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Questions and Answers
What is an ordered pitch class interval?
What is an ordered pitch class interval?
- Add the transposition level to the original set.
- Put in order on staff looking for the smallest distance between the first and last notes.
- Use the clock to find the shortest distance between notes.
- Use the clock, go ONLY clockwise, and do in the order in which the pitches are given. (correct)
What is an unordered pitch class interval?
What is an unordered pitch class interval?
- Use the clock, go ONLY clockwise, and do in the order in which the pitches are given.
- Use the clock to find the shortest distance between notes. (correct)
- To do this, add the Tx level to the original set.
- Put in order on staff looking for the smallest distance between the first and last notes.
What is normal order?
What is normal order?
Put in order on staff or use clock. Look for the smallest distance between the first and last notes. If that's a tie, then the smallest distance between first and second to last notes, etc.
What is prime form?
What is prime form?
What does transpositional equivalence refer to?
What does transpositional equivalence refer to?
What is inversional equivalence?
What is inversional equivalence?
What is a transposing set?
What is a transposing set?
How do you invert sets?
How do you invert sets?
What is the process for inversion and transposition?
What is the process for inversion and transposition?
What is an interval class vector?
What is an interval class vector?
What are invariant tones under transposition?
What are invariant tones under transposition?
What are common tones under inversion?
What are common tones under inversion?
What does abstract complement refer to?
What does abstract complement refer to?
What are abstract subsets?
What are abstract subsets?
What is transpositional symmetry?
What is transpositional symmetry?
What is inversional symmetry?
What is inversional symmetry?
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Study Notes
Ordered Pitch Class Interval
- Clockwise movement is used to determine the sequence of pitches.
- Pitches are arranged in the order they are presented without changing direction.
Unordered Pitch Class Interval
- Also referred to as "interval class."
- Determine the shortest distance between notes by traversing the clock.
Normal Order
- Arrange notes on staff or using the clock.
- Focus on the smallest interval between the first and last notes, breaking ties by examining subsequent pairs in sequence.
Prime Form
- Utilize the clock, converting the initial and last numbers to zero.
- Test the set in both directions; all results will start with zero.
Transpositional Equivalence
- Check if two sets are related via transposition by arranging in normal order.
- Compare adjacency interval series, which represents the distances between adjacent notes.
Inversional Equivalence
- Assess if two sets are related by inversion, starting with normal order.
- Compare adjacency interval series; if one is the reverse of the other, they are inversionally equivalent.
Transposing Set
- Perform transposition by adding a transposition level (Tx) to the original set.
- Example: T4 of (0,1,4) results in (4,5,8).
Inverting Sets
- Achieve inversion by subtracting each note in the set from 12 and reversing the order.
- For example, T0I of [0,1,4] results in [8,E,0] after calculations.
Inversion and Transposition
- To process T5I of [2,3,8]: Invert first by calculating 12 minus each element, then reverse the order before transposing.
Interval Class Vector
- Construct by identifying unordered pitch-class intervals across the set.
- For (0,1,4): from 0 to 1, the interval is 1; from 0 to 4, it’s 4; from 1 to 4, it’s 3.
Invariant Tones under Transposition
- Identified through the interval class vector, applying defined pairings based on transpositions.
- Different transpositions can share varying common tones, quantified in totals shown in the vector.
Common Tones under Inversion
- Utilize the Summation Square to derive the Index Vector, beginning at T0I for assessments.
Abstract Complement / Complementarity
- Convert the complement of a set to its prime form for analysis.
Abstract Subsets / Subsets
- To identify subsets, translate the subset into prime form.
Transpositional Symmetry
- Use the Interval Class Vector to find numbers corresponding to the note count, indicating levels of transpositional symmetry.
Inversional Symmetry
- Examine the Index Vector for matching values to the number of notes, determining levels of inversional symmetry present.
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