Commodore 16 - Creating Music and Melodies

APPENDIX
C
Deriving
Mathematical Functions
Functions
thai are nol intnnsic
lo
BASIC
3 5 may be
calculated
as
follows;
FUNCTION
BASIC EQUIVALENT
SEC
AN
t
SEC<X)-i/COSW
COSECANT
CSC<X)-1/SIN(X)
COTANGENT COT(X)-l/TAN(X)
INVERSE SINE
ARCSIN<X)=ATN(X,<SOfi(-X-Xtl))
INVERSE
COSINE
ARCCOSIX)- -ATNiX/SQR
(
X'X.i;j.a.'2
INVERSE SECANT
ARCSEC<X>=ATN<X/SGR{X*X-l)>
INVERSE COSECANT
arccsc(X)=atn:x<sor<x-«
. i
-|-)GN{X(-I'ai2)
INVERSE COTANGENT
ARCOT!X)-ATN(X).ir'2
HYPERBOLIC SINE SINH(X)
E
(EXP(X)-EXP|-X)K2
HYPERBOLIC
COSINE COSH(X)=<EXP(X)- *EXP( X]V2
HVPERBOUC TANGENT TANH(X)-EXP(-
X)/(EXPI«)
- EXP
l-Wt+1
HYPERBOLIC SECANT SECH(X)-a(EXP(X).EXP( X))
HYPERBOLIC COSECANT
C5CHtX)=?J(EXP(X)-EXP(-X))
HYPERBOLIC COTANGENT
COTH(X)-EXP(
-
XHEXP(X)
-EXPt-X))*:-'-
INVERSE HYPERBOLIC SINE
ARCS1NH(X)
=
L0G(X
i
SORfX'X
•
1»
INVERSE HYPERBOLIC COSINE ARCCOSH(X)
-
LOG(X. SORlX'X
-
1)|
INVERSE HYPERBOLIC
TANGENT ARCTANH<X)=LOG(|l »X^i X))/2
INVERSE HYPERBOLIC
SECANT ARCSECH(X)-LOG(*SOP
(
-
X'X 1 !)• ll'X)
INVERSE HYPERBOLIC COSECAN'
ARCCSCH(X)-LOGl(SGN(XrSOR
>'..H>
INVERSE HYPERBOLIC COTANGENT ARCCOTH(X)-LOGl(X.U'|.
\\y3
172
1
1
1
1
1 f
[
I
!
'
1
I I
1 1
1 r
1
i
'
i
1
i
1
i
1 I
i
i
:
'
i
1 (
[
i
1 f
1
1
APPENDIX
D
Musical Note Table
NOTE SOUND REGISTER
VALUE
ACTUAL
FREQUENCY (HZ)
A 7 110
B 118 1235
C 169 1308
D
262 146.8
E 345
164.7
F 383 174.5
G
453
195.9
A 516
220.2
B 571 246.9
C 596 261.4
D 643 293.6
E 685
330
F 704
3496
G 739
392.5
A 770
440.4
B 798 4949
C
810
522 7
D 834 588.7
E 854
658
F 864
699
G 881
782.2
A 897
880 7
B
911
989 9
C
917
1045
D
929 1177
E 939
1316
F
944
1398
G 953 1575
The
above table conlains the sound regisier values
of
toui octaves ot
notes The
sound registei values are used as ihe second parameter
ol the
SOUND command To
use
the first
note In the table (A—sound
173