Linear intervallic patterns (LIPs) are the series of intervals that govern what are commonly called "sequences" (= repeated melodic passages that, at each instance, move up or down a step,
and usually described according to the underlying harmonic progression, e.g. falling-fifth sequence).
A LIP is the subsurface pairs of intervals that guide such melodic passages. The subsurface LIP
may remain constant while the surface melodic patterning may change.
Example 1: 10-7 LIP
Assuming that the left-hand 16th rest at the beginning of m. 4 stands for a Bb, the interval between right and left hands on beat 1 is a 10th (Bb-D). As the harmony changes from I to IV at beat 2, an Eb enters in the left hand and forms a 7th with what we may assume to be a right-hand D at the 16th rest at the beginning of beat 2, as though the right-hand D from beat one were imaginarily held over to beat 2. That D, a dissonant 7th against the bass Eb, must resolve down by step to C, which it does on beat 3 as the harmony shifts to vii and the bass moves to A, forming another 10th (A-C), a step lower than the previous one (Bb-D). As the harmony falls another fifth on beat 4, to iii, the bass moves to D and forms another 7th with an imaginary right-hand C at the 16th rest on beat 4. The emerging, subsurface LIP is 10-7, 10-7, etc. That intervallic pattern guides and governs mm. 4-5. [Bach's Inventio 12 in A major, mm. 5-8, and Sinfonia 15 in B minor, mm. 7-11, provide two further, clear examples of 10-7 LIPs.]
Example 2: 10-5 LIP
Post-exposition LIPs in Inventions