4.5. Analyzing and Comparing PathVoices

As mentioned in above, a detailed voice leading analysis can be displayed for the active PathVoice of the active PathInstance. Enter PVan to view this display.

Example 4-14. Detailed map data of a PathVoice group

[PI(pathVL)TI()] :: pvan
PI: pathVL, PathVoice: uniform

Position 1,2: origin (6,2,9) destination (8,3,5)
MC 3:3-6 map (cba)
   VL     (6--5),(2--3),(9--8) 
   SMTH   vector:(0,3,0,0,0,0,0)            displacement:3                 
   UNIF   vector:(0,1,0,0,0,0,0,0,0,0,0,2)  offset:2 (Tn:11) max:2 span:3  
   BAL    vector:(0,0,0,0,0,2,0,0,0,0,0,1)  offset:6 (In:5) max:2 span:7   
   rank   S1 U1 B5 of6                                                     
Position 2,3: origin (8,3,5) destination (9,5,1)
MC 3:3-2 map (acb)
   VL     (8--9),(3--1),(5--5) 
   SMTH   vector:(1,1,1,0,0,0,0)            displacement:3                
   UNIF   vector:(1,1,0,0,0,0,0,0,0,0,1,0)  offset:3 (Tn:0) max:1 span:4  
   BAL    vector:(0,0,0,0,1,1,0,0,0,0,1,0)  offset:6 (In:5) max:1 span:7  
   rank   S1 U1 B4 of6

Instead of an analysis of each map employed in the active PathVoice for all pairs of Multisets, the user can, with the PVcm command, compare a single map with all possible maps between a single pair of Multisets. This comparison can be done between any two Multisets in the Path. Entering PVcm allows the user to view all possible maps between two sets, sorted either by Smoothness, Uniformity, or Balance. The user must supply the position of the Multisets to be compared, the sorting method, and the range of maps to return. In the following example, the user displays all the possible maps between a single pair of adjacent sets in a PathInstance, sorting by Balance:

Example 4-15. Viewing sorted map data between two sets

[PI(pathVL)TI()] :: PVcm
PathVoice uniform has map positions (1,2) through (2,3): enter position to compare: 2,3
enter ranking method: Smoothness, Uniformity or Balance? (s, u, or b): b
there are 6 maps in this ranking. enter a range: (beginRank,endRank): 1,6

PI: pathVL, VL BAL Comparison
Position 2,3: origin (8,3,5) destination (9,5,1)

