00001 #include "MusimatChapter9.h" 00002 MusimatChapter9Section(C091406b) { 00003 Print("*** Traversing the Cumulative Distribution Function ***"); 00004 /***************************************************************************** 00005 00006 Traversing the Cumulative Distribution Function 00007 00008 To automate this, we start at the top end of the cumulative distribution function and work 00009 down. As we go, we compare the value of R to the current step size. We've gone one step too far 00010 when the value of R exceeds the step size, so we return the previous step as the answer, and stop. 00011 *****************************************************************************/ 00012 para1(); // Step into this function to continue.) 00013 para2(); // Step into this function to continue.) 00014 } 00015 00016 Integer getIndex(RealList L, Real R){ 00017 Integer i; 00018 For (i = Length(L) - 1; i >= 0; i = i - 1) { 00019 If (R > L[i]) { 00020 Return(i + 1); 00021 } 00022 } 00023 Return( 0 ); 00024 } 00025 00026 Static Void para1() { 00027 Print("*** Invoking getIndex() ***"); 00028 /***************************************************************************** 00029 We can invoke getIndex() as follows: 00030 *****************************************************************************/ 00031 extern RealList f; // f was defined in C091406.cpp line 24 00032 00033 Real R = Random(); 00034 Integer p = getIndex(f, R); 00035 Print(p); 00036 } 00037 00038 Static Void para2() { 00039 /***************************************************************************** 00040 If R is 0.1, then p prints 0. Now let's bring all the pieces together. Here is a program that creates 00041 a melody of 25 pitches favoring pitches that are at the low end of the chromatic scale: 00042 *****************************************************************************/ 00043 Print("*** Melody of 25 low pitches ***"); 00044 RealList f(12.0, 11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0); 00045 StringList n("C", "Cs", "D", "Ds", "E", "F", "Fs", "G", "Gs", "A", "As", "B", "c"); 00046 f = normalize(f, sum(f)); // replace f with its normalized form 00047 f = accumulate(f); // calculate cumulative distribution function 00048 StringList s; // a place to put the result 00049 00050 For (Integer i = 0; i < 25; i = i + 1) { 00051 Integer p = getIndex(f, Random()); 00052 s[i] = n[p]; 00053 } 00054 00055 Print("Melody: ", s); // print the melody 00056 00057 /***************************************************************************** 00058 Running this program will generate something like figure 9.23, depending upon the values pro- 00059 duced by Random(). As we see, lower pitches are favored in approximately the proportions we 00060 specified. The longer the sample melody, the more likely the pitch choices would conform on aver- 00061 age to the distribution function. 00062 *****************************************************************************/ 00063 } 00064 00066 /* $Revision: 1.3 $ $Date: 2006/09/05 08:02:46 $ $Author: dgl $ $Name: $ $Id: C091406b.cpp,v 1.3 2006/09/05 08:02:46 dgl Exp $ */ 00067 // The Musimat Tutorial © 2006 Gareth Loy 00068 // Derived from Chapter 9 and Appendix B of "Musimathics Vol. 1" © 2006 Gareth Loy 00069 // and published exclusively by The MIT Press. 00070 // This program is released WITHOUT ANY WARRANTY; without even the implied 00071 // warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 00072 // For information on usage and redistribution, and for a DISCLAIMER OF ALL 00073 // WARRANTIES, see the file, "LICENSE.txt," in this distribution. 00074 // "Musimathics" is available here: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10916 00075 // Gareth Loy's Musimathics website: http://www.musimathics.com/ 00076 // The Musimat website: http://www.musimat.com/ 00077 // This program is released under the terms of the GNU General Public License 00078 // available here: http://www.gnu.org/licenses/gpl.txt 00079
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