imagined it to be 20 plus three. Is that enough? No, now what I have is 20. "So I should write it as sum times 10, "and then I'll see what happens." So how many 10s are there? And I see that there are two 10s. If I want to write 23, how should I think about it? So in my head, I'm going, Have an alphabet for it, so I'm just gonna use that. Put a question mark here because it's a different way of writing. And the same thing happensįor seven, five plus two. What is remaining here?" There's just one remaining. I'll go up here and ask, "What is the largest thing that I have "that's smaller than six?" So six lies between five and 10. Now, what should I do for six? It gets interesting for six because how do I write six? So when I look at six, And we've already made upĪ new alphabet for five. But then, what's going on? It's already becoming hard to read. So after this, what about five? I'm gonna up here. ![]() This is not how we do it, at least not anymore. (chuckles) So it seems right, right, to do this. And three is going toīe, that's right, III. And then two is, I need two ones, and I just have to write them So I'm gonna look at one, and what is one? I'll go here, I'll look at my table. So Roman numerals follows this idea of additive representation of numbers. I just add what's there individually because I know this I-like I just write them and say what I have is just one plus one plus one, three. And then if I wanted two, I might just write two ![]() ![]() Represent one of something, I might just write, hey, one of that.
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