pitch

Examples of pitch in the following topics:

• Symmetry and Centricity

  • When a particular pitch-class is regularly the lowest, highest, loudest, or longest in a passage, that pitch-class becomes something like a tonic.
  • Pitch symmetry always implies an axis of symmetry.
  • Pitch-class symmetry is very similar to pitch symmetry, but understood in pitch-class space.
  • Mapping this on the pitch-class circle shows the passage's pitch-class symmetry.
  • Unlike pitch space, pitch-class axes are always located at two different points in the pitch-class circle.

• Pitch

  • That is, "high" pitch means very rapid oscillation, and "low" pitch corresponds to slower oscillation.
  • Attitudinal: high declining pitch signals more excitement than does low declining pitch, as in "Good ↗morn↘ing" versus "Good morn↘ing. "
  • Avoid monotony, speaking with one pitch tone or little variety in pitch.
  • The higher pitch sounds move up the treble clef and the lower pitch sounds move down the bass clef.
  • Define pitch and describe how pitch changes can change the meaning of sentences

• Interval (Class)

  • Pitch intervals are the distance between pitches as measured in half steps.
  • Pitch-class intervals are the distance between pitch classes as measured in semitones.
  • The ordered pitch interval from G4 to B-flat5 is +15, but the ordered pitch interval from A-sharp5 to G4 is -15.
  • Unordered intervals represent the shortest distance between two pitches or pitch classes, without any reference to the order they are in.
  • The unordered pitch interval from G4 to A-sharp5 is 15.

• Pitches

  • On the illustration below, the pitch-class letter names are written on the keyboard.
  • When specifying a particular pitch precisely, we also need to know theregister.
  • In fact, if all you have is C-sharp or B-flat, you do not have a pitch, you have a pitch-class.
  • A pitch-class plus a register together designate a specific pitch.
  • So an ascending scale from middle C contains the following pitch designations:

• Pitch (Class)

  • Pitches are discrete tones with individual frequencies.
  • The concept of pitch, then, does not imply octave equivalence.
  • C4 is a pitch, and it is not the same pitch as C3.
  • Pitch classes are pitches under octave equivalence that are also spelled the same.
  • A4, A3, A2, etc. are all members of the pitch class A.

• Set Class and Prime Form (1)

  • A concept like pitch, for example, is very concrete, while pitch class is somewhat more abstract.
  • We can perform a pitch, but we can't really perform a pitch class.
  • Ordered pitch intervals are associated with a very specific sound (e.g., +15); unordered pitch-class intervals (e.g., interval class 1) are less vivid or real.
  • A basic concept in pitch-class set theory is that these levels of concreteness and abstractness encompass not only pitch and interval, but groups of pitch classes as well.
  • These groups of pitch classes are called pitch-class sets.

• Analyzing Atonal Music

  • Pitch transposition involves moving every pitch in a collection up or down by a specified interval.
  • Pitch-class transposition does the same thing.
  • For pitch-class transpositions, use ordered pitch-class intervals (numbers 0–11).
  • Pitch inversion occurs when all pitches are inverted, or flipped, around an axis of symmetry in pitch space (in other words, the axis of symmetry is a pitch).
  • Pitch-class inversion occurs when all pitch classes of a collection are inverted, or flipped, around an axis of symmetry in pitch-class space (in other words, the axis of symmetry is a pitch class).

• Normal Order

  • Normal order is the most compressed way to write a given collection of pitch classes.
  • Write as a collection of pitch classes (eliminating duplicates) in ascending order and within a single octave.
  • Write as a collection of pitch classes (eliminating duplicates) in ascending order and within a single octave. {8,9,3}
  • Find the largest ordered pitch-class interval between adjacent pitch classes.
  • In these cases, write the ordering implied by each tie and calculate the interval from the first to the penultimate pitch class.

• Transposition

  • Transposition is an operation—something that is done to a pitch, pitch class, or collection of these things—or alternatively a measurement—representing the distance between things.
  • We represent it as Tn, where n represents the ordered pitch-class interval between the two things.
  • Given the collection of pitch classes in m. 1 above and transposition by T4:
  • The result is the pitch classes in m. 18.
  • This is how I arrived at the T4 arrow label in the musical example above, by "subtracting" the pitch class integers of m. 1 from the pitch-class integers in m. 18.

• Inversion

  • You need to be able to (1) invert a collection of pitches and (2) determine the inversional relationship between two collections of pitches.
  • Inverting something is a two-step process, performed in this order: (1) Reflect the pitch classes in an object around the 0-6 axis of symmetry, and then (2) transpose it.
  • Fortunately, there is a much quicker way to invert a pitch or collection of pitches!
  • Given any collection of pitch classes and a TnI, simply subtract the the pitch classes from n:
  • Conversely, to determine the TnI that relates two collections of pitch classes, find a common value to which they all sum.