Helpful documents
Below are links to several PDFs that students may find helpful in their study of music theory.
Staff paper
- Blank staff paper
- Piano staff paper (two staves bracketed together)
- Half staff, half blank horizontal split
- Half staff, half blank vertical split
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> |
