Mercator family: Difference between revisions
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<center>'''[[Fractional-octave temperaments]]'''</center> | <center>'''[[Fractional-octave temperaments]]'''</center> | ||
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[[Category:Fractional-octave temperaments]] | [[Category:Fractional-octave temperaments]] | ||
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The '''Mercator family''' tempers out [[Mercator's comma]], {{monzo| -84 53 }}, and hence the fifths form a closed 53-note circle of fifths, identical to [[53edo]]. While the tuning of the fifth will be that of 53edo, 0.069 cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it. | The '''Mercator family''' tempers out [[Mercator's comma]], {{monzo| -84 53 }}, and hence the fifths form a closed 53-note circle of fifths, identical to [[53edo]]. While the tuning of the fifth will be that of 53edo, 0.069 cents flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it. | ||
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Mapping generators: ~531441/524288, ~5/1 | Mapping generators: ~531441/524288, ~5/1 | ||
[[Optimal tuning]] ([[POTE]]): ~5/4 = 386.264 | [[Optimal tuning]] ([[POTE]]): ~5/4 = 386.264 | ||
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Mapping generators: ~81/80, ~7/1 | Mapping generators: ~81/80, ~7/1 | ||
[[Optimal tuning]] ([[POTE]]): ~225/224 = 5.3666 | [[Optimal tuning]] ([[POTE]]): ~225/224 = 5.3666 | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Mercator family]] <!-- main article --> | [[Category:Mercator family]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||