3edt: Difference between revisions
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Despite its small size, 3edt has an excellent approximation to the 13th harmonic: 7 steps of 3edt is only 2.63 cents flat of 13/1. This is reinforced by 3edt having two good 13-limit [[Nearest just interval|rational approximations]], [[13/9]] and 75/52, both which are [[convergent]]s. 3edt thus tempers out (13/9)<sup>3</sup> / (3/1) = [[2197/2187]], the threedie, and (75/52)<sup>3</sup> / (3/1) = [[140625/140608]], the catasma. | Despite its small size, 3edt has an excellent approximation to the 13th harmonic: 7 steps of 3edt is only 2.63 cents flat of 13/1. This is reinforced by 3edt having two good 13-limit [[Nearest just interval|rational approximations]], [[13/9]] and 75/52, both which are [[convergent]]s. 3edt thus tempers out (13/9)<sup>3</sup> / (3/1) = [[2197/2187]], the threedie, and (75/52)<sup>3</sup> / (3/1) = [[140625/140608]], the catasma. | ||
=== | === Harmonics === | ||
{{Harmonics in equal|3|3|1}} | {{Harmonics in equal|3|3|1}} | ||