pemodelan matematika sederhana dalam membuat sebuah lagu
TRANSCRIPT
S e r g iu s L e s k i S in at u s Pu t r a
0 814 140 88
Tr i An g g a J iw an d an a
0 814 140 6 4
Pendahuluan
M a t e m a t i k a d a n m u s i k s u d a h
"b e r s a u d a r a " s e ja k z a m a n Y u n a n i
K u n o . Pythagoras (5 8 0 -5 0 0 S M )
s e o r a n g fi ls u f d a n
m a t e m a t i k a w a n t e r k e n a l p a d a
z a m a n Y u n a n i K u n o b e r s a m a
p a r a m u r i d n y a m e n e m u k a n
b a h w a h a r m o n i d a la m m u s i k
b e r k o r e s p o n d e n s i d e n g a n
p e r b a n d i n g a n d u a b u a h b i la n g a n
b u la t . B i la k i t a m e m p u n y a i d u a
u t a s k a w a t y a n g d i r e g a n g k a n
d e n g a n k e t e g a n g a n y a n g s a m a ,
m a k a p e r b a n d i n g a n p a n ja n g
k e d u a u t a s k a w a t t a d i m e s t i la h 2 :
1 u n t u k m e n g h a s i lk a n n a d a
k e e n a m (n o t y a n g s a m a p a d a
o k t a f b e r i k u t n y a ); 3 : 2 u n t u k n a d a
k e li m a , d a n 4 : 3 u n t u k n a d a
k e e m p a t .
D i z a m a n s e k a r a n g k i t a t i d a k
t e r la lu k e s u li t a n u n t u k
m e n g e r ja k a n s e s u a t u s e c a r a
m a n u a l. C u k u p m e n g e t a h u i
b e b e r a p a p e n g e t a h u a n d a s a r
y a n g s e la n ju t n y a d a p a t k i t a
k e m b a n g k a n s e n d i r i .
D i s i n i k i t a a k a n m e n g g u n a k a n
p e r a n m a t e m a t i k a s e b a g a i
d a s a r p e n g e t a h u a n k i t a d a la m
m e m b u a t s e b u a h la g u .
K ita misalkan : N o t p e n u h d e n g a n a ,
N o t d e n g a n ½ b ,
N o t d e n g a n ¼ c ,
N o t 1 /8 d e n g a n d ,
N o t 1 /1 6 d e n g a n e
u n t u k m a s a la h i n i k i t a
m e n g g u n a k a n b i r a m a 4 /4
D e n g a n m e m i s a lk a n 4 /4 = 1 ,
m a k a k i t a d a p a t m e li h a t
b a h w a
a = 1 (a r t i n y a a d a 1 n o t p e n u h
d a la m 1 b a r )
b + b = 1 (a r t i n y a a d a 2 n o t ½d a la m 1 b a r )
c + c + c + c = 1 ( a r t i n y a a d a 4 n o t
d a la m 1 b a r )¼d + d + d + d + d + d + d + d = 1 (a r t i n y a
a d a 8 n o t 1 /8 d a la m 1 b a r )
e + e + e + e + e + e + e + e + e + e + e + e + e +
e + e = 1 (a r t i n y a a d a 1 6 n o t
1 /1 6 d a la m 1 b a r )
a t a u
a = 2 b = 4 c = 8 d = 1 6 e
a t a u
a = b + b = 2 b
b = c + c = 2 c
c = d + d = 2 d
d = e + e = 2 e
Ja d i , k e t i k a k i t a a k a n
m e m b u a t s e b u a h la g u d a la m
1 b a r k i t a d a p a t m e n e n t u k a n
b e r a p a b a n y a k n o t y a n g h a r u s
k i t a m a s u k a n /d i b u a t
g ambar . 1 bar
P e r h a t i k a n g a m b a r -g a m b a r
b e r i k u t :
g ambar . a =1
Ja d i , h a n y a a d a 1 n o t y a n g
m u n g k i n k i t a b u a t d a la m 1
b a r .
Gambar. a = 2b
Ja d i , h a n y a a d a 2 n o t y a n g
m u n g k i n k i t a b u a t d a la m 1 b a r .
Gambar. a = 2b = 4c
Ja d i , h a n y a a d a 4 n o t y a n g
m u n g k i n k i t a b u a t d a la m 1 b a r .
Gambar. a = 8d
Ja d i , h a n y a a d a 8 n o t y a n g
m u n g k i n k i t a b u a t d a la m 1
b a r .
Gambar. a = 16e
Ja d i , h a n y a a d a 1 6 n o t y a n g
m u n g k i n k i t a b u a t d a la m 1
b a r .
Ja d i k i t a s u d a h m e n g e t a h u i
b a h w a
a = b+b = 2bb = c+c = 2cc = d+d = 2dd = e+e = 2eD a r i s i n i d a p a t k i t a t u r u n k a n
a = b+b= b + ( c + c)= b + c + ( d + d)= b + c + d + ( e + e)I n i la h a d a la h s a la h s a t u c o n t o h
p e n e r a p a n .
Gambar. c o n t o h p e n e r a p a n
S e la n ju t n y a k i t a a k a n
m e n g g u n a k a n s o ft w a r e
k o m p u t e r u n t u k m e m u d a h k a n
p e k e r ja a n k i t a .
D i s i n i k i t a a k a n m e n g g u n a k a n
a p li k a s i g u i t a r p r o 5
B e b e r a p a p e t u n ju k p e n t i n g
p e n g g u n a a n g u i t a r p r o
2. g a m b a r g i t a r , b e r fu n g s i u n t u k
m e m u d a h k a n m e n e m u k a n n a d a
y a n g i n g i n d i b u a t t e r m a s u k
c h o r d y a n g a k a n d i m u a t d a la m
b a r .
3. T e m p o , b e r fu n g s i u n t u k
m e n g a t u r s e b e r a p a c e p a t i r a m a
la g u y a n g a k a n k i t a b u a t .
4. a d d a t r a c k , b e r fu n g s i
m e n a m b a h i n s t r u m e n la i n ,
m i s a ln y a p e r c u s s i o n / d r u m
5. P a d a t r a c k a d a b a g i a n
i n s t r u m e n d i s i t u k i t a d a p a t
m e m i li h s u a r a a p a y a n g i n g i n
k i t a b u a t . T e r d a p a t b a n y a k
p i li h a n s u a r a .
6. C a t a t a n fi le y a n g d i h a s i lk a n
m a s i h b e r u p a m i d i .
S e t e la h a n d a m e m b u a t
g a m b a r a n m u s i k y a n g
d i i n g i n k a n , g a m b a r a n i n i
d a p a t m e n ja d i p e d o m a n
a n d a b i la a n d a i n g i n s e r i u s
b e r m u s i k a t a u s e b a g a i
p e n g h i b u r k e t i k a a n d a
b e la ja r m a t e m a t i k a .
B e r i k u t a d a la h c o n t o h
p e m b u a t a n n o t a s i d a n s u a r a
y a n g d i h a s i lk a n (sumber gitar pro 5)K li k u n t u k
m e m u t a r
la g u
D a r i b e n t u k m a t e m a t i s a = 2b = 4c = 8d = 16e
A n d a d a p a t b e la ja r
m e n g a r a n s e m e n d a n
m e m b u a t m u s i k s e s u a i
d e n g a n s e le r a a n d a .
Selamat mencoba dan bereksperimen !