WARNING: math freaks only

The calculation to ascertain the number of five note combinations (not to be confused with permutations) and, subsequently, the number of pentatonic modes per tonal center:

12!/[(12 - 5)! x 5!] = 792; 792/12 = 66; 66 x 5 = 330

792 possible five note combinations; 66 per tonal center; 330 unique five note modes

For example: Consider the seven note combinations which, coincidentally, also equal 792; one twelfth must be a unique combination containing a “C”; a combination of seven notes may be arranged in seven modes (giving a total of 462 unique seven note modes).

Remember that symmetric combinations, which occur in groupings of 2, 3, 4, 6, 8, 9 and 10 notes, must be taken into consideration to accurately calculate their respective scale numbers. For example, the second mode of c – e – g# in the “key” of G# is c – e – g#.