# Glossary of atonal musical terms

*this glossary is far from complete, in the very early stages of being built*

**collection** – The general term for treating multiple pitch classes as a single entity. Sets, set classes, scales, simultaneities, chords, and intervals are all specific kinds of collections.

**interval class** – The number of semitones between two *pitch classes*, counted as the shortest distance between them on a clock face. For instance, C and E make an interval class of 4. This is always the case, no matter which *pitch* is higher or lower, because interval class is concerned only with *pitch classes*. Interval classes are labeled **ic1**, **ic2**, . . . **ic6**. (There are none smaller than **ic1** or larger than **ic6**.)

**interval vector** – The interval vector of a set class describes all of the interval classes present in a set class. There are six interval classes (1–6). The interval vector gives the number of each of those intervals in order from 1 to 6, within angle brackets. An interval vector of **<101102>** means that the set has one ic1 (semitone/major seventh), no ic2s, one ic3 (minor third/major sixth), one ic4 (major third/minor sixth), no ic5s (perfect fourths), and two ic6s (tritones).

**ordered pitch interval** – The number of semitones from one pitch (not pitch class) to the next. Ascending intervals are denoted by positive numbers, descending intervals by negative numbers. Examples: B4–G5 would have an ordered pitch interval of 8 (eight ascending semitones). B3–G5 would be 20. B4–G4 would be –4.

**ordered pitch-class interval** – The number of *ascending* semitones from one pitch-class to another. G–B is four semitones, for an ordered PC interval of **4**. B–G is eight ascending semitones, for an ordered PC interval of **8**.

The ordered pitch-class interval is also the modulo12 version of the ordered pitch interval. For example, B4–G4 is –4 semitones (4 semitones down). mod12(–4) = 8. C3–D4 is 14 semitones. mod12(14) = 2.

**pitch** – A pitch class in a specific register, such as C4 (middle C).

**pitch class** – One of the twelve steps on the chromatic scale, summarized by a note name (C, D-sharp, B-flat, etc.) or a number 0–11 (C = 0, C-sharp = 1, . . . B = 11). In atonal music, spelling rarely matters except to make performance easier, so enharmonically equivalent pitch classes are considered identical (C = B-sharp = D-double-flat = 0).

**pitch-class set** – An *unordered* collection of pitch classes, usually grouped into curly brackets: {C, E, G}, {D, E-flat, G}, or {4, 5, 9}.

**pitch-class set class** or simply **set class** – A category of pitch-class sets that are all related by transposition or inversion. For example, the 12 major triads are all related by transposition. While each major triad is a different pitch-class set, they all belong to the same set class (the same category of sets). Note that minor triads are upside-down major triads (minor third–major third, instead of major third–minor third). Thus since major and minor triads can be related by inversion, they belong to the same set class. Set classes are typically named according to their *prime form* (see *prime form* in this glossary).

**prime form** – Since set classes come in as many as 24 different forms (12 transpositions times 2 inversions), one of those forms is chosen as its name or referential form, for ease of categorization. That form is the prime form. The prime form is, in a nutshell, the inversion and rotation of the set class that keeps the pitch classes most tightly packed on and above C (0).

For help finding the prime form of a set, Jay Tomlin’s set theory calculator can be helpful. The following video demonstrates how to use it.

SetTheoryCalculator from Kris Shaffer on Vimeo.

**simultaneity** – Any collection of more than one pitch (class) that sound at the same time. This includes dyads/intervals, chords, clusters, and “salami slices” of contrapuntal textures.

**unordered pitch-class interval** – A regular *simple* chromatic interval: the number of half steps between two pitches. Compound intervals (larger than an octave) are typically reduced to their corresponding simple interval. They are labeled with a lower-case **i**: **i4** is a major third, for example.