ComposerTools.com / Tools / Pitch Class Set Relationship Calculator - Copyright (c) 2003,2004 by Paul Nelson, all rights reserved.
intervalForteprimeinverted
vectorcount code formform
0 pitches, 0 intvls (1 vector, 1 quality, 1 total)
<000000>(1)i01() {silence}
1 pitch, 0 intvls (1 vector, 1 quality, 12 total)
<000000>(12)i11(0) {single-note}
2 pitches, 1 intvls (6 vectors, 6 qualities, 66 total)
<100000>(12)i21(0,1) {half-step}
<010000>(12)i22(0,2) {whole-step}
<001000>(12)i23(0,3) {minor-third}
<000100>(12)i24(0,4) {major-third}
<000010>(12)i25(0,5) {perfect}
<000001>(6)i26(0,6) {tritone}
3 pitches, 3 intvls (12 vectors, 19 qualities, 220 total)
<210000>(12)3-1:i31(0,1,2)
<111000>(24)3-2:i32(0,1,3)i32b[0,2,3]
<101100>(24)3-3:i33(0,1,4)i33b[0,3,4]
<100110>(24)3-4:i34(0,1,5)i34b[0,4,5]
<100011>(24)3-5:i35(0,1,6)i35b[0,5,6]
<020100>(12)3-6:i36(0,2,4)
<011010>(24)3-7:i37(0,2,5)i37b[0,3,5]
<010101>(24)3-8:i38(0,2,6) {It.}i38b[0,4,6]
<010020>(12)3-9:i39(0,2,7) {quar-3}
<002001>(12)3-10:i310(0,3,6) {dim}
<001110>(24)3-11:i311(0,3,7) {min}i311b[0,4,7]{maj}
<000300>(4)3-12:i312(0,4,8) {aug}
4 pitches, 6 intvls (28 vectors, 43 qualities, 495 total)
<321000>(12)4-1:i41(0,1,2,3)
<221100>(24)4-2:i42(0,1,2,4)i42b[0,2,3,4]
<212100>(12)4-3:i43(0,1,3,4)
<211110>(24)4-4:i44(0,1,2,5)i44b[0,3,4,5]
<210111>(24)4-5:i45(0,1,2,6)i45b[0,4,5,6]
<210021>(12)4-6:i46(0,1,2,7)
<201210>(12)4-7:i47(0,1,4,5)
<200121>(12)4-8:i48(0,1,5,6)
<200022>(6)4-9:i49(0,1,6,7)
<122010>(12)4-10:i410(0,2,3,5)
<121110>(24)4-11:i411(0,1,3,5)i411b[0,2,4,5]
<112101>(24)4-12:i412(0,2,3,6)i412b[0,3,4,6]
<112011>(24)4-13:i413(0,1,3,6)i413b[0,3,5,6]
<111120>(24)4-14:i414(0,2,3,7)i414b[0,4,5,7]
<111111>(48)4-Z15:i4Z15(0,1,4,6)i4Z15b[0,2,5,6]
4-Z29:i4Z29(0,1,3,7)i4Z29b[0,4,6,7]
<110121>(24)4-16:i416(0,1,5,7)i416b[0,2,6,7]
<102210>(12)4-17:i417(0,3,4,7)
<102111>(24)4-18:i418(0,1,4,7)i418b[0,3,6,7]
<101310>(24)4-19:i419(0,1,4,8) {mM7}i419b[0,3,4,8]
<101220>(12)4-20:i420(0,1,5,8) {maj7}
<030201>(12)4-21:i421(0,2,4,6)
<021120>(24)4-22:i422(0,2,4,7)i422b[0,3,5,7]
<021030>(12)4-23:i423(0,2,5,7) {quar-4}
<020301>(12)4-24:i424(0,2,4,8) {7+5}
<020202>(6)4-25:i425(0,2,6,8) {fr.,7-5}
<012120>(12)4-26:i426(0,3,5,8) {min7,maj6}
<012111>(24)4-27:i427(0,2,5,8) {hd7}i427b[0,3,6,8]{dom7}
<004002>(3)4-28:i428(0,3,6,9) {dd7}
