Music Analysis System

Larry Solomon, copyright © 2002, 1984

The Music Analysis System (MAS) is software that I designed for Windows computers. It runs in Windows or DOS. I am now making it available as freeware for scholars. You may download it from this Web page. See the end of this description for instructions. The following is a description of the functions of MAS.

This software does set theoretical analyses of two types: 1. Unordered or nonlinear sets, and 2. Ordered or linear sets, as in tone rows. Those unfamiliar with, yet curious about, set analysis are referred to Allen Forte's The Structure of Atonal Music (Yale, 1973), and to Larry Solomon's "The List of Chords, Their Properties and Use in Analysis," in Interface, Journal of New Music Research, 1982, v11/2.

Unordered set analysis is essentially a harmonic analysis of non-standard chords, although standard types can be included. The program contains a list of all the possible unordered set combinations in the chromatic scale. Any group of notes that is typed is immediately identified with its prime form, set-name, interval vector (IV), and any special characteristics or common names and enharmonic names. For example a,c,e is identified as a minor chord, Prime: 037, set name: 3-11, IV: 001110. The chord c,e,g is identified as a major chord, Prime: 047, set-name: 3-11B, IV: 001110. Thus, major chords are kept distinct from minor by the B-suffix, as are all inverse forms that are not "mirrors". This preserves Forte's original classification, yet provides a way to distinguish inverse sets. A hexachord like a#,d#,a,b,e,f is identified as 6-7* (* means mirror), 012678, 420243, second order all-combinatorial (linking it to ordered set analysis). The following shows the output for all the sets in Scriabin's Prelude, Op. 74 no. 3.

No.| notes
set name             prime form    interval vector  descriptive name

1  f#b#a#ega
6-Z23*..45          0 2 3 5 6 8................ 234222     Super-Locrian hexatonic/comb.=I8

2  f# b# gc#eac#
6-Z50*..29          0 1 4 6 7 9................ 224232    comb.=I1

3 f#b#a#ed#c#
6-Z23*..45          0 2 3 5 6 8................ 234222    Super-Locrian hexatonic/comb.=I8

4  f#b#c#ga#d#a
7-31                     0 1 3 4 6 7 9.............. 336333    Alternating heptatonic.1

5  f#b#ea#ag
6-Z23*..45          0 2 3 5 6 8................ 234222    Super-Locrian hexatonic/comb.=I8

6  ad#c#a#gf#
6-Z49*..28          0 1 3 4 7 9................ 224322    Prometheus Neapolitan scale/comb.=I4

7  ad#c#gf#e
6-Z23*..45          0 2 3 5 6 8................ 234222    Super-Locrian hexatonic/comb.=I8

8  b#f#ea#c#d#
6-Z23*..45          0 2 3 5 6 8................ 234222    Super-Locrian hexatonic/comb.=I8

9  d#ac#ecgf#
7-31                    0 1 3 4 6 7 9.............. 336333    Alternating heptatonic.a

10  d#ac#ecgf#
7-31                   0 1 3 4 6 7 9.............. 336333    Alternating heptatonic.a

11  b#f#a#ed#a
6-30                  0 1 3 6 7 9................   224223    minor-bitonal hexachord/comb.=P6/#I5+11

12  b#f#a#egac#d#
8-28*                0 1 3 4 6 7 9 10..........448444    Alternating-Octatonic/diminished scale

13  b#f#ed#c#a#
6-Z23*..45       0 2 3 5 6 8................ 234222     Super-Locrian hexatonic/comb.=I8

14  b#f#c#ga#d#
6-Z50*..29       0 1 4 6 7 9................ 224232    comb.=I1

15  b#f#ea#ag
6-Z23*..45      0 2 3 5 6 8................ 234222     Super-Locrian hexatonic/comb.=I8

16  b#f#gc#ead#
7-31                 0 1 3 4 6 7 9............. 336333    Alternating heptatonic.a

17  b#f#a#ed#c#a#
6-Z23*..45     0 2 3 5 6 8................ 234222    Super-Locrian hexatonic/comb.=I8

18  d#agc#b#e
6-Z49*..28     0 1 3 4 7 9................ 224322    Prometheus Neapolitan scale/comb.=I4

19  d#agc#b#a#
6-Z23*..45     0 2 3 5 6 8............... 234222    Super-Locrian hexatonic/comb.=I8

20  f#b#a#age
6-Z23*..45     0 2 3 5 6 8............... 234222    Super-Locrian hexatonic/comb.=I8

21  adg#a#f#c#b#d#
8-Z29B           0 2 3 4 6 7 8 9........ 555553

22  ad#ga#f#c#b#
7-31                0 1 3 4 6 7 9.............336333    Alternating heptatonic.a

23  f#b#ea#f#ad#
6-30                0 1 3 6 7 9................ 224223    minor-bitonal hexachord/comb.=P6/#I5+11

24  f#b#ea#af#ec#b#agd#
8-28*              0 1 3 4 6 7 9 10....... 448444    Alternating-Octatonic/diminished scale

25  d#c#b#a#ag
6-Z23*..45    0 2 3 5 6 8................ 234222    Super-Locrian hexatonic/comb.=I8

26  f#ega#b#d#
6-Z49*..28    0 1 3 4 7 9................ 224322    Prometheus Neapolitan scale/comb.=I4

After a list of chords is input, the program analyzes all the relationships that these sets may have. These relations are mapped onto a "relations triangle", the most concise format to visually show their relations. All the sets are listed in order on the diagonal of the triangle, by an identification-number (ID determined by the user) and set name. On the body of the triangle are symbols that show the relations as points of intersection, horizontally and vertically, with the set IDs. The relations shown are: 1. = (the sets are equal), 2. S and + (one set is the subset of the other), 3. Z (one set is the inverse of the other or has the same IV, 4. X (maximum similarity with interchange), 5. O (maximum similarity without interchange), and R (maximum similarity by percentage [optional]). Thus, the program can do a strictly Fortian analysis or it may be used in an extended way to include more information.

