Tone Clock · Set classes

Every set class

224 classes · 351 shapes · 4,096 sets

One page per class: its shapes, its interval content, its sets, and what it contains. Prime forms by Rahn’s packing; the empty set, 0-1, is the 224th class and has no page.

1 note · 1 class

Forte	Prime form	Vector	Name	Shapes	Sets
1-1	0	000000		1	12

2 notes · 6 classes

Forte	Prime form	Vector	Name	Shapes	Sets
2-1	01	100000		1	12
2-2	02	010000		1	12
2-3	03	001000		1	12
2-4	04	000100		1	12
2-5	05	000010		1	12
2-6	06	000001	tritone	1	6

3 notes · 12 classes

Forte	Prime form	Vector	Name	Shapes	Sets
3-1	012	210000		1	12
3-2	013	111000		2	24
3-3	014	101100		2	24
3-4	015	100110		2	24
3-5	016	100011		2	24
3-6	024	020100		1	12
3-7	025	011010		2	24
3-8	026	010101		2	24
3-9	027	010020		1	12
3-10	036	002001	diminished triad	1	12
3-11	037	001110	major or minor triad	2	24
3-12	048	000300	augmented triad	1	4

4 notes · 29 classes

Forte	Prime form	Vector	Name	Shapes	Sets
4-1	0123	321000		1	12
4-2	0124	221100		2	24
4-3	0134	212100		1	12
4-4	0125	211110		2	24
4-5	0126	210111		2	24
4-6	0127	210021		1	12
4-7	0145	201210		1	12
4-8	0156	200121		1	12
4-9	0167	200022		1	6
4-10	0235	122010		1	12
4-11	0135	121110		2	24
4-12	0236	112101		2	24
4-13	0136	112011		2	24
4-14	0237	111120		2	24
4-Z15	0146	111111	all-interval tetrachord	2	24
4-16	0157	110121		2	24
4-17	0347	102210		1	12
4-18	0147	102111		2	24
4-19	0148	101310		2	24
4-20	0158	101220	major seventh chord	1	12
4-21	0246	030201		1	12
4-22	0247	021120		2	24
4-23	0257	021030		1	12
4-24	0248	020301		1	12
4-25	0268	020202	French sixth	1	6
4-26	0358	012120	minor seventh chord	1	12
4-27	0258	012111	dominant or half-diminished seventh	2	24
4-28	0369	004002	diminished seventh chord	1	3
4-Z29	0137	111111	all-interval tetrachord	2	24

5 notes · 38 classes

Forte	Prime form	Vector	Name	Shapes	Sets
5-1	01234	432100		1	12
5-2	01235	332110		2	24
5-3	01245	322210		2	24
5-4	01236	322111		2	24
5-5	01237	321121		2	24
5-6	01256	311221		2	24
5-7	01267	310132		2	24
5-8	02346	232201		1	12
5-9	01246	231211		2	24
5-10	01346	223111		2	24
5-11	02347	222220		2	24
5-Z12	01356	222121		1	12
5-13	01248	221311		2	24
5-14	01257	221131		2	24
5-15	01268	220222		1	12
5-16	01347	213211		2	24
5-Z17	01348	212320		1	12
5-Z18	01457	212221		2	24
5-19	01367	212122		2	24
5-20	01568	211231		2	24
5-21	01458	202420		2	24
5-22	01478	202321		1	12
5-23	02357	132130		2	24
5-24	01357	131221		2	24
5-25	02358	123121		2	24
5-26	02458	122311		2	24
5-27	01358	122230		2	24
5-28	02368	122212		2	24
5-29	01368	122131		2	24
5-30	01468	121321		2	24
5-31	01369	114112		2	24
5-32	01469	113221		2	24
5-33	02468	040402	whole-tone pentachord	1	12
5-34	02469	032221		1	12
5-35	02479	032140	pentatonic scale	1	12
5-Z36	01247	222121		2	24
5-Z37	03458	212320		1	12
5-Z38	01258	212221		2	24

6 notes · 50 classes

Forte	Prime form	Vector	Name	Shapes	Sets
6-1	012345	543210		1	12
6-2	012346	443211		2	24
6-Z3	012356	433221		2	24
6-Z4	012456	432321		1	12
6-5	012367	422232		2	24
6-Z6	012567	421242		1	12
6-7	012678	420243		1	6
6-8	023457	343230		1	12
6-9	012357	342231		2	24
6-Z10	013457	333321		2	24
6-Z11	012457	333231		2	24
6-Z12	012467	332232		2	24
6-Z13	013467	324222		1	12
6-14	013458	323430		2	24
6-15	012458	323421		2	24
6-16	014568	322431		2	24
6-Z17	012478	322332		2	24
6-18	012578	322242		2	24
6-Z19	013478	313431		2	24
6-20	014589	303630	hexatonic scale	1	4
6-21	023468	242412		2	24
6-22	012468	241422		2	24
6-Z23	023568	234222		1	12
6-Z24	013468	233331		2	24
6-Z25	013568	233241		2	24
6-Z26	013578	232341		1	12
6-27	013469	225222		2	24
6-Z28	013569	224322		1	12
6-Z29	023679	224232		1	12
6-30	013679	224223	Petrushka chord	2	12
6-31	014579	223431		2	24
6-32	024579	143250	major hexachord	1	12
6-33	023579	143241		2	24
6-34	013579	142422		2	24
6-35	02468t	060603	whole-tone scale	1	2
6-Z36	012347	433221		2	24
6-Z37	012348	432321		1	12
6-Z38	012378	421242		1	12
6-Z39	023458	333321		2	24
6-Z40	012358	333231		2	24
6-Z41	012368	332232		2	24
6-Z42	012369	324222		1	12
6-Z43	012568	322332		2	24
6-Z44	012569	313431		2	24
6-Z45	023469	234222		1	12
6-Z46	012469	233331		2	24
6-Z47	012479	233241		2	24
6-Z48	012579	232341		1	12
6-Z49	013479	224322		1	12
6-Z50	014679	224232		1	12

