Helpful documents

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Staff paper

Technology

Set Theory

Table of Set Classes

The table has two vertical halves. The smaller set classes are in the left half, and the larger in the right. Together, the two set classes are complementary (together, they create the chromatic set).

Prime
Form
Forte
Number
Interval
Class
Vector
Prime
Form
Forte
Number
Interval
Class
Vector
(012) 3–1 <210000> (012345678) 9–1 <876663>
(013) 3–2 <111000> (012345679) 9–2 <777663>
(014) 3–3 <101100> (012345689) 9–3 <767763>
(015) 3–4 <100110> (012345789) 9–4 <766773>
(016) 3–5 <100011> (012346789) 9–5 <766674>
(024) 3–6 <020100> (01234568T) 9–6 <686763>
(025) 3–7 <011010> (01234578T) 9–7 <677673>
(026) 3–8 <010101> (01234678T) 9–8 <676764>
(027) 3–9 <010020> (01235678T) 9–9 <676683>
(036) 3–10 <002001> (01234679T) 9–10 <668664>
(037) 3–11 <001110> (01235679T) 9–11 <667773>
(048) 3–12 <000300> (01245689T) 9–12 <666963>
(0123) 4–1 <321000> (01234567) 8–1 <765442>
(0124) 4–2 <221100> (01234568) 8–2 <665542>
(0125) 4–4 <211110> (01234578) 8–4 <655552>
(0126) 4–5 <210111> (01234678) 8–5 <654553>
(0127) 4–6 <210021> (01235678) 8–6 <654463>
(0134) 4–3 <212100> (01234569) 8–3 <656542>
(0135) 4–11 <121110> (01234579) 8–11 <565552>
(0136) 4–13 <112011> (01234679) 8–13 <556453>
(0137) 4–Z29 <111111> (01235679) 8–Z29 <555553>
(0145) 4–7 <201210> (01234589) 8–7 <645652>
(0146) 4–Z15 <111111> (01234689) 8–Z15 <555553>
(0147) 4–18 <102111> (01235689) 8–18 <546553>
(0148) 4–19 <101310> (01245689) 8–19 <545752>
(0156) 4–8 <200121> (01234789) 8–8 <644563>
(0157) 4–16 <110121> (01235789) 8–16 <554563>
(0158) 4–20 <101220> (01245789) 8–20 <545662>
(0167) 4–9 <200022> (01236789) 8–9 <644464>
(0235) 4–10 <122010> (02345679) 8–10 <566452>
(0236) 4–12 <112101> (01345679) 8–12 <556543>
(0237) 4–14 <111120> (01245679) 8–14 <555562>
(0246) 4–21 <030201> (0123468T) 8–21 <474643>
(0247) 4–22 <021120> (0123568T) 8–22 <465562>
(0248) 4–24 <020301> (0124568T) 8–24 <464743>
(0257) 4–23 <021030> (0123578T) 8–23 <465472>
(0258) 4–27 <012111> (0124578T) 8–27 <456553>
(0268) 4–25 <020202> (0124678T) 8–25 <464644>
(0347) 4–17 <102210> (01345689) 8–17 <546652>
(0358) 4–26 <012120> (0134578T) 8–26 <456562>
(0369) 4–28 <004002> (0134679T) 8–28 <448444>
(01234) 5–1 <432100> (0123456) 7–1 <654321>
(01235) 5–2 <332110> (0123457) 7–2 <554331>
(01236) 5–4 <322111> (0123467) 7–4 <544332>
(01237) 5–5 <321121> (0123567) 7–5 <543342>
(01245) 5–3 <322210> (0123458) 7–3 <544431>
(01246) 5–9 <231211> (0123468) 7–9 <453432>
(01247) 5–Z36 <222121> (0123568) 7–Z36 <444342>
(01248) 5–13 <221311> (0124568) 7–13 <443532>
(01256) 5–6 <311221> (0123478) 7–6 <533442>
(01257) 5–14 <221131> (0123578) 7–14 <443352>
