athenaCL Tutorial Manual: Second Edition, Version 1.4.8 | ||
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One use of SetMeasures is to compare Multisets (as set classes) of a PathInstance. The PathSet "PS" commands deal with the PathInstance as a series of set classes. The user-entered pitch space or pitch-class representations have no relevance on set-class analysis as performed by these SetMeasures.
There are two methods of set class analysis. The first, PScma, compares each set with the adjacent set. Entering the PScma command will perform such an analysis on the active PathInstance with the active SetMeasure. In the example below, a different SetMeasure is first selected:
Example 4-19. Comparing adjacent sets in a Path
[PI(pathVL)TI()] :: smo rel SetMeasure REL now active. [PI(pathVL)TI()] :: PScma PI: pathVL, Lewin REL analysis Tn similarity range: 0(min) . | . (max)1 3-11B 0.50 ..............................+............................. 3-7A 0.00 +........................................................... 3-12 0.43 .........................+.................................. 3-11B
athenaCL produces text-based horizontal graphs to demonstrate relative similarities. The final graph compares the last SC to the first. It may seem odd that the comparison of 3-7A and 3-12 produces a minimum value of similarity (0.00). This can be explained by examining the Interval Class Vectors for these two sets, as done below:
Example 4-20. Examining interval class vectors
[PI(pathVL)TI()] :: scv 3-7a SC(3-7A), Z(none), mode(Tn) Pitch Space: (C4,D4,F4) Pitch Class: (0,2,5) Normal Form: (0,2,5) Prime Form: (0,2,5) Invariance Vector: (1,0,0,0,5,6,5,5) Interval Class Vector: (0,1,1,0,1,0) References: name incomplete minor-seventh chord Subset Vectors: 3CV(Tn) 0,0,0,0,0,0,0,0,0,0 - 1,0,0,0,0,0,0,0,0 [PI(4-3)TI()] :: scv 3-12 SC(3-12), Z(none), mode(Tn) Pitch Space: (C4,E4,G#4) Pitch Class: (0,4,8) Normal Form: (0,4,8) Prime Form: (0,4,8) Invariance Vector: (3,3,3,3,9,9,9,9) Interval Class Vector: (0,0,0,3,0,0) References: name augmented triad, equal 3-part octave division Subset Vectors: 3CV(Tn) 0,0,0,0,0,0,0,0,0,0 - 0,0,0,0,0,0,0,0,1
The SCv command shows that these two sets have exclusive Interval Class Vectors: the two sets have no vector entries (or intervals) in common, and thus are at maximum set class dissimilarity.
The second method of set class analysis is done by comparing one set to every set in a Path. This method of comparison, PScmb, is performed on the active PathInstance with the active SetMeasure. The user must provide the comparison, or reference, set class. In the example below, the reference set class is 4-11:
Example 4-21. Comparing one set to all sets in a Path
[PI(pathVL)TI()] :: PScmb enter a SC for comparison to the path... enter a pitch set, sieve, or set-class: 4-11 SC 4-11A as (C4,C#4,D#4,F4)? (y, n, or cancel): y PI: pathVL, Lewin REL analysis Tn reference SC 4-11A similarity range: 0(min) . | . (max)1 0.47 3-11B ............................+............................... 0.54 3-7A ................................+........................... 0.27 3-12 ................+...........................................