Rank-3 scale: Difference between revisions
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When associated with a mapping, product words are the rank-3 ''[[Fokker blocks]]''. Fokker blocks have ''unison vectors'', which generalize the concept of the chroma of MOS scales to higher ranks. If these intervals are plotted onto a plane representing rank-3 octave equivalent pitch space, they tile the space into Fokker blocks which differ by combinations of these unison vectors. Rank-2 Fokker blocks are the MOS scales, so Fokker blocks can be considered a generalization of MOS scales into higher ranks. | When associated with a mapping, product words are the rank-3 ''[[Fokker blocks]]''. Fokker blocks have ''unison vectors'', which generalize the concept of the chroma of MOS scales to higher ranks. If these intervals are plotted onto a plane representing rank-3 octave equivalent pitch space, they tile the space into Fokker blocks which differ by combinations of these unison vectors. Rank-2 Fokker blocks are the MOS scales, so Fokker blocks can be considered a generalization of MOS scales into higher ranks. | ||
Product words have maximum variety at most 4. The scale steps can be readily notated, sorted by size, as ''L'', '' | Product words have maximum variety at most 4. The scale steps can be readily notated, sorted by size, as ''L'', ''l'', ''S'', ''s'', and they satisfy ''L'' - ''l'' = ''S'' - ''s''. | ||
Any Fokker block where the unison vectors are smaller than the smallest steps will be constant structures (CS). Not all Fokker blocks are CS. | Any Fokker block where the unison vectors are smaller than the smallest steps will be constant structures (CS). Not all Fokker blocks are CS. | ||