FORMULA

On this page we publish the compositions, which have been written using The Beautiful Formula Language. Please, feel free to send us your comment or any kind of question: 

thebeautifulformula@googlemail.com
The Beautiful Formula Collective

Backjump, composition by Daniel Geiger
The Beautiful Formula Collective 2019
Daniel Geiger, Oleksiy Koval, Veronika Wenger
Marker on styropor, 79 x 49 cm

BACKJUMP
Daniel Geiger 2019

M

1/49b

E

a,e ≈
b,c,d ≈
f,g ≈

P

a {min 3 max 21} *1
b [5+3+5+3+5+1(+max 4x)] of a{n} #∞
c [5+3+5+3+5+1(+max 4x)] of a{n} #∞
d [3+2+3+2+3+1(+max 4x)] of a{n} #∞
e [*-+*1+-+*1…] of a{n} #∞
f a{n}+1+1+1+2+3(+max 2x) #∞
g a{n}+1+1+1+2+3(+max 2x) #∞

M METER
E ELEMENT
P PROCEDURE
# ENTRY

* hits the meter
(n) size of unit
[] within the same area
#(n) number of entries
∞ number of entries flexible
≈ size of the unit is corresponding for all elements
+ has to touch
{ n } polygon with n edges

----------------------------------------

Französischer Wein, composition by Veronika Wenger
The Beautiful Formula Collective 2019
Daniel Geiger, Oleksiy Koval, Veronika Wenger
Marker on paper, 50 x 40 cm

FRANZÖSISCHER WEIN
Veronika Wenger 2019

M

1/9 1/16b

E

a,b,c,d

P

a [1,2,1,2,1,2] max 15x
b *-+*-+*- max 5x
c -,-,-,-,-
d -,-,-,-,-

M METER
E ELEMENT
P PROCEDURE

* hits the meter
(n) size of unit
[] within the same area
+ has to touch

----------------------------------------

QUATTUOR NOVISSIMA (SYMPHONY N2)
Oleksiy Koval, 2018

E

a, b, c, d

P

1# a(-) T8 x 5
2# b(-) T5 x 5
3# c(-) T3 x 5
4# d(-) T2 x 5
5# a(-) T8 x 5
6# b(-) T5 x 5
7# c(-) T3 x 5
8# d 1, 1, 1, 2, 3, 2, 2, 3, 1, 1, 2, 1, 3, 1, 5
9# a(-) T8 x 5
10# b(-) T5 x 5
11# c¹(*-) c²(*-) c(-)+c¹+c² M 1/4b
12# d 1, 1, 1, 2, 3, 2, 2, 3, 1, 1, 2, 1, 3, 1, –
13# a(-) T8 x 5
14# b 5+1+5+2+5+3 max x5
15# c³(*-) c(-)+c²+c³ M 1/4b
16# d 1, 1, 1, 2, -, 2, 2, -, 1, 1, 2, 1, -, 1, –
17# a(-) T8 x 5
18# b+14#b 5+1+5+2+5+3 max x5
19# c⁴(*-) c(-)+c³+c⁴ M 1/4b
20# d 1, 1, 1, -, -, -, -, -, 1, 1, -, 1, -, 1, –

Signs and symbols:

M METER
T TAKT
E ELEMENT
P PROCEDURE
# ENTRY

* hits the meter
(n) size of unit
+ has to touch
ⁿ ordinal number

----------------------------------------

DIRIGENT, Daniel Geiger, 2016

M

1/25

R

a 1,2,1,3,1,5
b,d,f 1+1+1+2+3
c 2+2+3+1
e 3+1+3+2+3+3
g 1+2+1+3+1+5

E

a,b,c,d,e,f,g ≈

P

#1  a
#2  *a(1)+b+a(2)+c+a(1)+d+a(3)+e+a(1)+f+a(5)+g x3
#3  a

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



PHLEGMATIKER, Oleksiy Koval, 2015

M

1/144

T

1,2,3,4

E

a [*1]
b [*1][*1]
c [*1][*1][*1]
d [*1][*1][*1][*1]

