ComposerTools.com / Theory / Table of Prime Forms - 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)() {silence}
1 pitch, 0 intvls (1 vector, 1 quality, 12 total)
<000000>(12)(0) {single-note}
2 pitches, 1 intvls (6 vectors, 6 qualities, 66 total)
<100000>(12)(0,1) {half-step}
<010000>(12)(0,2) {whole-step}
<001000>(12)(0,3) {minor-third}
<000100>(12)(0,4) {major-third}
<000010>(12)(0,5) {perfect}
<000001>(6)(0,6) {tritone}
3 pitches, 3 intvls (12 vectors, 19 qualities, 220 total)
<210000>(12)3-1:(0,1,2)
<111000>(24)3-2:(0,1,3)[0,2,3]
<101100>(24)3-3:(0,1,4)[0,3,4]
<100110>(24)3-4:(0,1,5)[0,4,5]
<100011>(24)3-5:(0,1,6)[0,5,6]
<020100>(12)3-6:(0,2,4)
<011010>(24)3-7:(0,2,5)[0,3,5]
<010101>(24)3-8:(0,2,6) {It.}[0,4,6]
<010020>(12)3-9:(0,2,7) {quar-3}
<002001>(12)3-10:(0,3,6) {dim}
<001110>(24)3-11:(0,3,7) {min}[0,4,7]{maj}
<000300>(4)3-12:(0,4,8) {aug}
4 pitches, 6 intvls (28 vectors, 43 qualities, 495 total)
<321000>(12)4-1:(0,1,2,3)
<221100>(24)4-2:(0,1,2,4)[0,2,3,4]
<212100>(12)4-3:(0,1,3,4)
<211110>(24)4-4:(0,1,2,5)[0,3,4,5]
<210111>(24)4-5:(0,1,2,6)[0,4,5,6]
<210021>(12)4-6:(0,1,2,7)
<201210>(12)4-7:(0,1,4,5)
<200121>(12)4-8:(0,1,5,6)
<200022>(6)4-9:(0,1,6,7)
<122010>(12)4-10:(0,2,3,5)
<121110>(24)4-11:(0,1,3,5)[0,2,4,5]
<112101>(24)4-12:(0,2,3,6)[0,3,4,6]
<112011>(24)4-13:(0,1,3,6)[0,3,5,6]
<111120>(24)4-14:(0,2,3,7)[0,4,5,7]
<111111>(48)4-Z15:(0,1,4,6)[0,2,5,6]
4-Z29:(0,1,3,7)[0,4,6,7]
<110121>(24)4-16:(0,1,5,7)[0,2,6,7]
<102210>(12)4-17:(0,3,4,7)
<102111>(24)4-18:(0,1,4,7)[0,3,6,7]
<101310>(24)4-19:(0,1,4,8) {mM7}[0,3,4,8]
<101220>(12)4-20:(0,1,5,8) {maj7}
<030201>(12)4-21:(0,2,4,6)
<021120>(24)4-22:(0,2,4,7)[0,3,5,7]
<021030>(12)4-23:(0,2,5,7) {quar-4}
<020301>(12)4-24:(0,2,4,8) {7+5}
<020202>(6)4-25:(0,2,6,8) {fr.,7-5}
<012120>(12)4-26:(0,3,5,8) {min7,maj6}
<012111>(24)4-27:(0,2,5,8) {hd7}[0,3,6,8]{dom7}
<004002>(3)4-28:(0,3,6,9) {dd7}
5 pitches, 10 intvls (35 vectors, 66 qualities, 792 total)
<432100>(12)5-1:(0,1,2,3,4)
<332110>(24)5-2:(0,1,2,3,5)[0,2,3,4,5]
<322210>(24)5-3:(0,1,2,4,5)[0,1,3,4,5]
<322111>(24)5-4:(0,1,2,3,6)[0,3,4,5,6]
<321121>(24)5-5:(0,1,2,3,7)[0,4,5,6,7]
<311221>(24)5-6:(0,1,2,5,6)[0,1,4,5,6]
<310132>(24)5-7:(0,1,2,6,7)[0,1,5,6,7]
<232201>(12)5-8:(0,2,3,4,6)
<231211>(24)5-9:(0,1,2,4,6)[0,2,4,5,6]
<223111>(24)5-10:(0,1,3,4,6)[0,2,3,5,6]
<222220>(24)5-11:(0,2,3,4,7)[0,3,4,5,7]
