Hobbit: Difference between revisions
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A '''hobbit''', or '''hobbit scale''', is a generalization of [[MOS scale]] for arbitrary regular temperaments which is a sort of cousin to [[Dwarf|dwarf scales]]; examples may be found on the [[Scalesmith]] page. The idea is that MOS scales give us a means of contructing scales for a [[Regular Temperaments #Rank 2 (including "linear") temperaments|rank two regular temperament]] which gives priority to the intervals of least complexity in that temperament, and so makes efficient use of it; a hobbit does the same in higher ranks, and so using them is one way to make higher ranks, including especially the interesting rank three case, accessible for musical purposes. | A '''hobbit''', or '''hobbit scale''', is a generalization of [[MOS scale]] for arbitrary regular temperaments which is a sort of cousin to [[Dwarf|dwarf scales]]; examples may be found on the [[Scalesmith]] page. The idea is that MOS scales give us a means of contructing scales for a [[Regular Temperaments #Rank 2 (including "linear") temperaments|rank two regular temperament]] which gives priority to the intervals of least complexity in that temperament, and so makes efficient use of it; a hobbit does the same in higher ranks, and so using them is one way to make higher ranks, including especially the interesting rank three case, accessible for musical purposes. | ||
Given a regular temperament and an equal temperament val v which | Given a regular temperament and an equal temperament val v which [[support]]s (or belongs to) the temperament, there is a unique scale for the temperament, which can be tuned to any tuning of the temperament, containing ''v''<sub>1</sub> notes to the octave. | ||
== Definition == | == Definition == | ||