They are notated as follows:
- PI(a,b) = b - a
For example C) is 3 semitones:
- PI(0,3) = 3 - 0
While C4 to D♯5 ) is 15 semitones:
- PI(0,15) = 15 - 0
However, under #Pitch-interval class may be used.
The PIC is notated and related to the PI thus:
- PIC(0,15) = PI(0,15) mod 12 = (15 - 0) mod 12 = 15 mod 12 = 3
the other way.
One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, similar to the interval of tonal theory. This may be defined as:
The interval between pitch classes may be measured with ordered and unordered pitch class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. Thus the ordered pitch class interval, i<x, y>, may be defined as:
- (in modular 12 arithmetic)
Ascending intervals are indicated by a positive value, and descending intervals by a negative one.