7 notes · 38 classes

Forte	Prime form	Vector	Name	Shapes	Sets
7-1	0123456	654321		1	12
7-2	0123457	554331		2	24
7-3	0123458	544431		2	24
7-4	0123467	544332		2	24
7-5	0123567	543342		2	24
7-6	0123478	533442		2	24
7-7	0123678	532353		2	24
7-8	0234568	454422		1	12
7-9	0123468	453432		2	24
7-10	0123469	445332		2	24
7-11	0134568	444441		2	24
7-Z12	0123479	444342		1	12
7-13	0124568	443532		2	24
7-14	0123578	443352		2	24
7-15	0124678	442443		1	12
7-16	0123569	435432		2	24
7-Z17	0124569	434541		1	12
7-Z18	0145679	434442		2	24
7-19	0123679	434343		2	24
7-20	0125679	433452		2	24
7-21	0124589	424641		2	24
7-22	0125689	424542		1	12
7-23	0234579	354351		2	24
7-24	0123579	353442		2	24
7-25	0234679	345342		2	24
7-26	0134579	344532		2	24
7-27	0124579	344451		2	24
7-28	0135679	344433		2	24
7-29	0124679	344352		2	24
7-30	0124689	343542		2	24
7-31	0134679	336333		2	24
7-32	0134689	335442	harmonic minor scale	2	24
7-33	012468t	262623		1	12
7-34	013468t	254442	acoustic / melodic minor scale	1	12
7-35	013568t	254361	diatonic scale	1	12
7-Z36	0123568	444342		2	24
7-Z37	0134578	434541		1	12
7-Z38	0124578	434442		2	24

8 notes · 29 classes

Forte	Prime form	Vector	Name	Shapes	Sets
8-1	01234567	765442		1	12
8-2	01234568	665542		2	24
8-3	01234569	656542		1	12
8-4	01234578	655552		2	24
8-5	01234678	654553		2	24
8-6	01235678	654463		1	12
8-7	01234589	645652		1	12
8-8	01234789	644563		1	12
8-9	01236789	644464		1	6
8-10	02345679	566452		1	12
8-11	01234579	565552		2	24
8-12	01345679	556543		2	24
8-13	01234679	556453		2	24
8-14	01245679	555562		2	24
8-Z15	01234689	555553		2	24
8-16	01235789	554563		2	24
8-17	01345689	546652		1	12
8-18	01235689	546553		2	24
8-19	01245689	545752		2	24
8-20	01245789	545662		1	12
8-21	0123468t	474643		1	12
8-22	0123568t	465562		2	24
8-23	0123578t	465472		1	12
8-24	0124568t	464743		1	12
8-25	0124678t	464644		1	6
8-26	0134578t	456562		1	12
8-27	0124578t	456553		2	24
8-28	0134679t	448444	octatonic scale	1	3
8-Z29	01235679	555553		2	24

9 notes · 12 classes

Forte	Prime form	Vector	Name	Shapes	Sets
9-1	012345678	876663		1	12
9-2	012345679	777663		2	24
9-3	012345689	767763		2	24
9-4	012345789	766773		2	24
9-5	012346789	766674		2	24
9-6	01234568t	686763		1	12
9-7	01234578t	677673		2	24
9-8	01234678t	676764		2	24
9-9	01235678t	676683		1	12
9-10	01234679t	668664		1	12
9-11	01235679t	667773		2	24
9-12	01245689t	666963	enneatonic scale (Messiaen mode 3)	1	4

10 notes · 6 classes

Forte	Prime form	Vector	Shapes	Sets
10-1	0123456789	988884	1	12
10-2	012345678t	898884	1	12
10-3	012345679t	889884	1	12
10-4	012345689t	888984	1	12
10-5	012345789t	888894	1	12
10-6	012346789t	888885	1	6

11 notes · 1 class

Forte	Prime form	Vector	Name	Shapes	Sets
11-1	0123456789t	10101010105		1	12

12 notes · 1 class

Forte	Prime form	Vector	Name	Shapes	Sets
12-1	0123456789te	12121212126	chromatic aggregate	1	1