Music Theory: Pitch Class Intervals

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Questions and Answers

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?

  • 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?

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?

<p>Use the clock; convert first and last number to 0, and test in both directions. THESE ANSWERS ALWAYS BEGIN WITH ZERO.</p> Signup and view all the answers

What does transpositional equivalence refer to?

<p>To find out if the two sets are related by some level of Tx, put them in normal order first. Then, compare the adjacency interval series.</p> Signup and view all the answers

What is inversional equivalence?

<p>To find out if the two sets are related in some way by TxI, put them in normal order first. Then, compare adjacency interval series.</p> Signup and view all the answers

What is a transposing set?

<p>To do this, add the Tx level to the original set.</p> Signup and view all the answers

How do you invert sets?

<p>To do this, simply subtract the set from 12, and then reverse the order.</p> Signup and view all the answers

What is the process for inversion and transposition?

<p>Invert first, then transpose.</p> Signup and view all the answers

What is an interval class vector?

<p>Find the UNORDERED pitch-class intervals between all of the notes in a set, and place in a vector.</p> Signup and view all the answers

What are invariant tones under transposition?

<p>Displayed in the interval class vector, it shows the number of common tones at certain levels of transposition.</p> Signup and view all the answers

What are common tones under inversion?

<p>Use summation square to find the index vector.</p> Signup and view all the answers

What does abstract complement refer to?

<p>Put the complement into prime form.</p> Signup and view all the answers

What are abstract subsets?

<p>To find this, put the subset into prime form.</p> Signup and view all the answers

What is transpositional symmetry?

<p>To find this, use the interval class vector.</p> Signup and view all the answers

What is inversional symmetry?

<p>Use the index vector.</p> Signup and view all the answers

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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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