Step pattern product: Difference between revisions

Line 5:

For example, the product word of "aabaaab" and "xxyxyxy" is "(a,x)(a,x)(b,y)(a,x)(a,y)(a,x)(b,y)". For brevity, we can substitute each ordered pair of letters by a new single letter and say this is equivalent to the word "rrsrtrs". This construction has an obvious generalization to the product of three or more words.

The importance of product words in music theory is that every [[Fokker_blocks|Fokker block]] can be expressed as the product word of two or more [[MOS scale]]s in a unique way. Fokker blocks are therefore equivalent to product words of DE scales of the same size. If one or both of the MOS scales are rotated (into different [[mode|modes]]), then the product Fokker block scale is not always a mode, but is often a [[Dome|dome]] instead.

The importance of product words in music theory is that every [[Fokker_blocks|Fokker block]] can be expressed as the product word of two or more [[MOS scale]]s in a unique way. Fokker blocks are therefore equivalent to product words of MOS scales of the same size. If one or both of the MOS scales are rotated (into different [[mode|modes]]), then the product Fokker block scale is not always a mode, but is often a [[Dome|dome]] instead.

[[Category:math]]

[[Category:Scale]]

@@ Line 5: / Line 5: @@
 For example, the product word of "aabaaab" and "xxyxyxy" is "(a,x)(a,x)(b,y)(a,x)(a,y)(a,x)(b,y)". For brevity, we can substitute each ordered pair of letters by a new single letter and say this is equivalent to the word "rrsrtrs". This construction has an obvious generalization to the product of three or more words.
-The importance of product words in music theory is that every [[Fokker_blocks|Fokker block]] can be expressed as the product word of two or more [[MOS scale]]s in a unique way. Fokker blocks are therefore equivalent to product words of DE scales of the same size. If one or both of the MOS scales are rotated (into different [[mode|modes]]), then the product Fokker block scale is not always a mode, but is often a [[Dome|dome]] instead.
+The importance of product words in music theory is that every [[Fokker_blocks|Fokker block]] can be expressed as the product word of two or more [[MOS scale]]s in a unique way. Fokker blocks are therefore equivalent to product words of MOS scales of the same size. If one or both of the MOS scales are rotated (into different [[mode|modes]]), then the product Fokker block scale is not always a mode, but is often a [[Dome|dome]] instead.
 [[Category:math]]
 [[Category:Scale]]