Minimum Hitting Set

[Combinatorics]

Hypergraphs

Hypergraphs

0:00/ 0:00

Programme Description


This composition translates the logic of Baccarat into music.
The choice of notes is dictated by simulating the card game
using cryptographic hardware entropy, a Fisher-Yates shuffle,
and rejection sampling to ensure uniform probability without
modulo bias.

An Integer Linear Programming solver calculates the Minimum
Hitting Set of hypergraphs to construct both bass melodies and
structural polyrhythms. Harmony and pitch proximity are then
governed by modular arithmetic within a circular metric space,
resolving dissonance into consonance.

As the sequences interact, counterpoint develops, layering
perfect intervals against subharmonic series, whilst set theory
and complementary logic determine further harmonic voicing
during recurring game states. Throughout, traditional metre
dissolves into proportional temporal division.




Suite


[Suite]

no4

No4

0:00/ 0:00


no3

No3

0:00/ 0:00


no2

No2

0:00/ 0:00


no1

No1

0:00/ 0:00




sYmмeтRYЯтэмmYꙅ

(Symmetry)


[Symphony No1]

sYmмeтRYЯтэмmYꙅ

q p

0:00/ 0:00

Movement 1


q (0:00)
p (3:56)
ф (7:53)

Programme Description


Throughout Movement 1, the symmetrical properties of mathematics
are applied to the selection and arrangement of notes, the number
of instrument types, the quotients of measures, the durations of
parts q and p, the dynamics (volume) and rhythms of phrases,
the progression of visual patterns, the structures of parts q,
p, and ф, as well as the distances and angles within the
orchestra.

In part q, each instrument exposits the sound and atmosphere of
a specific component of a forest in nature, whilst in part p, this
representation develops into more complex, yet symmetrically
interrelated (micro)tonal combinations. In parallel, the intro-
ductions of parts q and p are recapitulated in part ф.

The conductor shall either add 32/455 seconds (~0.07032967032s)
to part q, or subtract it from part p, to complete the symmetry of
the two divisions. This may be achieved in the form of fermata,
incomplete rubato, accelerando or ritardando. Alternatively,
at the conductor’s discretion, adding 32/455 seconds of
silence is permitted as an instrumental element.

Instrumentation




아버지죽이기

(Patricide)


[Rondo]

아버지죽이기

Self-Portrait of Father

0:00/ 0:00

11 잠자는 아버지를 바라보며 (0:00)
10 아버지의 마지막 몸부림 (1:42)
9 움직이지 않는 아버지 (3:13)
8 그롙 매닉 에피소드 (5:26)
7 도깨비불 육과 팔 (6:58)
6 ∅∅∅∅∅∅ (10:40)



Begrafenis Wals

(Funeral Waltz)


[String Quartet in Polytonality:
simultaneous major & minor,
partly atonal & microtonal]

Begrafenis Wals
0:00/ 0:00

Storyline

In Andante Scherzando, despite the tragic news
of her friend's death, Mrs. VS attends a ballroom
party and dances with young gentlemen.

In La Reminiscenza, Mrs. VS delves deep into her
subconscious memories, including those that may
never have existed, and finds enlightenment.

In Veliero & Euforia, she then travels on a sailing
ship with dreams, against the wind and the waves,
and becomes euphoric before reaching

a rosy Romanza (Romance in between reality and
fantasy) state, where she dislocates her memories
and achieves self-realisation.

4 Movements




3 Impromptus from Wales


Ballet in Imagination


[Impromptu No3]

Ballet in Imagination

Ballerinas

0:00/ 0:00


The Adventures of Pwlldu Leaf


[Impromptu No2]

The Adventures of Pwlldu Leaf

Pwlldu Bay

0:00/ 0:00


Gwynt Gaeaf Cymreig

(Welsh Winter Wind)


[Impromptu No1 in Bitonality]

Welsh Winter Wind

Castle Graig

0:00/ 0:00


Godsgeschenk

(Gift From Heaven)


[Lied, for Countertenor/Alto]

Godsgeschenk
0:00/ 0:00

Storyline

Scene 1 depicts Annet meeting her mother in a dream,
which is followed by Scene 2, where a girl (Annet)
encounters a withered flower (Mother) with the help of
the sun, the cloud and the wind. In Scene 3, Annet
wakes up and says ‘Life goes the way it goes’.

Lyrics




The Capricious Woman


[Caprice]

The Capricious Woman
0:00/ 0:00

Mood Swings




Krasjemeisje - The Kitten


[Sonatina]

Krasjemeisje - The Kitten
0:00/ 0:00

4 Movements