MC 3:3-1 map (abc)
   VL     (8--9),(3--5),(5--1) 
   SMTH   vector:(0,1,1,0,1,0,0)            displacement:7                
   UNIF   vector:(0,1,1,0,0,0,0,0,1,0,0,0)  offset:6 (Tn:1) max:1 span:7  
   BAL    vector:(0,0,0,0,0,1,1,0,1,0,0,0)  offset:3 (In:6) max:1 span:4  
   rank   S2 U4 B1 of6                                                    
MC 3:3-4 map (bca)
   VL     (8--5),(3--1),(5--9) 
   SMTH   vector:(0,0,1,1,1,0,0)            displacement:9                
   UNIF   vector:(0,0,0,0,1,0,0,0,0,1,1,0)  offset:6 (Tn:9) max:1 span:7  
   BAL    vector:(0,1,1,0,1,0,0,0,0,0,0,0)  offset:3 (In:2) max:1 span:4  
   rank   S3 U5 B2 of6                                                    
MC 3:3-5 map (cab)
   VL     (8--1),(3--9),(5--5) 
   SMTH   vector:(1,0,0,0,0,1,1)            displacement:11                
   UNIF   vector:(1,0,0,0,0,1,1,0,0,0,0,0)  offset:6 (Tn:5) max:1 span:7   
   BAL    vector:(1,0,0,0,0,0,0,0,0,1,1,0)  offset:3 (In:10) max:1 span:4  
   rank   S5 U6 B3 of6                                                     
MC 3:3-2 map (acb)
   VL     (8--9),(3--1),(5--5) 
   SMTH   vector:(1,1,1,0,0,0,0)            displacement:3                
   UNIF   vector:(1,1,0,0,0,0,0,0,0,0,1,0)  offset:3 (Tn:0) max:1 span:4  
   BAL    vector:(0,0,0,0,1,1,0,0,0,0,1,0)  offset:6 (In:5) max:1 span:7  
   rank   S1 U1 B4 of6                                                    
MC 3:3-3 map (bac)
   VL     (8--5),(3--9),(5--1) 
   SMTH   vector:(0,0,0,1,1,0,1)            displacement:13               
   UNIF   vector:(0,0,0,0,0,0,1,0,1,1,0,0)  offset:3 (Tn:8) max:1 span:4  
   BAL    vector:(1,1,0,0,0,0,1,0,0,0,0,0)  offset:6 (In:1) max:1 span:7  
   rank   S6 U2 B5 of6                                                    
MC 3:3-6 map (cba)
   VL     (8--1),(3--5),(5--9) 
   SMTH   vector:(0,0,1,0,1,1,0)            displacement:11               
   UNIF   vector:(0,0,1,0,1,1,0,0,0,0,0,0)  offset:3 (Tn:4) max:1 span:4  
   BAL    vector:(0,0,1,0,0,0,0,0,1,1,0,0)  offset:6 (In:9) max:1 span:7  
   rank   S4 U3 B6 of6

In the above example, for each map entry a "rank" line is provided with a value for Smoothness, Uniformity and Balance. Since this display was sorted by Balance ("b"), each map's Balance rank can be seen in order from top to bottom, B1 through B6.

Non-adjacent Multisets can also be compared, allowing the user to investigate mappings that are not defined by a PathVoice. That is, since a PathVoice only defines maps for adjacent sets, PVcm allows the user to investigate maps between non-adjacent sets without creating a new Path. For example, the mappings between the first and the last Multiset of a three-Multiset Path can be compared. In the following example the user has selected a range of results smaller than the total number of maps possible. Instead of all six maps, the user has only selected the first three, ranked by Uniformity. This feature is useful when dealing with maps between large Multisets.

Example 4-16. Viewing fewer than the full range of map analysis data

[PI(pathVL)TI()] :: PVcm
PathVoice uniform has map positions (1,2) through (2,3): enter position to compare: 1,3
enter ranking method: Smoothness, Uniformity or Balance? (s, u, or b): u
there are 6 maps in this ranking. enter a range: (beginRank,endRank): 1,3

PI: pathVL, VL UNIF Comparison
Position 1,3: origin (6,2,9) destination (9,5,1)

MC 3:3-1 map (abc)
   VL     (6--9),(2--5),(9--1) 
   SMTH   vector:(0,0,0,2,1,0,0)            displacement:10               
   UNIF   vector:(0,0,0,2,1,0,0,0,0,0,0,0)  offset:1 (Tn:3) max:2 span:2  
   BAL    vector:(0,0,0,1,0,0,0,1,0,0,1,0)  offset:7 (In:7) max:1 span:8  
   rank   S4 U1 B4 of6                                                    
MC 3:3-4 map (bca)
   VL     (6--5),(2--1),(9--9) 
   SMTH   vector:(1,2,0,0,0,0,0)            displacement:2                 
   UNIF   vector:(1,0,0,0,0,0,0,0,0,0,0,2)  offset:1 (Tn:11) max:2 span:2  
   BAL    vector:(0,0,0,1,0,0,1,0,0,0,0,1)  offset:7 (In:3) max:1 span:8   
   rank   S1 U2 B5 of6                                                     
MC 3:3-5 map (cab)
   VL     (6--1),(2--9),(9--5) 
   SMTH   vector:(0,0,0,0,1,2,0)            displacement:14                
   UNIF   vector:(0,0,0,0,0,0,0,2,1,0,0,0)  offset:1 (Tn:7) max:2 span:2   
   BAL    vector:(0,0,1,0,0,0,0,1,0,0,0,1)  offset:7 (In:11) max:1 span:8  
   rank   S6 U3 B6 of6

Alternatively, the user can compare maps unrelated to any PathInstance or PathVoice. Using the MCcm command, the user can sort and view all maps between any pair of Multisets. After entering the command, the user is prompted for an origin and a destination Multiset, as well as a sort method and a result range.

