User:Inthar/MV3: Difference between revisions

Line 36:

== Definitions and theorems ==

Throughout, let ''S'' be a scale word in steps ''x'', ''y'', ''z'' (and assume all three of these letters are used).

=== PMOS ===

=== Definition: PMOS ===

~~Definition:~~ ''S'' is ''pairwise MOS'' (PMOS) if the result of equating any two of the step sizes is a MOS.

''S'' is ''pairwise MOS'' (PMOS) if the result of equating any two of the step sizes is a MOS.

=== AG ===

=== Definition: AG ===

~~Definition:~~ ''S'' satisfies the ''alternating generator property'' (AG) if it satisfies the following equivalent properties:

''S'' satisfies the ''alternating generator property'' (AG) if it satisfies the following equivalent properties:

# ''S'' can be built by stacking alternating generators, resulting in a circle of the form either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3.

# ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''m'', or one chain has size ''m'' and the second has size ''m-1''.

@@ Line 36: / Line 36: @@
 == Definitions and theorems ==
 Throughout, let ''S'' be a scale word in steps ''x'', ''y'', ''z'' (and assume all three of these letters are used).
-=== PMOS ===
+=== Definition: PMOS ===
-Definition: ''S'' is ''pairwise MOS'' (PMOS) if the result of equating any two of the step sizes is a MOS.
+''S'' is ''pairwise MOS'' (PMOS) if the result of equating any two of the step sizes is a MOS.
-=== AG ===
+=== Definition: AG ===
-Definition: ''S'' satisfies the ''alternating generator property'' (AG) if it satisfies the following equivalent properties:
+''S'' satisfies the ''alternating generator property'' (AG) if it satisfies the following equivalent properties:
 # ''S'' can be built by stacking alternating generators, resulting in a circle of the form  either g1 g2 ... g1 g2 g1 g3 or g1 g2 ... g1 g2 g3.
 # ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''m'', or one chain has size ''m'' and the second has size ''m-1''.