00001 #include "MusimatChapter9.h" 00002 MusimatChapter9Section(C091101) { 00003 Print("*** 9.11.1 Precomposition ***"); 00004 /***************************************************************************** 00005 00006 9.11.1 Precomposition 00007 00008 The process of composing atonal music is typically divided into two parts. 00009 00010 o Precomposing: assembling the musical materials 00011 00012 o Composing: applying the assembled materials in a design 00013 00014 Musimat already has a number of data types and operations, but a few more are needed: 00015 00016 o To represent pitches as symbols with integer values, such as: 00017 00018 Integer C = 0, Cs = Db = 1, D = 2, Ds = Eb = 3 . . ., B = 11; 00019 00020 o To represent motives as lists, such as: 00021 00022 IntegerList a = {F, F, G, A}; 00023 IntegerList b = {F, A, G}; 00024 IntegerList c = {F, E}; 00025 IntegerList d = {Bb, A, G, F}; 00026 IntegerList e = {E, C, D, E, F, F}; 00027 00028 o To combine motives and concatenate lists: 00029 00030 IntegerList y = Join(a, b, a, c, a, d, e); 00031 00032 (y is defined as the list of pitches of the tune "Yankee Doodle.") 00033 00034 The function transpose() below transposes a pitch set. 00035 *****************************************************************************/ 00036 para1(); // Step into this function to continue. 00037 para2(); // Step into this function to continue. 00038 para3(); // Step into this function to continue. 00039 } 00040 00041 IntegerList transpose(IntegerList L, Integer t) { 00042 For(Integer i = 0; i < Length(L); i = i + 1) { 00043 L[i] = PosMod(L[i] + t, 12); // BUG: given as Mod() in "Musimat", s.b. PosMod() 00044 } 00045 Return(L); 00046 } 00047 00048 Static Void para1() { 00049 /***************************************************************************** 00050 Here is an example of transposing a list: 00051 *****************************************************************************/ 00052 00053 Print("*** Transposing a list ***"); 00054 IntegerList L( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ); 00055 Print("Original row:", L); 00056 Print("Row transposed by 6: ", transpose(L, 6) ); 00057 00058 /***************************************************************************** 00059 To invert a pitch set: 00060 *****************************************************************************/ 00061 } 00062 00063 IntegerList invert(IntegerList L) { 00064 For(Integer i = 0; i < Length(L); i = i + 1) { 00065 L[i] = Mod(12 - L[i], 12); 00066 } 00067 Return(L); 00068 } 00069 00070 Static Void para2() { 00071 /***************************************************************************** 00072 Here is an example of inverting a list: 00073 *****************************************************************************/ 00074 Print("*** Inverting a list ***"); 00075 IntegerList L( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ); 00076 Print("Original row:", L); 00077 Print( "Inverted row:", invert(L) ); 00078 00079 /***************************************************************************** 00080 To take the retrograde of a set: 00081 *****************************************************************************/ 00082 } 00083 00084 IntegerList retrograde(IntegerList L) { 00085 Integer n = Length(L); 00086 IntegerList R = L; // make a new list as long as L 00087 For(Integer i = 0; i < n; i = i + 1) { 00088 R[i] = L[n - i - 1]; 00089 } 00090 Return(R); 00091 } 00092 00093 Static Void para3() { 00094 /***************************************************************************** 00095 Here is an example of retrograding a list: 00096 *****************************************************************************/ 00097 Print("*** Retrograding a list ***"); 00098 IntegerList L( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ); 00099 Print("Original row:", L); 00100 Print( "Retrograded row:", retrograde(L) ); 00101 00102 } 00103 00105 /* $Revision: 1.3 $ $Date: 2006/09/05 08:02:45 $ $Author: dgl $ $Name: $ $Id: C091101.cpp,v 1.3 2006/09/05 08:02:45 dgl Exp $ */ 00106 // The Musimat Tutorial © 2006 Gareth Loy 00107 // Derived from Chapter 9 and Appendix B of "Musimathics Vol. 1" © 2006 Gareth Loy 00108 // and published exclusively by The MIT Press. 00109 // This program is released WITHOUT ANY WARRANTY; without even the implied 00110 // warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 00111 // For information on usage and redistribution, and for a DISCLAIMER OF ALL 00112 // WARRANTIES, see the file, "LICENSE.txt," in this distribution. 00113 // "Musimathics" is available here: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10916 00114 // Gareth Loy's Musimathics website: http://www.musimathics.com/ 00115 // The Musimat website: http://www.musimat.com/ 00116 // This program is released under the terms of the GNU General Public License 00117 // available here: http://www.gnu.org/licenses/gpl.txt 00118
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