Fokker block: Difference between revisions

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Hence S satisfies the conditions for being a [[periodic scale]]~~, and since our unit~~ of ~~measurement is the octave, i.e. we are using log base two to define intervals, the repetition interval 1 represents an octave~~. This gives us our first definition of Fokker block.

Hence S satisfies the conditions for being a [[periodic scale]]; note that the value is pitch given in units of octaves. This gives us our first definition of Fokker block.

By choosing various ''a''''k'' satisfying 0 ≤ ''a''''k'' < ''P'', for any Fokker block we may find the various [[Periodic scale #Rotations|rotations]], of the block. However, other choices lead to blocks which are not rotations of our initial block, but instead belong to [[dome]]s which are disjoint from the dome of the initial block. The collection of all Fokker blocks for any of the allowed values of the ''a''''k'' offsets is an ''arena''; a Fokker arena is defined entirely by its chromas.

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 <math>S[i+P] = S[i] + e_1 t_1 + e_2 t_2 + … + e_n t_n = S[i] + 1</math>
-Hence S satisfies the conditions for being a [[periodic scale]], and since our unit of measurement is the octave, i.e. we are using log base two to define intervals, the repetition interval 1 represents an octave. This gives us our first definition of Fokker block.
+Hence S satisfies the conditions for being a [[periodic scale]]; note that the value is pitch given in units of octaves. This gives us our first definition of Fokker block.
 By choosing various ''a''<sub>''k''</sub> satisfying 0 ≤ ''a''<sub>''k''</sub> &lt; ''P'', for any Fokker block we may find the various [[Periodic scale #Rotations|rotations]], of the block. However, other choices lead to blocks which are not rotations of our initial block, but instead belong to [[dome]]s which are disjoint from the dome of the initial block. The collection of all Fokker blocks for any of the allowed values of the ''a''<sub>''k''</sub> offsets is an ''arena''; a Fokker arena is defined entirely by its chromas.