Rank-3 scale: Difference between revisions

Line 73:

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.

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.

@@ Line 73: / Line 73: @@
 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.
+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.