starts from a previously obtained sequence of triads. As each triad is associated with several harmonic loci, there is an associated family of combinatorially possible pathways to each chord sequence among which a shortest one has to be chosen. Each major chord signifies 6 harmonic loci. If is the center of a major region, there are six harmonic loci signified by one and the same major triad, e.g. with : With respect to the same regional center there are five harmonic loci signified by one and the same minor triad, e.g. with : Finally, there are three harmonic loci signified by each diminished triad, e.g. with : We may paraphrase these facts within our framework by attributing a boolean Riemann Logic sending each possible signification to if they are associated to one another like described above and to otherwise. If denote the total numbers of occurances of major, minor and diminished triads within the sequence the number of possible harmonic pathways equals .

Lerdahl reduces the Faith motive passage to the following sequence of 12 triads (7 major, 4 minor and 1 diminished):

The resulting number of possible pathway-analyses is Lerdahl proposes the following pathway out of these:

In order to make a clear balance, we first make the following observation: The devitions between the para-pseudo-distance and the pseudo-distance are not relevant in this particular example, as there are not transitions in the chord-sequence where such deviations occur. After reduction to the distance the number of possible pathways reduces to . Lerdahl’s analysis leads to a path length . There are 4676 paths with the same length. Furthermore, there are 8327 paths with lengths shorter than and thus representing better analyses in sense of Lerdahl’s theoretical approach. There are 22 analyses representing shortest possible paths of length :