For example, to label the arrow in Example 1, an analyst would “subtract” the pitch class integers of m. 1 from the pitch-class integers in m. 18. This is a list of pitch-class sets by Forte number. Notation of Notes, Clefs, and Ledger Lines, Half- and Whole-steps, Accidentals, and The Black Keys of the Piano, Major Scales, Scale Degrees, and Key Signatures, Minor Scales, Scale Degrees, and Key Signatures, Introduction to Diatonic Modes and the Chromatic "Scale", The Basics of Sight-singing and Dictation, Roman Numerals and SATB Chord Construction, III. • The PC Set for a C minor triad: [0, 3, 7] • The PC Set for a G major triad: [7, 11, 2] • In Pitch Class sets, octave doublings and displacements are ignored: 2.Duplicate the first pitch class at the end. [2, 4, 7] is inverted to become [1, 4, 6]. You can follow the links for each course to see more information including videos and example PDFs from many of the courses. Transposition is an operation—something that is done to a pitch, pitch class, or collection of these things. Every pitch that can be called "an F", say, is collected together into the pitch class that we just call "F". Inverting [2, 4, 7] in this way would yield [5, 8, 10]. This makes sense as a logical extension of the subtraction method above: if the inverted pitch y is the result of n–x, then it is also true that n = x + y. A pitch class set merely tells you how the frequencies of the notes will combine with each other within that particular chord (i.e. Inversion 1 © Megan Lavengood is licensed under a, inversion-2 © Megan Lavengood is licensed under a, Cross-addition for inversion © Megan Lavengood is licensed under a. This is always true no matter the spelling, pitch order, or musical context. This course shows you how you can combine various pitch class sets to make great sounding combinations that work well over modal situations. Any group of pitch classes can be a pitch class set. [footnote]These hybrid forms come from William Caplin (2013), Analyzing Classical Form. Occasionally you’ll have a tie in step 3. Mod-12 is short for modulo 12, where numbers wrap around upon reaching 12. n values for T n invariance:: n values for T n I invariance:: Subsets: Supersets: Pitches are discrete tones with individual frequencies. Another way to visualize this is on the clock face.If you have two sets that are 1) both in normal order and 2) related by inversion, the notes within each set will map onto one another in reverse order, as shown in Example 3 below. T4 [11, 2, 4] = [3, 6, 8]. if it is dissonant or consonant with itself, or somewhere in between). C4 is a pitch, and it is not the same pitch as C3. [/footnote], Structure of Individual Sections (Simple vs. Any group of pitch classes can be a pitch class set. The alternative notation for those chords are listed in the footnotes. n values for T n invariance:: n values for T n I invariance:: Subsets: Supersets: To invert a set by I8 follow this process, in this order: You can calculate the new set created by In by subtracting all the pitch classes of your first set from n. Any two pitches related by inversion can be added together to form the index number. All pitch-class sets that are transpositionally and inversionally related belong to the same set class, and they are represented by the same prime form. Given the collection of pitch classes in m. 1 above and transposition by T4: The result is the pitch classes in m. 18. Arithmetic in mod-12 is most familiar through clock time: after 12-o-clock, the time becomes 1-o-clock again. [3, 6, 8] and [11, 2, 4] are related by T4. Compound), Details about Refrains, Episodes, and Auxiliary Sections in Rondo Form, Authentic cadences (they sound conclusive! To transpose a set by Tn, add n to every integer in that set (mod 12). Technically, it is a list of pitch classes, but this wiki does not use pitch-class numbers. Transpose it so that the first pitch class is 0. The complement of 6 is 6: 6+6=12. Sets are listed next to their complements. Ordering the notes of a chord so that it is entirely stacked in thirds. There are two slightly different methods of obtaining a normal form.
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