Maximum variety: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 318: / Line 318: @@
 |}
 As the 6-note and 9-note addition tables prove, the requirement of having the same number of steps of different sizes makes max variety 3 scales with three step sizes rare.
+== Examples testing for MV ==
+=== MV2 ===
+==== positive ====
+Consider the 5L 2s diatonic scale: LLsLLLs. For each generic interval class, we must confirm that there are only 2 specific intervals:
+# L, s
+# LL, Ls
+# LLL, LLs
+# LLLs, LLss
+# LLLLs, LLLss
+# LLLLLs, LLLLss
+And so it's confirmed: this is an MV2.
+==== negative ====
+How about a counterexample, LsLLLLs:
+# L, s
+# LL, Ls
+# LLL, LLs, Lss — stop!
+We've found that for the generic interval class 3, this scale has three different specific intervals, so it is not MV2.
+=== MV3 ===
+==== positive ====
+Consider the 2L 2M 3s scale with pattern LsMLsMs.
+# L, M, s
+# Ls, Ms, LM
+# LMs, Mss, Lss
+# LLMs, LMss, LMMs
+# LLMss, LMMss, LMsss
+# LLMMss, LMMsss, LLMsss
+Great, this is MV3.
+==== negative ====
+Consider the 2L 2M 3s scale with pattern LssMLMs.
+# L, M, s
+# Ls, ss, Ms, LM — stop!
+This scale has more than three different specific intervals for a generic interval class, so it is not MV3.
+==== conditional ====
+How about the 2L 3M 2s scale with pattern LMMsMLs.
+# L, M, s
+# LM, MM, Ms, Ls — stop! ...but wait. What if MM=Ls? Then actually this would still be only 3 specific intervals. So let's go with that, and continue.
+# LMM=LLs, MMs, LMs
+# LMMs, MMMs=LMss, LLMs
+# LMMMs=LLMss, LMMss, LLMMs
+# LLMMMs, LLMMss, LMMMss
+So this scale is Conditionally MV3 (MM=Ls).
 [[Category:Scale theory]]
 [[Category:Terms]]