The Table of Pitch Class Sets

copyright © 1997, rev 2005 by Larry Solomon

About this table
Key to symbols

Note: to locate a prime form quickly, use your find (Ctrl-F) or search button and enter your set-name, prime form, or descriptive name with no spaces, e.g., 6-34, 013579, or "mystic chord".

# Forte cross-referenced Set-name Prime Interval Vector Descriptive name/properties
0 0-1 empty 000000 Null set
1 1-1* 0 000000 Unison
2 2-1* 01 100000 Semitone
3 2-2* 02 010000 Whole-tone
4 2-3* 03 001000 Minor Third
5 2-4* 04 000100 Major Third
6 2-5* 05 000010 Perfect Fourth
7 2-6*(6) 06 000001 Tritone
8 3-1* 012 210000 BACH /Chromatic Trimirror
9 3-2 013 111000 Phrygian Trichord
10 3-2B 023 111000 Minor Trichord
11 3-3 014 101100 Major-minor Trichord.1
12 3-3B 034 101100 Major-minor Trichord.2
13 3-4 015 100110 Incomplete Major-seventh Chord.1
14 3-4B 045 100110 Incomplete Major-seventh Chord.2
15 3-5 016 100011 Rite chord.2, Tritone-fourth.1
16 3-5B 056 100011 Rite chord.1, Tritone-fourth.2
17 3-6* 024 020100 Whole-tone Trichord
18 3-7 025 011010 Incomplete Minor-seventh Chord
19 3-7B 035 011010 Incomplete Dominant-seventh Chord.2
20 3-8 026 010101 Incomplete Dominant-seventh Chord.1/Italian-sixth
21 3-8B 046 010101 Incomplete Half-dim-seventh Chord
22 3-9* 027 010020 Quartal Trichord
23 3-10* 036 002001 Diminished Chord
24 3-11 037 001110 Minor Chord
25 3-11B 047 001110 Major Chord
26 3-12*(4) 048 000300 Augmented Chord
27 4-1* 0123 321000 BACH /Chromatic Tetramirror
28 4-2 0124 221100 Major-second Tetracluster.2
29 4-2B 0234 221100 Major-second Tetracluster.1
30 4-3* 0134 212100 Alternating Tetramirror
31 4-4 0125 211110 Minor Third Tetracluster.2
32 4-4B 0345 211110 Minor Third Tetracluster.1
33 4-5 0126 210111 Major Third Tetracluster.2
34 4-5B 0456 210111 Major Third Tetracluster.1
35 4-6* 0127 210021 Perfect Fourth Tetramirror
36 4-7* 0145 201210 Arabian Tetramirror
37 4-8* 0156 200121 Double Fourth Tetramirror
38 4-9*(6) 0167 200022 Double Tritone Tetramirror
39 4-10* 0235 122010 Minor Tetramirror
40 4-11 0135 121110 Phrygian Tetrachord
41 4-11B 0245 121110 Major Tetrachord
42 4-12< 0236 112101 Harmonic-minor Tetrachord
43 4-12B< 0346 112101 Major-third Diminished Tetrachord
44 4-13 0136 112011 Minor-second Diminished Tetrachord
45 4-13B 0356 112011 Perfect-fourth Diminished Tetrachord
46 4-14< 0237 111120 Major-second Minor Tetrachord
47 4-14B< 0457 111120 Perfect-fourth Major Tetrachord
48 4-Z15..29 0146 111111 All-interval Tetrachord.1
49 4-Z15B..29 0256 111111 All-interval Tetrachord.2
50 4-16 0157 110121 Minor-second Quartal Tetrachord
51 4-16B 0267 110121 Tritone Quartal Tetrachord
52 4-17* 0347 102210 Major-minor Tetramirror
53 4-18 0147 102111 Major-diminished Tetrachord
54 4-18B 0367 102111 Minor-diminished Tetrachord
55 4-19 0148 101310 Minor-augmented Tetrachord
56 4-19B 0348 101310 Augmented-major Tetrachord
57 4-20* 0158 101220 Major-seventh Chord
58 4-21* 0246 030201 Whole-tone Tetramirror
59 4-22 0247 021120 Major-second Major Tetrachord
60 4-22B 0357 021120 Perfect-fourth Minor Tetrachord
61 4-23* 0257 021030 Quartal Tetramirror
