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# C:/Musimathics_local/Musimat/MusimatChapter9/C091406a.cpp

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    00001 #include "MusimatChapter9.h"
    00002 MusimatChapter9Section(C091406a) {
    00003 Print("*** Accumulation ***");
    00004 /*****************************************************************************
    00005 Accumulation
    00006
    00007 If we index the y-axis of figure 9.22 with a random value in the unit interval, the corresponding
    00008 x-axis value will be one of the 12 pitches of the scale. Furthermore, the choice will more likely
    00009 fall on a step that occupies a wider footprint on the y-axis, corresponding in this case to the
    00010 lower pitches of the scale, just as we wanted. We can create the cumulative distribution function
    00011 in figure 9.22 as follows:
    00012 *****************************************************************************/
    00013         para1(); // Step into this function to continue.
    00014 }
    00015
    00016 RealList Reference accumulate(RealList Reference L){
    00017         For(Integer i = 1; i < Length(L); i = i + 1){
    00018                  L[i] = L[i] + L[i - 1];
    00019         }
    00020         Return(L);
    00021 }
    00022
    00023 Static Void para1() {
    00024 /*****************************************************************************
    00025 Starting with the second element in the list (indexed as 1), we replace this element with its original
    00026 value plus the value of the previous element. As we proceed through the list, each list element will
    00027 be equal to itself plus all previous elements. Given the preparation of the RealList r performed
    00028 above, Print(accumulate(r)); prints {0.15, 0.29, 0.42, 0.54, 0.64, 0.73, 0.81,
    00029 0.87, 0.92, 0.96, 0.99, 1.0}.
    00030
    00031 We have prepared the cumulative distribution function, and now we can access it with a random
    00032 value to select a pitch. Pick a number in the unit interval to be the next note of the melody:
    00033 *****************************************************************************/
    00034
    00035 Real R = Random();
    00036
    00037 /*****************************************************************************
    00038 R will fall within the range of one of the 12 steps in figure 9.22 because both Random() and the
    00039 cumulative distribution function exactly span the unit interval, 0 to 1. For example, if R equals 0.1,
    00040 then by inspection of figure 9.22, we can see that R lies within the first step, which covers the inter-
    00041 val [0, 0.15], so the pitch that this value of R selects is C.
    00042 *****************************************************************************/
    00043 }}
    00044
    00046 /* $Revision: 1.2 $ $Date: 2006/09/09 06:22:43 $ $Author: dgl $ $Name:  $ $Id: _c091406a_8cpp-source.html,v 1.2 2006/09/09 06:22:43 dgl Exp $ */
    00047 // The Musimat Tutorial © 2006 Gareth Loy
    00048 // Derived from Chapter 9 and Appendix B of "Musimathics Vol. 1" © 2006 Gareth Loy
    00049 // and published exclusively by The MIT Press.
    00050 // This program is released WITHOUT ANY WARRANTY; without even the implied
    00051 // warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
    00052 // For information on usage and redistribution, and for a DISCLAIMER OF ALL
    00053 // WARRANTIES, see the file, "LICENSE.txt," in this distribution.
    00054 // "Musimathics" is available here:     http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10916
    00055 // Gareth Loy's Musimathics website:    http://www.musimathics.com/
    00056 // The Musimat website:                 http://www.musimat.com/
    00057 // This program is released under the terms of the GNU General Public License
    00058 // available here:                      http://www.gnu.org/licenses/gpl.txt
    00059