Maximum variety: Difference between revisions
→Classification of MV3 scales: Linked to the relevant article, so I won't have to maintain a separate statement anymore. |
|||
| Line 12: | Line 12: | ||
When discussing scale patterns with three abstract step sizes a, b and c, unlike in the "rank-2" case one must distinguish between ''unconditionally MV3'' scale patterns or ''abstractly MV3'' ones, patterns that are MV3 regardless of what concrete sizes a, b, and c have, and ''conditionally MV3'' patterns, which have tunings that are not MV3. For example, MMLs is conditionally MV3 because it is only MV3 when L, M and s are chosen such that MM = Ls. When we say that an abstract scale pattern is MV3, the former meaning is usually intended. | When discussing scale patterns with three abstract step sizes a, b and c, unlike in the "rank-2" case one must distinguish between ''unconditionally MV3'' scale patterns or ''abstractly MV3'' ones, patterns that are MV3 regardless of what concrete sizes a, b, and c have, and ''conditionally MV3'' patterns, which have tunings that are not MV3. For example, MMLs is conditionally MV3 because it is only MV3 when L, M and s are chosen such that MM = Ls. When we say that an abstract scale pattern is MV3, the former meaning is usually intended. | ||
There is a theorem classifying MV3 scales; see [[Ternary scale theorems]]. | There is a theorem classifying all possible MV3 scales; see [[Ternary scale theorems]]. | ||
=== Generating MV3 scales === | === Generating MV3 scales === | ||