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and reversal. In this correspondence, a one in a binary sequence corresponds to a pitch that is present in a pitch class set, and a zero in a binary sequence corresponds to a pitch that is absent. The rotation of binary sequences corresponds to transposition of chords, and the reversal of binary
115:), each pitch class may be denoted by an integer in the range from 0 to 11 (inclusive), and a pitch class set may be denoted by a set of these integers. The prime form of a pitch class set is the most compact (i.e., leftwards packed or smallest in
196:, such as C major; 0, 2, 4, 5, 7, 9, and 11; is 11, 0, 2, 4, 5, 7, and 9; while its prime form is 0, 1, 3, 5, 6, 8, and 10; and its Forte number is 7-35, indicating that it is the thirty-fifth of the seven-member pitch class sets.
291:. "The 'Forte number' for a set class is composed of two digits separated by a hyphen. The first integer specifies the number of different pitch classes in the set class, the second the position of the set class on Forte's list."
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69:). The first number indicates the number of pitch classes in the pitch class set and the second number indicates the set's sequence in Forte's ordering of all pitch class sets containing that number of pitches.
91:
80:
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sequences corresponds to inversion of chords. The most compact form of a pitch class set is the lexicographically maximal sequence within the corresponding equivalence class of sequences.
312:. A Forte number, "consists of two numbers separated by a hyphen....The first number is the cardinality of the set form...and the second number refers to the ordinal position..."
192:, with pitch classes 0, 1, and 6, is given Forte number 3-5, indicating that it is the fifth in Forte's ordering of pitch class sets with three pitches. The normal form of the
188:
The major and minor chords are both given Forte number 3-11, indicating that it is the eleventh in Forte's ordering of pitch class sets with three pitches. In contrast, the
203:. Those that have different Forte numbers have different interval vectors with the exception of z-related sets (for example 6-Z44 and 6-Z19).
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213:
There are two prevailing methods of computing prime form. The first was described by Forte, and the second was introduced in John Rahn's
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contains the pitch classes 7, 0, and 4. The normal form would then be 0, 4, and 7. Its (transposed) inversion, which happens to be the
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had earlier (1960–1967) produced a numbered listing of pitch class sets, or "chords", as Carter referred to them, for his own use.
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Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form
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221:. For example, the Forte prime for 6-31 is {0,1,3,5,8,9} whereas the Rahn algorithm chooses {0,1,4,5,7,9}.
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Abstract
Musical Intervals: Group Theory for Composition and Analysis
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Sets of pitches which share the same Forte number have identical
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142:, contains the pitch classes 0, 3, and 7; and is the prime form.
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tuning system (or in any other system of tuning that splits the
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104:
36:
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367:"All About Set Theory: What is a Forte Number?"
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228:, the Forte numbers correspond to the binary
127:. The normal form of a set is that which is
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131:so as to be most compact. For example, a
281:Ear Training for Twentieth-century Music
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240:of length 12 under the operations of
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16:Classification of pitch class sets
14:
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219:Introduction to Post-Tonal Theory
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378:SetFinder: Prime Form Calculator
217:and used in Joseph N. Straus's
605:Structure implies multiplicity
589:Generic and specific intervals
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315:
294:
279:Friedmann, Michael L. (1990).
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389:The Table of Pitch Class Sets
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76:Major and minor chords on C
53:of three or more members in
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326:The Music of Elliott Carter
254:
10:
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568:Cardinality equals variety
551:
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447:
341:Carter, Elliott (2002).
330:Cornell University Press
452:All-interval tetrachord
232:of length 12: that is,
149:C major diatonic scale
457:All-trichord hexachord
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162:
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575:(Deep scale property)
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22:
600:Rothenberg propriety
584:Generated collection
507:Pitch-interval class
591:(Myhill's property)
524:Similarity relation
300:Tsao, Ming (2007).
261:List of set classes
234:equivalence classes
224:In the language of
215:Basic Atonal Theory
123:of a set or of its
117:lexicographic order
626:Musical set theory
441:Musical set theory
242:cyclic permutation
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101:
29:musical set theory
25:
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400:PC Set Calculator
393:SolomonsMusic.net
382:ComposerTools.com
190:Viennese trichord
55:The Structure of
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595:Maximal evenness
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345:, "Appendix 1".
343:The Harmony Book
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238:binary sequences
201:interval vectors
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133:second inversion
119:) of either the
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579:Diatonic scale
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332:, 1998. 324ff.
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371:JayTomlin.com
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351:9780825845949
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324:(1983/1998).
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322:Schiff, David
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310:9781430308355
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289:9780300045376
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467:Forte number
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170:Locrian mode
111:into twelve
102:
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33:Forte number
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573:Common tone
497:Pitch class
492:Permutation
207:Calculation
140:minor chord
136:major chord
121:normal form
48:pitch class
40:Allen Forte
555:set theory
534:Z-relation
462:Complement
267:References
129:transposed
44:prime form
230:bracelets
125:inversion
113:semitones
620:Category
563:Bisector
553:Diatonic
472:Identity
304:, p.98.
283:, p.46.
255:See also
46:of each
103:In the
61:(1973,
37:numbers
404:MtA.Ca
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308:
287:
109:octave
105:12-TET
65:
57:Atonal
172:on C
59:Music
517:List
347:ISBN
306:ISBN
285:ISBN
178:Play
155:Play
93:Play
82:Play
63:ISBN
31:, a
512:Set
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236:of
51:set
27:In
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