5 pitches, 10 intvls (35 vectors, 66 qualities, 792 total)
<432100>(12)5-1:i51(0,1,2,3,4)
<332110>(24)5-2:i52(0,1,2,3,5)i52b[0,2,3,4,5]
<322210>(24)5-3:i53(0,1,2,4,5)i53b[0,1,3,4,5]
<322111>(24)5-4:i54(0,1,2,3,6)i54b[0,3,4,5,6]
<321121>(24)5-5:i55(0,1,2,3,7)i55b[0,4,5,6,7]
<311221>(24)5-6:i56(0,1,2,5,6)i56b[0,1,4,5,6]
<310132>(24)5-7:i57(0,1,2,6,7)i57b[0,1,5,6,7]
<232201>(12)5-8:i58(0,2,3,4,6)
<231211>(24)5-9:i59(0,1,2,4,6)i59b[0,2,4,5,6]
<223111>(24)5-10:i510(0,1,3,4,6)i510b[0,2,3,5,6]
<222220>(24)5-11:i511(0,2,3,4,7)i511b[0,3,4,5,7]
<222121>(36)5-Z12:i5Z12(0,1,3,5,6)
5-Z36:i5Z36(0,1,2,4,7)i5Z36b[0,3,5,6,7]
<221311>(24)5-13:i513(0,1,2,4,8)i513b[0,2,3,4,8]
<221131>(24)5-14:i514(0,1,2,5,7)i514b[0,2,5,6,7]
<220222>(12)5-15:i515(0,1,2,6,8)
<213211>(24)5-16:i516(0,1,3,4,7)i516b[0,3,4,6,7]
<212320>(24)5-Z17:i5Z17(0,1,3,4,8)
5-Z37:i5Z37(0,3,4,5,8)
<212221>(48)5-Z18:i5Z18(0,1,4,5,7)i5Z18b[0,2,3,6,7]
5-Z38:i5Z38(0,1,2,5,8)i5Z38b[0,3,6,7,8]
<212122>(24)5-19:i519(0,1,3,6,7)i519b[0,1,4,6,7]
<211231>(24)5-20:i520(0,1,5,6,8)i520b[0,2,3,7,8]
<202420>(24)5-21:i521(0,1,4,5,8)i521b[0,3,4,7,8]
<202321>(12)5-22:i522(0,1,4,7,8)
<132130>(24)5-23:i523(0,2,3,5,7)i523b[0,2,4,5,7]
<131221>(24)5-24:i524(0,1,3,5,7)i524b[0,2,4,6,7]
<123121>(24)5-25:i525(0,2,3,5,8)i525b[0,3,5,6,8]
<122311>(24)5-26:i526(0,2,4,5,8)i526b[0,3,4,6,8]
<122230>(24)5-27:i527(0,1,3,5,8)i527b[0,3,5,7,8]{min9}
<122212>(24)5-28:i528(0,2,3,6,8)i528b[0,2,5,6,8]
<122131>(24)5-29:i529(0,1,3,6,8)i529b[0,2,5,7,8]
<121321>(24)5-30:i530(0,1,4,6,8)i530b[0,2,4,7,8]
<114112>(24)5-31:i531(0,1,3,6,9)i531b[0,2,3,6,9]{7-9}
<113221>(24)5-32:i532(0,1,4,6,9)i532b[0,2,5,6,9]{7+9}
<040402>(12)5-33:i533(0,2,4,6,8) {9+5,9-5}
<032221>(12)5-34:i534(0,2,4,6,9) {dom9}
<032140>(12)5-35:i535(0,2,4,7,9) {pentatonic,Quar-5}
intervalForteprimeinverted
vectorcount code formform
12 pitches, 66 intvls (1 vector, 1 quality, 1 total)
<CCCCC6>(1)iC1(0,1,2,3,4,5,6,7,8,9,A,B) {chromatic}
11 pitches, 55 intvls (1 vector, 1 quality, 12 total)
<AAAAA5>(12)iB1(0,1,2,3,4,5,6,7,8,9,A)
10 pitches, 45 intvls (6 vectors, 6 qualities, 66 total)
<988884>(12)iA1(0,1,2,3,4,5,6,7,8,9)
<898884>(12)iA2(0,1,2,3,4,5,6,7,8,A)
<889884>(12)iA3(0,1,2,3,4,5,6,7,9,A)
<888984>(12)iA4(0,1,2,3,4,5,6,8,9,A)
<888894>(12)iA5(0,1,2,3,4,5,7,8,9,A)
<888885>(6)iA6(0,1,2,3,4,6,7,8,9,A)
