It is because of this very strong effect of nonalignment and contradiction that I consider such associations of layers dissonant unlike Yeston, who considers them consonant on the basis of the numerical congruence of the constituent layers. Most displacement dissonance in tonal music involves a metrical layer and one antimetrical layer although the possibility of larger numbers of constituent layers exists whenever the shared cardinality is greater than 2; see the section on compound dissonance later in this chapter.
When a metrical layer is present within a displacement dissonance, we generally perceive the antimetrical layer or layers as a shifting out of the "normal position" designated by the metrical layer; the pulses of the metrical layer, in other words, function as a series of reference points in relation to which the pulses of the antimetrical layer are perceived as being displaced.
I refer to the constant number of pulse-layer attacks that separates the metrical and antimetrical layers throughout a particular displacement dissonance as the "displacement index. The amount of displacement must, of course, be smaller than the cardinality. Papillon op. Measuring in the direction of musical flow from these pulses intuitively seems more reasonable; I believe that it is possible to hear virtually all displacements in a "forward" manner.
There are, however, displacement dissonances that can also be perceived in a backward direction — dissonances whose antimetrical pulses can be heard as "early onset" in relation to the following metrical pulses.
It would be too hasty to conclude, however, that displaced pulses close to the end of a measure are always perceived in relation to the following downbeats. In the above passage from Schumann's tenth Papillon Example 2. There are two reasons why this displacement is more easily perceived in relation to the preceding downbeats.
Second, and more important, this displacement is more likely to be heard in relation to the preceding downbeats because the harmony during the displaced pulses is a continuation of that of the preceding downbeats. Harmony appears to be the main factor that can counteract our intuitive tendency to hear displacement in a "forward" direction.
I don't want to drag out the juicer and the blender for breakfast. Other than that, a solid little book. Apr 01, Bookish rated it liked it Shelves: There are some great recipes in this, no doubt. I just don't agree with the idea of "juicing" veggies or fruit, for that matter. Pureeing, yes, juicing, no.
The whole reason I eat or drink veggies is for the nutrients and benefits they provide, which includes fiber. Much fiber is lost from juicing. Same recipes, but blending instead of juicing,..
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Berry Melon Green Smoothie. Pineapple Detox Green Smoothie. Zingy Spring Green Smoothie. Berry Rocket Green Smoothie. Pear Delicious Green Smoothie. You can keep experimenting and delete wrong, functions can't be deleted the function f2 , then redefine it again with a different body. In the end, f1 will still work, because all it needs to know is how to access its scope and not what this scope used to contain at some point in time. Let's introduce closures with an illustration. There is the global scope. Think of it as the Universe, as if it contains everything.
It can contain variables such as a and functions such as F. Functions have their own private space and can use it to store other variables and functions. At some point, you end up with a picture like this: p84 - If you're at point a, you're inside the global space. If you're at point b, which is inside the space of the function F, then you have access to the global space and to the F-space. If you're at point c, which is inside the function N, then you can access the global space, the F-space and the N-space You cannot reach from a to b, because b is invisible outside F.
But you can get from c to b if you want, or from N to b. The interesting thing—the closure—happens when somehow N breaks out of F and ends up in the global space.
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What happens then? N is in the same global space as a. And since functions remember the environment in which they were defined, N will still have access to the F-space, and hence can access b. This is interesting, because N is where a is and yet N does have access to b, but a doesn't. And how does N break the chain? By making itself global omitting var or by having F deliver or return it to the global space. Let's see how this is done in practice. Think of it as N in the illustrations above.
This new function has access to its private space, to f 's space and to the global space. So it can see b.
Because f is callable from the global space it's a global function , you can call it and assign the returned value to another global variable. The final result of the next example will be the same as the previous example, but the way to achieve it is a little different. Let's start by declaring a placeholder for the global function-to-be. This is optional, but it's always good to declare your variables.
During definition time, n was inside f , so it had access to f 's scope. Based on what we have discussed so far, you can say that a closure is created when a function keeps a link to its parent's scope even after the parent has returned. When you pass an argument to a function it becomes available as a local variable. You can create a function that returns another function, which in turn returns its parent's argument.
This demonstrates how the function binds to its scope, not to the current variables and their values found in the scope. Let's loop three times, each time creating a new function that returns the loop sequence number. The new functions will be added to an array and we'll return the array at the end. Let's invoke them by adding parentheses after each array element. The expected behavior is to see the loop sequence printed out: 0, 1, and 2. What happened here?
We created three closures that all point to the same local variable i. Closures don't remember the value, they only link reference the i variable and will return its current value. After the loop, i's value is 3. So all the three functions point to the same value. Why 3 and not 2 is another good question to think about, for better understanding the for loop.
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So how do you implement the correct behavior? You need three different variables. For this function, i becomes the local value x, and x has a different value every time. Alternatively, you can use a "normal" as opposed to self-invoking inner function to achieve the same result. The key is to use the middle function to "localize" the value of i at every iteration. Let's see two more examples of using closures. The first one involves the creation of getter and setter functions.
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Imagine you have a variable that will contain a very specific range of values. You don't want to expose this variable because you don't want just any part of the code to be able to alter its value. You protect this variable inside a function and provide two additional functions—one to get the value and one to set it. The one that sets it could contain some logic to validate a value before assigning it to the protected variable let's skip the validation part for the sake of keeping the example simple.
It defines setValue and getValue as global functions, while the secret variable remains local and inaccessible directly. The last closure example also the last example in the chapter shows the use of a closure to accomplish Iterator functionality. You already know how to loop through a simple array, but there might be cases where you have a more complicated data structure with different rules as to what the sequence of values is.