Rank-3 scale theorems: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
Tags: Mobile edit Mobile web edit |
||
| Line 132: | Line 132: | ||
This proof shows that AG and unconditionally-MV3 scales must have odd size or size 4. | This proof shows that AG and unconditionally-MV3 scales must have odd size or size 4. | ||
==== An AG scale is unconditionally MV3 iff its cardinality is odd ==== | ==== An AG scale is unconditionally MV3 iff its cardinality is odd or 4 ==== | ||
We only need to see that AG + odd cardinality => MV3. But the argument in case 2 above works for any interval class (MV3 wasn't used), hence any interval class comes in at most 3 sizes regardless of tuning. | We only need to see that AG + odd cardinality => MV3. But the argument in case 2 above works for any interval class (MV3 wasn't used), hence any interval class comes in at most 3 sizes regardless of tuning. | ||