C:/Musimathics_local/Musimat/MusimatChapter9/C091101.cpp

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#include "MusimatChapter9.h"
MusimatChapter9Section(C091101) {
Print("*** 9.11.1 Precomposition ***");
/*****************************************************************************

9.11.1 Precomposition

The process of composing atonal music is typically divided into two parts.

o Precomposing: assembling the musical materials

o Composing: applying the assembled materials in a design

Musimat already has a number of data types and operations, but a few more are needed:

o To represent pitches as symbols with integer values, such as:

        Integer C = 0, Cs = Db = 1, D = 2, Ds = Eb = 3 . . ., B = 11;

o To represent motives as lists, such as: 

        IntegerList a = {F, F, G, A}; 
        IntegerList b = {F, A, G}; 
        IntegerList c = {F, E};
        IntegerList d = {Bb, A, G, F}; 
        IntegerList e = {E, C, D, E, F, F};

o To combine motives and concatenate lists:

        IntegerList y = Join(a, b, a, c, a, d, e);

(y is defined as the list of pitches of the tune “Yankee Doodle.”)

The following function transposes a pitch set.
*****************************************************************************/
        para1(); // Step into this function to continue.
        para2(); // Step into this function to continue.
        para3(); // Step into this function to continue.
}

IntegerList transpose(IntegerList L, Integer t) {
        For(Integer i = 0; i < Length(L); i = i + 1)
                 L[i] = PosMod(L[i] + t, 12); // BUG: given as Mod() in "Musimat", s.b. PosMod()
        Return(L);
}

Static Void para1() {
/*****************************************************************************
Here is an example of transposing a list:
*****************************************************************************/

                Print("*** Transposing a list ***");
                IntegerList L( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 );
                Print("Original row:", L);
                Print("Row transposed by 6: ", transpose(L, 6) );

/*****************************************************************************
To invert a pitch set:
*****************************************************************************/
}

IntegerList invert(IntegerList L) {
        For(Integer i = 0; i < Length(L); i = i + 1)
                L[i] = Mod(12 - L[i], 12);
        Return(L);
}

Static Void para2() {
/*****************************************************************************
Here is an example of inverting a list:
*****************************************************************************/
                Print("*** Inverting a list ***");
                IntegerList L( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 );
                Print("Original row:", L);
                Print( "Inverted row:", invert(L) );

/*****************************************************************************
To take the retrograde of a set:
*****************************************************************************/
}

IntegerList retrograde(IntegerList L) {
        Integer n = Length(L);
        IntegerList R = L;                                                              // make a new list as long as L
        For(Integer i = 0; i < n; i = i + 1)
                R[i] = L[n - i - 1];
        Return(R);
}

Static Void para3() {
/*****************************************************************************
Here is an example of retrograding a list:
*****************************************************************************/
                Print("*** Retrograding a list ***");
                IntegerList L( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 );
                Print("Original row:", L);
                Print( "Retrograded row:", retrograde(L) );

}}

/* $Revision: 1.4 $ $Date: 2006/09/12 17:37:25 $ $Author: dgl $ $Name:  $ $Id: _c091101_8cpp-source.html,v 1.4 2006/09/12 17:37:25 dgl Exp $ */
// The Musimat Tutorial © 2006 Gareth Loy
// Derived from Chapter 9 and Appendix B of "Musimathics Vol. 1" © 2006 Gareth Loy 
// and published exclusively by The MIT Press.
// This program is released WITHOUT ANY WARRANTY; without even the implied 
// warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
// For information on usage and redistribution, and for a DISCLAIMER OF ALL
// WARRANTIES, see the file, "LICENSE.txt," in this distribution.
// "Musimathics" is available here:     http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10916
// Gareth Loy's Musimathics website:    http://www.musimathics.com/
// The Musimat website:                 http://www.musimat.com/
// This program is released under the terms of the GNU General Public License
// available here:                      http://www.gnu.org/licenses/gpl.txt

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