Suggested Learning Resources
- Pitch-class: Refers to a pitch regardless of octave (C4 and C5 are both considered
C's... In integer notation, they are both considered 0 )
- Pitch-class-sets: A collection of pitches, usually written in integer notation.
They are UNORDERED, which means the order does not matter. They are written in
curly brackets. Because order does not matter {0 2 5 7} is the same as {2 7 5 0}
. However, even though the order does not mater in { } , we try to list them in ascending
order , in a way that has the fewest gaps… (lowest number is not always first) This
is comparable to thinking of a triad in root position.
- Ordered-pitch-intervals: These are the distance between two notes measured in half
steps, using a plus or minus sign to show direction. Intervals can be larger than
12 and use a + or – to show direction (example +15 is fifteen half-steps up). (The
distance from D up to F# is +4. In integer notation, the distance from 2 up to 6
is +4.)
- Unordered-pitch-intervals: These are the distance between two notes measured in
half steps, but they do not specify direction up or down. This is often used when
naming the interval size of two pitches that occur at the same time. Can be larger
than 12.
- Ordered-pitch-class-intervals: This is the distance between two notes X and Y where
the order (X before Y) matters, but the octave does not. To find, subtract Y-X using
mod 12 arithmetic. (Example: If you have the note A followed by the note D, you would
translate the notes to the numbers 9 and 2, subtract 2-9. Using mod12, you would
change the 2 to a 14, resulting in 14-9 = 5. 5 is the ordered pitch-class-interval
between A and D. The result will always be a number between 0 and 11.
- Unordered-pitch-class-interval: This is the distance between two pitch-classes
using the shortest possible distance. Order in which the notes occur does not matter.
The resulting number will be between 0 and 6. You can find the unordered-pitch-class-interval
of notes X and Y by calculating X-Y and Y-X (using mod12) and taking the smaller
of the two numbers. (NOTE: This is a precursor to the concept of interval-classes
and interval-class-vectors, to be studied later)
https://youtu.be/Jwj7avIYzbo?t=3m28s
Objective 47.2: Distinguish between pitch-class, pitch-class-sets, ordered-pitch-intervals,
unordered-pitch-intervals, ordered-pitch-class-intervals and unordered-pitch-class-intervals