62 4-24* 0248 020301 Augmented Seventh Chord
63 4-25*(6) 0268 020202 French-sixth Chord
64 4-26* 0358 012120 Minor-seventh Chord
65 4-27 0258 012111 Half-diminished Seventh Chord
66 4-27B 0368 012111 Dominant-seventh/German-sixth Chord
67 4-28*(3) 0369 004002 Diminished-seventh Chord
68 4-Z29..15 0137 111111 All-interval Tetrachord.3
69 4-Z29B..15 0467 111111 All-interval Tetrachord.4
70 5-1* 01234 432100 Chromatic Pentamirror
71 5-2 01235 332110 Major-second Pentacluster.2
72 5-2B 02345 332110 Major-second Pentacluster.1
73 5-3 01245 322210 Minor-second Major Pentachord
74 5-3B 01345 322210 Spanish Pentacluster
75 5-4 01236 322111 Blues Pentacluster
76 5-4B 03456 322111 Minor-third Pentacluster
77 5-5 01237 321121 Major-third Pentacluster.2
78 5-5B 04567 321121 Major-third Pentacluster.1
79 5-6 01256 311221 Oriental Pentacluster.1, Raga Megharanji (13161)
80 5-6B 01456 311221 Oriental Pentacluster.2
81 5-7 01267 310132 DoublePentacluster.1, Raga Nabhomani (11415)
82 5-7B 01567 310132 Double Pentacluster.2
83 5-8* 02346 232201 Tritone-Symmetric Pentamirror
84 5-9 01246 231211 Tritone-Expanding Pentachord
85 5-9B 02456 231211 Tritone-Contracting Pentachord
86 5-10 01346 223111 Alternating Pentachord.1
87 5-10B 02356 223111 Alternating Pentachord.2
88 5-11 02347 222220 Center-cluster Pentachord.1
89 5-11B 03457 222220 Center-cluster Pentachord.2
90 5-Z12*..36 01356 222121 Locrian Pentamirror
91 5-13 01248 221311 Augmented Pentacluster.1
92 5-13B 02348 221311 Augmented Pentacluster.2
93 5-14 01257 221131 Double-seconds Triple-fourth Pentachord.1
94 5-14B 02567 221131 Double-seconds Triple-fourth Pentachord.2
95 5-15* 01268 220222 Assymetric Pentamirror
96 5-16 01347 213211 Major-minor-dim Pentachord.1
97 5-16B 03467 213211 Major-minor-dim Pentachord.2
98 5-Z17*..37 01348 212320 Minor-major Ninth Chord
99 5-Z18<..38 01457 212221 Gypsy Pentachord.1
100 5-Z18B<..38 02367 212221 Gypsy Pentachord.2
101 5-19 01367 212122 Javanese Pentachord
102 5-19B 01467 212122 Balinese Pentachord
103 5-20 01378 211231 Balinese Pelog Pentatonic (12414), Raga Bhupala, Raga Bibhas
104 5-20B 01578 211231 Hirajoshi Pentatonic (21414), Iwato (14142), Sakura/Raga Saveri (14214)
105 5-21 01458 202420 Syrian Pentatonic/Major-augmented Ninth Chord, Raga Megharanji (13134)
106 5-21B 03478 202420 Lebanese Pentachord/Augmented-minor Chord
107 5-22* 01478 202321 Persian Pentamirror, Raga reva/Ramkali (13314)
108 5-23 02357 132130 Minor Pentachord
109 5-23B 02457 132130 Major Pentachord
110 5-24 01357 131221 Phrygian Pentachord
111 5-24B 02467 131221 Lydian Pentachord
112 5-25 02358 123121 Diminished-major Ninth Chord
113 5-23B 03568 123121 Minor-diminished Ninth Chord
114 5-26< 02458 122311 Diminished-augmented Ninth Chord
115 5-26B< 03468 122311 Augmented-diminished Ninth Chord
116 5-27 01358 122230 Major-Ninth Chord
117 5-27B 03578 122230 Minor-Ninth Chord
118 5-28< 02368 122212 Augmented-sixth Pentachord.1
119 5-28B< 02568 122212 Augmented-sixth Pentachord.2
120 5-29 01368 122131 Kumoi Pentachord.2
121 5-29B 02578 122131 Kumoi Pentachord.1
122 5-30 01468 121321 Enigmatic Pentachord.1
