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Fokker periodicity blocks are a concept in tuning theory used to mathematically relate musical intervals in just intonation to those in equal tuning .. tuning theory. tuning theory. musical intervals. interval ( music ). just intonation. just intonation. equal tuning. equal temperament. They are named after Adriaan Daniel Fokker .. Adriaan Daniel Fokker. Adriaan Fokker. These are included as the primary subset of what Erv Wilson refers to as constant structures , where `` each interval occurs always subtended by the same number of steps '' .. Erv Wilson. Erv Wilson. The basic idea of Fokker 's periodicity blocks is to represent just ratios as points on a lattice , and to find vectors in the lattice which represent very small intervals , known as commas .. lattice. lattice ( music ). vectors. vector space. commas. comma ( music ). Treating pitches separated by a comma as equivalent `` folds '' the lattice , effectively reducing its dimension by one ; mathematically , this corresponds to finding the quotient group of the original lattice by the sublattice generated by the commas .. lattice. lattice ( music ). commas. comma ( music ). quotient group. quotient group. For an n-dimensional lattice , identifying n linearly independent commas reduces the dimension of the lattice to zero , meaning that the number of pitches in the lattice is finite ; mathematically , its quotient is a finite abelian group .. lattice. lattice ( music ). commas. comma ( music ). linearly independent. linearly independent. finite. finite group. abelian group. abelian group. This zero-dimensional set of pitches is a periodicity block .. Frequently , it forms a cyclic group , in which case identifying the m pitches of the periodicity block with m-equal tuning gives equal tuning approximations of the just ratios that defined the original lattice .. equal tuning. equal temperament. lattice. lattice ( music ). cyclic group. cyclic group. Note that octaves are usually ignored in constructing periodicity blocks -LRB- as they are in scale theory generally -RRB- because it is assumed that for any pitch in the tuning system , all pitches differing from it by some number of octaves are also available in principle .. octaves. octaves. scale theory. scale theory. In other words , all pitches and intervals can be considered as residues modulo octave .. This simplification is commonly known as octave equivalence .. octave equivalence. octave equivalence