Comma-based lattices: Difference between revisions
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When plotted on the standard tonal lattice (in which the basis intervals have prime number frequency ratios up to some prime limit p) commas form a widely scattered cloud in which no obvious structure is discernible. But rebasing to a lattice in which the basis intervals are themselves of comma size has the effect of drawing a set of similar-sized commas into the region near the origin, where their interrelationships become apparent. The dual of such a '''comma-based lattice''' is a lattice of equal temperaments (ETs), which provides a means of visualising the relationships between ETs and commas. | When plotted on the standard tonal lattice (in which the basis intervals have prime number frequency ratios up to some prime limit p) commas form a widely scattered cloud in which no obvious structure is discernible. But rebasing to a lattice in which the basis intervals are themselves of comma size has the effect of drawing a set of similar-sized commas into the region near the origin, where their interrelationships become apparent. The dual of such a '''comma-based lattice''' is a lattice of equal temperaments (ETs), which provides a means of visualising the relationships between ETs and commas. | ||