123 5-30B 02478 121321 Enigmatic Pentachord.2, Altered Pentatonic (14223)
124 5-31 01369 114112 Diminished Minor-Ninth Chord
125 5-31B 02369 114112 Ranjaniraga/Flat-Ninth Pentachord
126 5-32 01469 113221 Neapolitan Pentachord.1
127 5-32B 01479 113221 Neapolitan Pentachord.2
128 5-33* 02468 040402 Whole-tone Pentamirror
129 5-34* 02469 032221 Dominant-ninth/major-minor/Prometheus Pentamirror, Dominant Pentatonic (22332)
130 5-35* 02479 032140 "Black Key" Pentatonic/Slendro/Bilahariraga/Quartal Pentamirror, Yo (23232)
131 5-Z36..12 01247 222121 Major-seventh Pentacluster.2
132 5-Z36B..12 03567 222121 Minor-seventh Pentacluster.1
133 5-Z37*..17 03458 212320 Center-cluster Pentamirror
134 5-Z38..18 01258 212221 Diminished Pentacluster.1
135 5-Z38B..18 03678 212221 Diminished Pentacluster.2
136 6-1* 012345 543210 Chromatic Hexamirror/1st ord. all-comb (P6, Ib, RI5)
137 6-2 012346 443211 comb I (b)
138 6-2B 023456 443211 comb I (1)
139 6-Z3..36B 012356 433221
140 6-Z3B..36 013456 433221
141 6-Z4*..37 012456 432321 comb RI (6)
142 6-5 012367 422232 comb I (b)
143 6-5B 014567 422232 comb I (3)
144 6-Z6*..38 012567 421242 Double-cluster Hexamirror
145 6-7* (6) 012678 420243 Messiaen's mode 5 (114114), 2nd ord.all-comb(P3+9,I5,Ib,R6,RI2+8)
146 6-8* 023457 343230 1st ord.all-comb (P6, I1, RI7)
147 6-9 012357 342231 comb I (b)
148 6-9B 024567 342231 comb I (3)
149 6-Z10..39 013457 333321
150 6-Z10B..39B 023467 333321
151 6-Z11..40B 012457 333231
152 6-Z11B..40 023567 333231
153 6-Z12..41B 012467 332232
154 6-Z12B..41 013567 332232
155 6-Z13*..42 013467 324222 Alternating Hexamirror/comb RI7)
156 6-14..14 013458 323430 comb P (6)
157 6-14B..14B 034578 323430 comb P (6)
158 6-15 012458 323421 comb I (b)
159 6-15B 034678 323421 comb I (5)
160 6-16 014568 322431 comb I (3)
161 6-16B 023478 322431 Megha or "Cloud" Raga/comb.I (1)
162 6-Z17..43B 012478 322332
163 6-Z17B..43 014678 322332
164 6-18 012578 322242 comb I (b)
165 6-18B 013678 322242 comb I (5)
166 6-Z19..44B 013478 313431
167 6-Z19B..44 014578 313431
168 6-20*(4) 014589 303630 Augmented scale, Genus tertium, 3rd ord. all-comb (P2+6+10, I3+7+b, R4+8, RI1+5+9)
169 6-21 023468 242412 comb I (1)
170 6-21B 024568 242412 comb I (3)
171 6-22 012468 241422 comb I (b)
172 6-22B 024678 241422 comb I (5)
173 6-Z23*..45 023568 234222 Super-Locrian Hexamirror/comb RI (8)
174 6-Z24..46B 013468 233331
175 6-Z24B..46 024578 233331 Melodic-minor Hexachord
176 6-Z25..47B 013568 233241 Locrian Hexachord/Suddha Saveriraga
177 6-Z25B..47 023578 233241 Minor Hexachord
178 6-Z26*..48 013578 232341 Phrygian Hexamirror/comb RI (8)
179 6-27 013469 225222 comb I (b)
180 6-27B 023569 225222 Pyramid Hexachord/comb I (1)
181 6-Z28*..49 013569 224322 Double-Phrygian Hexachord/comb RI (6)
182 6-Z29*..50 013689 224232 comb RI (9)
183 6-30 (6) 013679 224223 Minor-bitonal Hexachord/comb R (6), I (5,b)
184 6-30B (6) 023689 224223 Petrushka chord, Major-bitonal Hexachord, comb R (6), I (1,7)
185 6-31 013589 223431 comb I (7)
186 6-31B 014689 223431 comb I (b)
187 6-32* 024579 143250 Arezzo major Diatonic (221223), major hexamirror, quartal hexamirror, 1st ord.all-comb P (6), I (3), RI (9)
