This means that every possible combination of tones in the 12-tone set can be represented by a number between. The fun thing about binary power sets is that we can produce every possible combination, by merely invoking the integers from 0 (no tones) to 4095 (all 12 tones). Using a word of 12 bits, the power set (2^12) is equal to 4096. The number of sets in a power set of size n is (2^n). The total number of possible combinations of on and off bits is called the 'power set'. When represented as bits it reads from right to left - the lowest bit is the root, and each bit going from right to left ascends by one semitone. We can assign one bit to each degree of the chromatic scale, and use the power of binary arithmetic and logic to do some pretty awesome analysis with them. What we have in the 12-tone system is a binary 'word' made of 12 bits. Instead, we should regard a scale as being a set of 12 possibilities, and each one is either on or off. While this view of the scale is useful for understanding diatonic melodies, it's not a convenient paradigm for analysis.

The scale was essentially a stack of intervals piled up, that happened to add up to an octave. When I began piano lessons as a child, I learned that a scale was made up of whole- and half-steps. Other tuning systems have the notion of scales, but they're not being considered in this study. Equal temperament asserts that the perceptual (or functional) relationship between two pitches is the same as the relationship between two other pitches with the same chromatic interval distance. So it follows that if you're playing a scale in one octave, if you continue the pattern into the next octave you will play pitches with the same name.ġ2 tone equal temperament We're using the 12 tones of an equally-tempered tuning system, as you'd find on a piano. Octave Equivalence We assume that for the purpose of defining a scale, a pitch is functionally equivalent to another pitch separated by an octave. This exploration of scales is based in a musical universe founded on two assumptions: Where we discuss every possible combination of notes Assumptions

Chromatic music definition