I guess I should start out by providing a very brief historical context to the pitch class system of numbering
intervals. After the Romantic, Impressionistic and Post-Impressionistic styles, the complete dissolution of tonality was
eminent. With extended chord structures, harmonic chromaticism, denial of chord functions and extended phrases of
chromaticism being brought to the forefront of composition by people such as Wagner, Debussy, Ravel and Scriabin
to a name just a few, the beginning of a breakaway from the dominant-tonic system of analysis was in sight.
Using the pitch class system, every tone receives a number rather than a letter name. There are two ways to number
pitches, fixed-zero numbering and movable zero numbering. In the case of the former, the note "C" is always referred
to as "0". In movable zero numbering, any pitch may be given the number "0". Once numbered, all tones with that
name will be referred to by the number assigned to them, regardless of what octave the tone exists in. For example, if
middle "C" is represented by the number zero, then the "C" above middle "C" is also represented by the number zero,
as is the "C" above that and the "C" 5 octaves below that, etc., etc...
intervals. After the Romantic, Impressionistic and Post-Impressionistic styles, the complete dissolution of tonality was
eminent. With extended chord structures, harmonic chromaticism, denial of chord functions and extended phrases of
chromaticism being brought to the forefront of composition by people such as Wagner, Debussy, Ravel and Scriabin
to a name just a few, the beginning of a breakaway from the dominant-tonic system of analysis was in sight.
Using the pitch class system, every tone receives a number rather than a letter name. There are two ways to number
pitches, fixed-zero numbering and movable zero numbering. In the case of the former, the note "C" is always referred
to as "0". In movable zero numbering, any pitch may be given the number "0". Once numbered, all tones with that
name will be referred to by the number assigned to them, regardless of what octave the tone exists in. For example, if
middle "C" is represented by the number zero, then the "C" above middle "C" is also represented by the number zero,
as is the "C" above that and the "C" 5 octaves below that, etc., etc...
To be continued......