Barium: Difference between revisions
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'''Barium''' is a rank-2 temperament defined in the 5-limit by tempering out the comma which sets 56 syntonic commas equal to the octave. Extensions exist in the 7-limit and the 11-limit. It is named after the 56th chemical element. | '''Barium''' is a rank-2 temperament defined in the 5-limit by tempering out the comma which sets 56 syntonic commas equal to the octave. Extensions exist in the 7-limit and the 11-limit. It is named after the 56th chemical element. | ||
For technical data see: [[ | For technical data see: [[56th-octave temperaments#Barium]] | ||
== Theory == | == Theory == | ||
An octave is equal to <math>\frac{1}{\log{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament. | An octave is equal to <math>\frac{1}{\log{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament. | ||