Rank 3 scale: Difference between revisions

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Two MOS scales can be combined into a rank-3 scale as a ''[[Product word]]'', which reduces back to the two MOS scales when two of the three pairs of interval sizes are equated.
Two MOS scales can be combined into a rank-3 scale as a ''[[Product word]]'', which reduces back to the two MOS scales when two of the three pairs of interval sizes are equated.


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.  
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 max variety at most 4.
Product words have max variety at most 4.