Example 4-17. Viewing sorted map analysis data between any pair of sets

[PI(pathVL)TI()] :: MCcm
select SC X:
enter a pitch set, sieve, or set-class: g#, d
   SC 2-6 as (G#4,D4)? (y, n, or cancel): y
select SC Y:
enter a pitch set, sieve, or set-class: a, g, c#, c#, c#
   SC 3-8A as (9,7,1,1,1)? (y, n, or cancel): y
enter ranking method: Smoothness, Uniformity or Balance? (s, u, or b): b
there are 30 maps in this ranking. enter a range: (beginRank,endRank): 1,5

MC BAL Comparison
origin (8,2) destination (9,7,1,1,1)

MC 2:5-7 map ((ab)(cde))
   VL     (8--9),(8--7),(2--1),(2--1),(2--1) 
   SMTH   vector:(0,5,0,0,0,0,0)            displacement:5                 
   UNIF   vector:(0,1,0,0,0,0,0,0,0,0,0,4)  offset:2 (Tn:11) max:4 span:3  
   BAL    vector:(0,0,0,4,0,1,0,0,0,0,0,0)  offset:2 (In:3) max:4 span:3   
   rank   S1 U1 B1 of30                                                    
MC 2:5-24 map ((cde)(ab))
   VL     (8--1),(8--1),(8--1),(2--9),(2--7) 
   SMTH   vector:(0,0,0,0,0,5,0)            displacement:25               
   UNIF   vector:(0,0,0,0,0,4,0,1,0,0,0,0)  offset:2 (Tn:5) max:4 span:3  
   BAL    vector:(0,0,0,0,0,0,0,0,0,4,0,1)  offset:2 (In:9) max:4 span:3  
   rank   S30 U2 B2 of30                                                  
MC 2:5-8 map ((acde)b)
   VL     (8--9),(8--1),(8--1),(8--1),(2--7) 
   SMTH   vector:(0,1,0,0,0,4,0)            displacement:21               
   UNIF   vector:(0,1,0,0,0,4,0,0,0,0,0,0)  offset:4 (Tn:5) max:4 span:5  
   BAL    vector:(0,0,0,0,0,1,0,0,0,4,0,0)  offset:4 (In:9) max:4 span:5  
   rank   S25 U3 B3 of30                                                  
MC 2:5-23 map (b(acde))
   VL     (8--7),(2--9),(2--1),(2--1),(2--1) 
   SMTH   vector:(0,4,0,0,0,1,0)            displacement:9                 
   UNIF   vector:(0,0,0,0,0,0,0,1,0,0,0,4)  offset:4 (Tn:11) max:4 span:5  
   BAL    vector:(0,0,0,4,0,0,0,0,0,0,0,1)  offset:4 (In:3) max:4 span:5   
   rank   S6 U4 B4 of30                                                    
MC 2:5-3 map ((abc)(de))
   VL     (8--9),(8--7),(8--1),(2--1),(2--1) 
   SMTH   vector:(0,4,0,0,0,1,0)            displacement:9                 
   UNIF   vector:(0,1,0,0,0,1,0,0,0,0,0,3)  offset:8 (Tn:11) max:3 span:7  
   BAL    vector:(0,0,0,3,0,1,0,0,0,1,0,0)  offset:8 (In:3) max:3 span:7   
   rank   S2 U5 B5 of30