athenaCL Tutorial Manual: Second Edition, Version 1.4.8 | ||
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athenaCL contains numerous set-class similarity measures from the academic literature (Rahn 1980; Lewin 1987; Castren 1994). These similarity measures, as ways of evaluating set relations, are called SetMeasures.
The command SCcm allows the user to compare the similarity values of every similarity measure for any two sets. After entering SCcm, the user must provide the two sets to compare.
Example 8-7. Comparing two sets with all set class similarity measures
[PI()TI()] :: sccm select SC X: enter a pitch set, sieve, or set-class: 6-40 SC 6-40A as (C4,C#4,D4,D#4,F4,G#4)? (y, n, or cancel): y select SC Y: enter a pitch set, sieve, or set-class: c, d, e, f, g, a SC 6-32 as (C4,D4,E4,F4,G4,A4)? (y, n, or cancel): y SC similarity: 6-40A and 6-32 Tn classification {name,value,graph,range} ASIM 0.20 ......................................+......... 1--0 ATMEMB 0.68 ................................+............... 0--1 Ak 0.80 ......................................+......... 0--1 COST 0.91 ...........................................+.... 0--1 IcVD1 0.40 ......................................+......... 2--0 IcVD2 0.43 .................................+.............. 1.41--0 IcVSIM 0.82 .....................................+.......... 3.64--0 K 12 ..........+..................................... 0--55 MEMBn 29.00 ...........+.................................... 0--121 REL 0.65 ...............................+................ 0--1 SIM 6.00 ...........................................+.... 65--0 TMEMB 78.00 +............................................... 0--6118 T%Rel 50.83 .......................+........................ 100--0 %Rel 20.00 ......................................+......... 100--0 SI 3.16 ....................................+........... 8.49--1.41 sf 3.00 ...............................+................ 9--0 R0 0 + R1 0 + R2 0 +
The SCcm display provides the name of the measure, the value obtained from this comparison, and a graph of a normalized percentage of that measure's similarity range. Following the graph is the range of the measure, from least similar to most similar.
Single similarity measures, SetMeasures, can be selected for more extensive investigation. To see a list of available SetMeasures, enter SMls. To select a SetMeasure, enter SMo. Selecting SetMeasures is covered in greater detail in section 2.10. Here the user first browses the list of measures, and then selects "REL":
Example 8-8. Listing and selecting set class similarity measures
[PI()TI()] :: smls SetMeasures available: {name,reference,distinction} + ASIM Morris TnI ATMEMB Rahn Tn Ak Rahn TnI COST Rogers TnI IcVD1 Rogers TnI IcVD2 Rogers TnI IcVSIM Isaacson TnI K Morris TnI R2 Forte TnI REL Lewin Tn SIM Morris TnI TMEMB Rahn Tn TpRel Castren Tn [PI()TI()] :: smo rel SetMeasure REL now active.
The command SCs, for SetClass Search, like many commands within athenaCL, uses the active SetMeasure to process sets. Using the selected similarity measure, and given a set, SCs searches for sets with a similarity value within a user-provided similarity percentage range. Because similarity measures have a wide variety of ranges, percentage ranges between 0 and 1 are always used.
In the example below the user, having selected REL above, searches for sets that have a similarity value with set 6-40 corresponding to the top twenty-five percent of the REL range. Eleven sets are found, as shown below:
Example 8-9. Searching set classes by similarity range
[PI()TI()] :: scs select a SC: enter a pitch set, sieve, or set-class: 6-40 SC 6-40A as (0,1,2,3,5,8)? (y, n, or cancel): y enter a similarity percentage range: .75, 1 Set 6-40A: Lewin REL search TnI classification similarity percentage range: (0.75, 1.00) total found: 38 {set,value} 6-40A 1.00 7-23A 0.86 7-10A 0.86 7-14A 0.86 7-3A 0.85 7-36A 0.85 7-18A 0.83 6-46A 0.82 6-36A 0.82 6-9A 0.81 5-36A 0.81 6-39A 0.81 7-29A 0.80 6-25A 0.80 8-23 0.79 5-38A 0.79 8-10 0.79 6-47A 0.78 8-3 0.78 6-11A 0.78 5-5A 0.78 7-2A 0.77 7-11A 0.77 5-25A 0.77 6-12A 0.77 7-12 0.76 6-42 0.76 8-6 0.76 6-18A 0.76 8-13A 0.76 8-7 0.76 8-14A 0.76 5-27A 0.76 7-4A 0.75 6-8 0.75 8-11A 0.75 8-4A 0.75 6-41A 0.75
In athenaCL, Paths are ordered collections of sets. Using Paths allows the user additional control and analysis of pitch materials, not only in terms of sets, but also in terms of voice-leadings (mappings) between those sets. For more information on Paths, see Chapter 3.