## Interlaced Phasing – Basic Principles

uPhase+ was designed to explore phasing patterns, not to compose linear music. Phasing creates endless complexity out of very simple building blocks; a good understanding of phasing behaviours is key to master uPhase+.

Consider these two simple sequences :

Sequence 1 (3 notes, 1 beat per note) : A_B_C_

Sequence 2 (4 notes, 1 beat per note, offset by half a beat) : _A_B_C_D

If each is looped indepedently, we obtain a 24 notes sequence :

A_B_C_|A_B_C_|A_B_C_|A_B_C_|(4 times sequence 1)

_A_B_C_D|_A_B_C_D|_A_B_C_D| (3 times sequence 2)

AABBCCADBACBACBDCAABBCCD (resulting sequence of 24 notes)

To calculate the size of a sequence obtained by two interwoven phasing patterns, multiply their number of notes by each other, and double. Here, 3*4*2 = 24. Note that this works if the ratios are not reductible. If they are, reduce the ratio before multiplying :

6 and 4 phase like 3 and 2, meaning the 6 note sequence will have to loop 2 times while the 4 note sequence will loop 3 times, so the total number of notes of the new sequence will be 6*2 + 4*3 = 24. Since both sides of the sum will always be equal, calculating just one and doubling is enough. For example phasing of 8 and 6 : 8/6= 4/3, so the 8 note sequence will loop 3 times -> 8*3*2 = 48 notes in the resulting sequence.