P

#1 M1 a or b or c or d (if a)
#2 M2 b or c or d (if b)
#3 M4 a or c or d (if c)
#4 M8 a or b or d (if d)
#5 M13 a or b or c … stop if M144

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------

DOPPELGÄNGER, Karina Bugayova, 2015

M

M¹ 1/9
M² 1/9

R

a 1,1,2,3
b 3,8
c –

P

#1 *c>M5
#2 c
#3 c
#4 [a,a]>A5
#5 a,b
#6 *a,b
#7 *a,*b
#8 a,*b
#9 b,b
#10 c
#11 c
#12 c

P¹>M¹
P²>M²

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



SCHAR, Oleksiy Koval, 2012

M

1/16b

T

1,2,3,5

E

a,b,c,d,e,f ≈

P

a – (1-5) + #5 max
b – + – (1-5) + #5 max
c – (1-5) + #5 max
d – + – + – (1-5) + #5 max
e – (1-5) + #5 max
f – + – + – + – + – (1-5) + #5 max

*a+b+c+d+e+f

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



1,1,1,2,3, Oleksiy Koval, 2012

M

1/25

R

[*1,1,1,2,3]

E

|a,b,c,d,...| ≈

P

The rhythmical motive:
Element a starts with a solo using the rhythmical motive.
Then element a paints the same rhythmical motive, but in cooperation with the following two elements (b,c).
Element b has its solo and so on ...

[*a,a,a,aa,aaa]
[*a,a,a,ab,abc]
a makes four times a mark of the unit size 1
b chooses one of the four and makes a new unit of the size 2 by adding its mark in the unit size 1
a makes another mark of the unit size 1
b chooses again one of the four and makes a new unit of the size 2 by adding its mark in the unit size 1
c chooses one of the two units of the size 2 and makes one new unit of the size 3 by adding its mark in the unit size 1

[*b,b,b,bb,bbb]
[*b,b,b,bc,bcd]
[*c,c,c,cc,ccc]
[*c,c,c,cd,cde]
[*d,d,d,dd,ddd]
[*d,d,d,de,def]
...

The surface:
Start in area 1 or 5 and then move to the next area, either left to right, right to left or top to bottom until the row is completed.
The element wich comes next decides where to continue:
If you move horizontally it can be the area on the left or right border of the following row
or if you move vertically it can be the area on the top or bottom border of the following row.
This decision can be made for each row.

The idea behind this composition is to have a simple, repetitive structure, which allows for example to vary in speed while painting.

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------

SYMMETRIE, Kuros Nekouian, 2013

M

1/4

R

[–*,–,–,–,–,–] (1-3)

E

|a,b,c,d,e,f|

P

The leading element (marked) chooses an area and the following element may choose between the two opposite areas.

a,b,c,d,e,f
b,c,d,e,f,a
c,d,e,f,a,b
d,e,f,a,b,c
e,f,a,b,c,d
f,a,b,c,d,e

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



GAU, Oleksiy Koval, 2012

M

1/4 , 1/9

R

1,1,1,2,3,2,2,3,1,1,2,1,3,1,5

E

|a,b,c,d| ≈

P

a = 1
b = 2
c = 3
d = 5

#1 [*1,1,1,2,3][*2,2,3,1][*1,2,1,3,1,5]
#2 [*1,1,1,2,3][*2,2,3,1][*1,2,1,3,1,–]
#3 [*1,1,1,2,–][*2,2,–,1][*1,2,1,–,1,–]
#4 [*1,1,1,–,–][*–,–,–,1][*1,–,1,–,1,–]
#5 –,–,–,–,–,–,–,–,–,–,–,–,–,–,–

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



86, Veronika Wenger, 2013

E

a,b,c...

