TAMNAMS/Appendix: Difference between revisions

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### Let ''gen'' be the scale's generator and ''comp'' be the generator's octave complement for the mos ''z''L ''w''s. Recursively call this algorithm to find these intervals for ''z''L ''w''s; the final scale's generator and complement will be based on this.

### If {{nowrap|''x'' < ''y''}}, reverse the order of characters in ''gen'' and ''comp'', then swap ''gen'' and ''comp''. This is only needed if there are more L's than s's in the scale.

### To produce the scale's generator and complement, the L's and s's of both intervals must be replaced with substrings consisting of L's and s's. Let {{nowrap|''u'' {{=}} &lceil;''m2''/''m1''&rceil;}} and {{nowrap|''v'' {{=}} &lfloor;''m2''/''m1''&rfloor;}}.

### To produce the scale's generator and complement, the L's and s's of both intervals must be replaced with substrings consisting of L's and s's. Let {{nowrap|''u'' {{=}} &lceil;''m2''/''m1''&rceil;}} and {{nowrap|''v'' {{=}} &lfloor;''m2''/''m1''&rfloor;}}. (&lceil; &rceil; denotes the ceiling function and &lfloor; &rfloor; denotes the floor function.)

#### If {{nowrap|''x'' > ''y''}}, every instance of an L in both intervals is replaced with one L and ''u'' s's, and every s replaced with one L and ''v'' s's. This produces the final scale's generator and complement.

#### If {{nowrap|''x'' < ''y''}}, every instance of an L in both intervals is replaced with ''u'' L's and one s, and every s replaced with ''v'' L's and one s. This produces the final scale's generator and complement.

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 ### Let ''gen'' be the scale's generator and ''comp'' be the generator's octave complement for the mos ''z''L&nbsp;''w''s. Recursively call this algorithm to find these intervals for ''z''L&nbsp;''w''s; the final scale's generator and complement will be based on this.
 ### If {{nowrap|''x'' &lt; ''y''}}, reverse the order of characters in ''gen'' and ''comp'', then swap ''gen'' and ''comp''. This is only needed if there are more L's than s's in the scale.
-### To produce the scale's generator and complement, the L's and s's of both intervals must be replaced with substrings consisting of L's and s's. Let {{nowrap|''u'' {{=}} &lceil;''m2''/''m1''&rceil;}} and {{nowrap|''v'' {{=}} &lfloor;''m2''/''m1''&rfloor;}}.
+### To produce the scale's generator and complement, the L's and s's of both intervals must be replaced with substrings consisting of L's and s's. Let {{nowrap|''u'' {{=}} &lceil;''m2''/''m1''&rceil;}} and {{nowrap|''v'' {{=}} &lfloor;''m2''/''m1''&rfloor;}}. (&lceil; &rceil; denotes the ceiling function and &lfloor; &rfloor; denotes the floor function.)
 #### If {{nowrap|''x'' &gt; ''y''}}, every instance of an L in both intervals is replaced with one L and ''u'' s's, and every s replaced with one L and ''v'' s's. This produces the final scale's generator and complement.
 #### If {{nowrap|''x'' &lt; ''y''}}, every instance of an L in both intervals is replaced with ''u'' L's and one s, and every s replaced with ''v'' L's and one s. This produces the final scale's generator and complement.