9 pitches, 36 intvls (12 vectors, 19 qualities, 220 total)
<876663>(12)9-1:i91(0,1,2,3,4,5,6,7,8)
<777663>(24)9-2:i92(0,1,2,3,4,5,6,7,9)i92b[0,2,3,4,5,6,7,8,9]
<767763>(24)9-3:i93(0,1,2,3,4,5,6,8,9)i93b[0,1,3,4,5,6,7,8,9]
<766773>(24)9-4:i94(0,1,2,3,4,5,7,8,9)i94b[0,1,2,4,5,6,7,8,9]
<766674>(24)9-5:i95(0,1,2,3,4,6,7,8,9)i95b[0,1,2,3,5,6,7,8,9]
<686763>(12)9-6:i96(0,1,2,3,4,5,6,8,A)
<677673>(24)9-7:i97(0,1,2,3,4,5,7,8,A)i97b[0,1,3,4,5,6,7,8,A]
<676764>(24)9-8:i98(0,1,2,3,4,6,7,8,A)i98b[0,1,2,4,5,6,7,8,A]
<676683>(12)9-9:i99(0,1,2,3,5,6,7,8,A)
<668664>(12)9-10:i910(0,1,2,3,4,6,7,9,A)
<667773>(24)9-11:i911(0,1,2,3,5,6,7,9,A)i911b[0,1,2,4,5,6,7,9,A]
<666963>(4)9-12:i912(0,1,2,4,5,6,8,9,A)
8 pitches, 28 intvls (28 vectors, 43 qualities, 495 total)
<765442>(12)8-1:i81(0,1,2,3,4,5,6,7)
<665542>(24)8-2:i82(0,1,2,3,4,5,6,8)i82b[0,2,3,4,5,6,7,8]
<656542>(12)8-3:i83(0,1,2,3,4,5,6,9)
<655552>(24)8-4:i84(0,1,2,3,4,5,7,8)i84b[0,1,3,4,5,6,7,8]
<654553>(24)8-5:i85(0,1,2,3,4,6,7,8)i85b[0,1,2,4,5,6,7,8]
<654463>(12)8-6:i86(0,1,2,3,5,6,7,8)
<645652>(12)8-7:i87(0,1,2,3,4,5,8,9)
<644563>(12)8-8:i88(0,1,2,3,4,7,8,9)
<644464>(6)8-9:i89(0,1,2,3,6,7,8,9)
<566452>(12)8-10:i810(0,2,3,4,5,6,7,9)
<565552>(24)8-11:i811(0,1,2,3,4,5,7,9)i811b[0,2,4,5,6,7,8,9]
<556543>(24)8-12:i812(0,1,3,4,5,6,7,9)i812b[0,2,3,4,5,6,8,9]
<556453>(24)8-13:i813(0,1,2,3,4,6,7,9)i813b[0,2,3,5,6,7,8,9]
<555562>(24)8-14:i814(0,1,2,4,5,6,7,9)i814b[0,2,3,4,5,7,8,9]
<555553>(48)8-Z15:i8Z15(0,1,2,3,4,6,8,9)i8Z15b[0,1,3,5,6,7,8,9]
8-Z29:i8Z29(0,1,2,3,5,6,7,9)i8Z29b[0,2,3,4,6,7,8,9]
<554563>(24)8-16:i816(0,1,2,3,5,7,8,9)i816b[0,1,2,4,6,7,8,9]
<546652>(12)8-17:i817(0,1,3,4,5,6,8,9)
<546553>(24)8-18:i818(0,1,2,3,5,6,8,9)i818b[0,1,3,4,6,7,8,9]
<545752>(24)8-19:i819(0,1,2,4,5,6,8,9)i819b[0,1,3,4,5,7,8,9]
<545662>(12)8-20:i820(0,1,2,4,5,7,8,9)
<474643>(12)8-21:i821(0,1,2,3,4,6,8,A)
<465562>(24)8-22:i822(0,1,2,3,5,6,8,A)i822b[0,1,3,4,5,6,8,A]
<465472>(12)8-23:i823(0,1,2,3,5,7,8,A)
<464743>(12)8-24:i824(0,1,2,4,5,6,8,A)
<464644>(6)8-25:i825(0,1,2,4,6,7,8,A)
<456562>(12)8-26:i826(0,1,3,4,5,7,8,A)
<456553>(24)8-27:i827(0,1,2,4,5,7,8,A)i827b[0,1,3,4,6,7,8,A]
<448444>(3)8-28:i828(0,1,3,4,6,7,9,A) {octatonic}
7 pitches, 21 intvls (35 vectors, 66 qualities, 792 total)
<654321>(12)7-1:i71(0,1,2,3,4,5,6)
<554331>(24)7-2:i72(0,1,2,3,4,5,7)i72b[0,2,3,4,5,6,7]