P

#1 M1/4,  [*–,–,–] (5-7)
#2 M1/25b,  [1,1,1,2]
#3 M1/9,  [*1,2,1,3,1,5]

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



FIXER, Daniel Geiger, 2013

M

1/4, 1/16

R

a, d 1/4  [*–,–,–,–] (1-7)
b, c, e, f 1/16 2,2,3,1

E

a,b,c,d,e,f

P

[a]
[b] b > 1{4 [a] ( b is within a's choice )
[c] c > 1{4 [a]  ( c is within a's choice )
[d]
[e] e > 1{4 [d] ( e is within d's choice )
[f] f > 1{4 [d] ( f is within d's choice )

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



SUBLUNARE WELT, Oleksiy Koval, 2012

M

1/4, 1/9

R

1,2,1,3,1,5
5,–,–,–,–,1

E

|a,b,c,d,e,f| ≈

P

[a*1,b2,c1,d3,e1,f5] a*5,–,–,–,–,1
[b*1,c2,d1,e3,f1,a5] b*5,–,–,–,–,1
[c*1,d2,e1,f3,a1,b5] c*5,–,–,–,–,1
[d*1,e2,f1,a3,b1,c5] d*5,–,–,–,–,1
[e*1,f2,a1,b3,c1,d5] e*5,–,–,–,–,1
[f*1,a2,b1,c3,d1,e5] f*5,–,–,–,–,1

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------

GNADE, Oleksiy Koval, 2012

M

1/4 , 1/9 , 1/16

T

5 *–,–,–,–,– (1-5)

E

a,b,c,d,e,f ≈

P

[a] #=2 or 3 or 5
[b] #=2 or 3 or 5
[c] #=2 or 3 or 5
[d] #=2 or 3 or 5
[e] #=2 or 3 or 5
[f] #=2 or 3 or 5
stop if #=2:3, 2:3, 2:5

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



TLO, Oleksiy Koval, 2012

M

1/9

R
 
a 3,1,3,2,3,3
b *1,1,1,1,1
c *1,1,1,1,1
d *2,2,2,2,2
e *3,3,3,3,3
f *5,5,5,5,5

E

a,b,c,d,e,f ≈

P

a #∞
b #1
c #1
d #1
e #1
f #1

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------

SURROGATE, Oleksiy Koval, 2012

M

1/4, 1/9, 1/16, 1/25

R

a 1/4 [*–,–,–,–,–,–,–] (1-5)
b 1/9 [*2,2,3,1]
c 1/16 [*1,2,1,3,1,5]
d,(e,f) 1/25 [*1,1,1,2,3]

E

a,b,c,d,e,f ≈

P

d,e,f M1/25 [*1,1,1,2,3]
[d,d,d,dd,ddd]-
[d,d,d,de,def]-
[e,e,e,ee,eee]-
[e,e,e,ef,efd]-
[f,f,f,ff,fff]-
[f,f,f,fd,fde]-…

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------



STALKER, Oleksiy Koval, 2012

M

1/9

T

4 *–,–,–,– (1-3)

E

|a,b,c,d,e,f| ≈

P

1. [a]
2. [a]
3. [a]
4. [a,b] b > 1{4[a]
5. [a,b] b > 1{4[a]
6. [a,b,c] b > 1{4[a]; c > 1{3[a,b]
7. [a,b,c,d] b > 1{4[a]; c > 1{3[a,b]; d > 1{2[a,b,c]
8. [a,b,c,d,e] b > 1{4[a]; c > 1{3[a,b]; d > 1{2[a,b,c]; e > 1{2[a,b,c,d]
9. [a,b,c,d,e,f] b > 1{4[a]; c > 1{3[a,b]; d > 1{2[a,b,c]; e > 1{2[a,b,c,d]; f > 1{2[a,b,c,d,e]

M meter
U unit
T takt
R rhythmical motive
E element
P procedure
# entry

* hits the meter
[] within the same area
#(n) number of entries
∞ number of entries flexible
(n) size of unit
≈ size of the unit is corresponding for all elements
|| order fixed
> n occupy n
{ n out of n possible
+ has to touch
≠ not
V vertical
H horizontal
F flexibel
ⁿ ordinal number
----------------------------------------