Kite's thoughts on pergens: Difference between revisions

For (P8, P5), the pergen square has 4 notes, shown here with octave numbers (ignore the periods).

C1 -- G1

Splitting the 8ve or the multigen adds notes to the square. For (P8/2, P5), there are 6 notes. The new notes fall halfway between each 8ve:

C1 --- G1

A pergen square shows all alternate gens and multigens. The unreduced form of (P8/2, P5) is (P8/2, M2/2). The M2 becomes visible only after tiling the pergen square. From C2 to D2 is a M2, and C#v2 bisects it. G#v2 bisects the G2-A2 M2. Every "downed" note bisects an 8ve, a M2, a Wm7 (e.g. D1 to C3), a WM9 (e.g. C1 to D3), and many other intervals.

C1 --- G1 --- D2 --- A2

Splitting the 5th adds notes to the horizontal edges of the square:

C1 Ev1 G1

Each downed note also bisects a P11 (e.g. G1-C3), as well as many other intervals.

C1 Ev1 G1

From G1 to C2 is a 4th, so splitting the 4th adds a note halfway between them, in the center of the square.

C1 ---- G1