188 6-33 023579 143241 Dorian Hexachord/comb I (1)
189 6-33B 024679 143241 Dominant-11th/Lydian Hexachord/comb I (5)
190 6-34 013579 142422 Scriabin's Mystic Chord or Prometheus Hexachord/comb I (B)
191 6-34B 024689 142422 Harmonic Hexachord/Augmented-11th/comb I (7)
192 6-35*(2) 02468A 060603 Wholetone scale/6th ord.all-comb.(P+IoddT, R+RIevenT)
193 6-Z36..3B 012347 433221
194 6-Z36B..3 034567 433221
195 6-Z37*..4 012348 432321 comb RI (4)
196 6-Z38*..6 012378 421242 comb RI (3)
197 6-Z39..10 023458 333321
198 6-Z39B..10B 034568 333321
199 6-Z40..11B 012358 333231
200 6-Z40B..11 035678 333231
201 6-Z41..12B 012368 332232
202 6-Z41B..12 025678 332232
203 6-Z42*..13 012369 324222 comb RI (3)
204 6-Z43..17B 012568 322332
205 6-Z43B..17 023678 322332
206 6-Z44..19B 012569 313431 Schoenberg Anagram Hexachord
207 6-Z44B..19 012589 313431 Bauli raga (133131)
208 6-Z45*..23 023469 234222 comb RI (6)
209 6-Z46..24B 012469 233331
210 6-Z46B..24 024569 233331
211 6-Z47..25B 012479 233241
212 6-Z47B..25 023479 233241 Blues mode.1 (321132)
213 6-Z48*..26 012579 232341 comb RI (2)
214 6-Z49*..28 013479 224322 Prometheus Neapolitan mode (132312), comb RI (4)
215 6-Z50*..29 014679 224232 comb RI (1)
216 7-1* 0123456 654321 Chromatic Heptamirror
217 7-2 0123457 554331
218 7-2B 0234567 554331
219 7-3 0123458 544431
220 7-3B 0345678 544431
221 7-4 0123467 544332
222 7-4B 0134567 544332
223 7-5 0123567 543342
224 7-5B 0124567 543342
225 7-6 0123478 533442
226 7-6B 0145678 533442
227 7-7 0123678 532353
228 7-7B 0125678 532353
229 7-8* 0234568 454422
230 7-9 0123468 453432
231 7-9B 0245678 453432
232 7-10 0123469 445332
233 7-10B 0234569 445332
234 7-11 0134568 444441
235 7-11B 0234578 444441
236 7-Z12*..36 0123479 444342
237 7-13 0124568 443532
238 7-13B 0234678 443532
239 7-14 0123578 443352
240 7-14B 0135678 443352
241 7-15* 0124678 442443
242 7-16 0123569 435432
243 7-16B 0134569 435432
244 7-Z17*..37 0124569 434541
245 7-Z18<..38 0123589 434442
246 7-Z18B<..38 0146789 434442
247 7-19 0123679 434343
248 7-19B 0123689 434343
249 7-20 0124789 433452 Chromatic Phrygian inverse (1123113)
250 7-20B 0125789 433452 Pantuvarali Raga (1321131), Chromatic Mixolydian (1131132), Chromatic Dorian/Mela Kanakangi (1132113)
251 7-21 0124589 424641
252 7-21B 0134589 424641 Gypsy hexatonic (1312113)
253 7-22* 0125689 424542 Persian, Major Gypsy, Hungarian Minor, Double Harmonic scale, Bhairav That, Mayamdavagaula Raga (all: 1312131), Oriental (1311312)
254 7-23 0234579 354351
255 7-23B 0245679 354351 Tritone Major Heptachord
256 7-24 0123579 353442
257 7-24B 0246789 353442 Enigmatic Heptatonic (1322211)
258 7-25 0234679 345342
259 7-25B 0235679 345342
260 7-26< 0134579 344532
261 7-26B< 0245689 344532
262 7-27 0124579 344451
263 7-27B 0245789 344451 Modified Blues mode (2121132)
264 7-28< 0135679 344433
265 7-28B< 0234689 344433
266 7-29 0124679 344352
267 7-29B 0235789 344352
268 7-30 0124689 343542 Neapolitan-Minor mode (1222131), Mela Dhenuka
269 7-30B 0135789 343542
270 7-31 0134679 336333 Alternating Heptachord.1/Hungarian Major mode (3121212)
271 7-31B 0235689 336333 Alternating Heptachord.2
