54edo: Difference between revisions
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The 54cdd val makes for an excellent tuning of 7-limit [[hexe]] temperament, while the 54bdf val does higher limit [[muggles]] about as well as it can be tuned. The overall best val of 54edo in the 17-limit is probably 54c, which preserves the 2.3.5.7.13 mapping of 27edo and corrects the 11th and 17th harmonics with a consistently sharp tendency. | The 54cdd val makes for an excellent tuning of 7-limit [[hexe]] temperament, while the 54bdf val does higher limit [[muggles]] about as well as it can be tuned. The overall best val of 54edo in the 17-limit is probably 54c, which preserves the 2.3.5.7.13 mapping of 27edo and corrects the 11th and 17th harmonics with a consistently sharp tendency. | ||
However, even these best temperament interpretations of 54edo are quite high in [[badness]] compared to its immediate neighbours [[53edo|53-]] and [[55edo]], both of which are [[Historical temperaments|historically significant]] for different reasons, leaving it mostly unexplored so far. 54edo is still definitely usable to approximate low-complexity JI, since at this step size, every interval's direct approximation is within a maximum of about 11.1{{c}} [[error]], it's just | However, even these best temperament interpretations of 54edo are quite high in [[badness]] compared to its immediate neighbours [[53edo|53-]] and [[55edo]], both of which are [[Historical temperaments|historically significant]] for different reasons, leaving it mostly unexplored so far. 54edo is still definitely usable to approximate low-complexity JI, since at this step size, every interval's direct approximation is within a maximum of about 11.1{{c}} [[error]], it's just bad for its size. | ||
=== Odd harmonics === | === Odd harmonics === | ||