The following shows a sample output. It is an analysis of Scriabin's Prelude. The numbers in parentheses on the diagonal are the measure numbers from the Peters edition, unless specified as Dover.

Scriabin's Prelude Op. 74 no. 3, Relations Triangle

1___6-Z23*..45
X2___6-Z50*..29
=X3___6-Z23*..45
SSS4___7-31
=X=S5___6-Z23*..45
XXXSX6___6-Z49*..28
=X=S=X7___6-Z23*..45
=X=S=X=8___6-Z23*..45
SSS=SSSS9___7-31
SSS=SSSS=10__7-31
XRXSXXXXSS11__6-30
SSSSSSSSSSS12__8-28*
=X=S=X==SSXS13__6-Z23*..45
X=XSXXXXSSRSX14__6-Z50*..29
=X=S=X==SSXS=X15__6-Z23*..45
SSS=SSSS==SSSSS16__7-31
=X=S=X==SSXS=X=S17__6-Z23*..45
XXXSX=XXSSXSXXXSX18__6-Z49*..28
=X=S=X==SSXS=X=S=X19__6-Z23*..45
=X=S=X==SSXS=X=S=X=20__6-Z23*..45
21__8-Z29B (Dover)
SSS=SSSS==SSSSS=SSSS 22__7-31
XRXSXXXXSS=SXRXSXXXX S23__6-30
SSSSSSSSSSS=SSSSSSSS SS24__8-28*
=X=S=X==SSXS=X=S=X== SXS25__6-Z23*..45 (25)
XXXSX=XXSSXSXXXSX=XX SXSX26__6-Z49*..28 (26)

Set #21 (measures 21-22 of the Dover edition) shows no relationship to any of the other sets in the Prelude. An empty "tunnel" is displayed both horizontally and vertically from this set. Otherwise, the triangle is saturated with relationships. Set #22 (measures 21-22 of the Peters edition), however, is consistent with the other sets. Suspicion is therefore cast upon set #21 from the Dover edition.

If the set from the Dover edition is replaced with the one from Peters, MAS displays the following:

1___6-Z23*..45
X2___6-Z50*..29
=X3___6-Z23*..45
SSS4___7-31
=X=S5___6-Z23*..45
XXXSX6___6-Z49*..28
=X=S=X7___6-Z23*..45
=X=S=X=8___6-Z23*..45
SSS=SSSS9___7-31
SSS=SSSS=10__7-31
XRXSXXXXSS11__6-30
SSSSSSSSSSS12__8-28*
=X=S=X==SSXS13__6-Z23*..45
X=XSXXXXSSRSX14__6-Z50*..29
=X=S=X==SSXS=X15__6-Z23*..45
SSS=SSSS==SSSSS16__7-31
=X=S=X==SSXS=X=S17__6-Z23*..45
XXXSX=XXSSXSXXXSX18__6-Z49*..28
=X=S=X==SSXS=X=S=X19__6-Z23*..45
=X=S=X==SSXS=X=S=X=20__6-Z23*..45
SSS=SSSS==SSSSS=SSSS21__7-31
SSS=SSSS==SSSSS=SSSS=22__7-31
XRXSXXXXSS=SXRXSXXXXSS23__6-30
SSSSSSSSSSS=SSSSSSSSSSS24__8-28*
=X=S=X==SSXS=X=S=X==SSXS25__6-Z23*..45 (25)
XXXSX=XXSSXSXXXSX=XXSSXSX26__6-Z49*..28 (26)

A statistical table is also generated:

Total number of sets : 26
Number of each cardinality
C. 6 = 18      C. 7 = 6      C. 8 = 2
Number of mirror sets                               18   69 %
Number of sets showing S relation           26   100 %
Number of sets showing + relation           00   000 %
Number of sets showing + or S relation   26   100 %

Relations within equal cardinalities:
Number of sets showing equivalence        26   100 %
Number of sets showing Z                         00     00 %
Number of sets showing X+O                   18     69 %
Number of sets showing R                          4      15 %
Number of sets with =/R/X/O/Z               26    100 %

From the information shown in the final charts, the following questions can be answered:

1. How many different chords occur?
2. What percentage of the chords are mirrors?
3. What is the parent set?
4. What scale is being used?
5. What are the most and least significant chord relations?
6. Which chord functions as a tonic?
7. Is there a repeating harmonic progression?
8. What is the form, and how is it articulated?
9. Why is there a conspicuous gap in the triangle at chord #21 of the first chart?
10. Which chords occur most often?
11. Do all chords recur?
12. What does it mean to have such a density of relations displayed?
13. Do all sets display the subset relation?
14. Why are there no O or + relations?
15. Are there "non-harmonic tones", and if so, what are they?

Let me see the answers to these questions, along with a complete analysis and an incomplete theory of partitioning.

The ordered set portion of MAS will generate a row matrix, or analyze a "melodic line", analyze its ordered subset content and relationships, and also analyze unordered sets within the line. Properties of a row are also identified, such as symmetry (e.g., P=RI, R=I), source sets, directed-interval content, and combinatoriality. It can also be used to help trace lines in compositions by identifying short segments within a longer "row".

Please read the following if you are interested in downloading the Music Analysis System.

The MAS files are compressed and combined in MASTER.EXE and must be expanded. Make a new folder on your hard drive and move MASTER.EXE into the folder. Run MASTER.EXE to expand and install the files. Once installed, read the README file and print the DOC (documentation). MAS.BAT runs the program. It will also run with the file SOLOMON.EXE.

Download the Music Analysis System.