Hobbit: Difference between revisions

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After applying such a tuning, we discover than there seems to be a certain irregularity or inconsistency in action, in that some of the 11-limit intervals do not stem from the mapping for minerva, but represent additional temperings by 243/242 or 4000/3993. By adding one of these, we can flatten out the irregularity to a corresponding rank-2 temperament; by adding both, we obtain the rank-1 temperament with val {{val| 65 103 151 183 225 }}, giving a scale with steps 2, 4, 3, 3, 3, 3, 3, 2, 4, 2, 4, 3, 2, 4, 2, 4, 2, 3, 3, 3, 3, 3. Examples of this sort of inconsistency seem to increase with increasing rank.

== Notation ==

Hobbits are often assumed when a rank-3 temperament is appended with a number (e.g. [[Marvel9|marvel[9]]]), similar to how a rank-2 temperament appended with a number (e.g. [[Meantone7|meantone[7]]]) denotes a MOS.

[[Category:Hobbit| ]]

[[Category:Math]]

[[Category:Scale]]

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 After applying such a tuning, we discover than there seems to be a certain irregularity or inconsistency in action, in that some of the 11-limit intervals do not stem from the mapping for minerva, but represent additional temperings by 243/242 or 4000/3993. By adding one of these, we can flatten out the irregularity to a corresponding rank-2 temperament; by adding both, we obtain the rank-1 temperament with val {{val| 65 103 151 183 225 }}, giving a scale with steps 2, 4, 3, 3, 3, 3, 3, 2, 4, 2, 4, 3, 2, 4, 2, 4, 2, 3, 3, 3, 3, 3. Examples of this sort of inconsistency seem to increase with increasing rank.
+== Notation ==
+Hobbits are often assumed when a rank-3 temperament is appended with a number (e.g. [[Marvel9|marvel[9]]]), similar to how a rank-2 temperament appended with a number (e.g. [[Meantone7|meantone[7]]]) denotes a MOS.
 [[Category:Hobbit| ]] <!-- main page -->
 [[Category:Math]]
 [[Category:Scale]]