Glossary
Cardinality
Glossary
Set Theory
In musical set theory, cardinality just means the number of distinct pitch classes—as opposed to the number of notes—in a scale or chord. Harmonious focuses on chords and scales with cardinality three to nine.
The top examples 
have three notes and four notes, but both have cardinality of three, since the C note is duplicated. The bottom examples
have seven and eight notes, but with duplicate C note treated the same as a single C note, they both have cardinality of seven.
Cardinality values outside of three to nine are less useful or interesting harmonically for building chords and scales: cardinality zero is silence, cardinality one is just the individual notes of the chromatic scale, cardinality two is just the intervals, and cardinality ten and eleven are just the chromatic scale missing a few notes, like walking over to a piano and lying one’s forearm on most of the notes simultaneously.
See Clocks & Pitch Classes for a tutorial on pitch classes and cardinality-equivalence.
Set Theory
In musical set theory, cardinality just means the number of distinct pitch classes—as opposed to the number of notes—in a scale or chord. Harmonious focuses on chords and scales with cardinality three to nine.
The top examples have three notes and four notes, but both have cardinality of three, since the C note is duplicated. The bottom examples
have seven and eight notes, but with duplicate C note treated the same as a single C note, they both have cardinality of seven.
Cardinality values outside of three to nine are less useful or interesting harmonically for building chords and scales: cardinality zero is silence, cardinality one is just the individual notes of the chromatic scale, cardinality two is just the intervals, and cardinality ten and eleven are just the chromatic scale missing a few notes, like walking over to a piano and lying one’s forearm on most of the notes simultaneously.
See Clocks & Pitch Classes for a tutorial on pitch classes and cardinality-equivalence.