<544431>(24)7-3:i73(0,1,2,3,4,5,8)i73b[0,3,4,5,6,7,8]
<544332>(24)7-4:i74(0,1,2,3,4,6,7)i74b[0,1,3,4,5,6,7]
<543342>(24)7-5:i75(0,1,2,3,5,6,7)i75b[0,1,2,4,5,6,7]
<533442>(24)7-6:i76(0,1,2,3,4,7,8)i76b[0,1,4,5,6,7,8]
<532353>(24)7-7:i77(0,1,2,3,6,7,8)i77b[0,1,2,5,6,7,8]
<454422>(12)7-8:i78(0,2,3,4,5,6,8)
<453432>(24)7-9:i79(0,1,2,3,4,6,8)i79b[0,2,4,5,6,7,8]
<445332>(24)7-10:i710(0,1,2,3,4,6,9)i710b[0,2,3,4,5,6,9]
<444441>(24)7-11:i711(0,1,3,4,5,6,8)i711b[0,2,3,4,5,7,8]
<444342>(36)7-Z12:i7Z12(0,1,2,3,4,7,9)
7-Z36:i7Z36(0,1,2,3,5,6,8)i7Z36b[0,2,3,5,6,7,8]
<443532>(24)7-13:i713(0,1,2,4,5,6,8)i713b[0,2,3,4,6,7,8]
<443352>(24)7-14:i714(0,1,2,3,5,7,8)i714b[0,1,3,5,6,7,8]
<442443>(12)7-15:i715(0,1,2,4,6,7,8)
<435432>(24)7-16:i716(0,1,2,3,5,6,9)i716b[0,1,3,4,5,6,9]
<434541>(24)7-Z17:i7Z17(0,1,2,4,5,6,9)
7-Z37:i7Z37(0,1,3,4,5,7,8)
<434442>(48)7-Z18:i7Z18(0,1,4,5,6,7,9)i7Z18b[0,2,3,4,5,8,9]
7-Z38:i7Z38(0,1,2,4,5,7,8)i7Z38b[0,1,3,4,6,7,8]
<434343>(24)7-19:i719(0,1,2,3,6,7,9)i719b[0,1,2,3,6,8,9]
<433452>(24)7-20:i720(0,1,2,5,6,7,9)i720b[0,2,3,4,7,8,9]
<424641>(24)7-21:i721(0,1,2,4,5,8,9)i721b[0,1,3,4,5,8,9]
<424542>(12)7-22:i722(0,1,2,5,6,8,9) {hungar-min}
<354351>(24)7-23:i723(0,2,3,4,5,7,9)i723b[0,2,4,5,6,7,9]
<353442>(24)7-24:i724(0,1,2,3,5,7,9)i724b[0,2,4,6,7,8,9]
<345342>(24)7-25:i725(0,2,3,4,6,7,9)i725b[0,2,3,5,6,7,9]
<344532>(24)7-26:i726(0,1,3,4,5,7,9)i726b[0,2,4,5,6,8,9]
<344451>(24)7-27:i727(0,1,2,4,5,7,9)i727b[0,2,4,5,7,8,9]
<344433>(24)7-28:i728(0,1,3,5,6,7,9)i728b[0,2,3,4,6,8,9]
<344352>(24)7-29:i729(0,1,2,4,6,7,9)i729b[0,2,3,5,7,8,9]
<343542>(24)7-30:i730(0,1,2,4,6,8,9)i730b[0,1,3,5,7,8,9]
<336333>(24)7-31:i731(0,1,3,4,6,7,9)i731b[0,2,3,5,6,8,9]
<335442>(24)7-32:i732(0,1,3,4,6,8,9) {harm-min} i732b[0,1,3,5,6,8,9]
<262623>(12)7-33:i733(0,1,2,4,6,8,A)
<254442>(12)7-34:i734(0,1,3,4,6,8,A)
<254361>(12)7-35:i735(0,1,3,5,6,8,A) {diatonic}
6 pitches, 15 intvls (35 vectors, 80 qualities, 924 total)
intervalForteprimeinverted
vectorcount code formform
<543210>(12)6-1:i61(0,1,2,3,4,5)
<443211>(24)6-2:i62(0,1,2,3,4,6)i62b[0,2,3,4,5,6]
<433221>(48)6-Z3:i6Z3(0,1,2,3,5,6)i6Z3b[0,1,3,4,5,6]
6-Z36:i6Z36(0,1,2,3,4,7)i6Z36b[0,3,4,5,6,7]
<432321>(24)6-Z4:i6Z4(0,1,2,4,5,6)
6-Z37:i6Z37(0,1,2,3,4,8)
<422232>(24)6-5:i65(0,1,2,3,6,7)i65b[0,1,4,5,6,7]
