Copyright © 2006, 2007 by Ewen Leung Instruction Manual of Prime 2006

What is Prime 2006? An Excel program to find the Normal and Prime Forms of Pitch Class Sets

What are Pitch Classes ? Pitches belong to the same pitch class when they are, for example: Octave Apart Enharmonic Equivalent # bb or The above 5 pitches all belong to Pitch Class C

Pitch Classes There are only 12 pitch classes in a system and are also represented by numbers like the clock Pitch Class NumberPitch Class 012C 113C # (D b ) 214D 315D # (E b ) 416E 517F 618F # (G b ) 719G 820G # (A b ) 921A 1022A # (B b ) 1123B

What are Pitch Class Sets ? A Pitch Class Set is a list of pitch classes. It can have 2 to all 12 pitch classes, for example: As shown, Pitch Class Sets are usually represented by the pitch class numbers enclosed by square brackets [0, 7][0, 2, 5,10] # b

This program…… This program considers only the Pitch Class Sets containing 3 to 9 pitch classes ChordNo. of Pitch Class Tri3 Tetra4 Penta5 Hexa6 Septa7 Octa8 Nona9

What is the Normal Form of a Pitch Class Set ? Normal Form is defined as the form of a pitch class set with class numbers arranged in a way that the intervals between classes are the shortest Consider the Pitch Class Set [0, 2, 5, 10] It can be simplified to the one on the right [0, 2, 5,10] # b [0, 2, 5,10] #

Normal Form For the Pitch Class Set [0, 2, 5, 10], the interval between A # and C is 10 the interval between F and C is 5 the interval between D and C is 2 # # – 0 = 5 # – 0 = 2 10 – 0 = 10 C A#A# C F C D

Normal Form The Pitch Class Set [0, 2, 5, 10] is not Normal Because there exists another form with shorter intervals The other form is [10, 0, 2, 5] # [0, 2, 5,10] # [10, 0, 2, 5]

Normal Form For [10, 0, 2, 5], the interval between F and A # is 7 the interval between D and A # is 4 the interval between C and A # is 2 5 – 10 -> 17 – 10 = 7 A#A# # F 2 – 10 -> = 4 A#A# D # – 10 -> 12 – 10 = 2 A#A# C #

Normal Form The outermost interval of [10, 0, 2, 5] is shorter than that of [0, 2, 5, 10]. If there is NO other form with the outermost interval shorter than 7, then [10, 0, 2, 5] is the Normal Form. If there is another form with the outermost interval equal to 7, then the next inward interval are compared. Intervals are compared from the outermost pairs toward the inside until the shortest interval is found. Interval[0, 2, 5, 10][10, 0, 2, 5] Outermost107 Middle54 Innermost22

Please note that………. To determine the Normal form, the inverse form of the given pitch class set are also regarded as another form of the pitch class set and needed to be compared as well.inverse form

Inverse Form Inversion [0, 10, 7, 2] Flip 12 (C) 10 (A # ) 0 (C) 2 (D) 5 (F) 10 (A # ) 2 (D) 7 (G) = = = = = = 10 [0, 2, 5,10]

What is the Prime Form of a Pitch Class Set ? Prime Form is defined as the Normal Form transposed to 0. Thus, for [10, 0, 2, 5] to be transposed to 0, it becomes [0, 2, 4, 7] The Prime Form [0, 2, 4, 7] # The Normal Form [10, 0, 2, 5] # Given Pitch Class Set [0, 2, 5,10]

Don’t panic, this Program can do all these for you automatically.

How to do it ? 2. Enter the pitch classes in one of the yellow box bars according to the no. of class. 1. Select the type of accidental: 1 for # and 2 for b.

The program will……. 1. Show the corresponding Pitch Names of the given Pitch Class Set 2. Show the Normal Form of the given Pitch Class Set 3. Show the Prime Form of the given Pitch Class Set

Best Wishes! 祝生活愉快  hank You for Using Prime 2006 多謝支持多謝支持