**Scored for flute & piano**

*Duration: 3′ 00″*

PDF Score here.

**Inspiration…**

– The Compass School of Feng Shui “deals with numerology, calculation, orientation, and time… and utilises the *Luo Shu*, 3 × 3 magic square.

– Six cardinal directions = North, South, East, & West + Zenith & Nadir.

– Euler (magic) squares exist for all orders except 2 and 6.

– “In number theory, an integer… is called a quadratic residue modulo n if it is congruent to a perfect square modulo n” (wikipedia.org/wiki/Quadratic_residue).

**Sequence of Number of non zero quadratic residues (mod n) –
first 36 (http://oeis.org/A105612)**

0, 1, 1, 1, 2, 3,

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

6, 7, 5, 3, 8, 7,

9, 5, 7, 11, 11, 5,

10, 13, 10, 7, 14, 11,

15, 6, 11, 17, 11, 7,

18, 19, 13, 8, 20, 15,

21, 11, 11, 23, 23, 7,

21, 21, 17, 13, 26, 21,

17, 11, 19, 29, 29, 11,

30, 31, 15, 11, 20, 23,

33, 17, 23, 23, 35, 11, 36,

If C = 0, 12, 24…, B =11, 23, 35…

C4 -> C7 (flute range): Central point of reference = **G#5**

Potential isomorphic LIE scale (containign IC 2 & 6) = +1+5, “+2+6”, +3+7, +4+8…

Pitches ascending from G#4: (n=+1+2…)

G#4 (+1) A4 (+2 ) B4 (+3) D5 (+4) F#5 (+5) B5 (+6) F6 (+7) C7 (+8) G#7…

Pitches ascending from G#4: (n=+5+6…)

G#4 (+5) C#5 (+6 ) G5 (+7) D6 (+8) Bb6 (+9) G7…

Combinatory ascending scale:

**G#4 (+1) A4 (+2 ) B4 (+2) C#5 (+1) D5 (+4) F#5 (+1) G5 (+4) B5 (+3) D6 (+3) F6 (+5) Bb6 (+2) C7 (+7) G7 (+1 ) G#7…**

Pitches descending from G#4: (n=+1+2…)

G#4 (+1) G4 (+2 ) F4 (+3) D4 (+4) Bb3 (+5) F3 (+6) B2 (+7) E2 (+8) G#1 (+9) B0…

Pitches descending from G#4: (n=+5+6…)

G#4 (+5) Eb4 (+6 ) A3 (+7) D3 (+8) F#2 (+9) A1 (+10) B0…

Combinatory descending scale:

**B0 G#1 (+1 ) A1 (+7) E2 (+2) F#2 (+5) B2 (+3) D3 (+3) F3 (+4) A3 (+1) Bb3 (+4) D4 (+1) Eb4 (+2) F4 (+2) G4 (+1) G#4 **

IC 1,7,2,5,3,3,4,1 = Decimal expansion of 20th root of 2.

Corresponds to unique integer sequence: https://oeis.org/A010782

IC 1,2,2,1,4,1,4,3,3

Corresponds to unique integer sequence: https://oeis.org/A286582