2.5.7 subgroup: Difference between revisions
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==== Didacus ==== | ==== Didacus ==== | ||
'''Didacus''' temperament, the 2.5.7 restriction of [[hemimean]] and [[septimal meantone]], tempers out the comma [[3136/3125]] in the 2.5.7 subgroup, which splits the major third ([[5/4]]) into two intervals of [[28/25]]. It is one of the most accurate temperaments of its simplicity. While augmented and jubilic merge the middle interval of the triplets surrounding 1\6 and 5\6 with one of the two nearby intervals, didacus makes it an exact mean between the two. | '''Didacus''' temperament, the 2.5.7 restriction of [[orion]], [[hemimean]] and [[septimal meantone]], tempers out the comma [[3136/3125]] in the 2.5.7 subgroup, which splits the major third ([[5/4]]) into two intervals of [[28/25]]. It is one of the most accurate temperaments of its simplicity. While augmented and jubilic merge the middle interval of the triplets surrounding 1\6 and 5\6 with one of the two nearby intervals, didacus makes it an exact mean between the two. | ||
The [[DKW theory|DKW]] (2.5.7) optimum tuning states ~5/4 is tuned to 388.122c, and therefore ~28/25 to 194.061c; a chart of mistunings of simple intervals is below. | The [[DKW theory|DKW]] (2.5.7) optimum tuning states ~5/4 is tuned to 388.122c, and therefore ~28/25 to 194.061c; a chart of mistunings of simple intervals is below. | ||