272 7-32 0134689 335442 Harmonic-Minor mode (2122131), Spanish Gypsy, Mela Kiravani, Pilu That
273 7-32B 0135689 335442 Dharmavati Scale (2131221), Harmonic minor inverse (1312212), Mela Cakravana, Raga Ahir Bhairav
274 7-33* 012468A 262623 Neapolitan-major mode (1222221)/Leading-Whole-tone mode (222211)
275 7-34* 013468A 254442 Harmonic/Super-Locrian, Melodic minor ascending (1212222)/Aug.13th Heptamirror, Jazz Minor
276 7-35* 013568A 254361 Major Diatonic Heptachord/Dominant-13th, Locrian (1221222), Phrygian (1222122), Major inverse
277 7-Z36..12 0123568 444342
278 7-Z36B..12 0235678 444342
279 7-Z37*..17 0134578 434541
280 7-Z38..18 0124578 434442
281 7-Z38B..18 0134678 434442
282 8-1* 01234567 765442 Chromatic Octamirror
283 8-2 01234568 665542
284 8-2B 02345678 665542
285 8-3* 01234569 656542
286 8-4 01234578 655552
287 8-4B 01345678 655552
288 8-5 01234678 654553
289 8-5B 01245678 654553
290 8-6* 01235678 654463
291 8-7* 01234589 645652
292 8-8* 01234789 644563
293 8-9* (6) 01236789 644464 Messiaen's mode 4 (11131113)
294 8-10* 02345679 566452
295 8-11 01234579 565552
296 8-11B 02456789 565552
297 8-12< 01345679 556543
298 8-12B< 02345689 556543
299 8-13 01234679 556453
300 8-13B 02356789 556453
301 8-14< 01245679 555562
302 8-14B< 02345789 555562
303 8-Z15..29 01234689 555553
304 8-Z15B..29 01356789 555553
305 8-16 01235789 554563
306 8-16B 01246789 554563
307 8-17* 01345689 546652
308 8-18 01235689 546553
309 8-18B 01346789 546553
310 8-19 01245689 545752
311 8-19B 01345789 545752
312 8-20* 01245789 545662
313 8-21* 0123468A 474643
314 8-22 0123568A 465562
315 8-22B 0123579A 465562 Spanish Octatonic Scale (r9) (12111222)
316 8-23* 0123578A 465472 Quartal Octachord, Diatonic Octad
317 8-24* 0124568A 464743
318 8-25* (6) 0124678A 464644 Messiaen mode 6 (11221122)
319 8-26* 0124579A 456562 Spanish Phrygian (r9) (12112122)/ Blues mode.2 (21211212)
320 8-27 0124578A 456553
321 8-27B 0124679A 456553
322 8-28* (3) 0134679A 448444 Alternating Octatonic or Diminished scale (12121212)
323 8-Z29..15 01235679 555553
324 8-Z29B..15 02346789 555553
325 9-1* 012345678 876663 Chromatic Nonamirror
326 9-2 012345679 777663
327 9-2B 023456789 777663
328 9-3 012345689 767763
329 9-3B 013456789 767763
330 9-4 012345789 766773
331 9-4B 012456789 766773
332 9-5 012346789 766674
333 9-5B 012356789 766674
334 9-6* 01234568A 686763
335 9-7 01234578A 677673 Nonatonic Blues Scale (211111212)
336 9-7B 01234579A 677673
337 9-8 01234678A 676764
338 9-8B 01234689A 676764
339 9-9* 01235678A 676683 Raga Ramdasi Malhar (r2) (211122111)
340 9-10* 01234679A 668664
341 9-11 01235679A 667773
342 9-11B 01235689A 667773 Diminishing Nonachord
343 9-12* (4) 01245689A 666963 Tsjerepnin/Messiaen mode 3 (112112112)
344 10-1* 0123456789 988884 Chromatic Decamirror
345 10-2* 012345678A 898884
346 10-3* 012345679A 889884
347 10-4* 012345689A 888984
348 10-5* 012345789A 888894 Major-minor mixed (r7)
349 10-6* (6) 012346789A 888885 Messiaen mode 7 (1111211112)
350 11-1* 0123456789A AAAAA5 Chromatic Undecamirror
351 12-1*(1) 0123456789AB CCCCC6 Chromatic Scale/Dodecamirror (111111111111)