(01258) 5–Z38 <212221> (0124578) 7–Z38 <434442>
(01267) 5–7 <310132> (0123678) 7–7 <532353>
(01268) 5–15 <220222> (0124678) 7–15 <442443>
(01346) 5–10 <223111> (0123469) 7–10 <445332>
(01347) 5–16 <213211> (0123569) 7–16 <435432>
(01348) 5–Z17 <212320> (0124569) 7–Z17 <434541>
(01356) 5–Z12 <222121> (0123479) 7–Z12 <444342>
(01357) 5–24 <131221> (0123579) 7–24 <353442>
(01358) 5–27 <122230> (0124579) 7–27 <344451>
(01367) 5–19 <212122> (0123679) 7–19 <434343>
(01368) 5–29 <122131> (0124679) 7–29 <344352>
(01369) 5–31 <114112> (0134679) 7–31 <336333>
(01457) 5–Z18 <212221> (0145679) 7–Z18 <434442>
(01458) 5–21 <202420> (0124589) 7–21 <424641>
(01468) 5–30 <121321> (0124689) 7–30 <343542>
(01469) 5–32 <113221> (0134689) 7–32 <335442>
(01478) 5–22 <202321> (0125689) 7–22 <424542>
(01568) 5–20 <211231> (0125679) 7–20 <433452>
(02346) 5–8 <232201> (0234568) 7–8 <454422>
(02347) 5–11 <222220> (0134568) 7–11 <444441>
(02357) 5–23 <132130> (0234579) 7–23 <354351>
(02358) 5–25 <123121> (0234679) 7–25 <345342>
(02368) 5–28 <122212> (0135679) 7–28 <344433>
(02458) 5–26 <122311> (0134579) 7–26 <344532>
(02468) 5–33 <040402> (012468T) 7–33 <262623>
(02469) 5–34 <032221> (013468T) 7–34 <254442>
(02479) 5–35 <032140> (013568T) 7–35 <254361>
(03458) 5–Z37 <212320> (0134578) 7–Z37 <434541>
(012345) 6–1 <543210>
(012346) 6–2 <443211>
(012347) 6–Z36 <433221> (012356) 6–Z3 <433221>
(012348) 6–Z37 <432321> (012456) 6–Z4 <432321>
(012357) 6–9 <342231>
(012358) 6–Z40 <333231> (012457) 6–Z11 <333231>
(012367) 6–5 <422232>
(012368) 6–Z41 <332232> (012467) 6–Z12 <332232>
(012369) 6–Z42 <324222> (013467) 6–Z13 <324222>
(012378) 6–Z38 <421242> (012567) 6–Z6 <421242>
(012458) 6–15 <323421>
(012468) 6–22 <241422>
(012469) 6–Z46 <233331> (013468) 6–Z24 <233331>
(012478) 6–Z17 <322332> (012568) 6–Z43 <322332>
(012479) 6–Z47 <233241> (013568) 6–Z25 <233241>
(012569) 6–Z44 <313431> (013478) 6–Z19 <313431>
(012578) 6–18 <322242>
(012579) 6–Z48 <232341> (013578) 6–Z26 <232341>
(012678) 6–7 <420243>
(013457) 6–Z10 <333321> (023458) 6–Z39 <333321>
(013458) 6–14 <323430>
(013469) 6–27 <225222>
(013479) 6–Z49 <224322> (013569) 6–Z28 <224322>
(013579) 6–34 <142422>
(013679) 6–30 <224223>
(023679) 6–Z29 <224232> (014679) 6–Z50 <224232>
(014568) 6–16 <322431>
(014579) 6–31 <223431>
(014589) 6–20 <303630>
(023457) 6–8 <343230>
(023468) 6–21 <242412>
(023469) 6–Z45 <234222> (023568) 6–Z23 <234222>
(023579) 6–33 <143241>
(024579) 6–32 <143250>
(02468T) 6–35 <060603>

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Open Music Theory Copyright © 2023 by Mark Gotham; Kyle Gullings; Chelsey Hamm; Bryn Hughes; Brian Jarvis; Megan Lavengood; and John Peterson is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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