How to use -- Output format
Analyses of individual sets
Sample output of "verbose" option for segment 'a1' in the input example (i. e., the notes G#, A, Bb, Db):
===================================================================== segment a1 ===================================================================== set content: g# a bb db digitalized: 8 9 10 1 sorted, doubles deleted: 1 8 9 10 normal order, transp: 0 1 2 5 normal order, inv & transp: 0 3 4 5 prime form: 0 1 2 5 Forte's classification: 4-4 interval vector: 211110 complement: sorted, doubles deleted: 0 2 3 4 5 6 7 11 normal order, transp: 0 1 3 4 5 6 7 8 normal order, inv & transp: 0 1 2 3 4 5 7 8 prime form: 0 1 2 3 4 5 7 8 Forte's classification: 8-4 interval vector: 655552
The output is to be interpreted as follows:
- "set content" is exactly what was entered (including repetitions)
- "digitalized" is the same set transformed to digits (using the convention of C = 0);
- "sorted, doubles deleted" is rather self-explaining;
- "normal order, transp" is the most compact representation of the set, transposed so that the first pc is '0';
- "normal order, inv & transp" is the same but for the inversion of the set;
- "prime form" is the best normal order of the preceding two;
- "Forte's classification" (only for sets of size 3-9) is Forte's designation of the set
- "interval vector" is the number of respectively minor seconds, major seconds, minor thirds, major thirds, perfect fourths, and tritones within the set
The analysis is repeated for the complement of the original set. The "short" option performs the same calculations, but does not present all intermediate results.
Inclusion under transposition/transposition or inversion
Sample output of "inclusion under transposition or inversion" for the segments above.
a1 a2 b c1 c2
a1 - t i
a2 -
b t - i
c1 i -
c2 i -
This table tells us among other things that the smaller of the sets b and a1 (one of them must be smaller -- otherwise they must be equal, indicated by '=') is included in the larger after transposition (possibly by zero semitones, i.e., the inclusion may be literal). Likewise, the smaller of the sets a1 and c1 is included in the larger after inversion (which always is followed by transposition). Both inclusions could occur simultaneously; this would be indicated by 'ti'. The "inclusion under transposition" option behaves as expected.
Inclusion under transposition or inversion according to Forte/Cook
Sample output of "inclusion under transposition or inversion according to Forte" for the segments above:
a1 a2 b c1 c2
a1 - t i
a1c - i ti
a2 -
a2c - i i
b t - i
bc i i - t
c1 i -
c1c ti i t - i
c2 i -
c2c i -
This table looks like the previous one, only that now each set is compared not only to each other set (a1, a2 etc), but also to the (prime form of the) complement of that set (a1c, a2c etc). The "inclusion under transposition or inversion according to Cook" option behaves identically with the addition that the compared sets may be of complementary size (see "A very brief introduction...").
Kh-relations according to Forte/Cook
Sample output of "Kh-relations according to Forte/Cook" for the segments above:
a1 a2 b c1 c2
a1 - Kh Kh
a2 - K K
b Kh K - K K
c1 Kh K K - K
c2 K K -
This table tells us among other things that there is a 'K'-relation between set b and set a2; that is, there is a 't' and/or an 'i'-inclusive relation as described above either between b and a2 or between b and the complement of a2 (and, in the last case, automatically between a2 and the complement of b as well). Likewise, it tells us that there is a 'Kh' relation between b and a1; that is, there is a 't' and/or an 'i'-inclusive relation as described above both between b and a1 and between b and the complement of a1 (and, again, automatically between a1 and the complement of b as well).
Z-relations
Sample output of "Z-relations" for the segments above:
a1 a2 b c1 c2
a1 -
a1c
a2 - Z
a2c
b -
bc Zc
c1 -
c1c
c2 Z -
c2c
This table tells us among other things that set a2 and c2 are in z-related; that is, they share the same interval vector. The same goes for set b and bc; that is, set b has the same interval vector as its own complement.
Output preferences
For screen views, you may prefer spaces for separating columns and possibly extra blanklines between sets. If you want to export tables to a spread sheet or a word processor, you are probably better off with tabs between columns and no blanklines. Just copy the tables and use "paste as plain text", or whatever it may be called in your particular application.