<421242>(24)6-Z6:i6Z6(0,1,2,5,6,7)
6-Z38:i6Z38(0,1,2,3,7,8)
<420243>(6)6-7:i67(0,1,2,6,7,8)
<343230>(12)6-8:i68(0,2,3,4,5,7)
<342231>(24)6-9:i69(0,1,2,3,5,7)i69b[0,2,4,5,6,7]
<333321>(48)6-Z10:i6Z10(0,1,3,4,5,7)i6Z10b[0,2,3,4,6,7]
6-Z39:i6Z39(0,2,3,4,5,8)i6Z39b[0,3,4,5,6,8]
<333231>(48)6-Z11:i6Z11(0,1,2,4,5,7)i6Z11b[0,2,3,5,6,7]
6-Z40:i6Z40(0,1,2,3,5,8)i6Z40b[0,3,5,6,7,8]
<332232>(48)6-Z12:i6Z12(0,1,2,4,6,7)i6Z12b[0,1,3,5,6,7]
6-Z41:i6Z41(0,1,2,3,6,8)i6Z41b[0,2,5,6,7,8]
<324222>(24)6-Z13:i6Z13(0,1,3,4,6,7)
6-Z42:i6Z42(0,1,2,3,6,9)
<323430>(24)6-14:i614(0,1,3,4,5,8)i614b[0,3,4,5,7,8]
<323421>(24)6-15:i615(0,1,2,4,5,8)i615b[0,3,4,6,7,8]
<322431>(24)6-16:i616(0,1,4,5,6,8)i616b[0,2,3,4,7,8]
<322332>(48)6-Z17:i6Z17(0,1,2,4,7,8)i6Z17b[0,1,4,6,7,8]
6-Z43:i6Z43(0,1,2,5,6,8)i6Z43b[0,2,3,6,7,8]
intervalForteprimeinverted
vectorcount code formform
<322242>(24)6-18:i618(0,1,2,5,7,8)i618b[0,1,3,6,7,8]
<313431>(48)6-Z19:i6Z19(0,1,3,4,7,8)i6Z19b[0,1,4,5,7,8]
6-Z44:i6Z44(0,1,2,5,6,9)i6Z44b[0,1,4,5,6,9]
<303630>(4)6-20:i620(0,1,4,5,8,9)
<242412>(24)6-21:i621(0,2,3,4,6,8)i621b[0,2,4,5,6,8]
<241422>(24)6-22:i622(0,1,2,4,6,8)i622b[0,2,4,6,7,8]
<234222>(24)6-Z23:i6Z23(0,2,3,5,6,8)
6-Z45:i6Z45(0,2,3,4,6,9)
<233331>(48)6-Z24:i6Z24(0,1,3,4,6,8)i6Z24b[0,2,4,5,7,8]
6-Z46:i6Z46(0,1,2,4,6,9)i6Z46b[0,2,4,5,6,9]
<233241>(48)6-Z25:i6Z25(0,1,3,5,6,8)i6Z25b[0,2,3,5,7,8]
6-Z47:i6Z47(0,1,2,4,7,9)i6Z47b[0,2,3,4,7,9]
<232341>(24)6-Z26:i6Z26(0,1,3,5,7,8)
6-Z48:i6Z48(0,1,2,5,7,9)
<225222>(24)6-27:i627(0,1,3,4,6,9)i627b[0,2,3,5,6,9]
<224322>(24)6-Z28:i6Z28(0,1,3,5,6,9)
6-Z49:i6Z49(0,1,3,4,7,9)
<224232>(24)6-Z29:i6Z29(0,2,3,6,7,9)
6-Z50:i6Z50(0,1,4,6,7,9)
<224223>(12)6-30:i630(0,1,3,6,7,9)i630b[0,2,3,6,8,9]
<223431>(24)6-31:i631(0,1,4,5,7,9)i631b[0,2,4,5,8,9]
<143250>(12)6-32:i632(0,2,4,5,7,9) {min11}
<143241>(24)6-33:i633(0,2,3,5,7,9)i633b[0,2,4,6,7,9]{dom11}
<142422>(24)6-34:i634(0,1,3,5,7,9)i634b[0,2,4,6,8,9]
<060603>(2)6-35:i635(0,2,4,6,8,A) {wholetone}
Totals:
Total unique interval vectors: 200
Total prime forms: 208 (according to the Forte designations, does not include 0, 1, 2, 10, 11, 12 element PC sets)
Total unique qualities: 352 (the prime forms plus inversions of all PC sets shown above)
Total pitch collections: 4096 (all of the transpositions and inversions of all PC sets shown above)