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- Fokker_periodicity_block abstract "Fokker periodicity blocks are a concept in tuning theory used to mathematically relate musical intervals in just intonation to those in equal tuning. They are named after Adriaan Daniël 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".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. 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.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. 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.Note that octaves are usually ignored in constructing periodicity blocks (as they are in scale theory generally) 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. In other words, all pitches and intervals can be considered as residues modulo octave. This simplification is commonly known as octave equivalence.".
- Fokker_periodicity_block thumbnail Fokker_periodicity_block_12TET.svg?width=300.
- Fokker_periodicity_block wikiPageExternalLink fokkerpb.html.
- Fokker_periodicity_block wikiPageExternalLink fokker-gentle-1.aspx.
- Fokker_periodicity_block wikiPageExternalLink fokker-gentle-2.aspx.
- Fokker_periodicity_block wikiPageID "3303198".
- Fokker_periodicity_block wikiPageLength "9890".
- Fokker_periodicity_block wikiPageOutDegree "50".
- Fokker_periodicity_block wikiPageRevisionID "678510384".
- Fokker_periodicity_block wikiPageWikiLink 19-TET.
- Fokker_periodicity_block wikiPageWikiLink 19_equal_temperament.
- Fokker_periodicity_block wikiPageWikiLink 31-TET.
- Fokker_periodicity_block wikiPageWikiLink 31_equal_temperament.
- Fokker_periodicity_block wikiPageWikiLink 7-limit.
- Fokker_periodicity_block wikiPageWikiLink 7-limit_tuning.
- Fokker_periodicity_block wikiPageWikiLink Abelian_group.
- Fokker_periodicity_block wikiPageWikiLink Adriaan_Fokker.
- Fokker_periodicity_block wikiPageWikiLink Category:Dutch_inventions.
- Fokker_periodicity_block wikiPageWikiLink Category:Lattice_points.
- Fokker_periodicity_block wikiPageWikiLink Category:Pitch_space.
- Fokker_periodicity_block wikiPageWikiLink Cent_(music).
- Fokker_periodicity_block wikiPageWikiLink Comma_(music).
- Fokker_periodicity_block wikiPageWikiLink Cyclic_group.
- Fokker_periodicity_block wikiPageWikiLink Determinant.
- Fokker_periodicity_block wikiPageWikiLink Diesis.
- Fokker_periodicity_block wikiPageWikiLink Equal_temperament.
- Fokker_periodicity_block wikiPageWikiLink Erv_Wilson.
- Fokker_periodicity_block wikiPageWikiLink Finite_group.
- Fokker_periodicity_block wikiPageWikiLink Fundamental_domain.
- Fokker_periodicity_block wikiPageWikiLink Harmonic_seventh.
- Fokker_periodicity_block wikiPageWikiLink If_and_only_if.
- Fokker_periodicity_block wikiPageWikiLink Iff.
- Fokker_periodicity_block wikiPageWikiLink Integer.
- Fokker_periodicity_block wikiPageWikiLink Integer_lattice.
- Fokker_periodicity_block wikiPageWikiLink Interval_(music).
- Fokker_periodicity_block wikiPageWikiLink Invertible_matrix.
- Fokker_periodicity_block wikiPageWikiLink Just_intonation.
- Fokker_periodicity_block wikiPageWikiLink Lattice_(group).
- Fokker_periodicity_block wikiPageWikiLink Lattice_(music).
- Fokker_periodicity_block wikiPageWikiLink Limit_(music).
- Fokker_periodicity_block wikiPageWikiLink Linear_combination.
- Fokker_periodicity_block wikiPageWikiLink Linear_independence.
- Fokker_periodicity_block wikiPageWikiLink Linearly_independent.
- Fokker_periodicity_block wikiPageWikiLink Magic_temperament.
- Fokker_periodicity_block wikiPageWikiLink Major_third.
- Fokker_periodicity_block wikiPageWikiLink Musical_tuning.
- Fokker_periodicity_block wikiPageWikiLink Natural_number.
- Fokker_periodicity_block wikiPageWikiLink Octave.
- Fokker_periodicity_block wikiPageWikiLink Octave_equivalence.
- Fokker_periodicity_block wikiPageWikiLink Octaves.
- Fokker_periodicity_block wikiPageWikiLink Parallelepiped.
- Fokker_periodicity_block wikiPageWikiLink Parallelogram.
- Fokker_periodicity_block wikiPageWikiLink Perfect_fifth.
- Fokker_periodicity_block wikiPageWikiLink Quotient_group.
- Fokker_periodicity_block wikiPageWikiLink Royal_Netherlands_Academy_of_Arts_and_Sciences.
- Fokker_periodicity_block wikiPageWikiLink Scale_theory.
- Fokker_periodicity_block wikiPageWikiLink Septimal_kleisma.
- Fokker_periodicity_block wikiPageWikiLink Square_lattice.
- Fokker_periodicity_block wikiPageWikiLink Syntonic_comma.
- Fokker_periodicity_block wikiPageWikiLink Tessellation.
- Fokker_periodicity_block wikiPageWikiLink Tuning_theory.
- Fokker_periodicity_block wikiPageWikiLink Vector_space.
- Fokker_periodicity_block wikiPageWikiLink File:Fokker_periodicity_block_12TET.svg.
- Fokker_periodicity_block wikiPageWikiLinkText "Fokker periodicity block".
- Fokker_periodicity_block hasPhotoCollection Fokker_periodicity_block.
- Fokker_periodicity_block wikiPageUsesTemplate Template:Citation.
- Fokker_periodicity_block wikiPageUsesTemplate Template:Pitch_space.
- Fokker_periodicity_block wikiPageUsesTemplate Template:Reflist.
- Fokker_periodicity_block subject Category:Dutch_inventions.
- Fokker_periodicity_block subject Category:Lattice_points.
- Fokker_periodicity_block subject Category:Pitch_space.
- Fokker_periodicity_block hypernym Concept.
- Fokker_periodicity_block comment "Fokker periodicity blocks are a concept in tuning theory used to mathematically relate musical intervals in just intonation to those in equal tuning. They are named after Adriaan Daniël Fokker.".
- Fokker_periodicity_block label "Fokker periodicity block".
- Fokker_periodicity_block sameAs m.094f2l.
- Fokker_periodicity_block sameAs Q5464217.
- Fokker_periodicity_block sameAs Q5464217.
- Fokker_periodicity_block wasDerivedFrom Fokker_periodicity_block?oldid=678510384.
- Fokker_periodicity_block depiction Fokker_periodicity_block_12TET.svg.
- Fokker_periodicity_block isPrimaryTopicOf Fokker_periodicity_block.