About This Table

These Prime Forms reinstate the inverses of Forte's primes. They occur in the table with "B" suffixed to set-name.

Note that Allen Forte's "prime forms" are questionable as overly-reduced sets. As an example, 047, the major chord, does not appear in Forte's table, but is subsumed into 037, the minor chord. Thus, it becomes impossible to distinguish major from minor. This problem extends to all distinct pairs of set inverses. The dominant-seventh (0368), as another example, is subsumed into the half-diminished seventh (0258), making them indistinguishable. The above table retains all the original Forte set-names, but reinstates each inverse as the "B" form that is suffixed to the Forte name. Thus, these new primes are kept separate from their inverses. In no way does this subtract from the basic tenets of set theory, nor does it change Forte's foundational sets. Instead, it only adds more information -- information that was deleted by subsuming inverse sets under the same name. It also has the additional benefit of simplifying the determination of the prime form by elimination of the step that includes the inverse.

It is maintained by some theorists that the reduction in the Forte primes is valid because of the "atonal" context for which set theory was designed; i.e., major and minor chords are the same in an "atonal" context. But, the term "atonal" is itself a questionable, and perhaps undefinable term, as is what constitutes "atonal music". Aside from the problem of defining "atonality," there are additional problems with this categorical excuse. Forte himself uses set theory to analyze Stravinsky's Rite of Spring and other at least marginally tonal music, such as in Scriabin's work. Major and minor chords are found in the Rite, and they are rendered indistinguishable by Forteian analysis. It is simply incorrect that these chords are heard as the same sonority in the Rite or in the music of Scriabin. This problem may even be exacerbated in the early "atonal" work of Schoenberg. Thus, all "set analysis" that unquestioningly follows Forte's model must itself be questioned.