<222121>(36)5-Z12:(0,1,3,5,6)
5-Z36:(0,1,2,4,7)[0,3,5,6,7]
<221311>(24)5-13:(0,1,2,4,8)[0,2,3,4,8]
<221131>(24)5-14:(0,1,2,5,7)[0,2,5,6,7]
<220222>(12)5-15:(0,1,2,6,8)
<213211>(24)5-16:(0,1,3,4,7)[0,3,4,6,7]
<212320>(24)5-Z17:(0,1,3,4,8)
5-Z37:(0,3,4,5,8)
<212221>(48)5-Z18:(0,1,4,5,7)[0,2,3,6,7]
5-Z38:(0,1,2,5,8)[0,3,6,7,8]
<212122>(24)5-19:(0,1,3,6,7)[0,1,4,6,7]
<211231>(24)5-20:(0,1,5,6,8)[0,2,3,7,8]
<202420>(24)5-21:(0,1,4,5,8)[0,3,4,7,8]
<202321>(12)5-22:(0,1,4,7,8)
<132130>(24)5-23:(0,2,3,5,7)[0,2,4,5,7]
<131221>(24)5-24:(0,1,3,5,7)[0,2,4,6,7]
<123121>(24)5-25:(0,2,3,5,8)[0,3,5,6,8]
<122311>(24)5-26:(0,2,4,5,8)[0,3,4,6,8]
<122230>(24)5-27:(0,1,3,5,8)[0,3,5,7,8]{min9}
<122212>(24)5-28:(0,2,3,6,8)[0,2,5,6,8]
<122131>(24)5-29:(0,1,3,6,8)[0,2,5,7,8]
<121321>(24)5-30:(0,1,4,6,8)[0,2,4,7,8]
<114112>(24)5-31:(0,1,3,6,9)[0,2,3,6,9]{7-9}
<113221>(24)5-32:(0,1,4,6,9)[0,2,5,6,9]{7+9}
<040402>(12)5-33:(0,2,4,6,8) {9+5,9-5}
<032221>(12)5-34:(0,2,4,6,9) {dom9}
<032140>(12)5-35:(0,2,4,7,9) {pentatonic,Quar-5}
intervalForteprimeinverted
vectorcount code formform
12 pitches, 66 intvls (1 vector, 1 quality, 1 total)
<CCCCC6>(1)(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)(0,1,2,3,4,5,6,7,8,9,A)
10 pitches, 45 intvls (6 vectors, 6 qualities, 66 total)
<988884>(12)(0,1,2,3,4,5,6,7,8,9)
<898884>(12)(0,1,2,3,4,5,6,7,8,A)
<889884>(12)(0,1,2,3,4,5,6,7,9,A)
<888984>(12)(0,1,2,3,4,5,6,8,9,A)
<888894>(12)(0,1,2,3,4,5,7,8,9,A)
<888885>(6)(0,1,2,3,4,6,7,8,9,A)
9 pitches, 36 intvls (12 vectors, 19 qualities, 220 total)
<876663>(12)9-1:(0,1,2,3,4,5,6,7,8)
<777663>(24)9-2:(0,1,2,3,4,5,6,7,9)[0,2,3,4,5,6,7,8,9]
<767763>(24)9-3:(0,1,2,3,4,5,6,8,9)[0,1,3,4,5,6,7,8,9]
<766773>(24)9-4:(0,1,2,3,4,5,7,8,9)[0,1,2,4,5,6,7,8,9]
<766674>(24)9-5:(0,1,2,3,4,6,7,8,9)[0,1,2,3,5,6,7,8,9]
<686763>(12)9-6:(0,1,2,3,4,5,6,8,A)
<677673>(24)9-7:(0,1,2,3,4,5,7,8,A)[0,1,3,4,5,6,7,8,A]
<676764>(24)9-8:(0,1,2,3,4,6,7,8,A)[0,1,2,4,5,6,7,8,A]
<676683>(12)9-9:(0,1,2,3,5,6,7,8,A)
<668664>(12)9-10:(0,1,2,3,4,6,7,9,A)
<667773>(24)9-11:(0,1,2,3,5,6,7,9,A)[0,1,2,4,5,6,7,9,A]
<666963>(4)9-12:(0,1,2,4,5,6,8,9,A)
8 pitches, 28 intvls (28 vectors, 43 qualities, 495 total)
<765442>(12)8-1:(0,1,2,3,4,5,6,7)
<665542>(24)8-2:(0,1,2,3,4,5,6,8)[0,2,3,4,5,6,7,8]
<656542>(12)8-3:(0,1,2,3,4,5,6,9)
<655552>(24)8-4:(0,1,2,3,4,5,7,8)[0,1,3,4,5,6,7,8]
