Scales may also be identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale. The most common binary numbering scheme defines lower pitches to have lower numeric value (as opposed to low pitches having a high numeric value). Thus a single pitch class n in the pitch class set is represented by 2^n. This maps the entire power set of all pitch class sets in 12-TET to the numbers 0 to 4095. The binary digits read as ascending pitches from right to left, which some find discombobulating because they are used to low to high reading left to right, as on a piano keyboard. In this scheme, the major scale is 101010110101 = 2741. This binary representation permits easy calculation of interval vectors and common tones, using logical binary operators. It also provides a perfect index for every possible combination of tones, as every scale has its own number.Daniel Starr. ‘Sets, Invariance, and Partitions’. In: Journal of Music Theory 22.1 (1978), pp. 1–42Alexander Brinkman. Pascal Programming for Music Research. University of Chicago Press, 1990.
Scales may also be identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale The most common binary numbering scheme defines lower pitches to have lower numeric value (as opposed to low pitches having a high numeric value) Thus a single pitch class n in the pitch class set is represented by 2^n This maps the entire power set of all pitch class sets in 12-TET to the numbers 0 to 4095 The binary digits read as ascending pitches from right to left which some find discombobulating because they are used to low to high reading left to right as on a piano keyboard In this scheme the major scale is 101010110101 = 2741 This binary representation permits easy calculation of interval vectors and common tones using logical binary operators It also provides a perfect index for every possible combination of tones as every scale has its own numberDaniel Starr ‘Sets Invariance and Partitions’ In Journal of Music Theory 221 (1978) pp 1–42Alexander Brinkman Pascal Programming for Music Research University of Chicago Press 1990