The above table salvages the problem by reinstating the inverse forms. The only other changes to Forte's original list (SAM, Appendix I) are additional symbols that enhance the informational content of the table. For example, the asterisk * identifies the set as a mirror, thus one that has no distinct inverse. Complements can still be identified (see the Key).

Additions in this table, supplying even more information, are the descriptive or common names. Thus, when a set has a common name, such as dominant-seventh, it can easily be identified as such (as well as enharmonic equivalents). Scale names are also included when applicable. Some new "descriptive names" have been added that help to identify distinctive properties of a set. An example is 0347, the well-known superposed major-minor chord. It is tagged as the "major-minor tetramirror", which itself contains information about the nature of the chord: (1) that it is a 4-note chord (hence tetrachord), (2) that it is a mirror (symmetrical and having no distinct inverse), and (3) that it contains the major and minor chords.

More information is provided with hexachords, where the symbol "comb" may be encountered. This is an abbreviation for "combinatorial". The structure of a hexachord determines whether it can form a combinatorial 12-note set with its complement. Note that the order of the notes within each hexachord has no effect on the property of hexachordal combinatoriality. Thus, its combinatoriality can be identified (see the Key).

A new asset of this table is the exclusive use of single digit numbers for the prime form and the interval vector. This eliminates the need for commas, spaces, or other separators, resulting in a more elegant expression for each set. Hexadecimal notation is used. Thus, "10" is rendered as "A", "11" is rendered as "B", and "12" is C, rarely used in the last group of sets. It is worth the change because it makes it possible to express a set as a single line of numbers without separators; e.g., 02468A, the whole-tone scale. Other systems have been proposed, such as T for "10" and "E" for eleven, but these are Anglo-centric.


Key

symbol meaning
* The set is a mirror (see Glossary).
< The set has a complement with the same name ending1
(4) (1) The set has only 4 different unique transpositions, as opposed to the normal 12. (2) when occurring after "comb", indicates the transposition of comb when the set is in prime form.
B (at the end of a set-name) The set is the inverse of the set without the B and has the same IV.
..15 This is a Z set whose counterpart (having the same IV) is ordinal number 15 of the same cardinality. For hexachords this number also designates the set complement.
comb   This is a hexachord that is combinatorial.
comb RI This hexachord is combinatorial with RI (the number in parentheses indicates the transposition of comb form when set is prime form)
all-comb The set is known as an all-combinatorial set (see Glossary).
AAAA5 The last two sets in the table have their IVs designated in hexadecimal; A=10, B=11, C=12
   

1. Normally, sets with B names have complements without the B ending and vice versa. 8-12<, however, has the complement 4-12, and 8-12B has the complement 4-12B.


Selected Bibliography

Forte, Allen. The Structure of Atonal Music. New Haven: Yale, 1973

Rahn, John. Basic Atonal Theory. New York: Longman, 1980. Contains an extensive bibliography up to about 1978.

Solomon, Larry. "The List of Chords, Their Properties, and Uses", Interface, Journal of New Music Research, Vol. 11 (1982)

Strauss, Joseph N. Post-Tonal Theory, Prentice-Hall, 1990.


It should be noted that a number of authors have contributed to the development of the theory of set complexes for music. For comprehensive bibliographies see:

Rahn, John. Basic Atonal Theory. New York: Longman, 1980. Contains an extensive bibliography up to about 1978.

In Theory Only, V.3/7-11 (1977-78), Index of Music Theory in the United States 1955-1970, R. Browne, ed. This is an excellent source of bibliography on set theory, as well as all other aspects of music theory, from 1955-1970.

Richard Chrisman's bibliography in the Journal of Music Theory, V.21/1 (1977), pp.26-28.


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