<654553>(24)8-5:(0,1,2,3,4,6,7,8)[0,1,2,4,5,6,7,8]
<654463>(12)8-6:(0,1,2,3,5,6,7,8)
<645652>(12)8-7:(0,1,2,3,4,5,8,9)
<644563>(12)8-8:(0,1,2,3,4,7,8,9)
<644464>(6)8-9:(0,1,2,3,6,7,8,9)
<566452>(12)8-10:(0,2,3,4,5,6,7,9)
<565552>(24)8-11:(0,1,2,3,4,5,7,9)[0,2,4,5,6,7,8,9]
<556543>(24)8-12:(0,1,3,4,5,6,7,9)[0,2,3,4,5,6,8,9]
<556453>(24)8-13:(0,1,2,3,4,6,7,9)[0,2,3,5,6,7,8,9]
<555562>(24)8-14:(0,1,2,4,5,6,7,9)[0,2,3,4,5,7,8,9]
<555553>(48)8-Z15:(0,1,2,3,4,6,8,9)[0,1,3,5,6,7,8,9]
8-Z29:(0,1,2,3,5,6,7,9)[0,2,3,4,6,7,8,9]
<554563>(24)8-16:(0,1,2,3,5,7,8,9)[0,1,2,4,6,7,8,9]
<546652>(12)8-17:(0,1,3,4,5,6,8,9)
<546553>(24)8-18:(0,1,2,3,5,6,8,9)[0,1,3,4,6,7,8,9]
<545752>(24)8-19:(0,1,2,4,5,6,8,9)[0,1,3,4,5,7,8,9]
<545662>(12)8-20:(0,1,2,4,5,7,8,9)
<474643>(12)8-21:(0,1,2,3,4,6,8,A)
<465562>(24)8-22:(0,1,2,3,5,6,8,A)[0,1,3,4,5,6,8,A]
<465472>(12)8-23:(0,1,2,3,5,7,8,A)
<464743>(12)8-24:(0,1,2,4,5,6,8,A)
<464644>(6)8-25:(0,1,2,4,6,7,8,A)
<456562>(12)8-26:(0,1,3,4,5,7,8,A)
<456553>(24)8-27:(0,1,2,4,5,7,8,A)[0,1,3,4,6,7,8,A]
<448444>(3)8-28:(0,1,3,4,6,7,9,A) {octatonic}
7 pitches, 21 intvls (35 vectors, 66 qualities, 792 total)
<654321>(12)7-1:(0,1,2,3,4,5,6)
<554331>(24)7-2:(0,1,2,3,4,5,7)[0,2,3,4,5,6,7]
<544431>(24)7-3:(0,1,2,3,4,5,8)[0,3,4,5,6,7,8]
<544332>(24)7-4:(0,1,2,3,4,6,7)[0,1,3,4,5,6,7]
<543342>(24)7-5:(0,1,2,3,5,6,7)[0,1,2,4,5,6,7]
<533442>(24)7-6:(0,1,2,3,4,7,8)[0,1,4,5,6,7,8]
<532353>(24)7-7:(0,1,2,3,6,7,8)[0,1,2,5,6,7,8]
<454422>(12)7-8:(0,2,3,4,5,6,8)
<453432>(24)7-9:(0,1,2,3,4,6,8)[0,2,4,5,6,7,8]
<445332>(24)7-10:(0,1,2,3,4,6,9)[0,2,3,4,5,6,9]
<444441>(24)7-11:(0,1,3,4,5,6,8)[0,2,3,4,5,7,8]
<444342>(36)7-Z12:(0,1,2,3,4,7,9)
7-Z36:(0,1,2,3,5,6,8)[0,2,3,5,6,7,8]
<443532>(24)7-13:(0,1,2,4,5,6,8)[0,2,3,4,6,7,8]
<443352>(24)7-14:(0,1,2,3,5,7,8)[0,1,3,5,6,7,8]
<442443>(12)7-15:(0,1,2,4,6,7,8)
<435432>(24)7-16:(0,1,2,3,5,6,9)[0,1,3,4,5,6,9]
<434541>(24)7-Z17:(0,1,2,4,5,6,9)
7-Z37:(0,1,3,4,5,7,8)
<434442>(48)7-Z18:(0,1,4,5,6,7,9)[0,2,3,4,5,8,9]
7-Z38:(0,1,2,4,5,7,8)[0,1,3,4,6,7,8]
<434343>(24)7-19:(0,1,2,3,6,7,9)[0,1,2,3,6,8,9]
<433452>(24)7-20:(0,1,2,5,6,7,9)[0,2,3,4,7,8,9]
<424641>(24)7-21:(0,1,2,4,5,8,9)[0,1,3,4,5,8,9]
<424542>(12)7-22:(0,1,2,5,6,8,9) {hungar-min}
<354351>(24)7-23:(0,2,3,4,5,7,9)[0,2,4,5,6,7,9]
<353442>(24)7-24:(0,1,2,3,5,7,9)[0,2,4,6,7,8,9]
<345342>(24)7-25:(0,2,3,4,6,7,9)[0,2,3,5,6,7,9]
