Basis Vectors
All isomorphic keyboards derive their invariance from their relationship to rank-2 regular temperaments of Just Intonation.
A two-dimensional lattice is generated by two basis vectors, and so is a rank-2 regular temperament of Just Intonation. A keyboard lattice generated by two given musical intervals will be isomorphic in any rank-2 temperament that is also generated by those same two intervals. For example, an isomorphic keyboard generated by the octave and tempered perfect fifth will be isomorphic with both the syntonic and schismatic temperaments, which are both generated by those same two intervals.
Read more about this topic: Isomorphic Keyboard
Famous quotes containing the word basis:
“Adolescents, for all their self-involvement, are emerging from the self-centeredness of childhood. Their perception of other people has more depth. They are better equipped at appreciating others’ reasons for action, or the basis of others’ emotions. But this maturity functions in a piecemeal fashion. They show more understanding of their friends, but not of their teachers.”
—Terri Apter (20th century)