Chapter9 Namespace Reference

Functions
Void	C090400 ()
Void	C090703 ()
Void	C090703a ()
Void	C090703b ()
Void	C090703c ()
Void	C090903 ()
Void	C091101 ()
Void	C091102 ()
Void	C091200 ()
Void	C091201 ()
Void	C091201a ()
Void	C091201b ()
Void	C091201c ()
Void	C091201d ()
Void	C091201e ()
Void	C091201f ()
Void	C091204 ()
Void	C091204a ()
Void	C091204b ()
Void	C091204d ()
Void	C091405 ()
Void	C091406 ()
Void	C091406a ()
Void	C091406b ()
Void	C091406c ()
Void	C091704b ()
Void	C091704c ()
Void	C091704d ()
Static Void	para1 ()
Static Void	para2 ()
Static Void	para3 ()
Integer	LCRandom ()
Real	Random (Real L=0.0, Real U=1.0)
Integer	Random (Integer L, Integer U)
Integer	interpTendency (Real f, IntegerList L1, Integer Reference pos1, IntegerList L2, Integer Reference pos2, Integer inc)
RealList Reference	accumulate (RealList Reference L)
IntegerList	invert (IntegerList)
IntegerList	transpose (IntegerList, Integer)
Void	rotate (IntegerList Reference, Integer, Integer)
IntegerList	randomRow (Integer)
Integer	cycle (IntegerList, Integer Reference, Integer)
Integer	getIndex (RealList, Real)
RealList	normalize (RealList L, Real s)
Void	realToRational (Real f, Integer Reference num, Integer Reference den)
Real	sum (RealList L)
Variables
Integer	x
RealList	f

---

Function Documentation

Void Chapter9::C090400

(

)

Void Chapter9::C090703

(

)

Void Chapter9::C090703a

(

)

Void Chapter9::C090703b

(

)

Void Chapter9::C090703c

(

)

Void Chapter9::C090903

(

)

Void Chapter9::C091101

(

)

Void Chapter9::C091102

(

)

Void Chapter9::C091200

(

)

Void Chapter9::C091201

(

)

Void Chapter9::C091201a

(

)

Void Chapter9::C091201b

(

)

Void Chapter9::C091201c

(

)

Void Chapter9::C091201d

(

)

Void Chapter9::C091201e

(

)

Void Chapter9::C091201f

(

)

Void Chapter9::C091204

(

)

Void Chapter9::C091204a

(

)

Void Chapter9::C091204b

(

)

Void Chapter9::C091204d

(

)

Void Chapter9::C091405

(

)

Void Chapter9::C091406

(

)

Void Chapter9::C091406a

(

)

Void Chapter9::C091406b

(

)

Void Chapter9::C091406c

(

)

Void Chapter9::C091704b

(

)

Void Chapter9::C091704c

(

)

Void Chapter9::C091704d

(

)

Static Void Chapter9::para1

(

)

Definition at line 19 of file C090400.cpp.

References n(), Random(), and VossFracRand().

                    {
/*****************************************************************************
See "Musimathics" section B.2.1 for a description of PitchList. 
Then we need a source of judgment for which of Guido’s three vowel sequences 
should be chosen. We’ll use the integer Random( ) method to generate random values. 
Combining these, we obtain the program for Guido’s method:
*****************************************************************************/
}

Static Void Chapter9::para2

(

)

Definition at line 51 of file C090400.cpp.

References f, guido(), and sum().

                    {
/*****************************************************************************
The program indexes one Character at a time of text. 
If Character c is a vowel, it calculates offset based on which vowel it is. 
If it is not a vowel, the program sets offset to –1 so that the final step is skipped. 
If it is a vowel, the program chooses a random number 0, 1, or 2, corresponding to the 
three possible outcomes for each vowel. This is multiplied by 5, corresponding to the
number of vowels, and added to offset to arrive at the index of the selected element in 
the list of guidoPitches. The selected Character from that list is then stored in PitchList G. 
The method is repeated until text is exhausted. PitchList G then contains the list of pitches 
composed for this text. As its final action, the PitchList G is returned to the calling program.
To invoke the function guido(), we need a Latin text. I’ll use the first phrase of the text 
Guido used to name the solfeggio syllables, the medieval hymn Sanctus Joharines (St. John). 
This program fragment prints the pitches for a plain chant melody based on the text:
*****************************************************************************/

Print("*** Guidonian melody for the text: Ut queant laxis resonare ***");
Print(guido("Ut queant laxis resonare"));

/*****************************************************************************
An example result of this method is shown in "Musimathics" V1, figure 9.3.
*****************************************************************************/                                                                                  
}}

Static Void Chapter9::para3

(

)

Definition at line 90 of file C091101.cpp.

References f, retrograde(), sum(), and x.

                    {
/*****************************************************************************
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) );

}}

Integer Chapter9::LCRandom

(

)

Definition at line 53 of file C090703.cpp.

References a, b, c, and x.

