Questions and Answers
What is the pitch class represented by 0?
What is the pitch class represented by 1?
What is the pitch class represented by 2?
What is the pitch class represented by 3?
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What is the pitch class represented by 4?
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What is the pitch class represented by 5?
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What is the pitch class represented by 6?
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What is the pitch class represented by 7?
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What is the pitch class represented by 8?
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What is the pitch class represented by 9?
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What is the pitch class represented by 10?
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What is the pitch class represented by 11?
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What do you do with Mod-12 for positive numbers?
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What do you do with Mod-12 for negative numbers?
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What is a pitch class interval?
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What is an ordered pitch class interval?
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What is an unordered pitch class interval?
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What do you do with unordered pitch class intervals larger than 6?
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What is an interval class?
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What is a pitch class set?
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What is a dyad?
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What is a trichord?
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What is a tetrachord?
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What is a pentachord?
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What is a hexachord?
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What is an interval class vector?
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What is a normal order?
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How do you find the normal order of a set?
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Study Notes
Pitch-Class Set Theory Basics
- Pitch class is defined by notes sharing the same name but differing in octave.
- Each pitch class corresponds to an integer from 0 to 11.
Individual Pitch Classes
- 0 corresponds to C.
- 1 corresponds to C# (or Db).
- 2 corresponds to D.
- 3 corresponds to D# (or Eb).
- 4 corresponds to E.
- 5 corresponds to F.
- 6 corresponds to F# (or Gb).
- 7 corresponds to G.
- 8 corresponds to G# (or Ab).
- 9 corresponds to A.
- 10 corresponds to A# (or Bb).
- 11 corresponds to B.
Modulus Operations
- Mod-12 for positive numbers requires subtracting 12.
- Mod-12 for negative numbers requires adding 12 to return to a positive pitch class.
Pitch Class Intervals
- Pitch class interval indicates the exact number of half steps between two notes.
- Ordered pitch class interval is assessed by moving in an ascending (clockwise) direction.
- Unordered pitch class interval (or interval class) measures the shortest distance between two pitch classes; only six possible intervals exist.
- Intervals larger than six must be simplified to their complement.
Collections of Pitch Classes
- A pitch class set is an unordered collection of distinct pitch classes.
- Specific terms define the number of notes in a set:
- Dyad for a 2-note set.
- Trichord for a 3-note set.
- Tetrachord for a 4-note set.
- Pentachord for a 5-note set.
- Hexachord for a 6-note set.
Interval Class Vector and Normal Order
- The interval class vector is a tally of the interval classes present in a set.
- Normal order arranges pitch classes in ascending order (mod-12) to achieve the most compact representation.
- To determine the normal order:
- Exclude the largest interval.
- List remaining pitch classes in ascending order.
- For ties, list potential normal orders and select the one with the smallest ordered intervals.
Additional Pitch Classes
- Db corresponds to 1.
- Eb corresponds to 3.
- Gb corresponds to 6.
- Ab corresponds to 8.
- Bb corresponds to 10.
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Description
This quiz covers the fundamentals of pitch-class set theory, including the definition of pitch classes, their integer representations, and how to calculate pitch class intervals using modulus operations. Test your understanding of the relationships between notes and their intervals.