<344532>(24)7-26:(0,1,3,4,5,7,9)[0,2,4,5,6,8,9]
<344451>(24)7-27:(0,1,2,4,5,7,9)[0,2,4,5,7,8,9]
<344433>(24)7-28:(0,1,3,5,6,7,9)[0,2,3,4,6,8,9]
<344352>(24)7-29:(0,1,2,4,6,7,9)[0,2,3,5,7,8,9]
<343542>(24)7-30:(0,1,2,4,6,8,9)[0,1,3,5,7,8,9]
<336333>(24)7-31:(0,1,3,4,6,7,9)[0,2,3,5,6,8,9]
<335442>(24)7-32:(0,1,3,4,6,8,9) {harm-min} [0,1,3,5,6,8,9]
<262623>(12)7-33:(0,1,2,4,6,8,A)
<254442>(12)7-34:(0,1,3,4,6,8,A)
<254361>(12)7-35:(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:(0,1,2,3,4,5)
<443211>(24)6-2:(0,1,2,3,4,6)[0,2,3,4,5,6]
<433221>(48)6-Z3:(0,1,2,3,5,6)[0,1,3,4,5,6]
6-Z36:(0,1,2,3,4,7)[0,3,4,5,6,7]
<432321>(24)6-Z4:(0,1,2,4,5,6)
6-Z37:(0,1,2,3,4,8)
<422232>(24)6-5:(0,1,2,3,6,7)[0,1,4,5,6,7]
<421242>(24)6-Z6:(0,1,2,5,6,7)
6-Z38:(0,1,2,3,7,8)
<420243>(6)6-7:(0,1,2,6,7,8)
<343230>(12)6-8:(0,2,3,4,5,7)
<342231>(24)6-9:(0,1,2,3,5,7)[0,2,4,5,6,7]
<333321>(48)6-Z10:(0,1,3,4,5,7)[0,2,3,4,6,7]
6-Z39:(0,2,3,4,5,8)[0,3,4,5,6,8]
<333231>(48)6-Z11:(0,1,2,4,5,7)[0,2,3,5,6,7]
6-Z40:(0,1,2,3,5,8)[0,3,5,6,7,8]
<332232>(48)6-Z12:(0,1,2,4,6,7)[0,1,3,5,6,7]
6-Z41:(0,1,2,3,6,8)[0,2,5,6,7,8]
<324222>(24)6-Z13:(0,1,3,4,6,7)
6-Z42:(0,1,2,3,6,9)
<323430>(24)6-14:(0,1,3,4,5,8)[0,3,4,5,7,8]
<323421>(24)6-15:(0,1,2,4,5,8)[0,3,4,6,7,8]
<322431>(24)6-16:(0,1,4,5,6,8)[0,2,3,4,7,8]
<322332>(48)6-Z17:(0,1,2,4,7,8)[0,1,4,6,7,8]
6-Z43:(0,1,2,5,6,8)[0,2,3,6,7,8]
intervalForteprimeinverted
vectorcount code formform
<322242>(24)6-18:(0,1,2,5,7,8)[0,1,3,6,7,8]
<313431>(48)6-Z19:(0,1,3,4,7,8)[0,1,4,5,7,8]
6-Z44:(0,1,2,5,6,9)[0,1,4,5,6,9]
<303630>(4)6-20:(0,1,4,5,8,9)
<242412>(24)6-21:(0,2,3,4,6,8)[0,2,4,5,6,8]
<241422>(24)6-22:(0,1,2,4,6,8)[0,2,4,6,7,8]
<234222>(24)6-Z23:(0,2,3,5,6,8)
6-Z45:(0,2,3,4,6,9)
<233331>(48)6-Z24:(0,1,3,4,6,8)[0,2,4,5,7,8]
6-Z46:(0,1,2,4,6,9)[0,2,4,5,6,9]
<233241>(48)6-Z25:(0,1,3,5,6,8)[0,2,3,5,7,8]
6-Z47:(0,1,2,4,7,9)[0,2,3,4,7,9]
<232341>(24)6-Z26:(0,1,3,5,7,8)
6-Z48:(0,1,2,5,7,9)
<225222>(24)6-27:(0,1,3,4,6,9)[0,2,3,5,6,9]
<224322>(24)6-Z28:(0,1,3,5,6,9)
6-Z49:(0,1,3,4,7,9)
<224232>(24)6-Z29:(0,2,3,6,7,9)
6-Z50:(0,1,4,6,7,9)
<224223>(12)6-30:(0,1,3,6,7,9)[0,2,3,6,8,9]
<223431>(24)6-31:(0,1,4,5,7,9)[0,2,4,5,8,9]
<143250>(12)6-32:(0,2,4,5,7,9) {min11}
<143241>(24)6-33:(0,2,3,5,7,9)[0,2,4,6,7,9]{dom11}
<142422>(24)6-34:(0,1,3,5,7,9)[0,2,4,6,8,9]
<060603>(2)6-35:(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)