                  {
        x = Mod(a * x + b, c);                  // update x based on its previous value
        Integer r = x;                                  // x may be positive or negative
        If (r < 0)                                              // force the result to be positive
                r = -r;
        Return(r);
}

Real Chapter9::Random	(	Real	L = 0.0,
		Real	U = 1.0
	)

Definition at line 15 of file C090703b.cpp.

References c, and LCRandom().

                            {
        Integer i = LCRandom();                 // get a random integer value
        Real r = Real(i);                               // convert it to a real value
        r = r/Real(c);                                  // scale it to 0.0 <= r < 1.0
        Return(r * (U - L) + L);                // scale it to the range L to U
}

Integer Chapter9::Random	(	Integer	L,
		Integer	U
	)

Definition at line 33 of file C090703c.cpp.

References Random(), and x.

                                     {
        Real rL = L;                                                    // convert L to Real
        Real rU = U + 1.0;                                              // convert U to Real, add 1.0
        Real x = Random(rL, rU);                                // get a real random value
        Return( Integer(x));                                    // return it as an integer
}

Integer Chapter9::interpTendency	(	Real	f,
		IntegerList	L1,
		Integer Reference	pos1,
		IntegerList	L2,
		Integer Reference	pos2,
		Integer	inc
	)

Definition at line 55 of file C091201e.cpp.

References cycle(), unitInterp(), and x.

  {
        Integer x = cycle(L1, pos1, inc);
        Integer y = cycle(L2, pos2, inc);
        Return(Integer(Round(unitInterp(f, x, y))));
}

RealList Reference Chapter9::accumulate

(

RealList Reference

L

)

Definition at line 16 of file C091406a.cpp.

                                                   {
        For(Integer i = 1; i < Length(L); i = i + 1){
                 L[i] = L[i] + L[i - 1];
        }
        Return(L);
}

IntegerList Chapter9::invert

(

IntegerList

)

Definition at line 62 of file C091101.cpp.

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

IntegerList Chapter9::transpose	(	IntegerList	,
		Integer
	)

Definition at line 41 of file C091101.cpp.

                                                {
        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);
}

Void Chapter9::rotate	(	IntegerList	Reference,
		Integer	,
		Integer
	)

Definition at line 19 of file C090903.cpp.

References rotate(), and x.

                                                              {
        n = Mod(n, Length(f));                                          //constrain rotation to length of list
        Integer x = f[i];                                                       //store f[i] for use after recursion
        If(i < Length(f)-1)                                                     // reached the end?
                rotate(f, n, i+1);                                              // no, call rotate() recursively
        // continue from here when the recursion unwinds
        Integer pos = PosMod(i+n, Length(f));           // index list modulo its length
        f[pos] = x;                                                                     // assign value of x saved above
}

IntegerList Chapter9::randomRow

(

Integer

)

Definition at line 20 of file C091204a.cpp.

References Random(), and x.

                                 {
        IntegerList L;                                          // keep track of pitches chosen so far
        IntegerList M;                                          // used to build up random 12-tone row
        Integer i;
        
        // set all list elements to zero, which means "unused"
        For (i = 0; i < N; i = i + 1) {L[i] = 0;}

        // build up M, marking off elements in L when they are chosen
        i = 0;
        While (i < N) {
                Integer x = Random(0, N - 1);           // returns integer random value
                If (L[x] == 0) {                                        // hasn’t been chosen yet?
                         L[x] = 1;                                              // mark it "used"
                         M[i] = x;                                              // save result
                         i = i + 1;                                     // increment control variable
                }
        }
        Return(M);
}

Integer Chapter9::cycle	(	IntegerList	,
		Integer	Reference,
		Integer
	)

Definition at line 31 of file C091201a.cpp.

                                                                 {
        Integer i = PosMod(pos, Length(L)); // compute current index
        pos = PosMod(pos + inc, Length(L)); // compute index for next time
        Return(L[i]);
}

Integer Chapter9::getIndex	(	RealList	,
		Real
	)

Definition at line 15 of file C091406b.cpp.

                                    {
        Integer i;
        For (i = Length(L) - 1; i >= 0; i = i - 1){
                If (R > L[i]){
                        Return(i + 1);
                }
        }
        Return( 0 );
}

RealList Chapter9::normalize	(	RealList	L,
		Real	s
	)

Definition at line 60 of file C091406.cpp.

                                              {
                For (Integer i = 0; i < Length(L); i = i + 1){
                        L[i] = L[i]/s;
                }
                Return(L);
        }

Void Chapter9::realToRational	(	Real	f,
		Integer Reference	num,
		Integer Reference	den
	)

Real Chapter9::sum

(

RealList

L

)

Definition at line 38 of file C091406.cpp.

                             {
                Real s = 0.0;
                For (Integer i = 0; i < Length(L); i = i + 1) {
                        s = s + L[i];
                }
                Return(s);
        }

---

Variable Documentation

Integer Chapter9::x

Definition at line 51 of file C090703.cpp.

RealList Chapter9::f

---